arXiv subjects

Anurag Singh

Publications and source records attributed to Anurag Singh.

At least 19 recordsLinked to original sources

arXiv2026

A physics-informed inverse modeling framework for Moose-Wolf dynamics from limited and noisy data in Isle Royale National Park

The interaction of moose (Alces alces) and wolf (Canis lupus) populations in ecosystems such as Isle Royale National Park is a canonical benchmark for ecological modeling of prey-predator dynamics. Mathematical modeling is a useful tool for modeling these interactions. A central challenge in this domain is the inverse problem, recovering governing system parameters from observational data. Although classical parameter estimation methods have seen considerable progress, they mostly rely on data rather than physics and therefore largely fall short in capturing the time-varying nature of ecological interactions driven by environmental fluctuations, seasonal forcing, and habitat change. This study addresses that gap by solving the inverse problem for a non-autonomous prey-predator system that incorporates theta-logistic prey growth with temporally varying intrinsic growth and natural death rates, as well as Holling type-II and ratio-dependent functional responses. A deep learning framework (self-adaptive bc-PINN with transfer learning) is employed to estimate time-dependent and constant parameters directly from population time series data (1959-2019). Before estimating the parameters, we performed a structural identifiability analysis to ensure that the model parameters are identifiable. The framework demonstrates good reconstruction and prediction results across both functional responses. The ratio-dependent model has shown the better prediction trend beyond the training data. Our framework successfully predicts the sudden decline in the moose population in 2020.

math.DS↗

arXiv2026

A Multispectral Framework for the Detection of Calcium Carbide-Induced Ripening and Shelf-Life Estimation in Climacteric Fruits

Significant health risks are associated with the illegal, yet commonly practiced use of industrial-grade Calcium Carbide (CaC2) for ripening climacteric fruits like mango and banana, which leaves behind trace residues of arsenic and phosphorus. To address this, the proposed study explores a novel, non-invasive multispectral framework for distinguishing safely ripened fruits (naturally ripened and ethephon-induced) from calcium carbide-ripened samples, while also estimating their ripening progression (in percentage) and remaining shelf life (in days). The spectral profiles of mango (Mangifera indica) and banana (Musa acuminata) at 18 discrete wavelengths in the visible-near infrared (NIR) range (410 nm - 940 nm) are studied using the AS7265x spectral triad sensor. CaC2-treated samples exhibit sharper spectral intensity drops in the visible region, consistent with accelerated chlorophyll degradation and carotenoid development. To characterize these physiological changes, the feature engineering strategy integrates inter-method spectral variance, intensity ratios at distinct wavelengths, and environmental parameters including temperature and humidity. Dimensionality reduction using Principal Component Analysis (PCA) retains >90% of spectral variance within the first 5-7 components. The resulting feature set is used to train three independent eXtreme Gradient Boosting (XGBoost)-based learning algorithms for ripening method classification, along with quantitative estimation of remaining shelf life and ripening progression. A classification accuracy of 95% along with carbide class recall of 0.67 is observed for mango samples, while the model achieves an accuracy of 81% and carbide class recall of 0.74 for banana. This instrumentation and data-driven approach demonstrates the effectiveness of the proposed non-invasive framework.

cs.LG↗

arXiv2026

Incentive Aware AI Regulations: A Credal Characterisation

The rapid proliferation of AI applications has intensified debate on effective regulation of these black-box services. Effective regulation must balance two competing goals: (1) deterring non-compliant providers from entering the market, while (2) retaining compliant ones. We call this ideal the perfect market outcome (PMO). Regulators face two compounding obstacles that make PMO difficult to achieve: providers hold private information and can act strategically to evade compliance, while any evidence drawn or derived from a finite sample carries statistical uncertainty in proving non-compliance. As this information asymmetry and statistical uncertainty is inherent to any effective regulation, we formalise them through a mechanism design framework that explicitly accounts for such statistical uncertainty. This yields a sharp characterisation: a mechanism achieves PMO if and only if the set of non-compliant evidence distributions forms a closed, convex set of probability measures, known in imprecise probability as a credal set. This result serves as a diagnostic tool to determine whether PMO is achievable under a given regulation. We further show that PMO-achieving mechanisms can be constructed from a collection of hypothesis tests, and validate our theoretical contributions through experiments on spurious-feature and fairness-based regulations.

cs.LG↗

arXiv2026

Barile-Macchia Resolutions and the closed neighborhood ideal

We investigate the minimal free resolutions of closed neighborhood ideals of graphs within the framework of Barile-Macchia (BM) resolutions. We show that for any tree $T$, the closed neighborhood ideal $NI(T)$ is bridge-friendly, and hence its BM resolution is minimal. The combinatorial structure of trees further allows us to construct a maximal critical cell of size $α(T)$, leading to the equality $\operatorname{pd}(R/NI(T)) = α(T)$, where $α(T)$ denotes the independence number of $T$ and $\operatorname{pd}$ is the projective dimension. Using Betti splitting techniques, we also obtain explicit formulas for the graded Betti numbers of $NI(P_n)$, where $P_n$ is the path graph on $n$ vertices. Finally, we make some observations on the bridge-friendly condition of the closed neighborhood ideals of chordal and bipartite graphs.

math.AC↗

arXiv2026

Descent-restricted subsequences via RSK and evacuation

The length $\mathsf{is}(π)$ of a longest increasing subsequence in a permutation $π$ has been extensively studied. An increasing subsequence is one that has no descents. We study generalizations of this statistic by finding longest subsequences with other descent restrictions. We first consider the statistic which encodes the longest length of a subsequence with a given number of descents. We then generalize this to restrict the descent set of the subsequence. Extending the classical result for $\mathsf{is}(π)$, we show how these statistics can be obtained using the RSK correspondence and the Schützenberger involution. In particular, these statistics only depend on the recording tableau of the permutation.

math.CO↗

arXiv2026

Modified TSception for Analyzing Driver Drowsiness and Mental Workload from EEG

Driver drowsiness is a leading cause of traffic accidents, necessitating real-time, reliable detection systems to ensure road safety. This study proposes a Modified TSception architecture for robust assessment of driver fatigue and mental workload using Electroencephalography (EEG). The model introduces a five-layer hierarchical temporal refinement strategy to capture multi-scale brain dynamics, surpassing the original TSception's three-layer approach. Key innovations include the use of Adaptive Average Pooling (ADP) for structural flexibility across varying EEG dimensions and a two-stage fusion mechanism to optimize spatiotemporal feature integration for improved stability. Evaluated on the SEED-VIG dataset, the Modified TSception achieves 83.46% accuracy, comparable to the original model (83.15%), but with a significantly reduced confidence interval (0.24 vs. 0.36), indicating better performance stability. The architecture's generalizability was further validated on the STEW mental workload dataset, achieving state-of-the-art accuracies of 95.93% and 95.35% for 2-class and 3-class classification, respectively. These results show that the proposed modifications improve consistency and cross-task generalizability, making the model a reliable framework for EEG-based safety monitoring.

cs.HC↗

arXiv2026

Topology of total cut complexes and cut complexes of grid graphs

Inspired by the work of Fr{ö}berg (1990) and Eagon and Reiner (1998), Bayer et al. recently introduced two new graph complexes: total cut complexes and cut complexes. In this article, we investigate these complexes specifically for (rectangular) grid graphs, focusing on $2 \times n$ and $3 \times n$ cases. We extend and refine the work of Bayer et al., proving and strengthening several of their conjectures, thereby enhancing the understanding of these graph complexes' topological and combinatorial properties.

math.CO↗

arXiv2025

Independence Complexes of Hexagonal Grid Graphs

The independence complex of a graph is a simplicial complex whose faces correspond to the independent sets of $G$. While independence complexes have been studied extensively for many graph classes, including square grid graphs, relatively little is known about planar hexagonal grid graphs. In this article, we study the topology of the independence complexes of hexagonal grid graphs $H_{1 \times m \times n}$. For $ m=1, 2, 3$ and $n\geq 1$, we determine their homotopy types. In particular, we show that the independence complex of the hexagonal line tiling $H_{1 \times 1 \times n}$ is homotopy equivalent to a wedge of two $n$-spheres, and for $m=2$ and $m=3$, we obtain recursive descriptions that completely determine the spheres appearing in the homotopy type. Our proofs rely on link and deletion operations, the fold lemma, and a detailed analysis of induced subgraphs.

math.CO↗

arXiv2025

Climate Driven Interactions Between Malaria Transmission and Diabetes Prevalence

Climate change is intensifying infectious and chronic diseases like malaria and diabetes, respectively, especially among the vulnerable populations. Global temperatures have risen by approximately $0.6^\circ$C since 1950, extending the window of transmission for mosquito-borne infections and worsening outcomes in diabetes due to metabolic stress caused by heat. People living with diabetes have already weakened immune defenses and, therefore, are at an alarmingly increased risk of contraction of malaria. However, most models rarely include both ways of interaction in changing climate conditions. In the paper, we introduce a new compartmental epidemiological model based on synthetic data fitted to disease patterns of India from 2019 to 2021. The framework captures temperature-dependent transmission parameters, seasonal variability, and different disease dynamics between diabetic and non-diabetic groups within the three-compartment system. Model calibration using Multi-Start optimization combined with Sequential Quadratic Programming allows us to find outstanding differences between populations. The odds of malaria infection in diabetic individuals were found to be 1.8--4.0 times higher, with peak infection levels in 35--36\%, as compared to 20--21\% in the non-diabetic ones. The fitted model was able to capture well the epidemiological patterns observed, while the basic reproduction number averaged around 2.3, ranging from 0.31 to 2.75 in different seasons. Given that India's diabetic population is set to rise to about 157 million people by 2050, these findings point to a pressing need for concerted efforts toward climate-informed health strategies and monitoring systems that address both malaria and diabetes jointly.

cs.MA↗

arXiv2025

Matching complexes of $\bf 3 \times n$ grid graphs

The matching complex of a graph $G$ is a simplicial complex whose simplices are matchings in $G$. In the last few years the matching complexes of grid graphs have gained much attention among the topological combinatorists. In 2017, Braun and Hough obtained homological results related to the matching complexes of $2 \times n$ grid graphs. Further in 2019, Matsushita showed that the matching complexes of $2 \times n$ grid graphs are homotopy equivalent to a wedge of spheres. In this article we prove that the matching complexes of $3\times n$ grid graphs are homotopy equivalent to a wedge of spheres. We also give the comprehensive list of the dimensions of spheres appearing in the wedge.

math.CO↗

arXiv2025

The First Mathematical Model for Elk Wolf Interaction in Yellowstone National Park Using the E-SINDy Algorithm

In this study, we investigate the prey predator dynamics of the elk wolf system in northern Yellowstone National Park, USA, using a data driven modeling approach. We used yearly population data for elk and wolves from 1995 to 2022 to construct a mathematical model using a sparse regression modeling framework. To the best of our knowledge, no previous work has applied this framework to capture elk wolf interactions over this time period. Our modeling pipeline integrates Gaussian process regression for data smoothing, sparse identification of nonlinear dynamics for model discovery, and model selection techniques to identify the most suitable mathematical representation. The resulting model is analyzed for its nonlinear dynamics with ecologically meaningful parameters. Stability and bifurcation analyzes are then performed to understand the systems qualitative behavior. A saddle node bifurcation identifies parameter ranges where both species can coexist, while regions outside this range may lead to the extinction of one or both populations. Hopf and saddle node bifurcations together delineate zones of stable co existence, periodic oscillations, and extinction scenarios. Furthermore, co dimension two bifurcations, including Bogdanov Takens and cusp bifurcations, are explored by varying two parameters simultaneously. Ecologically, these bifurcations reflect the complex interplay between wolf pressure and elk defence mechanisms, such as grouping or herd behavior. They suggested that small changes in ecological parameters can lead to sudden shifts in population outcomes ranging from stable co existence to extinction or oscillatory cycles.

math.DS↗

arXiv2025

Truthful Elicitation of Imprecise Forecasts

The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their beliefs, limiting their use in safety-critical domains where decision-makers (DMs) prioritize proper uncertainty management. To address this, we propose a framework for scoring imprecise forecasts -- forecasts given as a set of beliefs. Despite existing impossibility results for deterministic scoring rules, we enable truthful elicitation by drawing connection to social choice theory and introducing a two-way communication framework where DMs first share their aggregation rules (e.g., averaging or min-max) used in downstream decisions for resolving forecast ambiguity. This, in turn, helps forecasters resolve indecision during elicitation. We further show that truthful elicitation of imprecise forecasts is achievable using proper scoring rules randomized over the aggregation procedure. Our approach allows DM to elicit and integrate the forecaster's epistemic uncertainty into their decision-making process, thus improving credibility.

cs.LG↗

arXiv2025

Perfect Matching Complexes of Polygonal Line Tilings

The perfect matching complex of a simple graph $G$ is a simplicial complex having facets (maximal faces) as the perfect matchings of $G$. This article discusses the perfect matching complex of polygonal line tilings and the $\left(2 \times n\right)$-grid graph in particular. We use tools from discrete Morse theory to show that the perfect matching complex of any polygonal line tiling is either contractible or homotopy equivalent to a wedge of spheres. While proving our results, we also characterize all the matchings of $\left(2 \times n\right)$-grid graph that cannot be extended to form a perfect matching.

math.CO↗

arXiv2025

Simplicial complexes and matroids with vanishing $T^2$

We investigate quotients by radical monomial ideals for which $T^2$, the second cotangent cohomology module, vanishes. The dimension of the graded components of $T^2$, and thus their vanishing, depends only on the combinatorics of the corresponding simplicial complex. We give both a complete characterization and a full list of one dimensional complexes with $T^2=0$. We characterize the graded components of $T^2$ when the simplicial complex is a uniform matroid. Finally, we show that $T^2$ vanishes for all matroids of corank at most two and conjecture that all connected matroids with vanishing $T^2$ are of corank at most two.

math.CO↗

arXiv2025

Bayesian Optimization for Building Social-Influence-Free Consensus

We introduce Social Bayesian Optimization (SBO), a vote-efficient algorithm for consensus-building in collective decision-making. In contrast to single-agent scenarios, collective decision-making encompasses group dynamics that may distort agents' preference feedback, thereby impeding their capacity to achieve a social-influence-free consensus -- the most preferable decision based on the aggregated agent utilities. We demonstrate that under mild rationality axioms, reaching social-influence-free consensus using noisy feedback alone is impossible. To address this, SBO employs a dual voting system: cheap but noisy public votes (e.g., show of hands in a meeting), and more accurate, though expensive, private votes (e.g., one-to-one interview). We model social influence using an unknown social graph and leverage the dual voting system to efficiently learn this graph. Our theoretical findigns show that social graph estimation converges faster than the black-box estimation of agents' utilities, allowing us to reduce reliance on costly private votes early in the process. This enables efficient consensus-building primarily through noisy public votes, which are debiased based on the estimated social graph to infer social-influence-free feedback. We validate the efficacy of SBO across multiple real-world applications, including thermal comfort, team building, travel negotiation, and energy trading collaboration.

cs.MA↗

arXiv2024

Castelnuovo-Mumford regularity of the closed neighborhood ideal of a graph

Let $G$ be a finite simple graph and let $NI(G)$ denote the closed neighborhood ideal of $G$ in a polynomial ring $R$. We show that if $G$ is a forest, then the Castelnuovo-Mumford regularity of $R/NI(G)$ is the same as the matching number of $G$, thus proving a conjecture of Sharifan and Moradi in the affirmative. We also show that the matching number of $G$ provides a lower bound for the Castelnuovo-Mumford regularity of $R/NI(G)$ for any $G$. Furthermore, we prove that, if $G$ contains a simplicial vertex, then $NI(G)$ admits a Betti splitting, and consequently, we show that the projective dimension of $R/NI(G)$ is also bounded below by the matching number of $G$, if $G$ is a forest or a unicyclic graph.

math.AC↗

arXiv2024

Robust Feature Inference: A Test-time Defense Strategy using Spectral Projections

Test-time defenses are used to improve the robustness of deep neural networks to adversarial examples during inference. However, existing methods either require an additional trained classifier to detect and correct the adversarial samples, or perform additional complex optimization on the model parameters or the input to adapt to the adversarial samples at test-time, resulting in a significant increase in the inference time compared to the base model. In this work, we propose a novel test-time defense strategy called Robust Feature Inference (RFI) that is easy to integrate with any existing (robust) training procedure without additional test-time computation. Based on the notion of robustness of features that we present, the key idea is to project the trained models to the most robust feature space, thereby reducing the vulnerability to adversarial attacks in non-robust directions. We theoretically characterize the subspace of the eigenspectrum of the feature covariance that is the most robust for a generalized additive model. Our extensive experiments on CIFAR-10, CIFAR-100, tiny ImageNet and ImageNet datasets for several robustness benchmarks, including the state-of-the-art methods in RobustBench show that RFI improves robustness across adaptive and transfer attacks consistently. We also compare RFI with adaptive test-time defenses to demonstrate the effectiveness of our proposed approach.

cs.LG↗

arXiv2024

Malaria Cell Detection Using Deep Neural Networks

Malaria remains one of the most pressing public health concerns globally, causing significant morbidity and mortality, especially in sub-Saharan Africa. Rapid and accurate diagnosis is crucial for effective treatment and disease management. Traditional diagnostic methods, such as microscopic examination of blood smears, are labor-intensive and require significant expertise, which may not be readily available in resource-limited settings. This project aims to automate the detection of malaria-infected cells using a deep learning approach. We employed a convolutional neural network (CNN) based on the ResNet50 architecture, leveraging transfer learning to enhance performance. The Malaria Cell Images Dataset from Kaggle, containing 27,558 images categorized into infected and uninfected cells, was used for training and evaluation. Our model demonstrated high accuracy, precision, and recall, indicating its potential as a reliable tool for assisting in malaria diagnosis. Additionally, a web application was developed using Streamlit to allow users to upload cell images and receive predictions about malaria infection, making the technology accessible and user-friendly. This paper provides a comprehensive overview of the methodology, experiments, and results, highlighting the effectiveness of deep learning in medical image analysis.

eess.IV↗