arXiv subjects

Majid Bani-Yaghoub

Publications and source records attributed to Majid Bani-Yaghoub.

9 recordsLinked to original sources

arXiv2026

Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters

We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale parameter defined as the geometric mean of all parameters. We thus augment the network input with a scale-aware feature, enabling it to capture sharp solution transitions intrinsically. Numerical experiments across a range of dynamical systems demonstrate that the proposed framework can handle coupled systems with multiple and high-contrast small parameters and obtain satisfactory accuracy in capturing solution features induced by small parameters.

math.NA↗

arXiv2026

On the Limits of Interpretable Machine Learning in Quintic Root Classification

Can Machine Learning (ML) autonomously recover interpretable mathematical structure from raw numerical data? We aim to answer this question using the classification of real-root configurations of polynomials up to degree five as a structured benchmark. We tested an extensive set of ML models, including decision trees, logistic regression, support vector machines, random forest, gradient boosting, XGBoost, symbolic regression, and neural networks. Neural networks achieved strong in-distribution performance on quintic classification using raw coefficients alone (84.3% + or - 0.9% balanced accuracy), whereas decision trees perform substantially worse (59.9% + or - 0.9\%). However, when provided with an explicit feature capturing sign changes at critical points, decision trees match neural performance (84.2% + or - 1.2%) and yield explicit classification rules. Knowledge distillation reveals that this single invariant accounts for 97.5% of the extracted decision structure. Out-of-distribution, data-efficiency, and noise robustness analyses indicate that neural networks learn continuous, data-dependent geometric approximations of the decision boundary rather than recovering scale-invariant symbolic rules. This distinction between geometric approximation and symbolic invariance explains the gap between predictive performance and interpretability observed across models. Although high predictive accuracy is attainable, we find no evidence that the evaluated ML models autonomously recover discrete, human-interpretable mathematical rules from raw coefficients. These results suggest that, in structured mathematical domains, interpretability may require explicit structural inductive bias rather than purely data-driven approximation.

math.NA↗

arXiv2026

Sparse Identification of Nonlinear Distributed-Delay Dynamics via the Linear Chain Trick

The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the recovery of discrete delay differential equations, where delay terms are represented explicitly in the candidate library. However, such formulations cannot capture the distributed delays that naturally arise in biological, physical, and engineering systems. In the present work, we extend SINDy to identify distributed-delay differential equations by incorporating the Linear Chain Trick (LCT), which provides a finite-dimensional ordinary differential equation representing the distributed memory effects. Hence, SINDy can operate in an augmented state space using conventional sparse regression while preserving a clear interpretation of delayed influences via the chain trick. From time-series data, the proposed method jointly infers the governing equations, the mean delay, and the dispersion of the underlying delay distribution. We numerically verify the method on several models with distributed delay, including the logistic growth model and a Hes1--mRNA gene regulatory network model. We show that the proposed method accurately reconstructs distributed delay dynamics, remains robust under noise and sparse sampling, and provides a transparent, data-driven approach for discovering nonlinear systems with distributed-delay.

math.NA↗

arXiv2025

Evaluating the Reasoning Abilities of LLMs on Underrepresented Mathematics Competition Problems

Understanding the limitations of Large Language Models, or LLMs, in mathematical reasoning has been the focus of several recent studies. However, the majority of these studies use the same datasets for benchmarking, which limits the generalizability of their findings and may not fully capture the diverse challenges present in mathematical tasks. The purpose of the present study is to analyze the performance of LLMs on underrepresented mathematics competition problems. We prompted three leading LLMs, namely GPT-4o-mini, Gemini-2.0-Flash, and DeepSeek-V3, with the Missouri Collegiate Mathematics Competition problems in the areas of Calculus, Analytic Geometry, and Discrete Mathematics. The LLMs responses were then compared to the known correct solutions in order to determine the accuracy of the LLM for each problem domain. We also analyzed the LLMs reasoning to explore patterns in errors across problem types and models. DeepSeek-V3 has the best performance in all three categories of Calculus, Analytic Geometry, and Discrete Mathematics, both in reasoning and correct final answers. All three LLMs exhibited notably weak performance in Geometry. The majority of errors made by DeepSeek-V3 were attributed to computational and logical mistakes, whereas GPT-4o-mini frequently exhibited logical and approach-related errors. Gemini, on the other hand, tended to struggle with incomplete reasoning and drawing rushed conclusions. In conclusion, evaluating LLMs on underrepresented mathematics competition datasets can provide deeper insights into their distinct error patterns and highlight ongoing challenges in structured reasoning, particularly within the domain of Geometry.

cs.AI↗

arXiv2025

Leveraging NCBI Genomic Metadata for Epidemiological Insights: Example of Enterobacterales

Numerous studies have utilized NCBI data for genomic analysis, gene annotation, and identifying disease-associated variants, yet NCBI's epidemiological potential remains underexplored. This study demonstrates how NCBI datasets can be systematically leveraged to extract and interpret infectious disease patterns across spatial and temporal dimensions. Using Enterobacterales as a case study, we analyzed over 477,000 genomic records and metadata, including collection date, location, host species, and isolation source. We compared trends of Escherichia coli and Salmonella in NCBI data with CDC's National Outbreak Reporting System (NORS). While both datasets showed consistent seasonal peaks and foodborne sources, NCBI data revealed broader host species (e.g., wildlife, environmental reservoirs), greater isolate diversity, and finer spatial-temporal resolution. These insights were enabled by our open-source Python package, EpiNCBI_V1, developed for real-time downloading, filtering, and cleaning of pathogen genomic metadata from NCBI. This work highlights the value of integrating genomic repositories into public health analytics to enhance surveillance, outbreak detection, and cross-species transmission tracking globally.

q-bio.QM↗

arXiv2021

Incorporating global dynamics to improve the accuracy of disease models: Example of a COVID-19 SIR model

Mathematical models of infectious diseases exhibit robust dynamics such as stable endemic or a disease-free equilibrium, or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics can be significantly improved by incorporating both local and global dynamics of the infection in disease models. To demonstrate improved accuracies, we extended a standard Susceptible-Infected-Recovered (SIR) model by incorporating global dynamics of the COVID-19 pandemic. The extended SIR model assumes three possibilities for the susceptible individuals traveling outside of their community: They can return to the community without any exposure to the infection, they can be exposed and develop symptoms after returning to the community, or they can be tested positive during the trip and remain quarantined until fully recovered. To examine the predictive accuracies of the extended SIR model, we studied the prevalence of the COVID-19 infection in Kansas City, Missouri influenced by the COVID-19 global pandemic. Using a two-step model-fitting algorithm, the extended SIR model was parameterized using the Kansas City, Missouri COVID-19 data during March to October 2020. The extended SIR model significantly outperformed the standard SIR model and revealed oscillatory behaviors with an increasing trend of infected individuals. In conclusion, the analytics and predictive accuracies of disease models can be significantly improved by incorporating the global dynamics of the infection in the models.

stat.AP↗

arXiv2017

Analysis and Applications of Delay Differential Equations in Biology and Medicine

The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior of solutions, which include destabilization of steady states, periodic and oscillatory solutions, bifurcations, and stability switches. The biological interpretations of delay effects are briefly discussed.

math.DS↗

arXiv2017

Introduction to Delay Models and Their Wave Solutions

In this paper, a brief review of delay population models and their applications in ecology is provided. The inclusion of diffusion and nonlocality terms in delay models has given more capabilities to these models enabling them to capture several ecological phenomena such as the Allee effect, waves of invasive species and spatio-temporal competitions of interacting species. Moreover, recent advances in the studies of traveling and stationary wave solutions of delay models are outlined. In particular, the existence of stationary and traveling wave solutions of delay models, stability of wave solutions, formation of wavefronts in the special domain, and possible outcomes of delay models are discussed.

q-bio.PE↗

arXiv2016

Social Network Analysis of a Grassland Rodent Community Using a Lotka-Volterra Modeling Approach

Although social network analysis is a promising tool to study the structure and dynamics of wildlife communities, the current methods require costly and detailed network data, which often are not available over long time periods (e.g. decades). The present work aims to resolve this issue by developing a new methodology that requires much less detailed data and it relies on well-established Lotka-Volterra models. Using the long-term abundance data (1973-2003) of northeastern Kansas rodents, the changes in the magnitude and direction of interactions (e.g., changes from cooperative behavior to competitive behavior or changes in the magnitude of competition) are quantified.

q-bio.PE↗