The Applied Math seminar has speakers twice a month during the
school year. We generally meet in POT 745 from 11noon. 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 UKAPPLIEDMATHL 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 201819
 April 4, 2019
POT 745 from 11:00am12:00 pm
Title: TBA
Speaker: Ami Radunskaya, Pomona College.
Abstract:
TBA.
 Mar 28, 2019
POT 745 from 11:00am12:00 pm
Title: Intermittent Preventive Treatment and the Spread of Drug Resistant Malaria
Speaker: Olivia Prosper, University of Kentucky.
Abstract:
TBA.
 Mar 21, 2019
POT 745 from 11:00am12:00 pm
Title: TBA
Speaker: Aida Maraj, University of Kentucky.
Abstract:
TBA.
 Mar 7, 2019
POT 745 from 11:00am12:00 pm
Title: TBA
Speaker: Jacob Adams, University of Kentucky.
Abstract:
TBA.
 February 21, 2019
POT 745 from 11:00am12:00 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 UrbanaChampaign.
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 contiguitybased computations in large practical districting problems are needed. This talk introduces the geograph framework for modeling geographic districting as a graph partitioning problem, discusses two geograph 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 geograph 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 geograph 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 11:00am12:00 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. Computeraided drug design and discovery has obtained a significant recognition recently. However, the geometric complexity of proteindrug complexes remains a grand challenge to conventional computational methods, including machine learning algorithms. We assume that the physics of interest of proteindrug complexes lies on lowdimensional manifolds or subspaces embedded in a highdimensional data space. We devise topological abstraction, differential geometry reduction, graph simplification, and multiscale modeling to construct lowdimensional representations of biomolecules in massive and diverse datasets. These representations are integrated with various deep learning algorithms for the predictions of proteinligand 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 computeraided drug design and discovery (http://users.math.msu.edu/users/wei/D3R_GC3.pdf).
 Nov 1, 2018
POT 745 from 11:00am12:00 pm
Title: Mathematics for Breast Cancer Research: investigating the role of iron
Speaker: Luis SordoVieira, 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 11:00am12:00 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 11:00am12:00 pm
Title: Preconditioning for Accurate Solutions of the Biharmonic Eigenvalue Problem
Speaker: Kasey Bray, University of Kentucky.
Abstract:
Solving illconditioned 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 illconditioning. 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 201718
 April 26, 2018
POT 745 from 11:00am12:00 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 1:00pm2:00 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 skewsymmetric 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 11:00am12:00 pm
Title: Effects of Thermoregulation on Human Sleep Patterns: A Mathematical Model of SleepWake Cycles with REMNREM Subcircuit
Speaker: Alicia Prieto Langarica, Youngstown State University.
Abstract:
In this paper we construct a mathematical model of human sleepwake 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 11:00am12:00 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 diseaseeconomic 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 11:00am12:00 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 11:00am12:00 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 postglacial 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 11:00am12:00 pm
Title: Simulating WithinVector 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 lifecycle 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 withinmosquito, generating a distribution of parasite densities at five parasite lifecycle 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 11:00am12:00 pm
Title: Modeldependent and modelindependent control of biological network models
Speaker: Jorge G. T. Zanudo, DanaFarber 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 modelindependent and modeldependent 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 11:00am12:00 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 coemerging 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 11:00am12:00 pm
Title: Ubiquitous Doubling Algorithms, General Theory, and Applications
Speaker: RenCang 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 $2^{i1}$st one than simply following the rule to generate every approximation between the $2^{i1}$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 discretetime 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 continuoustime and discretetime 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 11:00am12:00 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, highthroughput 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 SHAPEdirected 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 11:00am12:00 pm
Title: Spatial Dynamics of Vector Borne Diseases
Speaker: Omar Saucedo, Mathematical Biosciences Institute.
Abstract:
Vectorborne 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 vectorborne 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 vectorborne disease dynamics.
 November 30, 2017
FPAT 253 from 2:00pm3:00 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 ShortTerm 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 skewsymmetric 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 11:00am12:00 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 11:00am12:00 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 healthrelated research and provide access to new, better understood therapies.
The stateoftheart in many computational methodologies include machine learning approaches. In our digitalized, datadriven 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 druglike 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 offtarget interactions with kinases a common cause of adverse drug reactions.
 October 5, 2017
POT 745 from 11:00am12:00 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
\[
p_{mj}(h_n) = (1)^n p_j(h_n),\quad 0\leq n,j\leq m.
\]
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 11:00am12:00 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 11:00am12:00 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 illconditioning. Given a preconditioner M for an illconditioned 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 inverseequivalent 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 illconditioned matrices. Numerical examples are presented to illustrate the error analysis and the performance of the methods.
Academic Year 201617
 April 20, 2017
POT 745 from 11:00am12:00 pm
Title: TwoDimensional PCA with FNorm Minimization
Speaker: Jing Wei, University of Kentucky
Abstract: Master's Talk.
Twodimensional 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 Fnorm minimization (F2DPCA), which is intuitive and directly derived from 2DPCA. In F2DPCA, distance in spatial dimensions (attribute dimensions) is measured in Fnorm, while the summation over different data points uses 1norm. Thus it is robust to outliers and rotational invariant as well. To solve F2DPCA, we propose a fast iterative algorithm, which has a closedform 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 11:00am12:00 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): 123. Web. ISSN: 00219991 ; 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 11:00am12:00 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, 454477, 2003.
 March 9, 2017
POT 745 from 11:00am12:00 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 genegene interaction on cancer data obtained from the European casecontrol study GenAir extending previous work by Ricceri, Fassino, Matullo, Roggero, Torrente, Vineis, and Terracini.
 March 2, 2017
POT 745 from 11:00am12:00 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 11:00am12:00 pm
Title: The Inverse qNumerical Range Problem and Connections to the DavisWielandt 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 DavisWielandt shell, a
generalization of the numerical range. We found that the DavisWielandt
shell is in a sense conjugate to the the extreme singular values of the
resolvent of a matrix. Knowing the DavisWielandt shell allows for the
approximation of the $q$numerical range, the pseudospectra and the
DavisWielandt 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 11:00am12:00 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 11:00am12:00 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 agentbased 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 10:30am11:30 am
Title: Accurately Computing Eigenvalues of Extremely Illconditioned 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 illconditioned 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 11amnoon
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 11amnoon
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 11amnoon
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 structurefunction 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 bondlength distributions have revealed bondlength 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 nonaberrant CGs.
 October 27, 2016
POT 745 from 11amnoon
Title: Spatial heterogeneity, host movement, and the transmission of mosquitoborne disease
Speaker: Olivia Prosper, University of Kentucky
Abstract: The RossMacdonald framework, a suite of mathematical models for the transmission of mosquitoborne 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 vectorborne 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 vectorborne disease, based on the RossMaconald 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 realworld 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 11amnoon
Title: Synchrony in a Boolean network model of the Larabinose operon
Speaker: Matthew Macauley, Clemson University
Abstract: In genetics, an operon is a segment of DNA that contains several cotranscribed 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 Larabinose 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 11amnoon
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 11amnoon
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 longterm 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 nonsequential.
 September 22, 2016
POT 745 from 11amnoon
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 expost Nash equilibrium, and (iii) for given valuations, the auction ending prices and revenue depend only on starting prices. We establish sincere bidding and pathindependent 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 11amnoon
Title: Insight into Molecular through Subcellular Calcium Signaling via MultiScale Simulation
Speaker: Peter KekenesHuskey, 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. Calciumdependent signaling pathways enlist a variety of proteins and channels that must rapidly and selectively bind calcium against thousandfold higher cationic concentrations. Frequently these pathways further require the colocalization of these proteins within specialized subcellular structures to function properly. Our lab has developed multiscale simulation tools to elucidate how protein structure and colocalization 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 micronscale diffusion models, and reactiondiffusion simulations that leverage submicron microscopy data. In this seminar, I will describe these tools and their applications toward molecular mechanisms of calciumselective recognition and crosstalk between colocalized calcium binding proteins inside the cell.
 September 1, 2016
POT 745 from 11amnoon
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 201516
 April 28, 2016
POT 745 from 11amnoon
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 [1634]°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 firsttime infections. This study
emphasize the combined use of
mosquitoreduction 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,
mosquitoreduction 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 11amnoon
Title: Generative Neural Networks in SemiSupervised Learning
Speaker: Devin Willmott
Abstract: Semisupervised 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 semisupervised 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 23pm
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 11amnoon
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
 April 7, 2016
POT 745 from 11amnoon
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 highresolution
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 learningbased methods to extract
geospatial properties from imagery. In particular, I will
focus on two recent research thrusts: using deep
convolutional neural networks to geocalibrate social
network imagery and using such imagery to build
geotemporal models of human appearance.
 March 31, 2016
POT 745 from 11amnoon
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 11amnoon
Computing Exponentials of Essentially Nonnegative Matrices with
Entrywise Accuracy
Speaker: Qiang Ye, University of Kentucky
Abstract:
A real square matrix is said to be essentially nonnegative if all of
its offdiagonal entries are nonnegative. In this talk, I will present
new perturbation results and algorithms that demonstrate that the
exponential of an essentially nonnegative matrix can be computed
with entrywise relative accuracy.
 March 3, 2016
POT 745 from 11amnoon
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 11amnoon
Algebraic methods in computational biology
Speaker: Reinhard Laubenbacher, Director, Center for Quantitative Medicine, UConn Health Center
Abstract:
As biology has become a datarich 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 11amnoon
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 11amnoon
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 stateoftheart 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
intrinsicallyparallel, suitable for solving very large eigenproblems on
supercomputers.
 November 5, 2015
POT 745 from 11am1pm
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 wellconditioned matrix no matter how large the norm is.
In this dissertation, we derive new error bounds for computing \(e^{tA}v\) with nonsymmetric \(A\), 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 skewHermitian. 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 11amnoon
On the perfect reconstruction of the topology of dynamic networks
Speaker: Alan VelizCuba, University of Dayton Ohio
Abstract: The network inference problem consists in reconstructing the topology or wiring diagram of a dynamic network from timeseries 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 discretetime 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 11amnoon
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 11amnoon
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 12pm
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 shiftandinvert transformation
to accelerate the speed of convergence, which is not practical for
truly large problems. With this in mind, Golub and Ye proposes an
inversefree preconditioned Krylov subspace method, which uses
preconditioning instead of shiftandinvert to accelerate the
convergence. The inversefree 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 inversefree Krylov subspace method. We
generalize the original convergence theory for the inversefree
preconditioned Krylov subspace method to justify this deflation
scheme. We next extend the inversefree 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 socalled subspace clustering problem,
which aims for extracting a multisubspace structure from a collection
of points lying in a highdimensional 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 201415
 April 23, 2015
POT 945 from 11noon
Making Do with Less: An Introduction to Compressed Sensing
Master's Presentation
Speaker: Fouche Smith
 April 16, 2015
POT 745 from 2:153:30pm
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 56pm (refreshemnts at 4:30pm)
The Problem of BusBunching 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 3:304:30pm
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 distancebased 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 subtreepruneregraft 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 cladefaces are smallerdimensional 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 11noon
Convexity, starshapedness, and multiplicity of numerical range
and its generalizations
Speaker: TinYau Tam of the Auburn University Department of Mathematics
and Statistics
Abstract:
Given an
$n\backslash times\; n$
complex matrix
$A$, the
classical numerical range (field of values) of
$A$
is the following set associated with the quadratic
form:
$$W(A)\; =\; \backslash \{x^*Ax:\; x*x=1,\; x\backslash ,\backslash text\{\; is\; a\; complex\; \}\backslash ,\; n\backslash text\{tuple\}\backslash \}$$We will
start with the celebrated ToeplitzHausdorff (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,
starshapedness, and multiplicity will be reviewed, for example,
the results of Embry (1970), Westwick (1975), AuYeungTsing
(1983, 84), CheungTsing (1996), LiTam (2000), Tam (2002),
DokovicTam (2003), CheungTam (2008, 2011), Carden (2009),
CheungLiuTam (2011) and MarkusTam (2011). We will mention
some unsolved problems.
 March 12, 2015
DH 135 from 11amnoon
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 projecte.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 3:004:30pm
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 3:304:30pm
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 multiscale agentbased simulation model of FMD in northern
Cameroon, focusing on the mathematical SIRS epidemic model running
both inter and intraherd. 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 multiscale setting.
 October 16, 2014
POT 745 from 45pm
Efficient Solutions of Large SaddlePoint Systems
Speaker: Lola Davidson of the Unviersity of Kentucky Department of Mathematics
Abstract:
Linear systems of saddlepoint type arise in a range of applications including optimization, mixed finiteelement 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 saddlepoint systems.
 October 1, 2014
POT 745 from 34pm
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 Gausstype quadrature rules can be
applied to determine upper and lower bounds for quantities of interest.
 September 25, 2014
POT 145 from 3:304pm
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
