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APPLIED MATHEMATICS SEMINAR

Applied Math Seminar

Title: Understanding neutrophil dynamics during COVID-19 infection

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.

 

Date:
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Location:
POT 745

Applied Math Seminar

Title: Lightweight Deployable Automated Space Systems Using the Least Necessary Resources

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. 

Date:
-
Location:
POT 745

Applied Math Seminar

Title: Randomized Contour Integral Methods for Eigenvalue Problems with Probabilistic Error Analysis

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).

Date:
-
Location:
Zoom

Applied Math Seminar

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 Kansa
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 analysed. 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 recruit- ment 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.

Date:
-
Location:
POT 745

Applie Math Seminar:Qualifying Talk

Speaker: Devin Willmott

Title: Generative Neural Networks in Semi-Supervised Learning

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.

Date:
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Applied Math Seminar: Master's Talk

Title:   Matrix Factorization Techniques for Recommender Systems
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.

Date:
-
Location:
POT 110

Applied Math Seminar: Master's Talk

Jonathan Proctor will be giving a Master's Talk.  He will be presenting the paper

Numerical Methods for Electronic Structure Calculations of Materials

 

Date:
-
Location:
POT 745

Applied Math Seminar

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.

BIO:

Nathan Jacobs earned a PhD in Computer Science at Washington University in St. Louis (2010). Since then, he has been an Assistant Professor of Computer Science at the University of Kentucky. Dr. Jacobs' research area is computer vision; his specialty is developing learning-based algorithms and systems for processing large-scale image collections. His is a recipient of an NSF CAREER award, and his research has been funded by ARMY-SMDC, ARL, DARPA, Google, IARPA, NGA, and NIH. His current focus is on developing techniques for mining information about people and the natural world from geotagged imagery, including images from social networks, publicly available outdoor webcams, and satellites.

Date:
-
Location:
POT 745

Applied Math Seminar

Speaker: Luis Sordo Vieira
Title: The benefits of elliptic curve cryptography
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.
Date:
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Location:
POT 745

Applied Math Seminar

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.

Date:
-
Location:
POT 745
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