SCMB Final Symposium 

April 10 – 11, 2025 Poster Session 

Titles and Abstracts 

Hasif Ahmed - University of Wisconsin 

“Space Debris Oddity: A Population Dynamics Approach to Modeling Lower Earth Orbit Debris” 

Abstract: The proliferation of artificial space debris in Low Earth Orbit (LEO) presents a growing hazard to satellites, missions, and future access to space. In this work, we adopt a structured population dynamics perspective to model the temporal and spatial distribution of debris, treating orbiting objects not as discrete entities, but as a continuum population governed by birth, death, and transport-like mechanisms. 

Peter Alspaugh – University of South Florida 

“Structures of Monoids Motivated by DNA Origami” 

Abstract: DNA Origami provides a method to create DNA nanostructures via bottom-up self assembly rather than traditional top-down fabrication. A DNA Origami structure consists of a single long cyclic strand called a “scaffold” and numerous short “staple” strands, which force the scaffold into a desired shape during self-assembly. While many structures have been experimentally created, a mathematical framework and theoretical understanding of DNA Origami shapes and structures is still lacking. We propose an algebraic system, the Origami monoid, to describe varying staple arrangements within a rectangular fold of the scaffold. To each arrangement, we associate an element of the monoid and design the operation to represent concatenation of graphical representations of the origami shapes. We construct the monoid by doubling the generators and relations of the well-studied Jones monoid, then adding relations that describe plausible modifications to DNA Origami nanostructures. We prove several algebraic properties of the monoid, including restrictions on the forms of its elements, facts about its Green's classes, and we find an unexpected occurrence of contextual commutation between certain generators. Besides possible applications to DNA Origami, our approach also provides new ways to build and study algebraic structures. 

Emily Baker – Texas A&M University 

“Comparative Genomics of Schistocerca Gregaria” 

Abstract: The desert locust, Schistocerca Gregaria, is a species of locust prevalent in dry regions of northern and eastern Africa, the Arabian Peninsula, and southwest Asia This species is notorious as a major agricultural pest, forming swarms that decimate crops in its native regions. These swarms of S. gregaria form in response to an increase in conspeci@ic density, causing the population to display both behavioral and phenotypic changes -- a phenomenon known as locust phase polyphenism. This project seeks to determine the genetic mechanism behind these density-dependent changes and uncover the evolutionary history of the associated pathways by comparing the genome of S. gregaria to other members of the Schistocerca genus. Through identifying key genes involved in phase transition, we can gain insight into the genetic basis of swarm formation. Additionally, understanding the evolutionary divergence of these pathways may provide clues about the evolution of similar traits across different species, as well as provide possible methods of pest control for regions affected by these devastating outbreaks. 

Kasturi Barkataki – Arizona State University 

“Novel topological measures of multi-chain complexity in biopolymers” 

Abstract: Biopolymers live in crowded environments where they attain complex 3 dimensional conformations that are related to their sequence and function. To characterize the multi-component structure of biopolymers we employ methods from topology. A new framework in knot theory was introduced recently that enables one to characterize the complexity of collections of open curves in 3-space using the theory of knotoids and linkoids, which are equivalence classes of diagrams with open arcs. This gives rise to a collection of novel measures of entanglement of open curves in 3-space, which are continuous functions of the curve coordinates and tend to their corresponding classical invariants when the endpoints of the curves tend to coincide. In this talk, we show how knot theoretic measures, such as the Jones polynomial can be used to distinguish between systems of biopolymers and quantify the net entanglement present in such systems that is relevant to their function. 

Cory Brunson – University of Florida 

“Topological Feature Extraction for Texture Analysis of Lung CT Scans” 

Abstract: Background: Pulmonary sarcoidosis is a rare disease characterized by granulomatous inflammation. Given its heterogeneous presentation, sarcoidosis care stands to benefit from the identification of new markers for diagnosis, subtyping, and progression. One untapped texture-analytic approach is cubical persistent homology (CPH), a multiscale quantification of connectivity and enclosure in image data. Objective: Our primary goal is to apply this approach to important problems in pulmonary sarcoidosis care: distinguishing stages, identifying phenotypes within a heterogeneous population, and predicting progression. Methods: We hypothesize that topological features will support the classification of CT scans by disease subtype. As public image data on sarcoidosis is sparse, we tested this hypothesis using publicly available image data for adeno-, squamous cell, and small cell carcinoma from a research hospital in China. We applied a mesh to each 3D image array, computed CPH on each cell, and used feature averages to train (2/3) and test (1/3) a support vector machine. Results: The overall accuracy was 65.1%, with per-class accuracies of 74.3% (adeno-), 28.6% (squamous cell), and 0% (small cell). Conclusion: These preliminary results demonstrate that localized CPH can support lung disease subtyping. Ongoing data collection from our institutional EHR and refinement of our analysis pipeline will assess whether CPH can support subtyping and prognosis of sarcoidosis. 

Sam Clauss – Clemson University 

“Predicting mean time to extinction for Asian Longhorned Beetle infestations” 

Abstract: Asian Longhorned 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 infested trees over time. We employ a spatial agent-based model to predict the mean time to extinction, to investigate the mean time to extinction as a function of the initial number of infested trees, and explore the effect of spatial distribution on the infestation spread. Our model incorporates the spatial dynamics of ALB infestation and the removal of infested trees. Ideally, this model cango on to inform management practices to eradicate ALB from the United States.

Linh Do – Tulane University (SCMB Junior Researcher) 

“CPLASS: A segmentation analysis in noisy trajectories” 

Abstract: We introduce CPLASS, an algorithm for detecting generalized changes in slope problems within multidimensional data, addressing fundamental challenges in probability structure and search methodology. Unlike traditional changepoint detection methods that focus on mean shifts, detecting changes in slope requires specialized approaches due to continuity constraints and parameter dependencies. Existing algorithms, including binary segmentation and simple dynamic programming methods, struggle with these complexities. To overcome these limitations, we develop an MCMC-based approach with tailored proposal mechanisms for efficient parameter exploration. Our method is particularly suited for analyzing intracellular transport data, where molecular motor trajectories exhibit complex, multidimensional transitions. To enhance robustness in small-sample regimes, we introduce a speed penalty that improves statistical power while maintaining consistency in the large-sample limit. Additionally, we demonstrate that comparing the proportion of time spent at different speeds provides a more stable metric for trajectory characterization

Qijun He – University of Virginia 

“Inference of Antimicrobial Resistance Gene Mobilization via Weighted Simplicial Complexes” 

Abstract: Mobile genetic elements play a central role in the global spread of antibiotic resistance. To investigate the evolution of antimicrobial resistance over time, we reconstructed complete bacterial genomes and plasmid assemblies from isolates harboring the same bla_KPC carbapenemase gene, sampled from six confined hospital drain biofilms over a five-year period. From 82 isolates, we identified 14 unique strains spanning 10 species and characterized 113 bla_KPC-carrying plasmids across 16 distinct replicon types. To assess the dynamics of gene mobilization, we applied weighted simplicial complexes to encode the co-occurrence relationships between plasmids and chromosomes, enabling inference of the directional movement of resistance genes and identification of likely donor and recipient elements. Using this validated model, we demonstrate frequent transposition events of bla_KPC between plasmids, as well as integration into the bacterial chromosome within specific biofilm environments. We introduce a novel topological framework to estimate the directional mobilization of antimicrobial resistance genes, providing new insights into their spread across genetic elements in clinical environments. 

Yuta Hozumi – Georgia Tech 

“Revealing the Shape of Genome Space via K-mer Topology” 

Abstract: Despite decades of effort, understanding the shape of genome space in biology remains a challenge due to the similarity, variability, diversity, and plasticity of evolutionary relationships among species, genes, or other biological entities. We present a k-mer topology method, the first of its kind, to delineate the shape of the genome space. K-mer topology examines the topological persistence and the evolution of the homotopic shape of the sequences of k nucleotides in species, organisms, and genes using persistent Laplacians, a new multiscale combinatorial approach. We also propose a topological genetic distance between species by their topological invariants and non-harmonic spectra over scales. This new metric defines the topological phylogenetic trees of genomes, facilitating species classification and clustering. 

Irina Ivchenko – Cal Poly, San Luis Obispo 

“Characterizing the Structure of Seedling Roots with Fractal and Convex Hull Analysis” 

Abstract: The branching form of a plant’s seedling root structure mirrors the many branching structures that occur in nature. We argue that analysis on the structure of roots can be preformed on the 2-dimensional projection of a 3-dimensional root structure based on Marstrand’s Theorem and related conclusions. We use the statistical fractal dimension and the convex hull of the projection to characterize the structure of the roots, as metrics for the occupied space. The rhizosphere (the volume radially around the root branches from which the plant accesses nutrients and water) is then projected onto the same plane as the root structure to characterize the nutrients water gathering function of the root. Thus, we provide the foundation to determine the relationship of form of seedling roots with their function. 

Gabrianne Ivey – Clemson University 

"Modeling Oscillations in the Gene Expression of Components of the SOS Response in EscherIchia coli using a Boolean and a Stochastic Framework." 

Abstract: DNA can be damaged through both internal and external sources. Therefore, cells have created methods to repair DNA damage. In Escherichia coli, the system responsible for DNA repair is termed the SOS response. This system consists of more than 50 genes and contains three main repair pathways: nucleotide excision repair, translesion synthesis, and homologous recombination. The response is initiated when DNA lesions result in the accumulation of single-stranded DNA (ssDNA). The protein RecA is activated by binding to ssDNA and is then denoted RecA*. RecA* assists in the auto-cleavage of LexA which is the primary repressor protein involved in the SOS system. Inactivation of LexA allows for the transcription of operons, such as umuDC, uvrAB, recX, recN, recA, lexA, dinI, and yebG. In this study, we model the behavior of these genes and their gene products during the SOS response using a stochastic model and a Boolean model. In the stochastic model, we observe oscillations in some of the components of the system as well as two distinct responses: one in which DNA is repaired and the other where DNA is not repaired within 330 minutes. We find that the Boolean model exhibits two fixed points when the SOS system is induced which also suggests an oscillatory behavior and/or bistability. We hypothesize that these observations are due to 1) stalling/restarting the replication fork and 2) proteins inhibiting RecA*. In comparing our model to previous experimental results, we observe that it matches these data. 

Paria Karimi Kousalari – University of Iowa 

“Topoisomerases distance table” 

Abstract: DNA molecules are long polymers. Circular DNA can become knotted, which for proper biological function need to be resolved. Proteins such as topoisomerases play a crucial role in unknotting these molecules. The activity of type II topoisomerases can be thought of as a topological operation: these proteins resolve DNA knots by changing crossings. I am calculating distance tables modeling topoisomerase action on knots and links. 

Jakini Kauba – Clemson University 

“A Stochastic Approach to Modeling Drug Delivery Using Spatial Poisson Process”

Abstract: The focus of this research is to use computational biology to analyze the quantification of endosomal escape after successful peptide delivery of bioactive siRNAs into ovarian cancer cells. In this work, we 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. 

George Kennedy – University of Iowa 

“Aptamer Clustering using Mapper” 

Abstract: Aptamers are RNA molecules that can bind to a specific target, like antibodies, but are up to 20 times smaller and are chemically synthesized. Aptamer research ponders these molecules and searches for causes of aptamers binding or not binding to desired target molecules, as well as methods to construct new aptamers. A natural place to start is to cluster together groups of aptamers which bind to similar or different targets, and then look for similarities or differences between those aptamers. We use the Mapper algorithm from topological data analysis to investigate the reverse problem — do aptamers with genetic or structural similarities bind to similar targets, and do aptamers with significant genetic or structural differences bind to different targets? 

Anna Leinheiser – University of Iowa 

“A dynamical systems model for the total fission rate in Drp1-dependent mitochondrial fission” 

Abstract: Mitochondrial hyperfission in response to cellular insult is associated with reduced energy production and programmed cell death. Thus, there is a critical need to understand the molecular mechanisms coordinating and regulating the complex process of mitochondrial fission. We develop a nonlinear dynamical systems model of dynamin related protein one (Drp1)-dependent mitochondrial fission and use it to identify parameters which can regulate the total fission rate (TFR) as a function of time. The TFR defined from a nondimensionalization of the model undergoes a Hopf bifurcation with bifurcation parameter µ = k+M where M is the total concentration of mitochondrial fission factor (Mff) and k+ and k− are the association and dissociation rate constants between oligomers on the outer mitochondrial membrane. The variable µ can be thought of as the maximum build rate over the disassembling rate of oligomers. Though the nondimensionalization of the system results in four dimensionless parameters, we found the TFR and the cumulative total fission (TF) depend strongly on only one, µ. Interestingly, the cumulative TF does not monotonically increase as µ increases. Instead it increases with µ to a certain point and then begins to decrease as µ continues to increase. This non-monotone dependence on µ suggests interventions targeting k+, k−, or M may have a non-intuitive im- pact on the fission mechanism. Thus, understanding the impact of regulatory parameters, such as µ, may assist future therapeutic target selection.

Yilin Lu – Georgia Tech (SCMB Junior Researcher) 

“RNA directs a sequence-specific end-joining mechanism for double-strand break repair” 

Abstract: Studies have indicated that transcript RNA can serve as a donor sequence for DNA-homologous repair at double-strand break (DSB) sites. Unlike homologous recombination (HR), non-homologous end joining (NHEJ) and microhomology-mediated end joining (MMEJ) do not use a template to recover damaged or lost nucleotides. To explore how transcript RNA directly influences DSB repair mechanisms, we utilized the CRISPR/Cas9 system to induce targeted DSBs and double-strand gaps. Our experiments were conducted on human cell plasmid DNA and yeast chromosomal DNA, focusing on transcribed gene constructs to either allow or prevent intron splicing. DSBs were specifically generated within an exon or at exon-intron junctions. We identified specific sequences characteristic of each DSB repair mechanism to estimate their relative frequencies. Experiments were conducted in HEK293T that allows for plasmid replication, or HEK293 cells without plasmid replication. In yeast cells, in addition to wild-type cells, we used mutants of ribonuclease H1 and/or H2, the spt3-null mutant that prevents formation of cDNA, and the ku70-null mutant preventing NHEJ.

Moitrish Majumdar – UC Merced 

“Rapid recovery of protein-protein interactions using sparse signal reconstruction” 

Abstract: Proteins rarely act in isolation within cells but interact with specific partners to form functional complexes. Because such protein-protein interactions (PPIs) are crucial for understanding cellular information processing, numerous methods have been developed for mapping PPIs. One such method is immunopurification followed by mass spectrometry (IP-MS), which identifies all proteins that interact with a ‘bait’ protein of interest. While IP-MS is used widely, mapping large PPI networks is expensive since each experiment only profiles one bait. To overcome this limitation, we developed a pooled method that leverages ideas from compressed sensing to profile many baits using a limited number of IP-MS runs. This method first measures multiple linear combination of the PPIs by modifying the immunopurification step to use combinatorial antibody pools to pull down multiple bait proteins. The resulting signals are then decoded using a sparse signal reconstruction algorithm that estimates the PPIs for each bait. We here demonstrate the theoretical validity of the method using simulated experiments and test the practical feasibility using data from an initial pilot experiment. Overall, pooled IP-MS will allow researchers to map larger interaction networks at reduced cost, thus democratizing the study of PPIs.

Rayna Maleki – Clemson University 

“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. 

Francisco Martinez-Figueroa – University of South Florida (SCMB Junior Researcher) 

“Letter insertion Homology and complexity of word sets: A topological approach to DNA mutation in RNA-mediated repair” 

Abstract: When studying mechanisms of DNA repair, short mutations often arise at the repair site, frequently manifesting as the insertion of short nucleotide sequences from the alphabet {A, C, G, T}. Each of these insertions occurs across millions of DNA molecules, generating a set of short words with varying frequencies. Our goal is to identify a suitable mathematical object to analyze these word sets and distinguish patterns across different experimental conditions. We introduce the Insertion Chain Complex, a higher-dimensional generalization of insertion graphs, where homology serves as a measure of the complexity of a set of words. We present its construction, fundamental properties, and applications to biological data. In our case study, we analyze data from human cells in which DNA breaks were induced and the repaired sequences were sequenced. Our findings demonstrate that counting the highest-dimensional cells in these insertion complexes effectively distinguishes between different break locations. 

Aanushka Mehjabin – Georgia Tech (SCMB Junior Researcher) 

“Using NMR Spectroscopy to Refine the Interpretation of Gaussian Accelerated Molecular Dynamics Simulations of Phosphopeptides” 

Abstract: Recent advances in proteomics and computational biology have unveiled the vast extent of the proteomic "dark matter", comprised predominantly of intrinsically disordered proteins (IDPs) and regions (IDRs) that elude traditional structural characterization techniques like NMR. Protein phosphorylation, a key post-translational modification (PTM), is a reversible process known to crucially alter protein structure and functional capacity. Intrinsically Disordered Regions (IDRs) are segments of proteins that typically lack energetically stable three-dimensional structure, allowing them flexible functionality. These regions are also particularly rich in phosphorylation sites and existing experimental evidence supports the idea that phosphorylation can induce structural transitions in some IDRs. This has prompted the hypothesis that phosphorylation-induced structural change is encoded in the sequence and physicochemical properties of such IDRs. Our goal is to employ Gaussian Accelerated Molecular Dynamics (GAMD) simulations to elucidate the sequence and physicochemical properties of these phosphotransitional peptides. This will allow us to identify MD simulated peptide structures that best represent the conformational states observed in NMR experiments, thus providing a more accurate framework for studying the dynamic behavior of these proteins in MD simulations. 

Jacob Miller – University of Iowa 

“TDA Mapper on Natural Image Data” 

Abstract: Our research applies TDA Mapper as an alternative to persistent homology for analyzing natural images' topological structure. Building on Carlsson, Ishkhanov, de Silva, and Zomorodian's 2008 work, we examine whether Mapper algorithms can effectively detect the Klein bottle structure previously found in high-contrast 3x3 image patches. While the original study used persistent homology, we instead use Mapper constructions and a custom made mapper-complex visualization tool. We analyze identical data—high-contrast 3x3 patches from van Hateren's natural image collection—and contrast our results with similarly processed synthetic Klein bottle data. Our preliminary findings show that Mapper can reproduce these topological features while potentially offering better computational efficiency and interpretability. 

Audrey Nash – Florida State University 

“Exploring Gustatory Cortex Decoding of Chemosensory and Thermosensory Stimuli” 

Abstract: Eating behaviors are influenced by the integration of gustatory, olfactory, and somatosensory signals, which all contribute to the perception of flavor. Although extensive research has explored the neural correlates of taste in the gustatory cortex (GC), less is known about its role in encoding thermal information. This study investigates the encoding of oral thermal and chemosensory signals by GC neurons. In this study, we recorded the spiking activity of more than 900 GC neurons in mice allowed to freely lick small drops of gustatory stimuli or deionized water at varying non-nociceptive temperatures. We then developed and used a Bayesian-based analysis technique to assess neural classification scores based on spike rate and phase timing within the lick cycle. Our results indicate that GC neurons rely predominantly on rate information, although phase information is needed to achieve maximum accuracy, to effectively encode both chemosensory and thermosensory signals. GC neurons can effectively differentiate between thermal stimuli, excelling in distinguishing both large contrasts (14°C vs. 36°C) and, although less effectively, more subtle temperature differences. These findings highlight the GC's dual role in processing taste and temperature, emphasizing the importance of considering temperature in future studies of taste processing. 

Vanessa Newsome-Slade – Georgia Tech 

“Stanley-Reisner Theory and Unique Signed Minimal Wiring Diagrams” 

Abstract: Due to cost concerns, it is optimal to gain insight into biological networks using as few experiments as possible. Minimal wiring diagrams identify the minimal sets of variables for which a model that fits the data exists. In this work, the Stanley-Reisner correspondence between abstract simplicial complexes and squarefree monomial ideals is used to determine conditions under which a given set of inputs is guaranteed to have a unique signed minimal wiring diagram, regardless of the output assignment. 

Trung Nguyen – University of Tennessee, Knoxville 

“Multi-level, multi-color mathematical graph neural networks for molecular property prediction” 

Abstract: Graph Neural Networks (GNNs) have demonstrated significant potential in molecular property prediction. However, current GNN architectures mostly rely on standard node or edge features that overlook the complex, multi-scale interactions between atoms in small molecules. This research introduces a mathematics-driven approach that integrates concepts from Geometric Graph Learning (GGL) and Algebraic Graph Learning (AGL) to enhance molecular representations. Drawing upon GGL principles, we construct multi-color molecular graphs where nodes represent atoms and edges are weighted based on both spatial distances and local geometric features, such as curvatures derived from differential geometry applied to atomic interactions. Furthermore, we encode high-dimensional atomic interactions through the spectral properties of algebraic subgraphs, such as the Laplacian and adjacency matrices derived from these geometric graphs. The construction of these multi-level graphs and their connectivity follows the principles of Persistent Spectral Graph Theory, where a filtration process generates a family of graphs across different scales, capturing both topological persistence and geometric evolution of atomic relationships. This integrated approach enables reliable and robust molecular representations by incorporating both short- and long-range dependencies, thereby surpassing the limitations of conventional GNNs. Our approach significantly improves predictive performance in molecular property prediction tasks and provides a reliable framework to advance drug discovery and materials science applications. 

Logan Rose – University of Kentucky 

“When Does Additional Information Improve Accuracy of RNA Secondary Structure Prediction?” 

Abstract: Oftentimes, RNA chains will fold to form helices of paired bases and single stranded loops in what is known as the secondary structure. The secondary structure is often a major factor in determining sequence function, and thus accurate prediction is of major importance. One of the most common prediction techniques involves finding the possible structure with the minimum free energy (the MFE formation). Using two sets of RNA sequence data where secondary structures are known, we determine the MFE formation for each sequence. The base pairings of the MFE formation are compared to those of the true structure using two measures (PPV and sensitivity) which are combined into a single measure called accuracy, which is then used to assess the MFE prediction. Auxillary information (SHAPE) is then provided to improve prediction accuracy. Features for each sequence were determined by comparing competing substructures to the MFE formation (similarity measures) as well as using topological data analysis. Random forest classifiers in Python were built and used to classify sequences according to accuracy and directability (the improvement in accuracy gained using SHAPE). Sequences are classified as well-predicted if the accuracy is above a fixed threshold and directable if the improvement in accuracy using SHAPE is above a fixed threshold. Extensive testing was done using varying thresholds and feature importance was determined for each classifier. In general, similarity features were found to be more important in classifying sequences with similar structures while topological were more important in classifying those with unlike structures. 

Vardhan Satalkar – Georgia Tech (SCMB Junior Researcher) 

“Generative Approaches for Phosphopeptide Design” 

Abstract: Using experimentally-annotated phosphopeptide datasets overlayed with sequences known to undergo conditional folding, we constructed a new phosphorylation-dependent molecular recognition feature (phosphoMoRF) database of transitory peptides which undergo intrinsic disorder-to-ordered structural transitions upon phosphorylation. The extent peptide conformation changes were systematically determined and evaluated using combined in sillico enhanced Molecular Dynamics (MD) simulations and experimental protein structure determination methods including CD and NMR spectroscopy. The phosphoMoRF database was further utilized to create and test a custom phosphopeptide generative adversarial neural network (phosphoGAN) model, which yielded 77% classification accuracy in determining phosphorylation-dependent transitory peptides and generate artificial phosphopeptide sequences with minimum sequence identities around 40% when compared against the non-redundant phosphopeptide databases. These results highlight the potential of generative models specifically anchored by physicochemical and conformational property features of amino acids to expand functional phosphopeptide design beyond evolutionary limits. 

Fatemeh Shanehsazan – University of Iowa 

“Multi-Scale Visualization of Mapper Graphs via Filtration” 

Abstract: Topological Data Analysis (TDA) provides powerful tools for understanding high-dimensional data by capturing its underlying shape and structure. Mapper, a widely used TDA algorithm, enables the visualization of complex data structures and reveals significant patterns that may not be evident through traditional statistical methods. One of the main challenges in using Mapper is parameter selection—small variations in parameter choices can significantly impact the resulting graph structure. In this work, we use filtration on Mapper graphs to visualize a multi-scale perspective on Mapper’s output. 

Zach Thomas – University of Florida 

“Vectorizing the Shape of Data Through Dual Space” 

Abstract: Topological Data Analysis can encode the shape of a data set as a persistence diagram. In particular, it can encode the number and size of n-dimensional 'voids' in the data. These diagrams exist in a normed vector space, which has a dual space of Lipschitz functionals of compact support on half of the real plane. In a desire to apply statistics and machine learning tools to these persistence diagrams, I wish to embed them into a Hilbert space. I will present an approach which employs a Schauder basis of the dual space. This approach generalizes to certain persistence diagrams derived from multiparameter persistence on a data set. 

Hwai-Ray Tung – University of Utah 

“What to do if You Miss a Dose of Antibiotics?” 

Abstract: Despite the prevalence of missed antibiotic doses, there is vague or little guidance on what to do when a dose is forgotten. In this work, we consider the effects of different patient responses after missing a dose using a mathematical model that links antibiotic concentration with bacteria dynamics. We show using simulations that, in some circumstances, (a) missing just a few doses can cause treatment failure, and (b) this failure can be remedied by simply taking a double dose after a missed dose. We then develop an approximate model that is analytically tractable and use it to understand when it might be advisable to take a double dose after a missed dose. 

Himanshu Yadav – University of Florida 

“Topological Structure of the Cyclonic-Anticyclonic Interactions in Sea-Level Pressure Fields in the North Atlantic” 

Abstract: Understanding the interaction between cyclones and anticyclones is useful to understand the atmospheric dynamics that generates weather patterns in the North Atlantic region. Cyclones are associated with low-pressure systems, and anticyclones, associated with high-pressure systems. The interaction can affect storm formation, intensity, and distribution. Topological Data Analysis (TDA) is a field within applied mathematics that uses concepts from algebraic topology to extract topological information from data. Persistent homology is one of the tools in TDA which gives a topological summary of the data. We used persistent homology to obtain a topological summary of the following dynamics: a cyclonic system is surrounded by anticyclones and vice versa. We generate this topological summary for each day of years between 1948 and 2023. Our initial analysis reveals different patterns of activity for different seasons among both interactions. There is a change in the overall interaction from the past to the future, pointing to climate change. We also correlate this with the Atlantic Multidecadal Oscillation and whether this interaction has some similar oscillation. 

Nisha Yadav – Clemson University 

“Mathematical and Machine Learning Models for siRNA Delivery: Understanding Endosomal Escape in Cancer Therapy” 

Abstract: Small interfering RNA (siRNA) therapy is a promising approach for targeted cancer treatment, offering precise gene silencing with minimal off-target effects. However, effective delivery remains a challenge due to endosomal entrapment, where siRNA fails to escape into the cytoplasm. In this talk, we introduce a mathematical and machine learning framework to model and predict siRNA endosomal escape dynamics. We develop a stochastic compartmental model to simulate siRNA trafficking, integrate image processing techniques for time-lapse microscopy data, and generate synthetic datasets that reflect experimental conditions. Using these datasets, we train neural networks and random forest models to enhance predictive accuracy and optimize siRNA delivery strategies. Through this interdisciplinary approach, we demonstrate how mathematical modeling, stochastic simulations, and machine learning can collectively improve drug delivery systems in gene therapy. No prior biology background is required, this talk will provide an engaging introduction to the intersection of applied mathematics, data science, and biomedical research. 

Wanchen Zhao – University of Florida 

“Wasserstein Stability of Barcodes and Persistence Landscapes” 

Abstract: Barcodes represent interval decomposable persistence modules and are an important summary in topological data analysis. The space of barcodes is equipped with a canonical one-parameter family of metrics, the $p-$Wasserstein distances. However, the $p-$Wasserstein distances depend on a choice of a metric on the set of interval modules, and there is no canonical choice. One convention is to use the length of the symmetric difference of the intervals, which is also equivalent to the $L^1$ difference between the Hilbert functions of the interval modules. We propose a new metric on interval modules based on the rank invariants instead of the dimension invariants. We establish stability results from weighted CW complexes to barcodes, as well as from barcodes to persistence landscapes. In particular, we show that vectorization via persistence landscapes is 1-Lipschitz with a sharp bound with respect to our 1-Wasserstein distance on barcodes and the $L^1