Physical Sciences and Mathematics Commons^™

Rogue Peakon, Posedness And Blow-Up Phenomenon For An Integrable Camassa–Holm Type Equation, Mingxuan Zhu, Zhenteng Zeng, Zaihong Jiang, Baoqiang Xia, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study an integrable Camassa–Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon) solution – called rogue peakon, that is given in a rational form with some logarithmic function, but not a regular traveling wave. We also provide multi-rogue peakon solutions. Furthermore, we discuss the local well-posedness of the solution in the Besov space 𝐵𝑠𝑝,𝑟 with 1 ≤ p, r ≤ ∞, 𝑠 >max⁡{1+1/𝑝,3/2} or 𝐵3/22,1 , and then prove the ill-posedness …

Spectroscopic Investigations On Polyvinylidene Fluoride Nanofibers, Parinaz Amaniabdolmalaki, Jui Vitthal Kharade, Alexandro Trevino, Lydia Morales, Karen Lozano, Victoria Padilla, Karen S. Martirosyan, Horacio Vasquez, Mircea Chipara

Physics & Astronomy Faculty Publications

The production of polyvinylidene fluoride nanofibers by force-spinning from polymer solutions was confirmed by electron microscopy. The structural and phase characteristics of the resulting nanofiber mats were examined using Fourier Transform Infrared Spectroscopy in Attenuated Total Reflectance mode, Raman spectroscopy, and X-ray Diffraction. Results from all these techniques consistently indicated that both the powder and the mats of polyvinylidene fluoride predominantly contain the α phase, with a small admixture of the β phase. Within experimental errors, no other phases were noticed both in the powder and in the as-obtained mats. The ratios of the areas of the Raman lines at …

Optimal Quantization Of Finite Uniform Data On The Sphere, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

This paper develops a systematic and geometric theory of optimal quantization on the unit sphere 𝕊2, focusing on finite uniform probability distributions supported on the spherical surface—rather than on lower-dimensional geodesic subsets such as circles or arcs. We first establish the existence of optimal sets of n-means and characterize them through centroidal spherical Voronoi tessellations. Three fundamental structural results are obtained. First, a cluster-purity theorem shows that when the support consists of well-separated components, each optimal Voronoi region remains confined to a single component. Second, a ring allocation (discrete water-filling) theorem provides an explicit rule describing how optimal representatives are …

Interactive Effects Of Hyposalinity And Nitrate Loading On Growth, Physiology, And Nitrogen Status Of The Seagrass, Halodule Wrightii, Joseph L. Kowalski, Hudson R. Deyoe, Kirk Cammarata, Kristina P. Vatcheva

School of Earth, Environmental, & Marine Sciences Faculty Publications

The study goal was to examine the interactive physiological effects of two freshwater inflow stressors, nitrate pulses coupled with salinity decrease, on the seagrass Halodule wrightii. A microcosm experiment was designed to approximate an observed freshwater inflow event. Over a 13-day period plants were subjected to three sequential salinity drops (S35→ S23→ S15→ S5) with nitrate-nitrogen added simultaneously at 0, 30 or 60 µM. For comparisons, the Control was no salinity change and no nitrate added denoted by S35/No N. Measurements of H. wrightii shoot production, photosynthesis, respiration, quantum efficiency, %N, C:N ratios and δ¹⁵N …

Computational Insights Into Orthotropic Fracture: Crack-Tip Fields In Strain-Limiting Materials Under Non-Uniform Loads, Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah

School of Mathematical & Statistical Sciences Faculty Publications

A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress to linearized strain. Non-physical strain singularities at the crack apex are mitigated, ensuring bounded strain magnitudes. This methodology significantly advances boundary value problem (BVP) formulation, especially for first-order approximate theories. For a transversely isotropic elastic solid with a crack, the governing equilibrium equation, derived from linear momentum balance and the nonlinear constitutive model, is reduced to a second-order, vector-valued, quasi-linear elliptic BVP. This BVP is solved using a robust numerical scheme combining …

A Conceptual Framework For Cognitive Engagement And Human Agency In Ai-Mediated Learning, Sam Rhodes, Zuhal Yilmaz, Terrie Galanti, Younggon Bae, Victoria Delaney, Zareen Gul Aga, Stephen Hutt

School of Mathematical & Statistical Sciences Faculty Publications

The purpose of this chapter is to propose a conceptual framework that unpacks AI use in instructional practice across three interrelated dimensions: human agency, cognitive demand, and AI orchestration. We ground this work in historical perspectives on technology's mediating role in education. We then propose the conceptual framework and three characterizations of the use of AI in school instruction: cognitive load reducer, cognitive capacity builder, and cognitive companion. We then illustrate a worked example of each, including a curricular example and sample student prompts, and conclude with questions that educators might ask themselves as they consider if and how to …

Gain-Delay Decoupling In Human Stimulus Frequency Otoacoustic Emissions Reveals Constraints On Cochlear Nonlinear Amplification, Yoshita Sharma, Arturo Moleti, Renata Sisto, Teresa Botti, Hansapani Rodrigo, Sri Mishra

School of Mathematical & Statistical Sciences Faculty Publications

Purpose: The nonlinear cochlear amplifier, driven by outer hair cells, underlies the remarkable sensitivity and frequency selectivity of the mammalian auditory system. Stimulus frequency otoacoustic emissions (SFOAEs) provide a noninvasive window into these active cochlear processes, yet the relationship between emission gain and delay across stimulus levels remains incompletely understood. This study examined the level dependence of SFOAEs in normal-hearing human listeners to characterize cochlear nonlinear response properties. We tested how emission gain and delay vary with stimulus level and estimated the frequency of the apical–basal transition associated with the breakdown of the approximate local scaling symmetry.

Methods: SFOAEs were …

Fully Discrete Finite Element Methods For The Stochastic Kuramoto–Sivashinsky Equation With Multiplicative Noise, Hung D. Nguyen, Liet Vo

School of Mathematical & Statistical Sciences Faculty Publications

We investigate a fully discrete finite element approximation for the stochastic Kuramoto–Sivashinsky equation, combining the standard finite element methods in spatial discretization with the implicit Euler–Maruyama scheme in time. Rigorous error estimates are established for two distinct noise regimes. In the case of bounded multiplicative noise, we prove optimal strong convergence rates in full expectation. The analysis relies crucially on a stochastic Gronwall inequality and an exponential stability estimate for the PDE solution, which together control the interplay between the nonlinear drift and the multiplicative stochastic forcing. For general multiplicative noise, where boundedness no longer holds, we derive sub-optimal convergence …

Circle Actions On Oriented 4-Manifolds, Donghoon Jang, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

In this present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah–Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated fixed points that if an abstract graph satisfies the Atiyah–Hirzebruch formula, then there exists a corresponding 4-dimensional oriented S1-manifold.

The Classical Limit In Geometric Quantization By Group Extension, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Physical systems as a rule are associated with a symmetry group. The group approach to geometric quantization makes use of this to introduce a quantization by means of group extension. This procedure is discussed and applied to a physical system whose group law has its origin with the Galilean group. The main intention is to investigate the classical limit and its relationship under this approach to geometric quantization. The classical quantization conditions are obtained based on a deeper foundation.

Improving Pid Control With Bayesian Optimization For Adversarially Robust Federated Learning, Adrian Pena, Sergei Chuprov, Raman Zatsarenko, Leon Reznik

Computer Science Faculty Publications

Federated Learning (FL) often suffers from unstable convergence and reduced robustness under non-IID data and malicious attacks. In this paper, we present FedPIDAvg_tuned, a control-theoretic aggregation framework for improving stability and adversarial robustness in FL. In particular, our approach combines a server-side Proportional–Integral–Derivative (PID) controller with Bayesian optimization to tune controller gains for different data and attack conditions. The PID controller regulates global model updates through feedback on loss dynamics, providing adaptive scaling that improves stability and convergence. The tuned gains are applied within a trust-weighted trimmed-mean mechanism to remove adversarial or outlier updates. Using the Flower framework, we evaluate …

A Preliminary Investigation Of Research Collaboration Through Scientific Paper Co-Authorship In The Gulf Of Mexico, Juliet Vallejo, Evelyn Roozee, Dongkyu Kim, Andrew M. Song, Christopher A. Gabler, Jasper R. De Vries, Antonia Sohns, Gordon M. Hickey, Owen Temby

School of Earth, Environmental, & Marine Sciences Faculty Publications

It is well known that publications with collaborators from external institutions increase citations. This effect scales with spatial distance. There are also many barriers to long-distance collaborations, including linguistic differences, funding constraints, and the incremental costs of remote collaboration. This paper uses the Gulf of Mexico as a case study to examine long-distance research collaboration because it consists of three countries with diverse development levels and two prominent diplomatic languages, within a singular regional ecosystem of tremendous natural and economic value. This paper uses bibliometric network analysis to examine scientific research article co-authorship in the Gulf of Mexico from 2000 …

Histochemical Alteration, Protein Nitration, And Antioxidant Expression In Oysters As Early Warning Indicators For Microplastic Contamination In The Texas Gulf Coast, Rebecca Muñiz, Md Faisal Amin, Md. Saydur Rahman

School of Earth, Environmental, & Marine Sciences Faculty Publications

Microplastics are widely distributed in aquatic environments and have been detected in numerous organisms. Marine bivalves are among the most affected aquatic organisms by microplastics due to their filter-feeding behavior. In this study, 60 oysters were collected from two sites along the Texas Gulf Coast. Fourier transform infrared (FTIR) spectroscopy and Nile red staining were used to detect microplastics in oyster (Crassostrea virginica) tissues. We compared field and laboratory samples collected after a two-week depuration period to identify differences in the shape and size of microplastics in oyster tissues. Results from the field sites showed a large number of microplastics, …

Using Low-Cost Sensors For Source Attribution And Health Assessment: An Air Quality Study In Brownsville, Texas, Sai Deepak Pinakana, Kabir Bahadur Shah, Daniel Jaffe, Juan L. Gonzalez, Owen Temby, Gabriel Ibarra-Mejia, Amit U. Raysoni

School of Earth, Environmental, & Marine Sciences Faculty Publications

Air quality monitoring remains a challenge in areas lacking or having sparse federal monitoring infrastructure, posing significant barriers to public health research. This study demonstrates the usage of low-cost sensors in addressing gaps in air quality monitoring, source attribution, and health risk assessment in a Brownsville, TX neighborhood impacted by emissions from a barite and celestite mineral processing unit. PM2.5 concentrations were measured using PurpleAir sensors deployed across three residential locations, with the site nearest to the processing unit recording a 24-h averaged PM2.5 concentration of 25.12 μg/m3—approximately 2.79 times higher than the nearest Texas Commission of Environmental Quality (TCEQ) …

The Impact Of Regional Fishery Management Organization Structure On Collaborative Performance, Evelyn Roozee, Owen Temby, Gordon M. Hickey

School of Earth, Environmental, & Marine Sciences Faculty Publications

Collaboration is integral to understand, plan, coordinate, and implement management measures for fisheries that cross international borders. Regional Fishery Management Organizations (RFMOs) are the main arenas for countries to collaborate and make decisions for transboundary fisheries, but these organizations have generally failed to prevent the depletion of some of the world's most valuable fish stocks. It is unclear how the structure and functioning of RFMOs can improve collaborative performance to better manage transboundary fish stocks. Using fuzzy-set qualitative comparative analysis, our study analyzes 10 RFMOs to identify the combination of six organizational conditions associated with high and low collaborative performance. …

Patch-Moe Mamba: A Patch-Ordered Mixture-Of-Experts State Space Architecture For Medical Image Segmentation, Diego Adame, Fabian Vazquez Jr., Jose A. Nunez, Huimin Li, Jinghao Yang, Erik Enriquez, Dongchul Kim, Haoteng Tang, Bin Fu, Pengfei Gu

Computer Science Faculty Publications

CNN- and Transformer-based architectures have achieved strong performance in medical image segmentation, but CNNs are limited in modeling long-range dependencies, while Transformers often suffer from quadratic computational and memory complexity. State space models, especially Mamba-based networks, offer an efficient alternative with linear sequence complexity. However, existing Mamba segmentation models still face two limitations: pixel-wise directional scanning can disrupt local 2D spatial structure, and simple summation-based fusion of scan directions cannot adapt well to diverse object sizes, shapes, and boundaries. To address these issues, we propose Patch-MoE Mamba, a patch-ordered mixture-of-experts state space architecture for medical image segmentation. It introduces a …

Effects Of Short-Term Exposure To Environmentally Relevant Pesticides Mixture On Morphological Alterations, Oxidative-Nitrative Stress Biomarkers, Cellular Apoptosis, And Antioxidant Expression In Kidneys Of Goldfish, Esmirna Cantu, Md Saydur Rahman

School of Earth, Environmental, & Marine Sciences Faculty Publications

Chemical stressors are pervasive, affecting both terrestrial and aquatic environments. The continual influx of these toxins is damaging ecosystems and the organisms that inhabit them. The abundance of environmental toxins makes aquatic habitats inhospitable for aquatic life. These chemical stressors consistently disrupt the life processes of aquatic organisms, particularly their physiological functions. This study examined on the effects of environmentally relevant pesticides mixture (low-dose and high-dose: S-metolachlor: 2.4 go/L, 12 μg/L; linuron: 2.0 μg/L, 10 μg/L; isoproturon: 1.2 μg/L, 6.0 μg/L; tebucanozole: 1.2 μg/L, 6.0 μg/L; aclonifen: 0.8 μg/L, 4.0 μg/L; atrazine: 0.4 μg/L, 2.0 μg/L; pendimethalin: 0.4 μg/L, 2.0 …

Biomarkers Of Foraging And Reproduction In Captive Adult Female Hawksbill Sea Turtles (Eretmochelys Imbricata), Joslyn Blessing Kent, Kari Renee Dawson, Shingo Fukada, Masae Makabe, Isao Kawazu, Ken Maeda, Roldán A. Valverde

School of Earth, Environmental, & Marine Sciences Faculty Publications

Hawksbill sea turtles (Eretmochelys imbricata) are listed as critically endangered by the International Union for the Conservation of Nature (IUCN). To implement best conservation practices for this species, its biology should be well understood. Attempting to characterize the foraging physiology of free-ranging hawksbill sea turtles is complicated by the fact that sampling is typically limited to nesting females during the reproductive season. Without data from non-reproductive periods, it is difficult to determine whether observed physiological values reflect baseline conditions or are specific to the energetically demanding nesting season. Accordingly, in this study, we described the physiology of foraging in …

Strong Q-Analogues For Values Of The Dirichlet Beta Function, Ankush Goswami, Tim Huber

School of Mathematical & Statistical Sciences Faculty Publications

An infinite class of relations between modular forms is constructed that generalizes evaluations of the Dirichlet beta function at odd positive integers. The work is motivated by a base case appearing in Ramanujan’s Notebooks and a parallel construction for the Riemann zeta function. The identities are shown to be strong q-analogues by virtue of their reduction to the classical beta evaluations as 𝑞→1− and explicit evaluations at CM points for |𝑞|< 1. We also determine asymptotic formulas for the Fourier coefficients of the associated modular forms.

Optimal Quantization On Spherical Surfaces: Continuous And Discrete Models—A Beginner-Friendly Expository Study, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets ofthe sphere, emphasizing both continuous and discrete settings. We first present a detailedgeometric and analytical foundation for intrinsic quantization on the unit sphere, includingdefinitions of great and small circles, spherical triangles, geodesic distance, Slerp interpolation,the Fréchet mean, spherical Voronoi regions, centroid conditions, and quantizationdimensions. Building upon this framework, we develop explicit continuous and discretequantization models on spherical curves, namely great circles, small circles, and greatcircular arcs—supported by rigorous derivations and pedagogical exposition. For uniformcontinuous distributions, we compute optimal …

Gauge-Invariant Gravitational Wave Polarization In Metric F(R) Gravity With Cosmological Implications, Ramesh Radhakrishnan, David Mcnutt, Delaram Mirfendereski, Alejandro Pinero, Eric Davis, William Julius, Gerald Cleaver

Physics & Astronomy Faculty Publications

We develop a fully gauge-invariant analysis of gravitational-wave polarizations in metric 𝑓⁡(𝑅) gravity with a particular focus on the modified Starobinsky model 𝑓⁡(𝑅) =𝑅 +𝛼⁢𝑅2 −2⁢Λ, whose constant-curvature solution 𝑅𝑑 =4⁢Λ provides a natural de Sitter background for both early- and late-time cosmology. Linearizing the field equations around this background, we derive the Klein–Gordon equation for the curvature perturbation 𝛿⁢𝑅 and show that the scalar propagating mode acquires a mass 𝑚2𝜓 =1/(6⁢𝛼), highlighting how the same scalar degree of freedom governs inflationary dynamics at high curvature and the propagation of gravitational waves in the current accelerating Universe. Using the scalar–vector–tensor …

Gpu And Pso Accelerated Low-Latency Fully-Coherent All-Sky Search For Compact Binary Coalescences, Soumya D. Mohanty

Physics & Astronomy Faculty Publications

The fully-coherent all-sky (FCAS) search, which combines data from a gravitational wave detector network into a single likelihood function, is the preferred method prescribed by statistical theory for Gaussian noise. However, so far, its exorbitant computational cost has blocked its use for compact binary coalescence searches. We introduce a solution combining Particle Swarm Optimization with Graphics Processing Unit (GPU) acceleration that is ≈ 50-fold faster than real-time analysis. This transforms the prospect of a low-latency FCAS search on all GW data into a practical reality for the first time. With large-scale simulations enabled by this speedup, we examine the issue …

Efficient Search For Detection Candidates Using A Peak Finder Strategy For All-Sky-All-Frequency Gravitational Wave Radiometer, Arindam Sharma, Deepali Agarwal, Sanjit Mitra

Physics & Astronomy Faculty Publications

The first all-sky-all-frequency (ASAF) radiometer search was conducted using data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. The significance of this search lies in its fast and unmodeled approach, leveraging a cross-correlation technique to identify common signals across the detector network. As a result, this method serves as an excellent alternative to search for unknown or poorly modeled continuous wave sources and narrow band components of the gravitational wave (GW) background. For continuous wave sources whose waveform can be modeled, this method can serve as the first stage of a hierarchical scheme by …

Integrable Discrete Massive Thirring Model, Junchao Chen, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we are concerned with integrable semi- and fully discrete analogues of the massive Thirring model in light core coordinates. By using the Hirota’s bilinear approach and the Kadomtsev-Petviashvili (KP) hierarchy reduction method, we propose both the semi- and fully discrete massive Thirring models and construct their multi-bright soliton solutions.

Accurate Prediction Of Geometrical Parameters Of An Ultra-Broadband Metamaterial Absorber Using Machine Learning, Md. Rezwan Ahmed, Oishi Jyoti, Pritu Parna Sarkar, Mohammod Abdul Motin, Md. Selim Habib, Md. Samiul Habib

Electrical and Computer Engineering Faculty Publications

In this paper, we systematically demonstrate the design and analysis of a new type of ultra-broadband tunable metamaterial perfect absorber (MPA) comprising a top vanadium dioxide (VO2) based patterned resonating patch, a continuous metallic film at the bottom, and an intermediate dielectric substrate having a thickness of only 0.18 at the center working frequency. The simulation results reveal that the absorber achieves a bandwidth of 7.26 THz, ranging from 5.40 THz to 12.66 THz, with more than 90% absorptance and an average absorption of 98.21% under normal incidence of the incoming THz wave. Furthermore, absorptance exceeding 99% is achieved between …

Macroinvertebrate Community Dynamics In A Recovering, Hypersaline Estuary, Catherine M. Eckert, Claudia A. Tamez, Erin E. Easton, David Hicks

School of Earth, Environmental, & Marine Sciences Faculty Publications

The Bahia Grande is a 6,500—acre tidal basin located at the southernmost tip of Texas. Tidal flow into this coastal estuary was cut off in the 1930s, causing the basin to dry up for ~70 y. A pilot channel connecting the Bahia Grande to tidal waters was constructed in 2005, allowing flooding of the basin to occur. Throughout the period reported herein (2005–2019), the system remained characterized by persistent spatial and temporal episodes of extreme hypersalinity (>70)—a critical factor influencing estuarine community composition and driving key ecological processes. With additional rehabilitation actions forthcoming, characterization of the estuary is essential …

Orbital Stability Of Solitary Wave Solutions Of The Generalized Benjamin Equation, Leijin Cao, Binhua Feng, Zhaosheng Feng, Yichun Mo

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the existence and stability of solitary wave solutions for the generalized Benjamin equation in both the L2-critical and L2-supercritical cases by applying the variational methods and the non-homogeneous Gagliardo–Nirenberg inequality. Our main results generalize and complement the existing results in the literature.

Gwtc-4.0: An Introduction To Version 4.0 Of The Gravitational-Wave Transient Catalog, A. G. Abac, Teviet Creighton, Mario C. Diaz, Raul Alberto Espinosa Perez, J. Lawrence, Francisco Llamas Villarreal, Soma Mukherjee, Volker Quetschke, Wenhui Wang

Physics & Astronomy Faculty Publications

The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-wave signals identified by the LIGO–Virgo–KAGRA Collaboration in gravitational-wave data produced by the eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal’s source as inferred from the observational data. GWTC is the data release of this dataset, and version 4.0 extends the catalog to include observations made during the first part of the fourth LIGO–Virgo–KAGRA observing run up until 2024 January 31. This Letter marks an introduction to a collection of articles related …

Synthesis Of Antibody Functionalized Polyaniline/Polystyrene/N-Gqds Composite Fibermats For Sweat Based Cortisol Biosensing Applications, Ashwin James

Honors Theses

Noninvasive, wearable biosensors capable of detecting stress biomarkers in sweat require electrodes that are flexible, conductive, insoluble in water, and highly sensitive at low concentrations of analyte. In this work, bovine serum albumin blocked and anti-cmab immobilized nitrogen doped graphene quantum dots integrated polyaniline/polystyrene composite fibermat electrodes (BSA/Anti-Cmab/N-GQDs/PANI/PS electrodes) were synthesized and evaluated as a potential platform for an electrochemical cortisol biosensor in sweat based systems. Polyaniline was utilized in order to provide electrical conductivity, while polystyrene served as a carrying polymer for mechanical support and its hydrophobicity. Composite fibermats were manufactured through Forcespinning™, followed by a secondary polyaniline graft …

Gradient-Based Model Shortcut Detection For Time Series Classification, Salomon Ibarra, Frida Cantu, Kaixiong Zhou, Li Zhang

Computer Science Faculty Publications

Deep learning models have attracted lots of research attention in time series classification (TSC) task in the past two decades. Recently, deep neural networks (DNN) have surpassed classical distance-based methods and achieved state-of-the-art performance. Despite their promising performance, deep neural networks (DNNs) have been shown to rely on spurious correlations present in the training data, which can hinder generalization. For instance, a model might incorrectly associate the presence of grass with the label "cat" if the training set have majority of cats lying in grassy backgrounds. However, the shortcut behavior of DNNs in time series remain under-explored. Most existing shortcut …