UKY Applied Math Seminar

University of Kentucky Applied Math Seminar

The Applied Math seminar has speakers twice a month during the school year. This semester we will meet on Mondays in POT 715 during 4-5 pm. Past and upcoming speakers are listed below. If you would like to be added to the mailing list send an email to listserv@lsv.uky.edu with "subscribe UKAPPLIEDMATH-L YourFirstName YourLastName" in the message body (not the subject line!). The email address you send this from is the one that will be subscribed to the list. If you are interested in speaking in the seminar please send an email to murrugarra@uky.edu or qye3@uky.edu.

Academic Year 2024-25

April 7, 2025
POT 715 from 4:00-5:00 pm
Title: TBA
Speaker: Nathan Kirk, Illinois Institute of Technology.
Abstract:
TBA.
December 2, 2024
POT 715 from 4:00-5:00 pm
Title: The Joint Numerical Range and Its Uses in Optimization
Speaker: Aaron Davis, University of Kentucky.
Abstract:
In this talk, we consider the benefits of the Joint Numerical Range(JNR) as it relates to optimization problems. After reviewing the basics of the JNR, we show how to compute/visualize it. We then reformulate optimization problems of the Robust Rayleigh Quotient and the Sum of 2 Rayleigh Quotients(SRQ2) into optimizations over the JNR. Applications of these problems include Fair PCA and Eigenvalue Backward Errors respectively. These reformulations provide better solutions, assuming that the JNR is convex. However, JNR is only generally proven to be convex for a small number of matrices. Thus, future work is to be done to expand what is known about the convexity of JNR. We shall also consider the use of the approximate JNR to solve more difficult optimizations.
November 25, 2024
POT 715 from 4:00-5:00 pm
Title: Noise-Tolerant Coreset-Based Class Incremental Continual Learning
Speaker: Edison Mucllari, University of Kentucky.
Abstract:
This presentation introduces Continual/Lifelong Learning, a framework that enables systems to continuously acquire knowledge while retaining previously learned information. We will define this concept and explore various strategies within lifelong learning approaches, focusing on two innovative methods we have developed to enhance training efficiency. Our strategies outperform existing methods, particularly in real-world scenarios where data may be noisy, including issues like noisy labels and salt and pepper noise in images. Extensive experiments reveal compelling results that highlight the robustness and effectiveness of our approaches. Designed with practical applications in mind, our work emphasizes the relevance of these strategies in real-life contexts.
November 11, 2024
POT 715 from 4:00-5:00 pm
Title: An Introduction to Spiking Neural Networks
Speaker: Joshua Peterson, University of Kentucky.
Abstract:
In recent years, artificial neural networks (ANNs) have seen substantial increases in both methods available and use cases. We now have sophisticated large language models such as ChatGPT along with generative AI capable of producing videos such as Gen-3 Alpha. However, traditional ANNs struggle in areas such as energy efficiency and biological plausibility. In this talk, the concept of spiking neural networks, a relatively new model that seeks to address some of the concerns that are present in more traditional ANN models, will be discussed.
October 21, 2024
POT 715 from 4:00-5:00 pm
Title: Machine Learning and Optimization in Multi-Agent Multi-Objective Frameworks
Speaker: Peizhong Ju, University of Kentucky.
Abstract:
In many real-world machine learning and optimization applications, multiple participants often pursue diverse and sometimes conflicting objectives. This talk addresses several key challenges within such multi-agent, multi-objective frameworks through three focused parts. The first part of this talk examines the impacts of local updates on the generalization performance of federated learning, a popular machine learning framework involving multiple clients. The second part explores achieving fairness in multi-agent Markov Decision Processes (MDPs) via reinforcement learning, with an emphasis on finding policies that ensure fairness across agents. Finally, the talk tackles the challenge of finding the exact Pareto front in multi-objective MDPs, essential for optimizing policies that balance conflicting objectives. An efficient algorithm is presented, leveraging geometric properties to accurately identify the Pareto optimal set.
October 14, 2024
POT 715 from 4:00-5:00 pm
Title: Hyperspectral Band Selection based on Generalized 3DTV and Tensor CUR Decomposition
Speaker: Katherine Henneberger, University of Kentucky.
Abstract:
Hyperspectral Imaging (HSI) serves as an important technique in remote sensing. However, high dimensionality and data volume typically pose significant computational challenges. Band selection is essential for reducing spectral redundancy in hyperspectral imagery while retaining critical information. In this presentation, we propose a novel hyperspectral band selection model by decomposing the data into a low-rank and smooth component and a sparse component. In particular, we develop a generalized 3D total variation (G3DTV) by applying the $\ell_1^p$-norm to derivatives to preserve spatial-spectral smoothness. By employing the alternating direction method of multipliers (ADMM), we derive an efficient algorithm, where the tensor low-rankness is implied by the tensor CUR decomposition. We demonstrate the effectiveness of the proposed approach through comparisons with various other state-of-the-art band selection techniques using two benchmark real-world datasets.

Academic Year 2023-24

April 25, 2024
POT 745 from 11:00am-12:00 pm
Title: Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery
Speaker: Katherine Henneberger, University of Kentucky.
Abstract:
Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their convex relaxed versions are typically adopted in practice due to the computational efficiency, e.g., log-sum penalty. In this presentation, we propose novel log-sum regularized Kaczmarz algorithms for recovering high-order tensors with either sparse or low-rank structures. We present block variants along with convergence analysis of the proposed algorithms. Numerical experiments on synthetic and real-world data sets demonstrate the effectiveness of the proposed methods.
April 18, 2024
POT 745 from 11:00am-12:00 pm
Title: Understanding neutrophil dynamics during COVID-19 infection
Speaker: Quiyana Murphy, Virginia Tech.
Abstract:
Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in varied clinical outcomes, with virus-induced chronic inflammation and tissue injury being associated with enhanced disease pathogenesis. To determine the role of tissue damage on immune populations recruitment and function a mathematical model of innate immunity following SARS-CoV-2 infection has been proposed. The model was fitted to published longitudinal immune marker data from patients with mild and severe COVID-19 disease and key parameters were estimated for each clinical outcome. Analytical, bifurcation and numerical investigations were conducted to determine the effect of parameters and initial conditions on long-term dynamics. The results were used to suggest changes needed to achieve immune resolution.
April 11, 2024
POT 745 from 11:00am-12:00 pm
Title: Lightweight Deployable Automated Space Systems Using the Least Necessary Resources
Speaker: Muhao Chen, University of Kentucky.
Abstract:
Over six decades of space exploration have gradually solidified the belief, recently reinforced by advancements in the space economy, that humankind will leave the Earth's cradle and destine for stars. The critical challenge of deep space missions is the efficiency of payloads, constrained by rockets' limited size and capacity. Thus, reducing mass and volume is essential, driving aerospace research to innovate more mass- and volume-efficient structures. This talk will present newly developed analytical methods and advancements in the field of lightweight and deployable automated space systems, specifically focusing on 1) The design of highly flexible space structures that are both lightweight and deployable, utilizing structural paradigms such as tensegrity and origami. 2) Precise dynamic modeling of these structures. 3) Advanced control strategies for deployment and the optimal choice of sensors and actuators. The presentation will also highlight the vital role of interdisciplinary integration of structure and control, illustrating its significant benefits for developing space systems using the least necessary resources. These theoretical approaches are demonstrated by practical applications, such as autonomous lunar drilling rigs and solar panels for In-Situ Resource Utilization, space habitats with 1-g artificial gravity for In-Space Servicing, Assembly, and Manufacturing, space soft robotic arms for Debris Handling and Asteroid Capturing.
April 4, 2024
POT 745 from 11:00am-12:00 pm
Title: The inexact Matrix-Newton framework for solving NEPv
Speaker: Tom Werner, Technical University of Braunschweig.
Abstract:
The eigenvector-dependent nonlinear eigenvalue problem (NEPv), also known as nonlinear eigenvector problem, is a special type of eigenvalue problem where we seek to find $k$ eigenpairs of a Hermitian matrix function $H:\mathbb{C}^{n,k}\rightarrow\mathbb{C}^{n,n}$ that depends nonlinearly on the eigenvectors itself. That is, we have to find $V\in\mathbb{C}^{n,k}$ with orthonormal columns and $\Lambda=\Lambda^H\in\mathbb{C}^{k,k}$ such that $H(V)V=V\Lambda$.

NEPv arise in a variety of applications, most notably in quantum chemistry applications, such as discrete Kohn-Sham- or Gross-Pitaevskii-equations, and data science applications, such as robust linear discriminant analysis or trace ratio optimization.

This talk is concerned with solving NEPv by viewing it as a set of nonlinear matrix equations and using an inexact Newton method on a matrix level. In this setting, Newton's method is applied using the Fréchet derivative and exploiting the structure of the problem by using a global GMRES-approach to solve the Newton-update equation efficiently.

Preprint available from arXiv: An inexact Matrix-Newton method for solving NEPv, 2023, arxiv.org/abs/2311.09670.
March 21, 2024
POT 745 from 11:00am-12:00 pm
Title: Advancing Exascale Data Management with Trust-Driven Lossy Compression
Speaker: Xin Liang, University of Kentucky.
Abstract:
Today's extreme-scale scientific simulations and experiments are generating more data than that can be stored, transmitted, and analyzed. The upcoming exscale systems and high-resolution scientific instruments are going to exacerbate this problem with the imbalanced growth between storage systems and scientific data. In this talk, we will see how scientists address those data challenges via effective lossy data compression. This includes design and development of trust-driven data compression algorithms, optimizations on high-end computing clusters, and their interactions with storage and I/O systems. The ultimate goal is to provide effective scientific data management solutions to reduce time to insights on the cutting-edge computing systems for mission-critical applications.
February 29, 2024
Online from 11:00am-12:00 pm
Title: Randomized Contour Integral Methods for Eigenvalue Problems with Probabilistic Error Analysis
Speaker: Agnieszka Miedlar, Virginia Tech.
Abstract:
Randomized NLA methods have recently gained popularity because of their easy implementation, computational efficiency, and numerical robustness. We propose a randomized version of a well-established FEAST eigenvalue algorithm that enables computing the eigenvalues of the Hermitian matrix pencil (A, B) located in the given real interval I ⊂ [λmin, λmax]. In this talk, we present the analysis of this randomized variant of the subspace iteration method using a rational filter and propose several modifications of the original FEAST algorithm. First, we derive some new structural as well as probabilistic error analysis of the accuracy of approximate eigenpair and subspaces obtained using the randomized FEAST algorithm, i.e., bounds for the canonical angles between the exact and the approximate eigenspaces corresponding to the eigenvalues contained in the interval, and for the accuracy of the eigenvalues and the corresponding eigenvectors. Since this part of the analysis is independent of the particular distribution of an initial subspace, we denote it as structural. In the case of the starting guess being a Gaussian random matrix, we provide more informative, probabilistic error bounds. Our new algorithm allows to improve the accuracy of orthogonalization when B is ill-conditioned, efficiently apply the rational filter by using MPGMRES-Sh Krylov subspace method to accelerate solving shifted linear systems and estimate the eigenvalue counts in a given interval. Finally, we will illustrate numerically the effectiveness of presented error bounds and proposed algorithmic modifications. This is a joint work with E. de Sturler (VT) and A. K. Saibaba (NC State).
November 30, 2023
Online from 11:00am-12:00 pm
Title: Forecasting patient-specific treatment response to neoadjuvant chemotherapy in triple-negative breast cancer via MRI-based digital twins
Speaker: Chengyue Wu, The University of Texas MD Anderson Cancer Center.
Abstract:
Patients with locally advanced, triple-negative breast cancer (TNBC) typically receive neoadjuvant chemotherapy (NAT) to downstage the tumor and improve the outcome of subsequent breast conservation surgery. In this study, we integrated quantitative magnetic resonance imaging (MRI) data with biology-based mathematical modeling to address the currently unmet need for accurate prediction of TNBC response to NAT on an individual patient basis. Specifically, dynamic contrast-enhanced MRI and diffusion-weighted MRI was acquired in 56 patients before, after two, and after four cycles of Adriamycin/Cytoxan (A/C), and again after Taxol as part of the ARTEMIS (NCT02276443) trial. A biology-based mathematical model was established based on the reaction-diffusion equation to characterize the mobility of tumor cells, tumor proliferation, and treatment-induced cell death. Pre- and mid-treatment images were used for model calibration on a patient-specific basis. Two evaluation Frameworks were built: 1. using images acquired before and after two cycles of A/C for calibration and predicting tumor status after A/C, and 2. using images acquired before, after two cycles, and after four cycles of A/C for calibration and predicting response after NAT. For Framework 1, the Pearson correlation coefficients between the predicted and measured patient-specific, post-A/C changes in tumor cellularity and volume were 0.95 and 0.94, respectively. For Framework 2, the biologically-based model achieved an area under the receiver operator characteristic curve of 0.89 (sensitivity/specificity = 0.72/0.95) for differentiating pathological complete response (pCR) from non-pCR, which is statistically superior (P < 0.05) to the value of 0.78 (sensitivity/specificity = 0.72/0.79) achieved by the tumor volume measured after four cycles of A/C. Overall, our biology-based mathematical model successfully captured the patient-specific, spatiotemporal dynamics of TNBC response to NAT, providing highly accurate predictions of NAT response.
November 16, 2023
POT 745 from 11:00am-12:00 pm
Title: The Price of Fair PCA: One Extra Dimension
Speaker: Aaron Davis, University of Kentucky.
Abstract:
Principal Component Analysis (PCA) is a fundamental technique for dimension reduction in data analysis, but it may produce data representations with unequal fidelities across groups with different characteristics like gender, race, or education backgrounds. In this talk, we will present a novel Fair PCA technique aimed at addressing this fairness issue for two different groups. First, using the notion of reconstruction loss, we will establish the Fair PCA problem as a minimization of the worst reconstruction loss between the groups. We then talk about an algorithm to find the optimal projection matrix based on semi-definite relaxation techniques. This algorithm has polynomial-time complexity and guarantees to produce a projection matrix with at most one-extra dimension than the exact solution. Finally, we will demonstrate the effectiveness of the algorithm on two real-world data sets and provide evidence of fairness for the reduced data representation. This presentation is based on the work by Samadi et al. [The Price of Fair PCA: One Extra Dimension, in Advances in Neural Information Processing Systems 31 (2018).]
October 12, 2023
POT 745 from 11:00am-12:00 pm
Title: Is a Classification Procedure Good Enough?--A Goodness-of-Fit Assessment Tool for Classification Learning
Speaker: Jiawei Zhang, University of Kentucky.
Abstract:
In recent years, many nontraditional classification methods, such as random forest, boosting, and neural network, have been widely used in applications. Their performance is typically measured in terms of classification accuracy. While the classification error rate and the like are important, they do not address a fundamental question: Is the classification method underfitted? To our best knowledge, there is no existing method that can assess the goodness of fit of a general classification procedure. Indeed, the lack of a parametric assumption makes it challenging to construct proper tests. To overcome this difficulty, we propose a methodology called BAGofT that splits the data into a training set and a validation set. First, the classification procedure to assess is applied to the training set, which is also used to adaptively find a data grouping that reveals the most severe regions of underfitting. Then, based on this grouping, we calculate a test statistic by comparing the estimated success probabilities and the actual observed responses from the validation set. The data splitting guarantees that the size of the test is controlled under the null hypothesis, and the power of the test goes to one as the sample size increases under the alternative hypothesis. For testing parametric classification models, the BAGofT has a broader scope than the existing methods since it is not restricted to specific parametric models (e.g., logistic regression). Extensive simulation studies show the utility of the BAGofT when assessing general classification procedures and its strengths over some existing methods when testing parametric classification models.
September 28, 2023
POT 745 from 11:00am-12:00 pm
Title: Computational modeling using a novel continuum approach coupled with Pathway-informed neural networks to optimize Dynein-mediated centrosome positioning in Polarized cells
Speaker: Arka Ghosal, The Ohio State University.
Abstract:
Microtubules (MTs) are cytoskeletal polymers that interact with motor proteins such as dynein to position the centrosomes and nucleus within a cell. Centrosome positioning specifies the cell’s division plane by determining the location and orientation of the mitotic spindle. In polarized cells, centrosome alignment along the polarity axis causes the cell to divide asymmetrically, producing unequal daughter cells. Proper centrosome positioning is critical during development where it is required for important processes such as cell fate specification. Improper centrosome positioning is implicated in disease processes: cancer cells often exhibit abnormal centrosome positioning prior to division. While many studies have focused on centrosome movement during mitosis, centrosomes are often positioned prior to mitosis. This movement prior to mitosis when the centrosomes are associated with the intact pronuclear envelope is not well understood. Many aspects of dynein-mediated centrosome movement are highly nonlinear and rely on biochemical, mechanical and geometric features in the cell that are difficult to investigate experimentally. Mathematical modeling can easily deal with this complexity, bridging the varying time and space scales, and provide a fundamental understanding of the mechanisms of positioning centrosomes. This model provides the key features required to integrate modeling and experiments on early embryos of the C. elegans to elucidate the interplay between biochemical, mechanical and geometric signals that act to position centrosomes in polarized cells through the following aims. The same non-linear framework for confined geometries is extended to create a comprehensive data driven digital twin of an individual's mental health profile and analyze spatiotemporal behavior. Although dynamic study and modeling of depression-related behavior exist in literature, we employ a novel digital twin model that combines Sensitive, Exposed, Induced and Excluded models with Disease-informed neural networks to identify progression and intensity of depression related behavior.
September 7, 2023
POT 745 from 11:00am-12:00 pm
Title: RNA Landscapes
Speaker: David Murrugarra, University of Kentucky.
Abstract:
As the biomedical impact of non-coding RNAs grows, the interest for the development of tools that can accurately and reliably predict the secondary structure of RNAs has also increased. A common tool for computational prediction is based on the nearest neighbor thermodynamic model (NNTM) which is used to obtain the structure with minimum free energy. However, the NNMT approach is prone to ill-conditioning and accuracy errors in its predictions. Addressing the current challenges will require going beyond the single minimal free energy prediction such as studying the suboptimal structure formations to understand the competing alternatives. Boltzmann sampling of secondary structures allows the study of the competing substructural alternatives. RNA profiling is a tool based on graph theory techniques that allows the representation of the competing substructures as a partially ordered set which highlights the competing substructures in a Boltzmann sample. This talk will focus on the use of auxiliary information to improve the accuracy of data-directed RNA secondary structure prediction. We will investigate how auxiliary information affects the structure of RNA profile graphs and their directability. Using a new representation of RNA profiles based on persistent landscapes, we will measure how the structure of the RNA profile graphs changes as the intensity of the auxiliary information is increased.

Academic Year 2022-23

March 23, 2023
POT 745 from 11:00am-12:00 pm
Title: The Model Behind ChatGPT
Speaker: Qiang Ye, University of Kentucky.
Abstract:
This will be a general talk to introduce a deep learning model called Generative Pre-training Transformer (GPT). First, I will discuss in concept the machine learning approach for the task of question-answering. Then I will describe language modeling and some models such as recurrent neural networks (RNN) for that task. Finally, I will present the Transformer as well as the GPT models that have led to ChatGPT.
February 9, 2023
POT 745 from 11:00am-12:00 pm
Title: The nonlinearity of regulation in biological networks
Speaker: David Murrugarra, University of Kentucky.
Abstract:
The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed `regulatory nonlinearity', we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear interactions, using a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation, we used Taylor decomposition to approximate the models with various levels of nonlinearity. A comparison of the resulting series of approximations of the biological models with appropriate random ensembles revealed that biological regulation tends to be less nonlinear than expected. A further categorical analysis of the biological models revealed that the nonlinearity of cancer and disease networks could not only be sometimes higher than expected but are also relatively more variable. We show that this variation is caused by differences in the apportioning of information among the various orders of nonlinearity. Taken together, our results suggest, but do not imply, that biological regulation may have evolved to be more linear on average, and certain systems such as cancer may have, on the other hand, evolved to be more nonlinear.
January 26, 2023
POT 745 from 11:00am-12:00 pm
Title: Self-Correcting Discriminator Optimization for Image and Speech Enhancement GANs
Speaker: Vasily Zadorozhnyy, University of Kentucky.
Abstract:
Generative adversarial network (GAN) has become one of the most important neural network models for classical unsupervised machine learning. Various discriminator loss functions have been developed to train GAN's discriminators, most of which have a common structure: a sum of real and fake losses that depend only on the actual and generated data, respectively. One challenge associated with an equally weighted sum of two losses is that the training may benefit one loss but harm the other. We present self-correcting optimization for training a GAN discriminator, which helps avoid "harmful" training directions for parts of the discriminator loss function. Experiments validated the effectiveness of our loss functions on conditional and unconditional image generation tasks as well as speech enhancement tasks.
January 12, 2023
POT 745 from 11:00am-12:00 pm
Title: A generic framework to coarse-grain stochastic reaction networks by Abstract Interpretation
Speaker: Albin Salazar, École normale supérieure, Université PSL, CNRS, INRIA, Paris, France.
Abstract:
In the last decades, logical or discrete models have emerged as a successful paradigm for capturing and predicting the behaviors of systems of molecular interactions. Intuitively, they consist in sampling the abundance of each kind of biochemical entity within finite sets of intervals and deriving transitions accordingly. On one hand, formally-proven sound derivation from more precise descriptions (such as from reaction networks) may include many fictitious behaviors. On the other hand, direct modeling usually favors dominant interactions with no guarantee on the behaviors that are neglected. In this paper, we formalize a sound coarse-graining approach for stochastic reaction networks. Its originality relies on two main ingredients. Firstly, we abstract values by intervals that overlap in order to introduce a minimal effort for the system to go back to the previous interval, hence limiting fictitious oscillations in the coarse-grained models. Secondly, we compute for pairs of transitions (in the coarse-grained model) bounds on the probabilities on which one will occur first. We illustrate our ideas on two case studies and demonstrate how techniques from Abstract Interpretation can be used to design more precise discretization methods, while providing a framework to further investigate the underlying structure of logical and discrete models.
Apr 13, 2023
POT 745 from 11:00am-12:00 pm
Title: TBA
Speaker: Cole Pospisil, University of Kentucky.
Abstract:
TBA.
Apr 27, 2023
POT 745 from 11:00am-12:00 pm
Title: TBA
Speaker: Matthew McCarver, University of Kentucky.
Abstract:
TBA.
May 4, 2023
POT 745 from 11:00am-12:00 pm
Title: TBA
Speaker: Katherine Henneberger, University of Kentucky.
Abstract:
TBA.
December 8, 2022
POT 745 from 11:00am-12:00 pm
Title: Mathematical graph-based learner with extensive atomic interactions and a deep language model for drug development
Speaker: Farjana Mukta, University of Kentucky.
Abstract:
Drug discovery is a highly complicated and time-consuming process. Even after investing a considerable amount of money, time, and effort, the success of drugs cannot be assured. Many advanced machine learning models, including decision trees, deep neural networks, deep neural graphs, and deep language processing, have been widely used in the past few years to reduce the risk of failure in this field. Furthermore, the prediction of a possible interaction between a drug and a target enables biochemists and pharmacists to speed up the process of target validation and discovery. In this talk, we will present an algebraic graph-based learner featuring extended atom types to capture wide-range interactions between target and drug candidate. We then introduce several advanced machine learning and deep learning algorithms, such as Bidirectional Encoder Representations from Transformers (BERT) and gradient-boosting trees, integrating our novel graph-based molecular representations to form data-driven scoring functions (SF) named AGL-EAT-Score for protein-ligand binding affinity predictions. Our newly developed SF has outperformed numerous state-of-the-art models in CASF-2013, a famous benchmark for binding affinity scoring power, and the D3R dataset, a worldwide grand challenge in drug design.
December 1, 2022
POT 745 from 11:00am-12:00 pm
Title: A C0 finite element method for the biharmonic problem with Dirichlet boundary conditions in a polygonal domain
Speaker: Charuka Dilhara Wickramasinghe, University of Kentucky.
Abstract:
In this talk, we discuss the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourth-order problem into a system of two Poison equations and one Stokes equation, or a system of one Stokes equation and one Poisson equation. It is shown that the solution of each system is equivalent to that of the original fourth-order problem on both convex and non-convex polygonal domains. Two finite element algorithms are in turn proposed to solve the decoupled systems. In addition, we show the regularity of the solutions in each decoupled system in both the Sobolev space and the weighted Sobolev space, and we derive the optimal error estimates for the numerical solutions on both quasi-uniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings.
November 17, 2022
POT 745 from 11:00am-12:00 pm
Title: Robust Estimation of Smooth Graph Signals from Randomized Space-time Samples
Speaker: Longxiu Huang, Michigan State University.
Abstract:
Heat diffusion processes have found wide applications in modeling dynamical system over graphs. In this talk, I will talk about the recovery of a k-bandlimited graph signal that is an initial signal of a heat diffusion process from its space-time samples. In this work, we have proposed three random space-time sampling regimes, termed dynamical sampling techniques, that consist in selecting a small subset of space-time nodes at random according to some probability distribution. We show that the number of space-time samples required to ensure stable recovery for each regime depends on a parameter called the spectral graph weighted coherence, that depends on the interplay between the dynamics over the graphs and sampling probability distributions. Then, we propose a computationally efficient method to reconstruct k-bandlimited signals from their space-time samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we test dynamical sampling techniques on a wide variety of graphs. The numerical results on support our theoretical findings and demonstrate the efficiency.
November 10, 2022
POT 745 from 11:00am-12:00 pm
Title: Co-Separable Nonnegative Matrix Factorization
Speaker: Matthew McCarver, University of Kentucky.
Abstract:
Nonnegative matrix factorization (NMF) is a useful tool that has been widely used in the analysis of high dimensional data sets such as images and documents. In this talk, we consider a new variant of NMF with the separability assumption based on a 3-factor NMF, referred to as Co-Separable NMF (CoS-NMF). We introduce some properties of CoS-NMF, explore an optimization model for CoS-NMF, and implement a fast gradient descent based method to solve the model. Numerical experiments on synthetic data and images datasets for facial recognition are conducted to demonstrate the performance of this model.
October 20, 2022
POT 745 from 11:00am-12:00 pm
Title: Optimal Decision-Making in Social Networks
Speaker: Bhargav Karamched, Florida State University.
Abstract:
To make decisions we are guided by the evidence we collect and the opinions of friends and neighbors. How do we combine our private beliefs with information we obtain from our social network? To understand the strategies humans use to do so, it is useful to compare them to observers that optimally integrate all evidence. Here we derive network models of rational (Bayes optimal) agents who accumulate private measurements and observe the decisions of their neighbors to make an irreversible choice between two options. The resulting information exchange dynamics has interesting properties: When decision thresholds are asymmetric, the absence of a decision can be increasingly informative over time. In a recurrent network of two agents, the absence of a decision can lead to a sequence of belief updates akin to those in the literature on common knowledge. We then consider large networks under the same framework. Using a combination of asymptotic methods and first passage time calculations, we find that when the network is sufficiently large, most agents decide correctly irrespective of whether the first agent's decision is right or wrong. Interestingly, individuals in networks with both hasty and deliberate agents can make the right choice more quickly and more often than in networks of identical agents: Observing the choices of a small group of hasty agents can allow the more deliberate agents to make accurate decisions. Our model is tractable and readily generalizable, paving the way for the future study of different social network topologies. We conclude that diverse groups make quicker, more accurate decisions than homogenous groups.
October 6, 2022
POT 745 from 11:00am-12:00 pm
Title: Extrapolation for eigenvalue problems: Upcycling data for faster convergence
Speaker: Sara Pollock, University of Florida.
Abstract:
We will discuss accelerating convergence to numerical solutions of eigenvalue problems using a simple post-processing step applied to standard eigensolver techniques. First we will consider accelerating the standard power iteration, one of the most basic and powerful but sometimes very slow iterative methods. We will review some recent results on how we can make the power iteration faster by recombining previous iterates to form our next approximation to a solution; and, we will discuss why this works. We can also apply a similar technique to a restarted Arnoldi method to boost its performance with little additional computational cost. Numerical examples will illustrate the theory.
September 29, 2022
POT 745 from 11:00am-12:00 pm
Title: Low-Rank High-Order Tensor Completion with Applications in Visual Data
Speaker: Katherine Henneberger, University of Kentucky.
Abstract:
Tensors are the natural representation form for a broad range of real-world data, including images and videos. Tensor Completion (TC) aims to recover tensors with missing entries or with partial observations. In this talk a scalable low t-SVD rank TC model is presented, which successfully handles incomplete tensor data with arbitrary order. Using a convex TC model that minimizes the order-d tensor nuclear norm, one can accurately recover the underlying tensor with low t-SVD rank. We will review the preliminaries of TC, introduce the proposed recovery model, and implement an efficient algorithm. Several experiments on synthetic and visual data will be presented to demonstrate the performance of this model.
September 8, 2022
POT 745 from 11:00am-12:00 pm
Title: Theory and Algorithms for Nonlinear Eigenvector Problems with Affine-Linear Structures
Speaker: Ding Lu, University of Kentucky.
Abstract:
Eigenvector-dependent Nonlinear Eigenvalue Problems (NEPv) have long played critical roles in computational physics and chemistry and are becoming increasingly important in numerous data science applications. In this talk, we consider a class of NEPv where the coefficient matrices have a special affine-linear structure. One important origin of affine-linear NEPv is the Rayleigh-quotient-related optimization, including the trace-ratio optimization for dimension reduction and robust Rayleigh-quotient optimization for handling data uncertainties. We will establish variational characterizations for particular affine-linear NEPv, and then provide a geometric interpretation of a Self-Consistent Fields (SCF) iteration for solving the NEPv. The geometric interpretation reveals the global convergence of SCF in many cases and explains its potential non-convergence issues in others. New improvements to SCF, including the local acceleration schemes and the global verification techniques, are also discussed. Numerical experiments demonstrate the effectiveness of our approach.

Academic Year 2021-22

April 14, 2022
POT 745 from 11:00am-12:00 pm
Title: Enhanced 3DTV Regularization and Its Application in HSI Denoising
Speaker: Jonathan Benoit, University of Kentucky.
Abstract:
HSI denoising is one of the fundamental tasks in computer vision and medical imaging. In this talk, we discuss the Enhanced 3D Total Variation regularization method of HSI denoising. The enhancement comes from leveraging the low-rank nature of HSI gradients via a linear transformation. We will begin with the basics of image denoising, introduce the enhanced model, and derive an efficient numerical algorithm. Various numerical results will be presented to show the robustness and performance of this method.
April 7, 2022
POT 745 from 11:00am-12:00 pm
Title: An Adaptive Formation Control Architecture for A Team of Quadrotors with Performance and Safety Constraints
Speaker: Xu Jin, University of Kentucky.
Abstract:
We propose a novel adaptive formation control architecture for a group of quadrotor systems, under line-of-sight (LOS) distance and relative distance constraints, where the constraint requirements can be both asymmetric and time-varying in nature. Universal barrier functions are adopted in the controller design and analysis, which is a generic framework that can address system with different types of constraints in a unified controller architecture. Furthermore, each quadrotor's mass is unknown, and the system dynamics are subjected to time-varying external disturbance. Through rigorous analysis, an exponential convergence rate can be guaranteed on the distance tracking errors, while the constraints are satisfied during the operation. A simulation example further demonstrates the efficacy of the proposed control framework.
March 31, 2022
POT 745 from 11:00am-12:00 pm
Title: Cayley Orthogonal Gated Recurrent Units and its application in Bio-molecular data
Speaker: Edison Mucllari, University of Kentucky.
Abstract:
We are going to start with a quick introduction about Recurrent Neural Networks, Gated Recurrent Units(GRU) and Scaled Cayley Orthogonal Recurrent Neural Networks (scoRNN). Then, we are going to talk about Scaled Cayley Orthogonal GRU (scoGRU) and explain the model as well as the way it learns. During the talk we are going to see some results comparing our model with others. At the second part of my talk, we are going to talk about implementing scoGRU in an Autoencoder and how we use the Autoencoder to obtain the descriptors for the toxic data, logP, Lipophilicity and Freesolv. After understanding the Autoencoder, we are going to explain the model we use for the prediction of toxic data, logP, Lipophilicity and Freesolv. At the end we are going to see our results compared with GRU results (GRU is used at the Autoencoder same way we use scoGRU).
March 24, 2022 (Canceled)
POT 745 from 11:00am-12:00 pm
Title: Optimal Decision-Making in Social Networks
Speaker: Bhargav Karamched, Florida State University.
Abstract:
To make decisions we are guided by the evidence we collect and the opinions of friends and neighbors. How do we combine our private beliefs with information we obtain from our social network? To understand the strategies humans use to do so, it is useful to compare them to observers that optimally integrate all evidence. Here we derive network models of rational (Bayes optimal) agents who accumulate private measurements and observe the decisions of their neighbors to make an irreversible choice between two options. The resulting information exchange dynamics has interesting properties: When decision thresholds are asymmetric, the absence of a decision can be increasingly informative over time. In a recurrent network of two agents, the absence of a decision can lead to a sequence of belief updates akin to those in the literature on common knowledge. We then consider large networks under the same framework. Using a combination of asymptotic methods and first passage time calculations, we find that when the network is sufficiently large, most agents decide correctly irrespective of whether the first agent's decision is right or wrong. Interestingly, individuals in networks with both hasty and deliberate agents can make the right choice more quickly and more often than in networks of identical agents: Observing the choices of a small group of hasty agents can allow the more deliberate agents to make accurate decisions. Our model is tractable and readily generalizable, paving the way for the future study of different social network topologies. We conclude that diverse groups make quicker, more accurate decisions than homogenous groups.
March 3, 2022
Online from 11:00am-12:00 pm
Title: Eigenvalue solution via the use of a single random vector
Speaker: Jianlin Xia, Purdue University.
Abstract:
In this talk, we show the design of reliable and efficient eigensolvers based on the use of a single random vector in eigenvalue detection strategies. Given a region of interest, some randomized estimators applied to a spectral projector are used to detect the existence of eigenvalues. The reliability of the estimators with a single random vector are studied so as to obtain robust thresholds for eigenvalue detection. This is then combined with repeated domain partitioning to find eigenvalues to a desired accuracy. Preconditioned Krylov subspace methods are used to solve multiple shifted linear systems in the eigenvalue detection scheme and Krylov subspaces are reused for multiple shifts. We also show how another randomized strategy can be used to obtain eigenvectors reliably with little extra costs.
February 10, 2022
Online from 11:00am-12:00 pm
Title: Uncovering potential interventions for pancreatic cancer patients via mathematical modeling
Speaker: Daniel Plaugher, University of Kentucky.
Abstract:
While any cancer diagnosis is life-altering, pancreatic cancer is among the most discouraging to receive because of its extreme difficulty to overcome. Recent literature suggests that the surrounding environment of pancreatic cancer cells could play a key role in their therapeutic response. Thus, there is a growing need for the discovery of intervention strategies that can attack these cancer cells and the microenvironment that protects them. To address this problem, we have built a mathematical model to computationally predict patient outcomes and test discovered control targets. Using amenable control approaches, we were able discover novel control targets as well as validate previously known results. Further, we were able to predict a hierarchy of disease aggression based on which mutations were present, in the sense that some combinations may be more difficult to treat or that the patient might see a faster decline. This is a step forward in aiding the development of personalized medicine, as treatment protocols progress in becoming more patient-specific.
Jan 13, 2022
Online from 11:00am-12:00 pm
Title: Low-rank Structured Data Analysis
Speaker: Longxiu Huang, University of California, Los Angeles.
Abstract:
In modern data analysis, the datasets are often represented by large-scale matrices or tensors( the generalization of matrices to higher dimensions). To have a better understanding of the data, an important step is to construct a low-dimensional/compressed representation of the data that may be better to analyze and interpret in light of a corpus of field-specific information. To implement the goal, a primary tool is the matrix/tensor decomposition. In this talk, I will talk about novel matrix/tensor decompositions, CUR decompositions, which are memory efficient and computationally cheap. Besides, I will also discuss how CUR decompositions are applied to develop efficient algorithms or models to robust decomposition and completions and show the efficiency of the algorithms on some real and synthetic datasets.
December 9, 2021
POT 745 from 11:00am-12:00 pm
Title: Symmetry Structured Convolutional Neural Networks
Speaker: Vasily Zadorozhnyy, University of Kentucky.
Abstract:
We will consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for example a sequential recommendation problem. We will introduce a CNN architecture that generates and preserves the symmetry structure in the network's convolutional layers. We will present parameterizations for the convolutional kernels that produce update rules to maintain symmetry throughout the training. Lastly, we will show that the symmetric structured networks produce improved results using fewer numbers of machine parameters.
December 2, 2021
POT 745 from 11:00am-12:00 pm
Title: Video Denoising via Directional Fractional Order Total Variation
Speaker: Jonathan Benoit, University of Kentucky.
Abstract:
Video denoising is one of the fundamental tasks in computer vision and medical imaging. In this talk, we propose a novel denoising method for spatiotemporal video data based on the Directional Fractional Order Total Variation (DFTV) regularization and Huber loss. We will begin with the basics of image denoising, introduce our DFTV regularized video denoising model, and derive an efficient numerical algorithm. Various numerical results will be presented to show the robustness and performance of our method.
November 11, 2021
Online from 11:00am-12:00 pm
Title: Reliable computation of exterior eigenvalues through matrix functions
Speaker: Fei Xue, Clemson University.
Abstract:
Exterior eigenvalues of large sparse matrices are needed for various applications, such as linear stability analysis. These eigenvalues are difficult to compute efficiently and reliably if they are much smaller than the dominant eigenvalues in modulus. Traditional spectral transformations such as Cayley transform are far from reliable. In this talk, we discuss a simple idea of spectral transformation based on functions of matrices that maps the desired exterior eigenvalues to dominant ones. Approximations of the action of matrix functions on vectors is fundamental for this approach, which can be performed by rational Krylov subspace methods (RKSM). Numerical experiments for linear and nonlinear eigenvalue problems demonstrate the reliability of this method.
October 14, 2021
POT 745 from 11:00am-11:30 am
Title: A Feedback Control Architecture for Bioelectronic Devices with Applications to Wound Healing
Speaker: Marcella Gomez, University of California, Santa Cruz.
Abstract:
Bioelectronic devices can provide an interface for feedback control of biological processes in real-time based on sensor information tracking biological response. The main control challenges are guaranteeing system convergence in the presence of saturating inputs into the bioelectronic device and complexities from indirect control of biological systems. In this talk, we first derive a saturated-based robust sliding mode control design for a partially unknown nonlinear system with disturbance. Next, we develop a data informed model of a bioelectronic device for in silico simulations. Our controller is then applied to the model to demonstrate controlled pH of a target area. A modular control architecture is chosen to interface the bioelectronic device and controller with a bistable phenomenological model of wound healing to demonstrate closed-loop biological treatment. External pH is regulated by the bioelectronic device to accelerate wound healing, while avoiding chronic inflammation.
October 14, 2021
POT 745 from 11:30am-12:00 pm
Title: Identification of control targets in Boolean networks via computational algebra
Speaker: Alan Veliz Cuba, University of Dayton.
Abstract:
Many problems in systems biology have the goal of finding strategies to change an undesirable state of a biological system into another state through an intervention. The identification of such strategies is typically based on a mathematical model such as Boolean networks. In this talk we will see how to find node and edge interventions using computational algebra.
September 30, 2021
POT 745 from 11:00am-12:00 pm
Title: Geometry and Statistics: New Developments in Statistics on Manifolds
Speaker: Lizhen Lin, University of Notre Dame.
Abstract:
With the increasing prevalence of modern complex data in non-Euclidean (e.g., manifold) forms, there is a growing need for developing models and theory for inference of non-Euclidean data. This talk first presents some recent advances in nonparametric inference on manifolds and other non-Euclidean spaces. The initial focus is on nonparametric inference based on Fréchet means. In particular, we present omnibus central limit theorems for Fréchet means for inference, which can be applied to general metric spaces including stratified spaces, greatly expanding the current scope of inference. A robust framework based on the classical idea of median-of-means is then proposed which yields estimates with provable robustness and improved concentration. In addition to inferring i.i.d data, we also consider nonparametric regression problems where predictors or responses lie on manifolds. Various simulated or real data examples are considered.
September 2, 2021
Online from 11:00am-12:00 pm
Title: Evaluation of the United States COVID-19 vaccine allocation strategy
Speaker: Claus Kadelka, Iowa State University.
Abstract:
Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. In this talk, I present our recent study that evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested). We developed a compartmental disease model that incorporates key elements of the current pandemic including age-varying susceptibility to infection, age-varying clinical fraction, an active case-count dependent social distancing level, and time-varying infectivity (accounting for the emergence of more infectious virus strains). The CDC allocation strategy is compared to all other possibly optimal allocations that stagger vaccine roll-out in up to four phases (17.5 million strategies). The CDC allocation strategy performed well in all vaccination goals but never optimally. Under the developed model, the CDC allocation deviated from the optimal allocations by small amounts, with 0.19\% more deaths, 4.0% more cases, 4.07% more infections, and 0.97% higher YLL, than the respective optimal strategies. The CDC decision to not prioritize the vaccination of individuals under the age of 16 was optimal, as was the prioritization of health-care workers and other essential workers over non-essential workers. Finally, a higher prioritization of individuals with comorbidities in all age groups improved outcomes compared to the CDC allocation. The developed approach can be used to inform the design of future mass vaccine rollouts in the United States, or adapted for use by other countries seeking to optimize the effectiveness of their vaccine allocation strategies.

Academic Year 2020-21

April 29, 2021
Online from 11:00am-12:00 pm
Title: Global-in-time domain decomposition methods for the coupled Stokes and Darcy flows
Speaker: Thi-Thao-Phuong Hoang, Auburn University.
Abstract:
In many engineering and biological applications (e.g., groundwater flow problems, flows in vuggy porous media, industrial filtrations, biofluid-organ interaction and cardiovascular flows), the Stokes-Darcy system is used to model the interaction of fluid flow with porous media flow, where the Stokes equations represent an incompressible fluid, and the Darcy equations represent a flow through a porous medium. The time scales in the Stokes and Darcy regions could be largely different, thus it is inefficient to use the same time step throughout the entire spatial domain. In this talk, we present decoupling iterative algorithms based on domain decomposition for the time-dependent Stokes-Darcy model, in which different time step sizes can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on either physical interface conditions or equivalent Robin-Robin interface conditions. Such an interface problem is solved iteratively by a Krylov subspace method (e.g., GMRES) which involves at each iteration parallel solution of time-dependent Stokes and Darcy problems. Consequently, local discretizations in both space and time can be used to efficiently handle multiphysics systems with discontinuous parameters. Numerical experiments with nonconforming time grids are considered to illustrate the performance of the proposed methods.
April 22, 2021
Online from 11:00am-12:00 pm
Title: Modeling and topological methods to better understand pattern formation in fish
Speaker: Alexandria Volkening, Northwestern University.
Abstract:
Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, voters in an election, or locusts in a swarm. Self-organization also occurs at much smaller scales in biology, though, and here I will focus on elucidating how brightly colored cells interact to form skin patterns in zebrafish. Wild-type zebrafish are named for their dark and light stripes, but mutant zebrafish feature variable skin patterns, including spots and labyrinth curves. All these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells. This leads to the question: how do cell interactions change to create mutant patterns? The longterm motivation for my work is to help shed light on this question and better link genes, cell behavior, and visible animal characteristics. Toward this goal, we combine different modeling approaches (including agent-based and continuum) to simulate pattern formation and make experimentally testable predictions. In this talk, I will overview our models and highlight how topological data analysis can be used to quantitatively describe self-organization in silico and in vivo.
April 15, 2021
Online from 11:00am-12:00 pm
Title: A Self-consistent-field Iteration for Orthogonal Canonical Correlation Analysis
Speaker: Li Wang, University of Texas at Arlington.
Abstract:
We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a useful criterion for visualization, pattern recognition and feature extraction, existing methods for solving OCCA problem are either numerically unstable by relying on a deflation scheme, or less efficient by directly using generic optimization methods. In this paper, we propose an alternating numerical scheme whose core is the sub-maximization problem in the trace-fractional form with an orthogonality constraint. A customized self-consistent-field (SCF) iteration for this sub-maximization problem is devised. It is proved that the SCF iteration is globally convergent to a KKT point and that the alternating numerical scheme always converges. We further formulate a new trace-fractional maximization problem for orthogonal multiset CCA and propose an efficient algorithm with an either Jacobi-style or Gauss-Seidel-style updating scheme based on the SCF iteration. Extensive experiments are conducted to evaluate the proposed algorithms against existing methods, including real-world applications of multi-label classification and multi-view feature extraction. Experimental results show that our methods not only perform competitively to or better than the existing methods but also are more efficient.
April 8, 2021
Online from 11:00am-12:00 pm
Title: Boolean canalization in the micro and macro scales
Speaker: Santosh Manicka, Tufts University.
Abstract:
Canalization is a property of Boolean automata that characterizes the extent to which subsets of inputs determine (canalize) the output. In this presentation, I describe the role of canalization as a determinant of the dynamical character of Boolean networks (BN). I consider two different measures of canalization introduced by Marques-Pita and Rocha, namely 'effective connectivity' and 'input symmetry,' in a three-pronged approach. First, we show that the mean 'effective connectivity,' a measure of the true mean in-degree of a BN, is a better predictor of the dynamical regime (order or chaos) of random BNs with homogeneous connectivity than the mean in-degree. Next, I combine effective connectivity and input symmetry in a single measure of 'unified canalization' by using a common yardstick of Boolean hypercube "dimension" - a form of fractal dimension. I show that the unified measure is a better predictor of dynamical regime than effective connectivity alone for BNs with large in-degrees. Finally, I introduce 'integrated effective connectivity' as a macro-scale extension of effective connectivity that characterizes the canalization present in BNs coarse-grained in time obtained by iteratively composing a BN with itself. I show that the integrated measure is a better predictor of long-term dynamical regime than just effective connectivity for a small class of BNs known as the elementary cellular automata. The results also help partly explain the chaotic properties of Rule 30 and why it makes sense to use it as a random number generator.
March 25, 2021
Online from 11:00am-12:00 pm
Title: A New Block Preconditioner for Implicit Runge-Kutta Methods for Parabolic PDE Problems
Speaker: Masud Rana, Texas Tech University.
Abstract:
Explicit time integrators for parabolic PDE are subject to a restrictive timestep limit, so A-stable integrators are essential. It is well known that although there are no A-stable explicit linear multistep methods and implicit multistep methods cannot be A-stable beyond order two, there exist A-stable and L-stable implicit Runge-Kutta (IRK) methods at all orders. IRK methods offer an appealing combination of stability and high order; however, these methods are not widely used for PDE because they lead to large, strongly coupled linear systems. An s-stage IRK system has s-times as many degrees of freedom as the systems resulting from backward Euler or implicit trapezoidal rule discretization applied to the same equation set. In this talk, I will introduce a new block preconditioner for IRK methods, based on a block LDU factorization with algebraic multigrid subsolves for scalability. I will demonstrate the effectiveness of this preconditioner on two test problems, a 2-D heat equation and a model advection-difusion problem. I compare this preconditioner in condition number and eigenvalue distribution, and in numerical experiments with other preconditioners currently in the literature. Experiments are run using IRK methods with two to seven stages. We find that the new preconditioner outperforms the others, with the improvement becoming more pronounced as spatial discretization is refined and as temporal order is increased.
March 11, 2021
Online from 11:00am-12:00 pm
Title: Data-driven hierarchical kernel matrix methods
Speaker: Yuanzhe Xi, Emory University.
Abstract:
The explosion of datasets from diverse applications and the increasing computational power of computer hardware call for the need of scalable algorithms and software. In this talk, I will focus on the computational bottlenecks associated with fully populated kernel matrices that are ubiquitous in machine learning as well as scientific simulations. Those dense matrices usually induce large computation costs that scale quadratically or cubically with problem size. The complexity can be significantly reduced by exploiting the hierarchical rank structure inside the kernel matrices. Representing a kernel matrix in an appropriate hierarchical format enables (nearly) optimal storage and computations. I will demonstrate the newly developed data-driven techniques for hierarchical representations and compare their performance with state-of-the-art methods/software on several real-world applications.
March 4, 2021
Online from 11:00am-12:00 pm
Title: Statistics, Topology and Data Analysis
Speaker: Vasileios Maroulas, University of Tennessee.
Abstract:
In this talk, I will discuss how statistics and topological data analysis are beautifully complement each other to solve real data problems. As a paradigm, I will discuss supervised learning, and present a classification approach using a novel Bayesian framework for persistent homology. An application to materials science will be discussed.
February 25, 2021
Online from 11:00am-12:00 pm
Title: Mathematical modelling of blood coagulation system
Speaker: Ksenia Zlobina, University of California, Santa Cruz.
Abstract:
Blood is an important liquid organ performing transport functions. Any injury may lead to dangerous blood loss, but fortunately we have a reliable emergency blood coagulation system that quickly reacts to injuries and prevents massive blood loss. Disorders in blood coagulation may induce thrombosis, stroke, myocardial infarction and other complications, including lethal ones. In the early months of coronavirus pandemic, the first important achievement in medicine was including anticoagulant therapy in protocols of treatment that decreased percentage of deaths. Many aspects of blood coagulation are still to be understood in the future. Blood coagulation is an interesting object of investigation by mathematical models. It includes a nonlinear threshold system of activation, polymerization of fibrin leading to gelation, activation of blood cells and others. All this biochemical system works in a branched network of blood vessels with a variety of hydrodynamical conditions in them. This research is related to nonlinear dynamical systems and reaction-diffusion-convection models.
February 18, 2021
Online from 11:00am-12:00 pm
Title: Modeling of Emergent Patterns Within Stem Cell Colonies
Speaker: Daniel A. Cruz, Georgia Tech.
Abstract:
The differentiation of stem cell colonies into specified tissue types is possible through local and long-distance intercellular communication; however, it is unclear which mechanisms take priority in context-specific situations. Here we consider human induced pluripotent stem cells (hiPSCs) whose therapeutic potential arises from their ability to differentiate into all germ lineages. Prior work in the literature suggests that both cell-autonomous and non-autonomous (e.g. positional) mechanisms determine cell fate during the differentiation of hiSPCs, producing patterns and other system-level features in the process. Informed by experimental data, we develop a collection of agent-based models (ABMs) whose agents (i.e. cells) are each equipped with local rules that govern how the agents interact with their environment and with each other. The purpose of each ABM is to simulate the early differentiation of hiPSCs according to a different set of biological assumptions, with some ABMs using a Boolean network to model potential mechanisms of intercellular communication. We also extend an existing mathematical framework by M. Yereniuk and S.D. Olson which formalizes ABMs to estimate long-term model behavior with respect to time. Our extensions introduce the birth and death of agents into the framework, and our estimates aim to establish connections between local interactions and certain system-level observations. Thus, we study both the emergent behaviors of our ABMs and the dynamics of the local rules governing each agent in order to ascertain which modes of intercellular communication determine cell fate.
February 4, 2021
Online from 11:00am-12:00 pm
Title: Applied Math Group Open House
Panel: Ding Lu, David Murrugarra, Duc Nguyen, Jing Qin, Qiang Ye.
Abstract:
This will be an opportunity for students to learn more about the applied math research group and for faculty to put faces with names of our first- and second-year students.

Academic Year 2019-20

April 23, 2020
POT 745 from 11:00am-12:00 pm
Title: First-order Upwind Scheme for Solving the Adjoint Euler Equations
Speaker: Chase Ashby, University of Kentucky.
Abstract:
A first-order upwind scheme based on matrix splitting is developed for solving the 2D adjoint Euler equations. We prove that the adjoint advection equation is a suitable model for the 1D adjoint Euler equations and use this knowledge to develop and study our proposed numerical scheme. Solution behavior is first discussed from a mathematical perspective and later demonstrated numerically for both the model equations and adjoint Euler equations.
April 16, 2020
POT 745 from 11:00am-12:00 pm
Title: TBA
Speaker: Hasan Poonawala, University of Kentucky.
Abstract:
April 9, 2020
POT 745 from 11:00am-12:00 pm
Title: TBA
Speaker: Chenglong Ye, University of Kentucky.
Abstract:
April 2, 2020
POT 745 from 11:00am-12:00 pm
Title: TBA
Speaker: Jon Lee, University of Michigan.
Abstract:
March 26, 2020
POT 745 from 11:00am-12:00 pm
Title: TBA
Speaker: Kit Newton, University of Wisconsin-Madison.
Abstract:
March 12, 2020
POT 745 from 11:00am-12:00 pm
Title: Improved Training of Generative Adversarial Network
Speaker: Vasily Zadorozhnyy, University of Kentucky.
Abstract:
The original Generative Adversarial Network was introduced by Ian Goodfellow et al. in 2014, together with a discriminator loss function, called binary cross-entropy. Later, other discriminator loss functions were developed: WGAN loss, hidge loss, Dragan loss, etc. We introduce a new family of discriminator loss functions. Experiments validated the effectiveness of our loss functions on unconditional image generation task.
March 5, 2020
POT 745 from 11:30am-12:00 pm
Title: Designing multistability with AND gates
Speaker: Alan Veliz Cuba, University of Dayton.
Abstract:
Systems of differential equations have been used to model biological systems such as gene and neural networks. A problem of particular interest is to understand and control the number of stable steady states. Here we propose conjunctive networks (systems of differential equations equations created using AND gates) to achieve any desired number of stable steady states. Our approach uses combinatorial tools to easily predict the number of stable steady states from the structure of the wiring diagram.
March 5, 2020
POT 745 from 11:00am-11:30 am
Title: Mechanisms of stabilization and development in early multicellular evolution
Speaker: Pedro Marquez Zacarias, Georgia Tech.
Abstract:
The evolution of life on Earth is marked by a few biological innovations that profoundly changed downstream evolutionary trajectories. John Maynard Smith and Eörs Szathmáry termed these innovations Major Evolutionary Transitions and among others, they include the evolution of multicellular organisms from unicellular ancestors. Although the fossil record is scarce to understand what happened in the early evolution of multicellularity, we can conduct experiments in the laboratory to evolve primitive multicellular organisms. Using an experimental model of multicellularity, called 'snowflake yeast', and some theoretical tools, we asked: how is multicellularity stabilized over evolutionary time? and, how simple developmental rules can lead to an increase in multicellular size? The understanding of multicellular evolution can inform us about the mechanisms underlying other major evolutionary transitions, and more generally, this research can deepen our understanding of the evolution of biological complexity.
Feb 13, 2020
POT 745 from 11:00am-12:00 pm
Title: Particle collision model embedded into an optimization graph theory problem
Speaker: Darleen Perez-Lavin, University of Kentucky.
Abstract:
The color reconnection model is used to explain and predict the production of particles in high energy collisions of hadrons. According to this model, the colored partons produced in an event can lose their original color quantum numbers and acquire new ones if this reduces a type of free energy. The computation of the ground state of the free energy is combinatorially complex. In this note, we demonstrate the limitations of traditional techniques for solving this problem and the possibility of using quantum solvers. In particular, we present an Ising model formulation for quantum annealers and a gate-based formulation. During my time at FermiLab, given by the MSGI-NSF program, I was able to jump in on this problem to help construct an optimal Hamiltonian for quantum annealers. I will be providing an introduction to the physics problem and my contribution in how we used AMPL to help us construct a Hamiltonian.
Jan 30, 2020
POT 745 from 11:00am-12:00 pm
Title: Linearized Krylov subspace Bregman iteration with nonnegativity constraint
Speaker: Lothar Reichel, Kent State University.
Abstract:
Bregman-type iterative methods have attracted considerable attention in recent years due to their ease of implementation and the high quality of the computed solutions they deliver. However, these iterative methods may require alarge number of iterations and this reduces their attractiveness. This talk describes a linearized Bregman algorithm defined by projecting the problem tobe solved into an appropriately chosen low-dimensional Krylov subspace. The projection reduces both the number of iterations and the computational effort required for each iteration. A variant of this solution method, in which nonnegativity of each computed iterate is imposed, also is described. The talk presents joint work with A. Buccini and M. Pasha.
December 12, 2019
POT 745 from 11:00am-12:00 pm
Title: Algebraic Data Science
Speaker: Brandilyn Stigler, Southern Methodist University.
Abstract:
Data science has emerged as an important field for making decisions based on data collected from sectors as varied as health care and housing. Two important steps in a data-science pipeline are data collection strategies and predictive modeling. In this talk, we introduce an algebraic-geometric platform for unifying experimental design for discrete data sets and model selection for polynomial dynamical systems. We will illustrate the utility of the platform on a few biological systems.
November 14, 2019
POT 745 from 11:00am-12:00 pm
Title: Recovering data sparse in a frame
Speaker: Xuemei Chen, New Mexico State University.
Abstract:
In this talk, we will first review some classical results on compressed sensing, a subject about recovering sparse signals from undersampled linear measurements. The theory developed in compressed sensing is transformative as it has been applied to a broader class of data recovery problems such as matrix completion. Then we will focus on its generalization where signals are sparse in a redundant frame. We will discuss the challenges faced in this case, as well as some new results. A preliminary image inpainting application will also be addressed at the end of the talk.
October 31, 2019
POT 745 from 11:00am-12:00 pm
Title: Enhancing mechanistic modeling with machine learning
Speaker: Tongli Zhang, University of Cincinnati.
Abstract:
At their core, biological systems are information processing systems. In response to numerous environmental cues, the complex molecular interaction networks within human cells integrate these signals and orchestrate a number of intricate cellular behaviors. Verbal argument and intuition alone are insufficient to understand how these complex networks control cellular behaviors or to rationally design treatment, and it is beneficial to translate these molecular networks into realistic and predictive mathematical models. However, the development of such models faces several fundamental challenges: 1) the control network is complex and full of interacting feedbacks, 2) the kinetic constants characterizing the biological reactions are often unavailable, 3) it is often impossible to derive analytical solutions of these models, and 4) once the models become increasingly realistic and complex, they are often as difficult to understand as the original biological system. To address these above mentioned challenges, we have developed an integrated computational pipeline that combines Mechanistic modeling, Machine learning and nonlinear dynamical analysis. By integrating different methods with unique strength and limitations, this innovative pipeline can potentially overcome each other's limitations. This novel, integrated pipeline has been applied to study several different biological systems, and the results have been verified experimentally. Based on our theoretical analysis and experimental confirmation, we propose that his novel pipeline can be generally applied to understand any complex and uncertain biological systems.
October 24, 2019
POT 745 from 11:00am-12:00 pm
Title: Generative Adversarial Networks
Speaker: Vasily Zadorozhnyy, University of Kentucky.
Abstract:
In 2014, Ian Goodfellow et al. proposed a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. In this talk, I will talk about the structure of such a framework, how we train it as well as some theoretical results and applications.
October 17, 2019
POT 745 from 11:00am-12:00 pm
Title: Parameter space analysis and automatic theorem proving in SageMath
Speaker: Yuan Zhou, University of Kentucky.
Abstract:
A metaprogramming trick transforms algebraic programs for testing a property for a given input parameter into programs that compute semialgebraic descriptions of the input parameters for which the property holds. Our implementation of this trick is for the Python-based computer algebra system SageMath. We borrow techniques from global optimization for simplification of semialgebraic sets. We investigate practical representations of proof cells and efficient strategies that lead to shorter proofs. We illustrate it with an application to the theory of integer linear optimization, the automatic discovery and proof of certain cutting plane theorems in integer programming.
October 3, 2019
POT 745 from 11:00am-12:00 pm
Title: Efficient control methods for stochastic Boolean networks
Speaker: David Murrugarra, University of Kentucky.
Abstract:
The development of efficient methods for finding intervention strategies that can direct a system from an undesirable state into a more desirable state is an important problem in systems biology. The identification of potential interventions can be achieved through mathematical modeling by finding appropriate input manipulations that represent external interventions in the system. This talk will describe a stochastic modeling framework generalized from Boolean networks, which will be used to formulate an optimal control problem. The optimal control method requires a set of control inputs, each representing the silencing of a gene or the disruption of an interaction between two molecules. Several methods from Markov decision processes can be used to generate an optimal policy that dictates the action to be taken at each state. However, the computational complexity of these algorithms limits the applications of standard algorithms to small models. This talk will discuss alternate methods that can be used for large models.
September 26, 2019
POT 745 from 11:00am-12:00 pm
Title: Information Theoretic Learning with Infinitely Divisible Kernels
Speaker: Luis Sanchez Giraldo, University of Kentucky.
Abstract:
In this work, we introduce a framework for information theoretic learning based on an entropy-like functional defined on positive definite matrices. The proposed functional, which is based on Renyi's axiomatic definition of entropy, provides a quantity that can be estimated from data and applied as an objective function in different machine learning problems. As an application example, we derive a supervised metric learning algorithm using a matrix-based analogue to conditional entropy with results comparable with the state of the art.
September 5, 2019
POT 745 from 11:00am-12:00 pm
Title: On the Real-time Learning-based Control of Dynamical Systems
Speaker: Mohammad Jafari, University of California, Santa Cruz.
Abstract:
Understanding actuation mechanisms, sensing systems, and behavior patterns of humans has been a subject of scientific inquiry for centuries. The brain is arguably the most important organ in the human body. It controls and coordinates actions and reactions, allows us to think and feel, and enables us to have memories and feelings-all the things that make us human. In most applications, controllers are not designed after humans. In general, unique applications in controls require custom controller designs based on systems information. This becomes problematic when there are un-modeled disturbances and/or full knowledge of the system dynamics is not available, etc., if we can mimic human behavior, this allows us to adaptively learn the control law without a priori knowledge about the system dynamics. To mimic human behavior, we must explore methods that can adapt to unknown environments with minimal system information. However, limitations include insufficient data a priori, computational complexity of learning algorithms, and lack of methods for real-time implementation of said algorithms, etc. We will overcome these challenges by considering real-time learning-based methods. I will present the Emotional Learning and Neural Network (-based) approaches for utilization in real-time control of unknown dynamical systems. Specifically, we will demonstrate applications in Robotic, Power Systems, and Process Industries.

Academic Year 2018-19

April 25, 2019
POT 745 from 11:00am-12:00 pm
Title: Correct Model Selection in Big Data Analysis
Speaker: Katherine Thompson, University of Kentucky.
Abstract:
Although recent attention has focused on improving predictive models, less consideration has been given to variability introduced into models through incorrect variable selection. Here, the difficulty in choosing a scientifically correct model is explored both theoretically and practically, and the performance of traditional model selection techniques is compared with that of more recent methods. The results in this talk show that often the model with the highest R-squared (or adjusted R-squared) or lowest Akaike Information Criterion (AIC) is not the scientifically correct model, suggesting that traditional model selection techniques may not be appropriate when data sets contain a large number of covariates. This work starts with the derivation of the probability of choosing the scientifically correct model in data sets as a function of regression model parameters, and shows that traditional model selection criteria are outperformed by methods that produce multiple candidate models for researchers' consideration. These results are demonstrated both in simulation studies and through an analysis of a National Health and Nutrition Examination Survey (NHANES) data set.
April 18, 2019
POT 745 from 11:00am-12:00 pm
Title: Modeling the emergence of Division of labor in social systems
Speaker: Oyita Udiani, University of Tennessee.
Abstract:
Division of labor (DOL) is a key pattern of social organization that has evolved in a diverse array of systems from microbes, insects and, of course, humans. Theoretical models predict that division of labor is optimal (and that evolutionary selection can favor it) if there are increasing efficiency (or fitness) benefits arising from individual specialization. One main open question about DOL is 'What proximate (behavioral) mechanisms are responsible for its initial emergence?' In this talk, I will propose a novel theory using a framework of individual energetics and optimization in social dynamics. The key assumption is that individuals are myopic optimizers of a utility function that reflects the tradeoffs of energy/ time needed to perform, and become proficient in, a set of alterative (fitness-bearing) tasks. This hypothesis serves as counterpoint to existing theory of inter-individual variation in 'response thresholds' popularized by studies of task allocation in social insect colonies. Simulation findings show that DOL can emerge from individual optimization and can be enhanced by varying parameters of fatigue and group size. This result has broader implications for understanding the evolutionary transition to sociality (the period in which previously solitary animals began living together in groups).
April 4, 2019
POT 745 from 11:00am-12:00 pm
Title: Using mathematics to fight cancer
Speaker: Ami Radunskaya, Pomona College.
Abstract:
What can mathematics tell us about the treatment of cancer? In this talk I will present some of work that I have done in the modeling of tumor growth and treatment over the last fifteen years. Cancer is a myriad of individual diseases, with the common feature that an individual's own cells have become malignant. Thus, the treatment of cancer poses great challenges, since an attack must be mounted against cells that are nearly identical to normal cells. Mathematical models that describe tumor growth in tissue, the immune response, and the administration of different therapies can suggest treatment strategies that optimize treatment efficacy and minimize negative side-effects. However, the inherent complexity of the immune system and the spatial heterogeneity of human tissue gives rise to mathematical models that pose unique challenges for the mathematician. In this talk I will give a few examples of how mathematicians can work with clinicians and immunologists to understand the development of the disease and to design effective treatments. I will use mathematical tools from dynamical systems, optimal control and network analysis. This talk is intended for a general math audience: no knowledge of biology will be assumed.
Mar 28, 2019
POT 745 from 11:00am-12:00 pm
Title: Intermittent Preventive Treatment and the Spread of Drug Resistant Malaria
Speaker: Olivia Prosper, University of Kentucky.
Abstract:
Over the last decade, control measures have significantly reduced malaria morbidity and mortality. However, the burden of malaria remains high, with more than 70% of malaria deaths occurring in children under the age of five. The spread of antimalarial resistant parasites challenges the efficacy of current interventions, such as Intermittent Preventive Treatment (IPT), whose aim it is to protect this vulnerable population. Under IPT, a curative dose of antimalarial drugs is administered along with a child's routine vaccinations, regardless of their infection status, as both a protective measure and to treat subclinical infections. We have developed mathematical models to study the relative impact of IPT in promoting the spread of drug resistant malaria (compared with treatment of clinically ill individuals), and the combined effect of different drug half-lives, age-structure and local transmis- sion intensity on the number of childhood deaths averted by using IPT in both the short and long-term in malaria endemic settings. I will also discuss some potential consequences of unstable and seasonal transmission of malaria on the efficacy of IPT.
Mar 21, 2019
POT 745 from 11:00am-12:00 pm
Title: On Toric Ideals of some Statistical Models
Speaker: Aida Maraj, University of Kentucky.
Abstract:
We introduce hierarchical models from statistics and their associated Markov bases. These bases are often large and difficult to compute. We introduce certain toric ideals and their algebraic properties as an alternative way of thinking about these objects. One challenge is to describe hierarchical models with infinitely many generators in a finite way. Using a symmetric group action, we describe certain classes of models including progress made for the non-reducible Models. This is joint work with Uwe Nagel.
Mar 7, 2019
POT 715 from 11:00am-12:00 pm
Title: Exponential convergence rates for Batch Normalization
Speaker: Jacob Adams, University of Kentucky.
Abstract:
Batch Normalization is a normalization technique that has been used in training deep Neural Networks since 2015. In spite of its empirical benefits, there exists little theoretical understanding as to why this normalization technique speeds up learning. From a classical optimization perspective, we will discuss specific problem instances in which we can prove that Batch Normalization can accelerate learning, and how this acceleration is due to the fact that Batch Normalization splits the optimization task into optimizing length and direction of parameters separately.
February 21, 2019
POT 745 from 11:00am-12:00 pm
This talk is sponsored by the SIAM Student Chapter at UK.
Title: Efficient Methods for Enforcing Contiguity in Geographic Districting Problems
Speaker: Sheldon Jacobson, University of Illinois Urbana-Champaign.
Abstract:
Every ten years, United States Congressional Districts must be redesigned in response to a national census. While the size of practical political districting problems is typically too large for exact optimization approaches, heuristics such as local search can help stakeholders quickly identify good (but suboptimal) plans that suit their objectives. However, enforcing a district contiguity constraint during local search can require significant computation; tools that can reduce contiguity-based computations in large practical districting problems are needed. This talk introduces the geo-graph framework for modeling geographic districting as a graph partitioning problem, discusses two geo-graph contiguity algorithms, and applies these algorithms to the creation of United States Congressional Districts from census blocks in several states. The experimental results demonstrate that the geo-graph contiguity assessment algorithms reduce the average number of edges visited during contiguity assessments by at least three orders of magnitude in every problem instance when compared with simple graph search, suggesting that the geo-graph model and its associated contiguity algorithms provide a powerful constraint assessment tool to political districting stakeholders. Joint work with Douglas M. King and Edward C. Sewell.
Nov 15, 2018
CB 211 from 11:00am-12:00 pm
Title: Mathematical deep learning for drug discovery
Speaker: Guowei Wei, Michigan State University.
Abstract:
Designing efficient drugs for curing diseases is of essential importance for the 21st century's life science. Computer-aided drug design and discovery has obtained a significant recognition recently. However, the geometric complexity of protein-drug complexes remains a grand challenge to conventional computational methods, including machine learning algorithms. We assume that the physics of interest of protein-drug complexes lies on low-dimensional manifolds or subspaces embedded in a high-dimensional data space. We devise topological abstraction, differential geometry reduction, graph simplification, and multiscale modeling to construct low-dimensional representations of biomolecules in massive and diverse datasets. These representations are integrated with various deep learning algorithms for the predictions of protein-ligand binding affinity, drug toxicity, drug solubility, drug partition coefficient and mutation induced protein stability change, and for the discrimination of active ligands from decoys. I will briefly discuss the working principle of various techniques and their performance in D3R Grand Challenges, a worldwide competition series in computer-aided drug design and discovery (http://users.math.msu.edu/users/wei/D3R_GC3.pdf).
Nov 1, 2018
POT 745 from 11:00am-12:00 pm
Title: Mathematics for Breast Cancer Research: investigating the role of iron
Speaker: Luis Sordo-Vieira, The Jackson Laboratory.
Abstract:
Breast cancer cells are addicted to iron. The mechanisms by which malignant cells acquire and contain high levels of iron are not completely understood. Furthermore, other cell types in a tumor, such as immune cells, can either aid or inhibit cancer cells from acquiring high levels of iron. In order to shed light in the question of how iron affects breast cancer growth, we are applying mathematical tools including polynomial dynamical systems over finite fields and 3D multiscale mathematical modeling. In this talk we will survey how mathematics is aiding in understanding the mechanisms of this addictive iron behavior of malignant cells, and present some preliminary work.
Sept 27, 2018
POT 745 from 11:00am-12:00 pm
Title: A Mathematical Model for the Force and Energetics in Competitive Running
Speaker: Margaret Grogan, University of Kentucky.
Abstract:
Competitive running has been around for thousands of years and many people have wondered what the optimal form and strategy is for running a race. In his paper, Behncke develops a simple mathematical model that focuses on the relationships and dynamics between the forces and energetics at play in order to find an optimal strategy for racing various distances. In this talk, I will describe the biomechanics, energetics, and optimization of running in Behncke's model and present his findings. Note: you do not have to like running to come to this talk :)
Sept 13, 2018
POT 745 from 11:00am-12:00 pm
Title: Preconditioning for Accurate Solutions of the Biharmonic Eigenvalue Problem
Speaker: Kasey Bray, University of Kentucky.
Abstract:
Solving ill-conditioned systems poses two basic problems: convergence and accuracy. Preconditioning can overcome slow convergence, but this is only practical if the preconditioned system can be formed sufficiently accurately. In fact, for a fourth order operator, existing eigenvalue algorithms may compute smaller eigenvalues with little or no accuracy in standard double precision. In this talk, we combine standard matrix eigenvalue solvers with an accurate preconditioning scheme in order to compute the smallest eigenvalue of the biharmonic operator to machine precision in spite of ill-conditioning. The results on various domains are compared with the best known computations from the literature to demonstrate the accuracy and applicability of the method.

Academic Year 2017-18

April 26, 2018
POT 745 from 11:00am-12:00 pm
Title: Finding cycles in discrete dynamical systems
Speaker: Mihai Tohaneanu, University of Kentucky.
Abstract:
Discrete dynamical systems often exhibit chaotic behavior, and as a result finding cycles can be computationally expensive. I present a new approach to this problem, based on adding a nonlinear feedback that stabilizes the cycles. We are then able to find cycles numerically in polynomial time. The main theoretical new insight is casting the problem in the language of complex analysis, and finding new complex polynomials that generalize work of Ted Suffridge that optimize the number of steps one needs in order to stabilize the system. This is joint work with D. Dmitrishin, A. Khamitova and A. Stokolos.
April 26, 2018
POT 745 from 1:00pm-2:00 pm
Title: Complex unitary recurrent neural networks using scaled Cayley transform
Speaker: K.D.Gayan Maduranga, University of Kentucky.
Abstract:
Recurrent neural networks (RNNs) have been successfully used in wide range of sequential problems. Despite this success, RNNs suffer from the vanishing or exploding gradients problem. One recent method ''scaled Cayley orthogonal recurrent neural network'' (scoRNN) addresses this issue by maintaining an orthogonal recurrent weight matrix by parametrizing a skew-symmetric matrix through a scaled Cayley transform. The initial implementation of scoRNN used an orthogonal recurrent matrix and we extend the idea to the complex case using unitary matrices. We discuss the advantage the complex scoRNN has over the traditional scoRNN and implementation issues.
April 19, 2018
POT 745 from 11:00am-12:00 pm
Title: Effects of Thermoregulation on Human Sleep Patterns: A Mathematical Model of Sleep-Wake Cycles with REM-NREM Subcircuit
Speaker: Alicia Prieto Langarica, Youngstown State University.
Abstract:
In this paper we construct a mathematical model of human sleep-wake regulation with thermoregulation and temperature effects. Simulations of this model show features previously presented in experimental data such as elongation of duration and number of REM bouts across the night as well as the appearance of awakenings due to deviations in body temperature from thermoneutrality. This model helps to demonstrate the importance of temperature in the sleep cycle. Further modifications of the model to include more temperature effects on other aspects of sleep regulation such as sleep and REM latency are discussed.
April 12, 2018
POT 745 from 11:00am-12:00 pm
Title: Disease ecology meets economics
Speaker: Calistus Ngonghala, University of Florida
Abstract:
Understanding why some human populations remain extremely poor despite current development trends around the world remains a mystery to the natural, social and mathematical sciences. The poor rely on their immediate natural environment for subsistence and suffer from high burdens of infectious diseases. We present a general framework for modeling the ecology of poverty and disease, focusing on infectious diseases and renewable resources. Interactions between these ecological drivers of poverty and economics create reinforcing feedbacks resulting in three possible development regimes: 1) globally stable wealthy/healthy development, 2) globally stable unwealthy/unhealthy development, and 3) bistability. We show that the proportion of parameters leading to poverty is larger than that resulting in healthy/wealthy development; bistability consistently emerges as a general property of generalized disease-economic systems and that the systems under consideration are most sensitive to human disease parameters. The framework highlights feedbacks, processes and parameters that are important to measure in future studies of development, to identify effective and sustainable pathways out of poverty.
April 5, 2018
POT 745 from 11:00am-12:00 pm
Title: Epidemiological models examining two susceptible classes
Speaker: Christina Edholm, University of Tennessee
Abstract:
Be it the Ebola or Buruli ulcers, we are constantly informed about infectious diseases and the ramifications. We can combat infectious diseases using mathematics to gain insight into diseases dynamics and outbreaks. We will explore using two susceptible classes in epidemiological models. I concentrate on a model for Buruli Ulcers and briefly discuss two other disease models. Buruli Ulcers is a debilitating disease induced by Mycobacterium ulcerans. The transmission mechanism is not known at this time, but the bacteria is known to live in natural water environments. To understand the role of human contact with water environments in the spread of this disease, we formulate a model to emphasize the interaction between humans and the pathogen in a water environment. Therefore, we included two susceptible classes with one having more exposure to the water environment than the other in our system of differential equations. This work gives insight into the importance of various components of the mechanisms for transmission dynamics.
March 29, 2018
POT 745 from 11:00am-12:00 pm
Title: Investigating the structure of Earth's interior
Speaker: Keely O'Farrell, University of Kentucky.
Abstract:
This talk will focus on the fluid dynamics of Earth and planetary mantles (interiors) and their surface manifestations. By necessity, convection in planetary mantles is largely studied using numerical models on supercomputers, though the right parameter range is still often out of reach. In order to solve the equations governing fluid dynamics inside the Earth, we need to know about the velocity, temperature density and general structure (such as viscosity) of the interior. Over the past few decades, much work has been done to constrain the viscosity structure of the Earth's mantle using inverse techniques, viscoelastic modelling and post-glacial rebound data. Variations in the Earth's gravitational potential anomalies (geoid) provide constraints on the density structure in the mantle. Seismic tomography can be used to investigate radial viscosity variations on instantaneous flow models. By specifying a possible viscosity structure and predicting a synthetic geoid, we can compare with the observed geoid to see how well our viscosity structure matches the real Earth. Examining over 50 tomographic models we found 2 possible profiles for the viscosity structure inside the Earth.
March 22, 2018
POT 745 from 11:00am-12:00 pm
Title: Simulating Within-Vector Generation of the Malaria Parasite Diversity
Speaker: Olivia Prosper, University of Kentucky.
Abstract:
Plasmodium falciparum, the malaria parasite causing the most severe disease in humans, undergoes an asexual stage within the human host, and a sexual stage within the vector host, Anopheles mosquitoes. Because mosquitoes may be superinfected with parasites of different genotypes, this sexual stage of the parasite life-cycle presents the opportunity to create genetically novel parasites. To investigate the role that mosquitoes' biology plays on the generation of parasite diversity, which introduces bottlenecks in the parasites' development, we first constructed a stochastic model of parasite development within-mosquito, generating a distribution of parasite densities at five parasite life-cycle stages: gamete, zygote, ookinete, oocyst, and sporozoite, over the lifespan of a mosquito. We then coupled a model of sequence diversity generation via recombination between genotypes to the stochastic parasite population model. Our model framework shows that bottlenecks entering the oocyst stage decrease diversity from the initial gametocyte population in a mosquito's blood meal, but diversity increases with the possibility for recombination and proliferation in the formation of sporozoites. Furthermore, when we begin with only two distinct parasite genotypes in the initial gametocyte population, the probability of transmitting more than two unique genotypes from mosquito to human is over 50% for a wide range of initial gametocyte densities.
March 1, 2018
POT 745 from 11:00am-12:00 pm
Title: Model-dependent and model-independent control of biological network models
Speaker: Jorge G. T. Zanudo, Dana-Farber Cancer Institute and Broad Institute.
Abstract:
Network models of intracellular signaling and regulation are ubiquitous in systems biology research because of their ability to integrate the current knowledge of a biological process and test new findings and hypotheses. An often asked question is how to control a network model and drive it towards its dynamical attractors (which have been found to be identifiable with phenotypes or stable patterns of activity of the modeled system), and which nodes and interventions are required to do so. In this talk, we will introduce two recently developed network control methods -feedback vertex set control and stable motif control- that use the graph structure of a network model to identify nodes that drive the system towards an attractor of interest (i.e., nodes sufficient for attractor control). Feedback vertex set control makes predictions that apply to all network models with a given graph structure and stable motif control makes predictions for a specific model instance, and this allows us to compare the results of model-independent and model-dependent network control. We illustrate these methods with various examples and discuss the aspects of each method that makes its predictions dependent or independent of the model.
February 22, 2018
POT 745 from 11:00am-12:00 pm
Title: The Potential Role of Subclinical Infection in Outbreaks of Emerging Pathogens
Speaker: Nourridine Siewe, NIMBIOS.
Abstract:
Many rare or emerging diseases exhibit different epidemioligical behaviors from outbreak to outbreak, leaving it unclear how to best characterize the relevant facets that could be exploited for outbreak mitigation/control. Some studies have already proposed considering the role of active subclinical infections co-emerging and cocirculating as part of the process of emergence of a novel pathogen. However, consideration of the role of subclinical infections in emerging disease dynamics have usually avoided considering the full set of possible influences. Most recently, the Ebola outbreak 2014 seems to fit all the criteria for possible involvement of subclinical circulation. We argue that an understanding of the potential mechanism for diversity in observed epidemiological dynamics may be of considerable importance in understanding and preparing for outbreaks of novel and/or emerging diseases.
February 15, 2018
POT 745 from 11:00am-12:00 pm
Title: Ubiquitous Doubling Algorithms, General Theory, and Applications
Speaker: Ren-Cang Li, University of Texas at Arlington.
Abstract:
Iterative methods are widely and indispensably used in numerical approximations. Basically, any iterative method is a rule that produces a sequence of approximations and with a reasonable expectation that newer approximations in the sequence are better. The goal of a doubling algorithm is to significantly speed up the approximation process by seeking ways to skip computing most of the approximations in the sequence but sporadically few, in fact, extremely very few: only the $2^i$-th approximations in the sequence, kind of like computing $\alpha^{2^i}$ via repeatedly squaring. However, this idea is only worthwhile if there is a much cheaper way to directly obtain the $2^i$-th approximation from the $2^{i-1}$-st one than simply following the rule to generate every approximation between the $2^{i-1}$-st and $2^i$-th approximations in order to obtain the $2^i$-th approximation. Anderson (1978) had sought the idea to speed up the simple fixed point iteration for solving the discrete-time algebraic Riccati equation via repeatedly compositions of the fixed point iterative function. As can be imagined, under repeatedly compositions, even a simple function can usually and quickly turn into nonetheless a complicated and unworkable one. In the last 20 years or so in large part due to an extremely elegant way of formulation and analysis, the research in doubling algorithms thrived and continues to be very active, leading to numerical effective and robust algorithms not only for the continuous-time and discrete-time algebraic Riccati equations from optimal control that motivated the research in the first place but also for $M$-matrix algebraic Riccati equations (MARE), structured eigenvalue problems, and other nonlinear matrix equations. But the resulting theory is somewhat fragmented and sometimes ad hoc. In this talk, we will seek to provide a general and coherent theory, discuss new highly accurate doubling algorithm for MARE, and look at several important applications.
February 1, 2018
POT 745 from 11:00am-12:00 pm
Title: Modeling RNA secondary structure with auxiliary information
Speaker: David Murrugarra, University of Kentucky.
Abstract:
The secondary structure of an RNA sequence plays an important role in determining its function, but directly observing RNA secondary structure is costly and difficult. Therefore, researchers have developed computational tools to predict the secondary structure of RNAs. One of the most popular methods is the Nearest Neighbor Thermodynamic Model (NNTM). More recently, high-throughput data that correlates with the state of a nucleotide being paired or unpaired has been developed. This data, called SHAPE for `selective 2'-hydroxyl acylation analyzed by primer extension', has been incorporated as auxiliary information into the objective function of NNTM with the goal of improving the accuracy of the predictions. This type of prediction is referred to as SHAPE-directed RNA secondary structure modeling. The addition of auxiliary information usually improves the accuracy of the predictions of NNTM. This talk will discuss challenges in RNA secondary structure modeling using NNTM and will provide ideas for developing synthetic auxiliary information that can be incorporated into NNTM to improve the accuracy of the predictions.
January 18, 2018
POT 745 from 11:00am-12:00 pm
Title: Spatial Dynamics of Vector Borne Diseases
Speaker: Omar Saucedo, Mathematical Biosciences Institute.
Abstract:
Vector-borne diseases affects approximately 1 billion people and accounts for 17% of all infectious diseases. With travel becoming more frequent across the global, it is important to understand the spatial dynamics of vector-borne diseases. Host movement plays a key part on how a disease can be distributed as it enables a pathogen to invade a new environment, and helps the persistence of a disease in locations that would otherwise be isolated. In this talk, we will explore how spatial heterogeneity combines with mobility network structure to influence vector-borne disease dynamics.
November 30, 2017
FPAT 253 from 2:00pm-3:00 pm
Title: Orthogonal Recurrent Neural Networks with Scaled Cayley Transform
Speaker: Kyle Helfrich, University of Kentucky
Abstract:
Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases, exceed the capabilities of Long Short-Term Memory networks (LSTMs). We propose a simpler and novel update scheme to maintain orthogonal recurrent weight matrices without using complex valued matrices. This is done by parametrizing with a skew-symmetric matrix using the Cayley transform. Such a parametrization is unable to represent matrices with negative one eigenvalues, but this limitation is overcome by scaling the recurrent weight matrix by a diagonal matrix consisting of ones and negative ones. The proposed training scheme involves a straightforward gradient calculation and update step. In several experiments, the proposed scaled Cayley orthogonal recurrent neural network (scoRNN) achieves superior results with fewer trainable parameters than other unitary RNNs.
November 14, 2017
POT 745 from 11:00am-12:00 pm
Title: Dynamic Programming in Secondary Structure Inference
Speaker: Devin Willmott, University of Kentucky
Abstract:
Given an RNA sequence, secondary structure inference is the problem of predicting that sequence's base pairs. A variety of methods for this problem exist; among the most popular are minimum free energy (MFE) methods, which assign each possible secondary structure an energy based on the presence or absence of various substructures, with negative energy structures being more likely to occur naturally. These methods then use dynamic programming to predict the lowest free energy structure(s) efficiently. We will give an introduction to dynamic programming, talk about why it is necessary for approaching this problem efficiently, and discuss some of the shortcomings of the method. If time permits, we will also talk about connections to machine learning methods for secondary structure prediction.
October 19, 2017
POT 745 from 11:00am-12:00 pm
Title: Computational Polypharmacology: A Machine Learning Approach
Speaker: Sally Ellingson, UK Division of Biomedical Informatics
Abstract:
Drug discovery is a lengthy, expensive, and sometimes fatal process. It is also an extremely difficult task to perform with a full understanding of experimental results. Drugs are studied in test tubes which lack a realistic in vivo environment and in animal models having limited validity for human conditions. Even when new drugs pass screening experiments with no red flags, they fail during human clinical trials after a great amount of time and money has been invested. Thus, an economic burden is created that eventually must be recuperated with the few drugs that do pass FDA approval. Computational methods that consistently improve predictive accuracy over laboratory and animal testing for the entire human proteome and huge chemical space of potential drugs could revolutionize pharmaceutical research and development. The utilization of such computational tools will increase the return on future investments in health-related research and provide access to new, better understood therapies. The state-of-the-art in many computational methodologies include machine learning approaches. In our digitalized, data-driven world, there is a wealth of knowledge available that is beyond the processing power of an individual researcher or even team of researchers. The goal of my work is to improve the prediction of novel drug safety and efficacy by increasing the accuracy of predicting polypharmacological networks, investigating how drugs interact with the entire proteome. We integrate traditional computational simulations of protein and drug interactions (such as the efficient molecular docking calculation), cheminformatics features of drug-like molecules, and features describing individual proteins to improve the prediction of drug and protein binding. Each component investigated provides some level of predictive utility in isolation. For example, I have seen in my own work that a small number of drug features calculated from current cheminformatics programs can identify active compounds for a given protein with greater than 99% accuracy. These same drug features have been used in machine learning models in combination with docking scores to rescore interactions with one candidate drug to multiple proteins. The individual components of a molecular docking scoring function can be used as features in a machine learning model to greatly improve the accuracy of identifying active compounds in models specific for one protein. From a different perspective, protein features have been used in machine learning models to predict the druggability of a protein. The hypothesis of this work is that the combination of all these components can be used in one model that would vastly improve the accuracy of predicting the effects of new proteins and classes of drugs. Presented here is a first step of showing that it can be done for a class of functionally related proteins (kinases). Kinases have been chosen to study because kinase inhibitors are the largest class of new cancer therapies and selectively inhibiting a kinase is difficult due to their high sequence similarity, making off-target interactions with kinases a common cause of adverse drug reactions.
October 5, 2017
POT 745 from 11:00am-12:00 pm
Title: Application of Orthogonal Polynomials and the Euclidean Algorithm to Interpolation and Cubature
Speaker: Larry Harris, University of Kentucky
Abstract:
Numbers $h_0 > h_1 > \cdots > h_m$ are alternation points for corresponding orthogonal polynomials $p_0, p_1,\ldots, p_m$ if \[ p_{m-j}(h_n) = (-1)^n p_j(h_n),\quad 0\leq n,j\leq m. \] For example, the Chebyshev points $h_n = \cos(n\pi/m)$, $0 \leq n \leq m$ are alternation points for the Chebyshev polynomials $T_0,\ldots, T_m$. We show that any decreasing numbers are alternation points for some corresponding orthogonal polynomials. This is applied to produce Lagrange polynomials and cubature formulas for nodes in $R^2$ whose coordinates are even and odd pairs of points from a finite decreasing sequence.
September 14, 2017
POT 745 from 11:00am-12:00 pm
Title: Radiative transport and optical tomography
Speaker: Francis Chung, University of Kentucky
Abstract:
Optical tomography is the process of reconstructing the optical parameters of the inside of an object from measurements taken on the boundary. This problem is hard if light inside the object is scattered -- if it bounces around a lot and refuses to travel in straight lines. To solve optical tomography problems, we need a mathematical model for light propagation inside a scattering medium. In this talk I'll give a brief introduction to one such model -- the radiative transport model -- and talk a little bit about its behavior and its implications for optical tomography.
August 31, 2017
POT 745 from 11:00am-12:00 pm
Title: Preconditioning for Accurate Solutions of Linear Systems and Eigenvalue Problems
Speaker: Qiang Ye, University of Kentucky
Abstract:
This paper develops the preconditioning technique as a method to address the accuracy issue caused by ill-conditioning. Given a preconditioner M for an ill-conditioned linear system Ax=b, we show that, if the inverse of the preconditioner can be applied to vectors accurately, then the linear system can be solved accurately. A stability concept called inverse-equivalent accuracy is introduced to describe higher accuracy that is achieved and an error analysis will be presented. As an application, we use the preconditioning approach to accurately compute a few smallest eigenvalues of certain ill-conditioned matrices. Numerical examples are presented to illustrate the error analysis and the performance of the methods.

Academic Year 2016-17

April 20, 2017
POT 745 from 11:00am-12:00 pm
Title: Two-Dimensional PCA with F-Norm Minimization
Speaker: Jing Wei, University of Kentucky
Abstract:
Master's Talk.
Two-dimensional principle component analysis (2DPCA) has been widely used for face image representation and recognition. But it is sensitive to the presence of outliers. To alleviate this problem, we propose a novel robust 2DPCA, namely 2DPCA with F-norm minimization (F-2DPCA), which is intuitive and directly derived from 2DPCA. In F-2DPCA, distance in spatial dimensions (attribute dimensions) is measured in F-norm, while the summation over different data points uses 1-norm. Thus it is robust to outliers and rotational invariant as well. To solve F-2DPCA, we propose a fast iterative algorithm, which has a closed-form solution in each iteration, and prove its convergence. Experimental results on face image databases illustrate its effectiveness and advantages.
April 13, 2017
POT 245 from 11:00am-12:00 pm
Title: Theory and Application of a Direct Solution Algorithm for Large Dense Matrices of Boundary Element Methods
Speaker: Robert John Thomas, University of Kentucky
Abstract:
Master's Talk
Subject Paper: Martinsson, and Rokhlin. "A Fast Direct Solver for Boundary Integral Equations in Two Dimensions." Journal of Computational Physics 205.1 (2005): 1-23. Web. ISSN: 0021-9991 ; DOI: 10.1016/j.jcp.2004.10.033 In computational science and engineering, the numerical solution of partial differential equations is effected through the solution of extremely large linear systems. Finite element and finite difference methods give rise to sparse matrices that admit iterative solution techniques. Acoustic and electromagnetic scattering problems, however, are often better approached via boundary element methods. These result in huge dense matrices that would be prohibitively expensive to solve conventionally. The subject paper details a method to construct the matrix inverse directly. The nature of the boundary integrals causes the system matrix to exhibit rank deficiency of blocks further removed from the diagonal. A modified QR algorithm from the literature both reveals the rank and approximates the nullspace basis of such blocks. An algorithm based on the Schur complement is then applied iteratively, inverting selected pivot blocks. The approach is extended to a hierarchical application reminiscent of Greengard and Rokhlin's Fast Multipole Method. This Master's Degree examination talk will present the theory of the key elements of the method, as well as the performance metrics of the derived algorithms. A sample implementation with numerical results will also be described.
March 30, 2017
POT 745 from 11:00am-12:00 pm
Title: Master's talk
Speaker: Kehelwala Dewage Maduranga, University of Kentucky
Abstract:
This master's talk will present the following paper: Theory of Inexact {Krylov} Subspace Methods and Applications to Scientific Computing Valeria Simoncini and Daniel B. Szyld SIAM Journal on Scientific Computing, 25, 454-477, 2003.
March 9, 2017
POT 745 from 11:00am-12:00 pm
Title: Algebraic Statistics Applications in Epidemiology
Speaker: Luis Garcia Puente, Sam Houston State University
Abstract:
Interactions between single nucleotide polymorphisms (SNPs) and complex diseases have been an important topic throughout epidemiological studies. Previous studies have mostly focused on gene variables at a single locus. In this talk, I will discuss a focused candidate gene study to test the interaction of multiple SNPs with the risk of different types of cancer. We will exemplify the fact that traditional asympotic results in statistical analysis do not apply in our setting. This is due mainly to the fact that we have a relatively small fixed data set. In our work we develop a new statistical approach using techniques from the field of algebraic statistics. Algebraic statistics focuses on mathematical aspects of statistical models, where algebraic, geometric and combinatorial insights can be useful to study behavior of statistical procedures. Using the R package algstat, developed by Kahle, Garcia Puente, and Yoshida, we implemented an algebraic statistics method that can test for independence between several variables and the desease. We applied our methods to the study of gene-gene interaction on cancer data obtained from the European case-control study Gen-Air extending previous work by Ricceri, Fassino, Matullo, Roggero, Torrente, Vineis, and Terracini.
March 2, 2017
POT 745 from 11:00am-12:00 pm
Title: Tallgrass Prairie Ecosystem Restoration: Modeling the Impact of the Conservation Reserve Program
Speaker: Anna Mummert, Marshall University
Abstract:
The tallgrass prairie ecosystem has been reduced to a fraction of its original extent, due to rapid conversion to other land use types, especially agricultural and urban. Restoration is a relatively new process to convert agricultural land back to communities dominated by native vegetation, including prairies. The most notable restoration project for prairies is the Conservation Reserve Program (CRP) administered by the USDA Farm Service Agency. We develop a compartmental model for the Midwestern tallgrass prairie ecosystem, incorporating the impact of human population on land use changes. Restoration via participation in CRP is included. Historical data is used to determine model parameter ranges. Local and global sensitivity analyses are performed. Our findings emphasize the importance of increasing incentives for CRP enrollment as a means to restoring the tallgrass prairie ecoregion.
February 23, 2017
POT 745 from 11:00am-12:00 pm
Title: The Inverse q-Numerical Range Problem and Connections to the Davis-Wielandt Shell and the Pseudospectra of a Matrix
Speaker: Russell Carden, University of Kentucky
Abstract:
Numerical ranges and related sets provide insights into the behavior of iterative algorithms for solving systems of equations and computing eigenvalues. Inverse numerical range problems attempt to enhance these insights. We generalize the inverse numerical range problem, as proposed by Uhlig, to the inverse $q$-numerical range problem, and propose an algorithm for solving the problem that relies on convexity. To determine an approximation to the boundary of the $q$-numerical range, as needed by our algorithm, we must approximate the top of the Davis-Wielandt shell, a generalization of the numerical range. We found that the Davis-Wielandt shell is in a sense conjugate to the the extreme singular values of the resolvent of a matrix. Knowing the Davis-Wielandt shell allows for the approximation of the $q$-numerical range, the pseudospectra and the Davis-Wielandt shell for any allowed M\"{o}bius transformation of a matrix. We provide some examples illustrating these connections, as well as how to solve the inverse $q$-numerical range problem.
February 16, 2017
POT 745 from 11:00am-12:00 pm
Title: RNA Secondary Structure Inference with Recurrent Neural Networks
Speaker: Devin Willmott, University of Kentucky
Abstract:
RNA secondary structure inference is the problem of taking an RNA sequence and predicting which elements of the sequence are paired together. We will begin by converting the problem into a mathematically palatable form, and then look at some currently popular methods for inferring RNA secondary structure. Our work centers around the comparison of two methods that work with sequential data: hidden Markov models (HMMs) and recurrent neural networks (RNNs). We will discuss some of the particular strengths and weaknesses of each in the context of RNA secondary structure inference, see some preliminary results of each method's application to the problem, and (if time permits) talk about future research directions that exploit the combinatorial structure of RNA.
February 9, 2017
POT 745 from 11:00am-12:00 pm
Title: A quantitative comparison of quarantine and symptom monitoring
Speaker: Lauren Childs, Virginia Tech
Abstract:
Quarantine and symptom monitoring of contacts with suspected exposure to an infectious disease are key interventions for the control of emerging epidemics; however, there does not yet exist a quantitative framework for comparing the control performance of each. Here, we use an agent-based branching model of seven case study diseases to show how the choice of intervention is influenced by the natural history of the infectious disease, its inherent transmissibility, and the intervention feasibility in the particular healthcare setting. We use this information to identify the most important characteristics of the disease and setting that need to be characterized for an emerging pathogen in order to make an informed decision between quarantine and symptom monitoring.
December 8, 2016
POT 745 from 10:30am-11:30 am
Title: Accurately Computing Eigenvalues of Extremely Ill-conditioned Matrices, with an Application to the Biharmonic Operator
Speaker: Kasey Bray, University of Kentucky
Abstract:
We are primarily concerned with computing smaller eigenvalues of large, extremely ill-conditioned matrices. After discussing where the standard algorithms fail to compute such eigenvalues with any accuracy, we offer a solution to the problem for diagonally dominant matrices. We will then apply this solution to accurately compute an eigenvalue of the biharmonic operator on the unit circle.
December 1, 2016
POT 745 from 11am-noon
Title: Optical tomography on graphs
Speaker: Jeremy Hoskins, University of Michigan
Abstract:
Diffuse optical tomography is an imaging modality frequently used in imaging biomedical systems. Here we discuss a discrete analog defined on graphs, which we call discrete diffuse optical tomography (DDOT). The goal of DDOT is to recover a vertex potential from boundary measurements. In this talk, we present a novel method for solving the inverse problem associated with DDOT, proving necessary conditions for recovery. Finally, we show how to modify our method to incorporate additional information on the structure of the potential and multifrequency measurements.
November 17, 2016
POT 745 from 11am-noon
Title: Applications of Singular Value Decomposition to cryptography and privacy
Speaker: Luis Sordo Vieira, University of Kentucky
Abstract:
There have been recent attempts to encrypt images and text using the singular Value decomposition of a matrix. We talk about some of these protocols and results and possible benefits. We also mention some protocols to preserve privacy in data mining. We will quickly overview SVD in the beginning.
November 3, 2016
POT 745 from 11am-noon
Title: Structural and Functional Characterization of Expected and Aberrant Metal Ion Coordination in Proteins
Speaker: Hunter Moseley, University of Kentucky
Abstract:
Metalloproteins bind and utilize metal ions for a variety of biological purposes. Due to the ubiquity of metalloprotein involvement throughout these processes across all domains of life, how proteins coordinate metal ions for different biochemical functions is of great relevance to understanding the implementation of these biological processes. Towards these ends, we have improved our methodology for structurally and functionally characterizing metal binding sites in metalloproteins. Our new ligand detection method is statistically much more robust, producing estimated false positive and false negative rates of ~0.11% and ~1.2%, respectively. Additional improvements expand both the range of metal ions and their coordination number that can be effectively analyzed. Also, the inclusion of many additional quality control filters has significantly improved structure-function Spearman correlations as demonstrated by rho values greater than 0.90 for several metal coordination analyses and even one rho value above 0.95. Also, improvements in bond-length distributions have revealed bond-length modes specific to chemical functional groups involved in multidentation. Using these improved methods, we analyzed all single metal ion binding sites with Zn, Mg, Ca, Fe, and Na ions in wwPDB, producing statistically rigorous results supporting the existence of both a significant number of unexpected compressed angles and subsequent aberrant metal ion coordination geometries (CGs) within structurally known metalloproteins. By recognizing these aberrant CGs in our clustering analyses, high correlations are achieved between structural and functional descriptions of metal ion coordination. Moreover, distinct biochemical functions are associated with aberrant CGs versus non-aberrant CGs.
October 27, 2016
POT 745 from 11am-noon
Title: Spatial heterogeneity, host movement, and the transmission of mosquito-borne disease
Speaker: Olivia Prosper, University of Kentucky
Abstract:
The Ross-Macdonald framework, a suite of mathematical models for the transmission of mosquito-borne disease, made numerous simplifying assumptions including that transmission occurs in a homogeneous environment. Despite these assumptions, this modeling framework has been invaluable to the study of vector-borne disease and to informing public health policy. In recent years, more attention has been paid to the role of human movement in regions with spatially heterogeneous disease transmission. In this talk, I will introduce a metapopulation framework for vector-borne disease, based on the Ross-Maconald model, in which human movement connects discrete populations with different levels of malaria transmission. I will discuss properties of this model, compare these properties to the homogeneous case, and will discuss the implications for malaria control. Next, I will present some of the challenges that arise when linking this theoretical framework to a real-world problem. Finally, I will discuss an approach developed to address one of these challenges, namely identifying the appropriate network structure for the metapopulation model, using either mobile phone or geographical data.
October 20, 2016
POT 745 from 11am-noon
Title: Synchrony in a Boolean network model of the L-arabinose operon
Speaker: Matthew Macauley, Clemson University
Abstract:
In genetics, an operon is a segment of DNA that contains several co-transcribed genes, which together form a functional regulatory unit. Operons have primarily been studied in prokaryotes, with both the lactose and tryptophan operons in E. Coli having been classically modeled with differential equations and more recently, with Boolean networks. The L-arabinose operon in E. coli encodes proteins that function in the catabolism of arabinose. This operon has several complex features, such as a protein that acts both as an activator, a DNA looping repressing mechanism, and the lack of inducer exclusion by glucose. In this talk, I will propose a Boolean network model of the ara operon, and then show how computational algebra in Sage establishes that for 11 of the 12 choices of initial conditions, the state space contains a single fixed point that correctly predicts the biology. The final initial condition describes the case where there are medium levels of arabinose and no glucose, and it successfully predicts bistability of the system. Finally, I will compare the state space under synchronous and asynchronous update, and show how the former has several artificial cycles that go away under a general asynchronous update.
October 13, 2016
POT 745 from 11am-noon
Title: The role of networks on disease spread and intervention strategies
Speaker: Michael Kelly, Transylvania University
Abstract:
The interconnectedness of communities has played a major role in disease spread within a population. This has become especially true in the case of waterborne diseases such as cholera, where multiple transmission pathways exist. Understanding the role of networks on disease outbreaks has become crucial when considering where intervention strategies should be focused. We investigate questions of optimal vaccination distributions on heterogeneous community networks in the case of cholera outbreaks; both in response to and preemptively before an outbreak. For responsive strategies, optimal control on a system of ordinary differential equations is developed to minimize the number of infected individuals in the population. For preemptive strategies, a constrained optimization problem is used that seeks to minimize the risk of outbreak on the network while incorporating uncertainty in disease transmissibility. Both also focus on minimizing the associated cost of implementation. The two methods will be discussed, simulations are shown for varying scenarios and networks, and results provide guidance on where to prioritize vaccination in light of outbreaks.
September 29, 2016
POT 745 from 11am-noon
Title: Long Short Term Memory
Speaker: John A. Hirdt, Department of Mathematics, University of Kentucky
Abstract:
Long Short Term Memory or LSTMs as they are more commonly known, are the most popular type of Recurrent Neural Network used in Machine Learning. LSTMs popularity comes from their ability to capture long-term dependencies in sequential data sets. LSTMs often outperform other RNNs and many Hidden Markov Models when applied to various applications. One popular example of LSTM use is the Netflix user rating example. Users watch a movie, rate it and then watch another movie, and continue with this pattern creating a sequence of reviews. Using LSTMs we can model this sequence and make predictions about a users favorite genre of movie as well as make predictions about future movies a user may want to watch. Finally, we look at how LSTMs can be applied to a variety of problems, including those that are non-sequential.
September 22, 2016
POT 745 from 11am-noon
Title: An Efficient Ascending Auction for Assignment Problems
with De Liu, Carlson School of Management- University of Minnesota
Speaker: Adib Bagh, Department of Mathematics, University of Kentucky
Abstract:
We review basic concepts in the theory of auctions. We then introduce a simple ascending auction that allocates heterogeneous objects among bidders with purely private unit demands. Our auction design differs from existing dynamic auctions in a number of ways: it solicits a single new bid from selected bidders at a time, thus minimizing bidder information revelation; it uses a simple and intuitive price adjustment procedure; the seller can set starting prices above his valuations. Despite these new features, (i) the auction stops in a finite time, (ii) sincere bidding at every stage of the auction is an ex-post Nash equilibrium, and (iii) for given valuations, the auction ending prices and revenue depend only on starting prices. We establish sincere bidding and path-independent ending prices using combinatorial arguments. We demonstrate via simulations that our proposed auctions is better than existing auctions in preserving the privacy of the bidders.
September 8, 2016
POT 745 from 11am-noon
Title: Insight into Molecular through Subcellular Calcium Signaling via Multi-Scale Simulation
Speaker: Peter Kekenes-Huskey, Department of Chemistry, University of Kentucky
Abstract:
Calcium is critical to a wide range of physiological processes, including neurological function, immune responses, and muscle contraction. Calcium-dependent signaling pathways enlist a variety of proteins and channels that must rapidly and selectively bind calcium against thousand-fold higher cationic concentrations. Frequently these pathways further require the co-localization of these proteins within specialized subcellular structures to function properly. Our lab has developed multi-scale simulation tools to elucidate how protein structure and co-localization facilitate intracellular calcium signaling. Developments include combining molecular simulations with a statistical mechanical model of ion binding, a homogenization theory to upscale molecular interactions into micron-scale diffusion models, and reaction-diffusion simulations that leverage sub-micron microscopy data. In this seminar, I will describe these tools and their applications toward molecular mechanisms of calcium-selective recognition and cross-talk between co-localized calcium binding proteins inside the cell.
September 1, 2016
POT 745 from 11am-noon
Title: Hidden Markov Models with Applications to RNA Folding
Speaker: David Murrugarra, Department of Mathematics, University of Kentucky
Abstract:
This talk will give an introduction to RNA secondary structure prediction using the Nearest Neighborhood Thermodynamic Model (NNTM) and then will present Hidden Markov Models (HMMs) and potential applications for the problem of RNA folding.

Academic Year 2015-16

April 28, 2016
POT 745 from 11am-noon
Title: Qualitative Assesment of the Role of Temperature Variations on Malaria Transmission Dynamics
Speaker: Folashade B. Agusto, Department of Ecology and Evolutionary Biology, University of Kansas
Abstract:
A new mechanistic deterministic model for assessing the impact of temperature variability on malaria transmission dynamics is developed. The effects of sensitivity and uncertainty in estimates of the parameter values used in numerical simulations of the model are analyzed. These analyses reveal that, for temperatures in the range [16-34]°C, the parameters of the model that have the dominant influence on the disease dynamics are the mosquito carrying capacity, transmission probability per contact for susceptible mosquitoes, human recruitment rate, mosquito maturation rate, biting rate, transmission probability per contact for susceptible humans, and recovery rate from first-time infections. This study emphasize the combined use of mosquito-reduction strategy and personal protection against mosquito bite during the periods when the mean monthly temperatures are in the range [16.7, 25]°C. For higher daily mean temperatures in the range [26, 34]°C, mosquito-reduction strategy should be emphasized ahead of personal protection. Numerical simulations of the model reveal that mosquito maturation rate has a minimum sensitivity (to the associated reproduction threshold of the model) at T = 24°C and maximum at T = 30°C. The mosquito biting rate has maximum sensitivity at T = 26°C, while the minimum value for the transmission probability per bite for susceptible mosquitoes occurs at T = 24°C. Furthermore, disease burden increases for temperatures between 16°C and 25°C and decreases beyond 25°C. This finding, which supports a recent study by other authors, suggests the importance of the role of global warming on future malaria transmission trends.
April 21, 2016
POT 745 from 11am-noon
Title: Generative Neural Networks in Semi-Supervised Learning
Speaker: Devin Willmott
Abstract:
Semi-supervised learning is a relatively new machine learning concept that seeks to use both labeled and unlabeled data to perform supervised learning tasks. We will look at two network types with some promising applications to semi-supervised learning: ladder networks and adversarial networks. For each, we will discuss the motivations behind their architectures & training methods, and derive some favorable theoretical properties about their capabilities.
April 20, 2016
POT 110 from 2-3pm
Title: Matrix Factorization Techniques for Recommender Systems
Speaker: Zhen Luo
Abstract:
Recommendation Systems apply Information Retrieval techniques to select the online information relevant to a given user. Collaborative Filtering (CF) is currently most widely used approach to build Recommendation System. To address this issue, the collaborative filtering recommendation algorithm is based on singular value decomposition (SVD) . How the SVD works to make recommendations is presented in this master talk.
April 14, 2016
POT 745 from 11am-noon
Master's Talk
Speaker: Jonathan Proctor, University of Kentucky
Abstract:
Jonathan will be presenting the paper
SIAM Rev., 52(1), 3-54. (52 pages)

Numerical Methods for Electronic Structure Calculations of Materials

Yousef Saad, James R. Chelikowsky, and Suzanne M. Shontz

DOI:10.1137/060651653
April 7, 2016
POT 745 from 11am-noon
Learning About When and Where from Imagery
Speaker: Nathan Jacobs, University of Kentucky
Abstract:
Every day billions of images are uploaded to the Internet. Together they provide many high-resolution pictures of the world, from panoramic views of natural landscapes to detailed views of what someone had for dinner. Many are tagged with when and where the picture was taken, thus providing an opportunity to better understand how the appearance of objects and scenes varies with respect to location and time. This talk describes my work in using learning-based methods to extract geo-spatial properties from imagery. In particular, I will focus on two recent research thrusts: using deep convolutional neural networks to geo-calibrate social network imagery and using such imagery to build geo-temporal models of human appearance.
March 31, 2016
POT 745 from 11am-noon
The benefits of elliptic curve cryptography
Speaker: Luis Sordo Vieira, University of Kentucky
Abstract:
We will introduce the basis of elliptic curve cryptography. Roughly speaking ECC is based on the group structure of the points defined on an elliptic curve over a finite field and the difficulty of solving the discrete log problem. The applications are many, such as signature verification and pseudo random generators. No knowledge of algebraic geometry is required.
March 10, 2016
POT 745 from 11am-noon
Computing Exponentials of Essentially Non-negative Matrices with Entry-wise Accuracy
Speaker: Qiang Ye, University of Kentucky
Abstract:
A real square matrix is said to be essentially non-negative if all of its off-diagonal entries are non-negative. In this talk, I will present new perturbation results and algorithms that demonstrate that the exponential of an essentially non-negative matrix can be computed with entrywise relative accuracy.
March 3, 2016
POT 745 from 11am-noon
Learning Algorithms for Restricted Boltzmann Machines
Speaker: Devin Willmott, University of Kentucky
Abstract:
Restricted Boltzmann machines (RBMs) have played a central role in the development of deep learning. In this talk, we will introduce the theoretical framework behind stochastic binary RBMs, give motivation and a derivation for the most commonly used RBM learning algorithm (contrastive divergence), and prove some analytic results related to its convergence properties.
February 4, 2016
POT 745 from 11am-noon
Algebraic methods in computational biology
Speaker: Reinhard Laubenbacher, Director, Center for Quantitative Medicine, UConn Health Center
Abstract: As biology has become a data-rich science, more biological phenomena have become amenable to modeling and analysis using mathematical and statistical methods. At the same time, more mathematical areas have developed applications in the biosciences, in particular algebra, discrete mathematics, topology, and geometry. This talk will present some case studies from algebra and discrete mathematics applied to the construction and analysis of dynamic models of biological networks. Some emerging themes will be highlighted, outlining a broader research agenda at the interface of biology and algebra and discrete mathematics. No special knowledge in any of these fields is required to follow the presentation.
January 28, 2016
POT 745 from 11am-noon
Estimating Propensity Parameters using Google PageRank and Genetic Algorithms
Speaker: David Murrugarra, University of Kentucky
Abstract: Stochastic Boolean networks, or more generally stochastic discrete networks, are an important class of computational models for molecular interaction networks. The stochasticity stems from the updating schedule. The standard updating schedules include the synchronous update, where all the nodes are updated at the same time and gives a deterministic dynamic, and the asynchronous update, where a random node is updated at each time step that gives a stochastic dynamics. A more general stochastic setting considers propensity parameters for updating each node. SDDS is a modeling framework that considers two propensity values for updating each node, one when the update has a positive impact on the variable, that is, when the update causes the variable to increase its value, and the other when the update is negative, that is, when the update causes it to decrease its value. This extension adds a complexity in parameter estimation of the propensity parameters. This talk presents a method for estimating the propensity parameters for SDDS. The method is based on adding noise to the system using the Google PageRank approach to make the system ergodic and thus guaranteeing the existence of a stationary distribution and then with the use of a genetic algorithm the propensity parameters are estimated.
November 12, 2015
POT 745 from 11am-noon
Fast algorithms for large scale eigenvalue and singular value calculations
Speaker: Yunkai Zhou, Southern Methodist University
Abstract: The first part of this talk is on accelerating a block Davidson method for computing large scale eigenvalue decomposition (EVD) and singular value decomposition (SVD). We use two type of filters for the acceleration, one based on polynomial filters, the other based on rational filters. Our method uses the least amount of memory comparing with other state-of-the-art algorithms, but can achieve similar or better computational speed.
The second part of the talk is on a recently developed spectrum partition methods based on ARPACK (or the eigs() in Matlab). It can be used to conveniently compute several thousands of eigenpairs for matrices with large dimensions. In comparison, eigs() without partition applied to the same problems would either take very long to converge or run out of memory. Our partitioned method is designed to be intrinsically-parallel, suitable for solving very large eigenproblems on supercomputers.
November 5, 2015
POT 745 from 11am-1pm
The Krylov Subspace Methods for the Computation of Matrix Exponentials
Speaker: Hao Wang, University of Kentucky
Abstract: The problem of computing the matrix exponential $e^{tA}$ arises in many theoretical and practical problems. Many methods have been developed to accurately and efficiently compute this matrix function or its product with a vector, i.e., $e^{tA}v$. In the past few decades, with the increasing need of the computation for large sparse matrices, iterative methods such as the Krylov subspace methods have proved to be a powerful class of methods in dealing with many linear algebra problems. The Krylov subspace methods have been introduced for computing matrix exponentials by Gallopoulos and Saad, and the corresponding error bounds that aim at explaining the convergence properties have been extensively studied. Many of those bounds show that the speed of convergence depends on the norm of the matrix, while some others emphasize the important role played by the spectral distribution for some special matrices. For example, it is shown in a recent work by Ye that the speed of convergence is closely related to the condition number, namely the convergence is fast for a well-conditioned matrix no matter how large the norm is.
In this dissertation, we derive new error bounds for computing $e^{tA}v$ with non-symmetric $A$, using the spectral information of $A$. Our result is based on the assumption that the field of values of $A$ lies entirely in the left half of the complex plane, such that the underlying dynamic system is stable. The new bounds show that the speed of convergence is related to the size and shape of the rectangle containing the field of values, and they agree with the existing results when $A$ is nearly symmetric. Furthermore, we also derive a simpler error bound for the special case when $A$ is skew-Hermitian. This bound explains an observed convergence behavior where the approximation error initially stagnates for certain iterations before it starts to converge. In deriving our new error bounds, we use sharper estimates of the decay property of exponentials of Hessenberg matrices, by constructing polynomial approximations of the exponential function in the region containing the field of values. The Jacobi elliptic functions are used to construct the conformal mappings and generate the Faber polynomials. We also present numerical tests to demonstrate the behavior of the new error bounds.
October 22, 2015
POT 745 from 11am-noon
On the perfect reconstruction of the topology of dynamic networks
Speaker: Alan Veliz-Cuba, University of Dayton Ohio
Abstract: The network inference problem consists in reconstructing the topology or wiring diagram of a dynamic network from time-series data. Even though this problem has been studied in the past, there is no algorithm that guarantees perfect reconstruction of the topology of a dynamic network. In this talk I will present a framework and algorithm to solve the network inference problem for discrete-time networks that, given enough data, is guaranteed to reconstruct the topology of a dynamic network perfectly. The framework uses tools from algebraic geometry.
October 8, 2015
POT 745 from 11am-noon
An Introduction to Wavelets Speaker: David Roach, Western Kentucky University
Abstract: In this talk, I will introduce the concept of a wavelet from a theoretical perspective as well as how the wavelet can used to approximate data which contains high frequency data at multiple resolutions.
September 24, 2015
POT 745 from 11am-noon
Multivariate Decomposition Method for $\infty$-Variate Integration Speaker: Grzegorz W. Wasilkowski, University of Kentucky
Abstract: We present a Multivariate Decomposition Method (MDM) for approximating integrals of functions with countably many variables. We assume that the integrands have mixed first order partial derivatives bounded in a $\gamma=\{\gamma_u\}_{u\subset \mathbb{N}_+}$-weighted $L_p$ norm. We also assume that the integrands can be evaluated only at points with finitely many $(d)$ coordinates different than zero and that the cost of such a sampling is equal to $\$(d)$ for a given cost function $\$$. We show that MDM can approximate the integrals with the worst case error bounded by $\varepsilon$ at cost proportional \[\varepsilon^{-1+|O(\ln(1/\varepsilon)/\ln(\ln(1/\varepsilon)))|}\] even if the cost function is exponential in $d$ , i.e., $\$(d)=e^{O(d)}$. This is an almost optimal method since all algorithms for univariate functions $(d=1)$ from this space have the cost bounded from below by $\Omega(1/\varepsilon)$.
September 10, 2015
No Seminar.
We will meet for lunch around noon to discuss future activities of the seminar.
We encourage you to attend the Math Biology journal club that will bee meeting at 2pm in POT 945.
September 1, 2015
POT 745 from 1-2pm
Singular Value Computation and Subspace Clustering
Speaker: Qiao Liang, University of Kentucky

Abstract: In this dissertation we discuss two problems. In the First part, we consider the problem of computing a few extreme singular values of a symmetric defnite generalized eigenvalue problem or a large and sparse matrix C. Most existing numerical methods are based on reformulating the singular value problem as an equivalent symmetric eigenvalue problem. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, which uses preconditioning instead of shift-and-invert to accelerate the convergence. The inverse-free Krylov subspace method focuses on the computation of one extreme eigenvalue and a deflation technique is needed to compute additional eigenvalues. The Wielandt deflation has been considered and can be used in a straightforward manner. However, the Wielandt deflation alters the structure of the problem and may cause some difficulties in certain applications such as the singular value computations. So we First propose to consider a deformation by restriction method for the inverse-free Krylov subspace method. We generalize the original convergence theory for the inverse-free preconditioned Krylov subspace method to justify this deflation scheme. We next extend the inverse-free Krylov subspace method with deflation by restriction to the singular value problem. We consider preconditioning based on robust incomplete factorization to accelerate the convergence. Numerical examples are provided to demonstrate effciency and robustness of the new algorithm. In the second part of this thesis, we consider the so-called subspace clustering problem, which aims for extracting a multi-subspace structure from a collection of points lying in a high-dimensional space. Recently, methods based on Self Expressive Property(SEP) such as Sparse Subspace Clustering(SSC) and Low Rank Representations( LRR) have been shown to enjoy superior performances than other methods. Self Expressive Property means the points can be expressed as linear combinations of themselves. However, methods with SEP may result in representations that are not amenable to clustering through graph partitioning. We propose a method where the points are expressed in terms of an orthonormal basis. The orthonormal basis is optimally chosen in the sense that the representation of all points is sparsest. Nnumerical results are given to illustrate the effectiveness and effciency of this method.

Academic Year 2014-15

April 23, 2015
POT 945 from 11-noon
Making Do with Less: An Introduction to Compressed Sensing
Master's Presentation
Speaker: Fouche Smith
April 16, 2015
POT 745 from 2:15-3:30pm
A Matrix Analysis of Centrality Measures
Master's Presentation
Speaker: Sarach Orchard

Abstract: When analyzing a network, one of the most basic concerns is identifying the "important" nodes in the network. What defines "important" can vary from network to network, depending on what one is trying to analyze about the network. In this paper by Benzi and Klymko several different centrality measures, methods of computing node importance, are introduced and compared. We will see that some centrality measures give more information about the network on a local scale, while others help to analyze on a more global scale. In particular, the paper analyzes the behavior of these measures as we let the parameters defining them approach certain limits that appear to be problematic.
April 9, 2015
CP 222 from 5-6pm (refreshemnts at 4:30pm)
The Problem of Bus-Bunching and What to Do About It
SIAM Talk
Speaker: Dr. John Bartholdi of Georgia Institute of Technology
Abstract: The main challenge for an urban bus system is to maintain constant headways between successive buses. Most bus systems try to adhere to a schedule, but the natural dynamics of the system tends to collapse headways so that buses travel in bunches. What can be done about it? We discuss some models of the phenomenon and show some ways to coordinating buses. In addition, we introduce a new idea that abandons the idea of a schedule and any a priori headway and enables equal headways to emerge spontaneously. We also report on the implementation for a public bus route in Atlanta.

(joint work with Donald D. Eisenstein, University of Chicago)
April 2, 2015
POT 245 from 3:30-4:30pm
Optimality of the Neighbor Joining Algorithm and Faces of the Balanced Minimum Evolution Polytope
Speaker: Dr. Ruriko Yoshida of the University of the University of Kentucky Department of Statistics

Abstract: Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2008, Eickmeyer, Huggins, Pachter, and myself developed a notion of the BME polytope, the convex hull of the BME vectors obtained from Pauplin's formula applied to all binary trees. We also showed that the BME can be formulated as a linear programming problem over the BME polytope. The BME is related to the Neighbor Joining (NJ) algorithm, now known to be a greedy optimization of the BME principle. Further, the NJ and BME algorithms have been studied previously to understand when the NJ algorithm returns a BME tree for small numbers of taxa. In this talk we aim to elucidate the structure of the BME polytope and strengthen knowledge of the connection between the BME method and NJ algorithm. We first show that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope. Moreover, we describe an entire family of faces parametrized by disjoint clades. We show that these clade-faces are smaller-dimensional BME polytopes themselves. Finally, we show that for any order of joining nodes to form a tree, there exists an associated distance matrix (i.e., dissimilarity map) for which the NJ algorithm returns the BME tree. More strongly, we show that the BME cone and every NJ cone associated to a tree T have an intersection of positive measure. We end this talk with the current and future projects on phylogenomics with biologists in University of Kentucky and Eastern Kentucky University. This work is supported by NIH.
March 26, 2015
POT 245 from 11-noon
Convexity, star-shapedness, and multiplicity of numerical range and its generalizations
Speaker: Tin-Yau Tam of the Auburn University Department of Mathematics and Statistics

Abstract: Given an $n\times n$ complex matrix $A$ , the classical numerical range (field of values) of $A$ is the following set associated with the quadratic
form:
$W(A) = \{x^*Ax: x*x=1, x\,\text{ is a complex }\, n\text{-tuple}\}$ We will start with the celebrated Toeplitz-Hausdorff (1918, 1919) convexity theorem for the classical numerical range. Then we will move on to introduce various generalizations and we will focus on those in the framework of semisimple Lie algebras and compact Lie groups. In our discussions, results on convexity, star-shapedness, and multiplicity will be reviewed, for example, the results of Embry (1970), Westwick (1975), Au-Yeung-Tsing (1983, 84), Cheung-Tsing (1996), Li-Tam (2000), Tam (2002), Dokovic-Tam (2003), Cheung-Tam (2008, 2011), Carden (2009), Cheung-Liu-Tam (2011) and Markus-Tam (2011). We will mention some unsolved problems.
March 12, 2015
DH 135 from 11am-noon
Text as Data
Speaker: J.P. Wedeking of the University of Kentucky Department of Political Science

Abstract: Professor Wedeking will give a summary of three projects that he has been involved in using text as data (1 is published, 1 is under review, and 1 is ongoing). Specifically, for each of the 3 projects, He will: (1) describe the method he's using, what it generally is used for; (2) the motivation for the project-e.g., the substantive research question and relevant background information; (3) a brief description of the data; and (4) the results of the method and the substantive conclusions. The three projects are: (1) measuring how legal issues are framed (e.g., free speech vs. right to privacy, etc) and how that helps parties win; (2) uncovering the clarity of texts using readability formulas; and (3) scaling justices with texts- uncovering their ideological positions (how liberal or conservative they are) using their words.
December 4, 2014
POT 145 from 3:00-4:30pm
Hubs and Authorities Master's Presentation
Speaker: Nicholas Benthem of the University of Kentucky Department of Mathematics

Abstract: We introduce the idea of Hub and Authority rankings inside large scale networks with appropriate historical context, and introduce a new form for calculating Hubs and Authorities by turning a directed network into a bipartite network, along with efficient computational tools to evaluate these rankings in large scale networks.
November 6, 2014
POT 145 from 3:30-4:30pm
Modeling Foot and Mouth Disease in cattle in northern Cameroon
Speaker: Matt Orelam of the Ohio State Universsity Mathematical Biosciences Institute

Abstract: Foot and Mouth Disease (FMD) is endemic in cattle in the Far North Region of Cameroon. While many cattle herds remain in a fixed location throughout the year, there are a small number of mobile herds that migrate depending on the season. These mobile herds share grazing space with many other cattle throughout the year, leading to increased disease transmission. In this talk I will present a multi-scale agent-based simulation model of FMD in northern Cameroon, focusing on the mathematical SIRS epidemic model running both inter- and intra-herd. Various parameters are determined by data from researchers on the ground while others are determined via in silico experimentation. The goal of the first phase of the project is to determine how each herd type contributes to the overall number of secondary infections. This model is a work in progress and the talk is meant to stimulate discussion about means of incorporating epidemic models in a multi-scale setting.
October 16, 2014
POT 745 from 4-5pm
Efficient Solutions of Large Saddle-Point Systems
Speaker: Lola Davidson of the Unviersity of Kentucky Department of Mathematics

Abstract: Linear systems of saddle-point type arise in a range of applications including optimization, mixed finite-element methods for mechanics and fluid dynamics, economics, and finance. Due to their indefiniteness and generally unfavorable spectral properties, such systems are difficult to solve, particularly when their dimension is very large. In some applications - for example, when simulating fluid flow over large periods of time - such systems have to be solved many times over the course of a single run, and the linear solver rapidly becomes a major bottleneck. For this reason, finding an efficient and scalable solver is of the utmost importance. In this talk, we examined various solution strategies for saddle-point systems.
October 1, 2014
POT 745 from 3-4pm
Network Analysis with Matrix Functions
Speaker: Lothar Reichel of Kent State University

Abstract: Networks arise in many applications. It is often of interest to be able to identify the most important nodes of a network or to determine the ease of traveling between them. We are interested in carrying out these tasks for large undirected and directed networks. Many quantities of interest can be determined by computing certain matrix functionals. We discuss how for directed and undirected graphs a few steps of the Lanczos method in combination with Gauss-type quadrature rules can be applied to determine upper and lower bounds for quantities of interest.
September 25, 2014
POT 145 from 3:30-4pm
Accurate Computations of Matrix Eigenvalues with Applications to Differential Operators
Speaker: Qiang Ye of the University of Kentucky Department of Mathematics

Abstract: In this talk, we present our recent works on high relative accuracy algorithms for computing eigenvalues of diagonally dominant matrices. We present an algorithm that computes all eigenvalues of a symmetric diagonally dominant matrix to high relative accuracy. We further consider using the algorithm in an iterative method for a large scale eigenvalue problem and we show how smaller eigenvalues of finite difference discretizations of differential operators can be computed accurately. Numerical examples are presented to demonstrate the high accuracy achieved by the new algorithm.

Corrections to: murrugarra@uky.edu