Abstracts

Short Talk Abstracts

Name: Sha Wan

School: Clemson University

Title: Change-Point Detection With Quantile Autoregression Model

Abstract: This study investigates change-point detection within Quantile Autoregression (QAR) models, a key tool for identifying structural shifts in time series data across fields like economics, climate studies, and quality control. We examine both traditional and advanced techniques for detecting single and multiple change-points, including methods like CUSUM, Likelihood Ratio Tests, Binary Segmentation, and Penalized Likelihood approaches.

The research addresses the challenges of applying these techniques to autocorrelated data, proposing modifications to improve their eMectiveness. Additionally, we highlight the efficiency of the of the Pruned Exact Linear Time (PELT) algorithm in detecting change-points.

Future work will focus on enhancing QAR model fitting through gradient-based

optimization, particularly for data with periodic components.

Name: Sahil Chindal

School: Virginia Commonwealth University

Title: Neural Network Approaches for Predicting Dengue Incidence in the Dominican Republic

Abstract: Dengue is a mosquito-borne disease endemic to many tropical and subtropical regions around the world, including the Dominican Republic. Temperature, precipitation, humidity, and other climate variables play a crucial role in dengue spread due to their association with mosquito growth and proliferation. Using climate and dengue case data, we aim to determine which climate factors are associated with dengue cases. We have developed various machine-learning models utilizing either artificial neural networks (ANNs) or physics-informed neural networks (PINNs) to study dengue spread in several provinces of the Dominican Republic. One model uses ANN and incorporates climate and previous dengue case data to predict future cases. Our second model utilizes the PINN framework and previous dengue case data and the SIR compartment model framework to predict future cases. We train those models with dengue incidence data from 2015-2019, compare their prediction accuracy, and discuss the insights from the fitted models. Our predictive model that utilizes ANN and PINN can be integrated with geographic, sociodemographic, and other types of information as part of a comprehensive early warning system that predicts outbreaks and informs public health and mosquito control policies.

Name: Jakini Kauba

School: Clemson University

Title: Modeling Endosomal Escape using Spatial Poisson Processes

Abstract: The focus of this research is to use computational biology to model the quantification of endosomal escape after successful peptide delivery of bioactive siRNAs into ovarian cancer cells. In this work, we want to show that endosomal escape exhibits features similar to spatial population models.

We model the random spatial properties of siRNA by using a combination of stochastic population modeling, continuous-time Markov Chains, and doubly stochastic Gaussian-Poisson processes. While previous work relies solely on pixel counts for quantification, we aim to develop a model that not only efficiently quantifies endosomal escape but also allows for the prediction and further exploration of this random motion. Our hope is that such modeling can be used experimentally in practice for bioengineers, chemists, pharmacists, and other scientists. This work will contribute to the ever-growing body of research on effective drug delivery and cancer therapy.

Name: Rakhi Goswami

School: Clemson University

Title: On Solving Two-Stage Biobjective Linear Programs

Abstract: Two-stage biobjective linear programs (TSBOLPs) model decision situations under uncertainty with conflicting objectives at every stage. The assumptions about discrete or continuous uncertainty in the right-hand-side vector, the number of objectives in the second stage, and the application of the weighted-sum scalarization lead to four parametric single objective optimization problems (SOPs) resulting from the TSBOLP. These SOPs have bilinear terms composed of parameters and variables in different configurations, making them difficult to solve. A methodology is developed to solve the TSBOLP, defined as the computation of the first-stage robust solutions of the TSBOLP which are efficient for all objective functions and all uncertainty scenarios. The methodology relies on parametric linear programming and Benders’ decomposition and includes three Parametric Benders’ Decomposition algorithms that solve TSBOLPs for two or more first-stage objective functions and one or more second-stage objective functions. The algorithms are supported by examples.

Name: Sumit Banerjee

School: Clemson University

Title: Aluminium-26 emission from Galactic Fountains

Abstract: The measurement and interpretations of the characteristic diffused Gamma ray emissions from the decays of radioisotopes like Aluminum-26 and Iron-60 has been a central topic in astrophysical research. Designated missions like INTEGRAL with its spectrometer SPI and COMPTEL have revealed various intricacies of these emissions including their distribution, placing constraints on their amount in the Galaxy which in turn puts a constraint on the possible sources of such emissions. Past works have revealed that these emissions are clumpy and scattered throughout the Galaxy, signifying that the likely origin is from massive star groups. We now understand that the majority of these radioisotopes come from supernovae and stellar winds from the Wolf-Rayet stars. Detailed sky maps produced by INTEGRAL and COMPTEL further show that the emission is localized to the Galactic midplane, further constraining the sources. Several modeling attempts have been made to model this distribution of the isotopes in the Galaxy none of which have been satisfactory in the regards that none of these simulations explain the amount of the radioisotopes found in the Galaxy. In this study, we explore one such possibility of Galactic fountains serving as a source. Galactic fountains eject gas and dust into the Interstellar medium of the Galaxy which after some time falls back to the Galactic midplane due to gravity. We are hopeful that the emissions from these Galactic fountains bridge the gap between the modeled and observed emissions of the radioisotopes in the Interstellar medium.

Name: Rayna Maleki

School: Clemson University

Title: Applications of Stochastic Processes and Markov Modeling to In Vitro Fertilization

Abstract: We propose a comprehensive stochastic model of the most common form of assisted reproductive technology, in vitro fertilization (IVF), a process in which

individuals seeking to get pregnant go through hormonal treatments, ovarian stimulation for optimal oocyte retrieval, and embryo fertilization and culture in a lab setting in hopes of increasing the probability of conceiving. IVF is a complex and often cyclic process with well-defined clinical states, which makes Markov modeling an accessible tool for researchers, clinicians, and patients to gain insight on the fertility treatment process. Using a mixture of discrete and continuous time Markov chains, we can simulate a series of random walks through the chain, compute the limiting and stationary distributions, compare transition functions for differing types of treatments at each stage, and find the mean time until an outcome of interest. Our design of a Markov chain with both fixed time transition probabilities between states and continuous transitions where time is a random variable can be broadly applied to other kinds of medical treatments, clinical trials, and biological processes.

Name: Samuel Orr

School: Clemson University

Title: An Introduction to Error Correction and Gabidulin Codes

Abstract: Error correcting codes are used to correct errors that occur during data transmission or during storage of data. Several public key cryptosystems have been created using these codes, notably the McEliece cryptosystem, which utilizes Binary Goppa Codes and the Hamming metric. We will discuss another type of metric as well: the rank metric. One code defined using this metric is the Gabidulin code, first seen in Ernst Gabidulin's 1985 paper "Theory of Codes with Maximum Rank Distance". We will introduce a cryptosystem based off of these codes and explain how attempts at making these codes secure have thus far been unsuccessful.

Name: Tyler Moore

School: Clemson University

Title: Computational Analysis of the Maximum Clique Problem

Abstract: The maximum clique problem (MCP) finds itself in the intersection of discrete optimization and graph theory–analyzing the cliques of a graph and finding the largest, complete subgraph by cardinality. We explore public solvers and mathematical formulations of the MCP, which are tested on benchmark graphs to compare algorithm performances. Variations naturally derive from the problem, including the maximum vertex weight and, more interestingly, the maximum edge weight clique problem, which will be highlighted with mathematical formulations, computational results, and real-world applications. We observe the effectiveness of computational algorithms and explore the behavior of the problem and variations as graph size increases using mixed-integer, linear, and quadratic programming.

Name: Fabrice Razafimahatratra

School: Clemson University

Title: Shifting The Spell

Abstract: The Banach-Tarski paradox is one of the most intriguing results in mathematics. Its most famous form states that we can decompose a ball into a finite number of pieces and reassemble them to form two balls of the same shape and volume as the original. One can blame the axiom of choice (AC) for this nonphysical result, which resembles a spell in a world of witchcraft. To shift away from this particular nonphysical consequence of AC, we will recreate the (mathematical) universe using opens (Topological objects)—fundamentally in dialectic, a la Lawvere, to the concept of points (element of a set)—as a base. We will conclude that such an approach does not produce a nonphysical result.

Name: Sam Clauss

School: Clemson University

Title: From infestation to eradication: Modeling extinction probabilities of Asian Long-horned Beetle Infestations

Abstract: Asian Long-horned Beetles (ALB) (Anoplophora glabripennis) are an invasive species native to China and Korea. Female ALB burrow to create oviposition cavities in trees where they lay their eggs. Larvae then feed on the tree, which can often end in the death of the tree. ALB infestations have occurred in several states in the eastern United States such as Massachusetts, Ohio, New York, and South Carolina. This project aims to calculate the probability of extinction of ALB. We employ a Multiple Population Viability Analysis on populations of ALB with different management scenarios using data generated from a Spatial Poisson Process to mimic infestation patterns. We compare this to an stochastic branching process to estimate the probability of extinction. The goal is to find critical thresholds for parameters of interest such as the removal rates of infested trees to maximize the probability of extinction. Ideally, this model will go on to inform management practices to eradicate ALB and other invasive species.

Name: Lauren Henderson

School: Clemson University

Title: Bounding the Convex Hull Relaxation of the Unit Commitment Problem with the Shapley-Folkman Theorem

Abstract: The Unit Commitment (UC) problem finds an optimal schedule for a set of generators by minimizing the total operation cost subject to demand and operational constraints. The UC problem is often modeled with a mixed-integer linear program (MILP). We employ the Shapley-Folkman Theorem to provide a bound on the size of fractional solutions of its convex hull relaxation. This result is used to obtain a bound on the optimality gap between the MILP and the convex hull relaxation, which is further tightened using several problem-specific properties of UC. We conduct extensive numerical experiments to study the tightness of this threshold, and how it is impacted by different parameters.

Name: Ben Gobler

School: Clemson University

Title: Why does 6 come after 7?

Abstract: The Calkin-Wilf tree is a binary tree with nodes labeled by reduced fractions. In this talk, we will investigate the integers which appear in early rows of the Calkin-Wilf tree, as well as those which take longer to make an appearance.

Poster Abstracts

Name: Ethan Doherty

School: Clemson University

Title: Stochastic modeling of an Asian longhorned beetle invasion

Abstract: The Asian long-horned beetle (Anoplophora glabripennis) in an invasive wood-boring pest in the eastern United States. It destructively feeds on maples and other hardwood trees, often killing its host and disrupting native ecologies. A multi-institutional effort has been made to mark the presence and distribution of the beetle in the US states. Currently, metapopulation models are used to calculate infestation rates based on tree species, type of land usage, and patch size. Utilizing raw field data, we have constructed several models to evaluate factors influencing beetle spatial distribution, identify high-risk areas, and anticipate its spread. Agent-based models explored the probabilities of tree infestation, detection, and removal by incorporating host availability, infestation intensity, dispersal distances, and survey methodologies.

Name: Chinthaka Weerarathna

School: University of Tennessee Chattanooga

Title: An Introduction to Error Correction and Gabidulin Codes

Name: Rabin Baral

School: Clemson University

Title: Enhancement of Actin Bundle Rigidity by β-CaMKII for Synaptic Stability

Abstract: Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) is a serine/threonine kinase that plays a key role in synaptic plasticity by regulating the actin cytoskeleton within dendritic spines. These spines, where CaMKII is highly concentrated, undergo structural changes driven by modifications in the actin network, which are essential for synaptic plasticity. However, the mechanisms underlying the stability and adaptability of the actin cytoskeleton, particularly how it withstands or transmits mechanical forces, remain unclear. We hypothesize that CaMKII-actin interactions contribute to the mechanical stability of dendritic spines during synaptic activity by enhancing the resilience of the actin network to physical stress. To test this, we used passive microrheology to track the movement of polystyrene beads (ranging from 0.79 to 5 micrometers) in solutions containing actin, CaMKII-bundled actin, α-actinin-bundled actin, and fascin-bundled actin. The mean square displacement (MSD) analysis revealed significant differences among the conditions, with β-CaMKII showing notably lower MSD values and reduced particle mobility compared to the other tested actin-binding proteins (ABPs). The MSD data were further used to calculate the complex viscoelastic modulus, demonstrating that β-CaMKII uniquely stiffens actin filament bundles. These findings suggest that the rigidity imparted by β-CaMKII to actin bundles is critical for the structural reorganization and expansion of the spine cytoskeleton. This increased rigidity could support spine stabilization during synaptic activity, enabling spine enlargement associated with enhanced synaptic strength, a process known as structural plasticity.

Name: Preethika Yetukuri

School: Clemson University

Title: Time-Series Analysis & Markov Chains for Predicting SDG Progress

Abstract: The United Nations Sustainable Development Goals (SDGs) provide a global framework for addressing critical challenges. However, tracking progress toward these goals remains complex due to uncertainties in policy effectiveness, economic fluctuations, and external shocks. This research utilizes time-series analysis and Markov Chains to model and predict SDG progress across different countries, offering insights into the likelihood of achieving these targets by 2030. This research aims to contribute to data-driven policymaking by showing how stochastic models have the power to strategize decision making toward sustainable development efforts.

Name: Abideen Ayangbemi

School: Clemson University

Title: Application of Worm-Like Chain Model in Single-Molecule Force Spectroscopy

Abstract: The worm-like chain (WLC) model is a fundamental statistical mechanics framework used to describe the elasticity of biopolymers like DNA, proteins and actin filaments. This model is important in interpreting experimental data from single-molecule techniques such as atomic force microscopy, optical tweezers and magnetic tweezers. This model, which is an extension of the Kratky-Porod model, treats the polymer as a continuously flexible rod with a finite persistence length. The WLC model predicts the polymer's conformational properties, the end-to-end distance and radius of gyration, relating it to the polymer’s persistence length and contour length. In a Single-Molecule Force Spectroscopy (SMFS) experiment, mechanical force is applied to biomolecules to probe the extension properties as a factor of applied force. By analyzing force-extension curves obtained from these SMFS studies, the WLC model can be used to determine the mechanical response of polymers under tension, revealing insights into biological processes like intermediates of the unfolding of proteins, DNA-protein interactions and chromatin organization. This study discusses the mathematical formulation of the WLC model, modification to include the energy function, end-to-end distance distribution and force-extension behavior under external forces focusing on their applications in single-molecule force spectroscopy and polymer physics. The continuous modification to this model can improve our understanding of polymer mechanics yielding advancement in molecular biology and nanotechnology.

Name: Belen Gandrud

School: Clemson University

Title: REVAMP - Resilience and Evolution of Viscoelastic Accumulation in Materials and Polymers

Abstract: Visco-elastic materials are susceptible to damage accumulation when subjected to sequential cycles of loading and unloading, particularly under varied temperature and loading conditions. The research aims to develop methods both analytical and experimental to assess the long-term behavior of polymer materials, including damage accumulation, lifetime prediction, and stress-strain state of the material, accounting for both environmental effects loading and temperature. The proposed approach requires only a limited number of short-term experiments and will provide insight into the scattered failure behavior of viscoelastic materials. The analysis seeks to establish correlations between the time-dependent properties of polymers and the optimization of parameters for the analytical model. The analytical framework will be based on a phenomenological approach using hereditary-type equations in order to assess the time-dependent deformation and fracture process. The economical impact of implementing analytical and experimental software packages is evaluated and presented for marketing applications.