Showing 1–50 of 77 results for author: Ghosh, I

Stochastic Spatial Metapopulation Modelling of HPAI Control and Poultry Restocking on Jolly Island

Authors: Hammed O. Fatoyinbo, Indranil Ghosh, Parul Tiwari, Peter O. Olanipekun, Afeez Abidemi, Ryan H. L. Ip

Abstract: Highly pathogenic avian influenza (HPAI) outbreaks require rapid control during active transmission and evidence-based decisions on the safe restocking of depopulated farms. We developed a stochastic spatial SEIR-based metapopulation model for a synthetic HPAI outbreak on the fictional Jolly Island. Farms were classified as `Broiler-2', `organic duck', or `Other' production systems. The model inco… ▽ More Highly pathogenic avian influenza (HPAI) outbreaks require rapid control during active transmission and evidence-based decisions on the safe restocking of depopulated farms. We developed a stochastic spatial SEIR-based metapopulation model for a synthetic HPAI outbreak on the fictional Jolly Island. Farms were classified as `Broiler-2', `organic duck', or `Other' production systems. The model incorporated local, environmental, movement-mediated, and distance-dependent transmission, together with reactive and preventive culling, production-specific confinement, and capacity-based restocking. The simulated epidemic was geographically concentrated and differed substantially among production classes. Preventive culling reduced mean cumulative burden from 16,362.7 to 13,631.9 infectious-farm-days, with an overall reduction of 16.7\%. Earlier confinement substantially reduced epidemic magnitude, while stronger environmental transmission increased the epidemic peak. Restocking risk declined as the epidemic approached resolution. Under the model assumptions, 24 May 2026 was the first candidate date satisfying the predefined rebound-probability threshold of 0.20. For restocking on 15 March 2026, none of the tested restocking fractions met this criterion. Capacity-based restocking reduced cumulative burden by 8.45\% and rebound probability from 0.780 to 0.533, compared with restocking relative to the baseline population. These findings demonstrate the value of integrating epidemic control and post-outbreak recovery within a single modelling framework. Timely confinement, targeted preventive culling, and phased capacity-based restocking may reduce both epidemic burden and resurgence risk, although operational decisions should also incorporate surveillance, biosecurity, economic considerations, and regulatory requirements. △ Less

Submitted 13 August, 2026; originally announced August 2026.

Comments: 32 pages, 19 figures

MSC Class: 37N25; 93E03; 91B70; 62P12;

A Complete Characterization of Cartan Inclusions of Finite Dimensional $C^*$-algebras

Authors: Indrajit Ghosh, Sumit Kumar

Abstract: We give a complete characterization of Cartan inclusions of finite dimensional $C^*$-algebras in terms of their inclusion matrices. More precisely, for a unital inclusion $\mathcal{B}\subseteq\mathcal{A}$ with inclusion matrix $Λ=(Λ_{ij})$, where Cartan means that $\mathcal{B}$ is a \emph{generalised Cartan subalgebra} of $\mathcal{A}$ in the sense of Exel, we prove that the inclusion is Cartan if… ▽ More We give a complete characterization of Cartan inclusions of finite dimensional $C^*$-algebras in terms of their inclusion matrices. More precisely, for a unital inclusion $\mathcal{B}\subseteq\mathcal{A}$ with inclusion matrix $Λ=(Λ_{ij})$, where Cartan means that $\mathcal{B}$ is a \emph{generalised Cartan subalgebra} of $\mathcal{A}$ in the sense of Exel, we prove that the inclusion is Cartan if and only if \[ \sum_i Λ_{ij}\leq 1 \] for every $j$. We call matrices satisfying this condition \emph{multiplicity free}. Thus, our characterization provides a purely combinatorial criterion for determining when a finite dimensional inclusion is Cartan. We further prove that every Cartan inclusion admits a unique conditional expectation from $\mathcal{A}$ onto $\mathcal{B}$. Conversely, we show that, for unital inclusions of finite dimensional $C^*$-algebras, the uniqueness of the conditional expectation is sufficient for the inclusion to be Cartan. Consequently, a unital inclusion $\mathcal{B}\subseteq\mathcal{A}$ of finite dimensional $C^*$-algebras is Cartan if and only if there exists a unique conditional expectation from $\mathcal{A}$ onto $\mathcal{B}$. △ Less

Submitted 13 August, 2026; v1 submitted 12 August, 2026; originally announced August 2026.

Comments: 15 pages

MSC Class: Primary 46L05; 47L40; Secondary 46L10

A Complete Characterization of Regular Inclusions of Finite Dimensional $C^*$-algebras

Authors: Keshab Chandra Bakshi, Indrajit Ghosh, Sumit Kumar

Abstract: We give a complete characterization of regular (in the sense of Kumjian and Renault) unital inclusions of finite-dimensional $C^*$-algebras. For subalgebras $\bigoplus_j( \mathbb{M}_{d_j}(\mathbb{C}) \otimes \mathbb{I}_{p_j})$ of $\mathbb{M}_n(\mathbb{C})$, we show that regularity depends only on equality of the multiplicities $p_j$, while unitary regularity---characterized recently by the first a… ▽ More We give a complete characterization of regular (in the sense of Kumjian and Renault) unital inclusions of finite-dimensional $C^*$-algebras. For subalgebras $\bigoplus_j( \mathbb{M}_{d_j}(\mathbb{C}) \otimes \mathbb{I}_{p_j})$ of $\mathbb{M}_n(\mathbb{C})$, we show that regularity depends only on equality of the multiplicities $p_j$, while unitary regularity---characterized recently by the first author and Silambarasan---additionally requires equality of the $d_j$; we recover the latter via a streamlined alternative proof. Extending this to inclusions of arbitrary finite-dimensional $C^*$-algebras, encoded by an inclusion matrix $Λ$, we show that regularity is equivalent to an explicit row/column condition on $Λ$---coinciding with the normalizer matrix introduced by the first author and Silambarasan ---so that the device used there to detect unitary regularity is shown to characterize regularity in general; unitary regularity is recovered by a further dimension-equality condition. △ Less

Submitted 5 August, 2026; originally announced August 2026.

Comments: 24 pages

MSC Class: Primary 46L05; 47L40; Secondary 46L10

Collective Phase Reorganization and Cluster Synchronization in Networks of Coupled Gumowski--Mira Maps

Authors: Hammed Olawale Fatoyinbo, Indranil Ghosh

Abstract: We investigate the collective dynamics of networks composed of diffusively coupled Gumowski-Mira maps and analyze how modifications in the intrinsic dynamics of the local oscillator reorganize the emergent phase structure of the network. The coupling strength and the local control parameter are treated as bifurcation parameters, and the resulting collective states are quantified using the largest… ▽ More We investigate the collective dynamics of networks composed of diffusively coupled Gumowski-Mira maps and analyze how modifications in the intrinsic dynamics of the local oscillator reorganize the emergent phase structure of the network. The coupling strength and the local control parameter are treated as bifurcation parameters, and the resulting collective states are quantified using the largest Lyapunov exponent, a synchronization error measure, cluster-count statistics, and collective phase-classification diagrams. Two representative regimes of the local dynamics are examined. In the first regime, the network exhibits a smooth and highly organized collective parameter space, featuring a synchronization wedge embedded within an extended region of periodic cluster states. In the second regime, the same coupling architecture yields a fragmented phase organization, comprising disconnected synchronization islands, incoherent domains, and enhanced chaotic-cluster states. These results indicate that variations in the intrinsic dynamics of the individual Gumowski-Mira oscillator do not simply shift synchronization thresholds but can fundamentally restructure the topology of the collective phase space. Our findings thus establish a direct relationship between local nonlinear dynamics and the emergent organization of collective phases in coupled discrete-time networks. △ Less

Submitted 3 July, 2026; originally announced July 2026.

Comments: 18 pages, 11 figures

ForceBand: Learning Forceful Manipulation with sEMG

Authors: Botao He, Zhi Wang, Linna Kuang, Ishaan Ghosh, Jitendra Malik, Cornelia Fermuller, Tingfan Wu, Jiayuan Mao, Ruoshi Liu, Haozhi Qi, Yiannis Aloimonos

Abstract: Human demonstrations are a scalable data source for learning robot manipulation policies. However, common sources of human demonstration data, such as motion-capture trajectories and internet videos, capture mostly motion and appearance while missing the contact forces that are critical for force-sensitive manipulation. In this paper, we introduce ForceBand, a low-cost wrist-worn sEMG system that… ▽ More Human demonstrations are a scalable data source for learning robot manipulation policies. However, common sources of human demonstration data, such as motion-capture trajectories and internet videos, capture mostly motion and appearance while missing the contact forces that are critical for force-sensitive manipulation. In this paper, we introduce ForceBand, a low-cost wrist-worn sEMG system that turns human muscle activity into force-enriched demonstrations. We first collect a 10-hour multimodal dataset containing egocentric video, sEMG, IMU, and fingertip force measurements across diverse actions and objects. Using this dataset, we pre-train an EMG2Force model that predicts per-finger forces from sEMG and IMU signals. After a short user-specific calibration, users can collect target-task demonstrations using only ForceBand and video; EMG2Force then labels these demonstrations with per-finger force traces, producing force-augmented demonstrations for robot policy learning. Experiments show that ForceBand recovers fine-grained fingertip interactions with over 50% lower force prediction error than vision-based baselines and achieves an 87% success rate on pick, squeeze, and place tasks that require object-specific force control across objects with diverse shapes, sizes, and weights. Project website: https://forceband-emg.github.io △ Less

Submitted 24 June, 2026; originally announced June 2026.

M-SDT: A modelling framework for dengue transmission, forecasting, and intervention strategies in Ahmedabad Municipal Corporation

Authors: Sourav Roy, Rajendra Gadhavi, Bhavin Solanki, Chirag Shah, Raj C. Sharma, Indrajit Ghosh

Abstract: Dengue fever poses a persistent public health challenge in rapidly urbanizing Indian cities such as Ahmedabad, where spatial heterogeneity and seasonal variability complicate forecasting and control. In this study, we develop a data-driven compartmental framework to simulate transmission dynamics, generate forecasts, and evaluate intervention strategies across the Ahmedabad Municipal Corporation (… ▽ More Dengue fever poses a persistent public health challenge in rapidly urbanizing Indian cities such as Ahmedabad, where spatial heterogeneity and seasonal variability complicate forecasting and control. In this study, we develop a data-driven compartmental framework to simulate transmission dynamics, generate forecasts, and evaluate intervention strategies across the Ahmedabad Municipal Corporation (AMC). We employ a Mechanistic Seasonal Dengue Transmission (M-SDT) model that incorporates symptomatic and asymptomatic infections. We calibrated the proposed model using zone-wise dengue case data during 2020--2024. Parameter uncertainty is rigorously quantified using a bootstrap sampling framework with negative binomial noise. The calibrated model reveals pronounced spatial heterogeneity across AMC zones, with persistent hotspots and distinct transmission regimes. Forecasts for 2026--2028 indicate continued endemic circulation with moderate inter-annual variability. Sensitivity analysis identifies the mosquito biting rate and vector mortality as dominant drivers of long-term disease burden, highlighting the central role of vector ecology in shaping epidemic outcomes. Evaluating seasonal vector control strategies shows a notable difference in operation; periodic fogging has a cumulative effect over the years, while sustained residual spraying can quickly curb outbreaks and decrease incidence by over 80%. The zone-wise analysis reveals that the mosquito-to-human ratio governs not only the baseline outbreak potential but also each zone's responsiveness to control strategies. Overall, the M-SDT modelling framework enables reconstruction of unobserved dynamics, rigorous uncertainty quantification, and evaluation of targeted, zone-specific interventions, underscoring the importance of integrating fine-scale surveillance data with mechanistic modelling for adaptive urban dengue control. △ Less

Submitted 18 May, 2026; originally announced May 2026.

Comments: 38 pages, 17 figures

MSC Class: 92-10;

PULSE: Agentic Investigation with Passive Sensing for Proactive Affective Intervention in Cancer Survivorship

Authors: Zhiyuan Wang, Subigya Nepal, Ariful Islam, Indrajeet Ghosh, Xinyu Chen, Katharine E. Daniel, Laura E. Barnes, Philip Chow

Abstract: Cancer survivors face elevated rates of depression, anxiety, and emotional distress, yet self-report may be unavailable at some moments when support is relevant, a challenge we term the diary paradox. We present PULSE, a system for agentic sensing investigation: LLM agents equipped with eight purpose-built tools query smartphone sensing data, compare current behavior with personal baselines, and r… ▽ More Cancer survivors face elevated rates of depression, anxiety, and emotional distress, yet self-report may be unavailable at some moments when support is relevant, a challenge we term the diary paradox. We present PULSE, a system for agentic sensing investigation: LLM agents equipped with eight purpose-built tools query smartphone sensing data, compare current behavior with personal baselines, and retrieve outcome-labeled historical cases. Rather than receiving only a fixed feature summary, agents choose which modalities and time windows to inspect. We evaluate PULSE through a two-by-two evaluation design crossing system architecture (structured single-pass vs. multi-turn agentic) with concurrent input modality (no current diary vs. sensing plus current diary) on 50 cancer survivors. The agentic multimodal condition achieves balanced accuracy of 0.743 for emotion-regulation desire; the agentic no-current-diary condition achieves 0.713 for self-reported intervention availability. This is a system-level comparison because the architecture conditions also differ in tool-mediated information access. The results provide a retrospective benchmark for interactive sensing investigation and motivate prospective evaluation at diary non-response moments. △ Less

Submitted 7 August, 2026; v1 submitted 17 May, 2026; originally announced May 2026.

Handwriting decoding as a challenging motor task for EEG Foundation Models

Authors: Srinivas Ravishankar, Ishayu Ghosh, Nora Zajzon, Teng Fei, Virginia de Sa

Abstract: Recent attempts at creating Foundation Models (FMs) for Electroencephalography (EEG) have achieved state-of-the-art performance on multiple tasks including Motor Imagery (MI). These MI tasks have typically involved coarse classification between imagined limb movements. However, the development of foundation models necessitates diverse datasets, both for pretraining and evaluating the progress of t… ▽ More Recent attempts at creating Foundation Models (FMs) for Electroencephalography (EEG) have achieved state-of-the-art performance on multiple tasks including Motor Imagery (MI). These MI tasks have typically involved coarse classification between imagined limb movements. However, the development of foundation models necessitates diverse datasets, both for pretraining and evaluating the progress of these models. In this work, we propose handwriting decoding as a challenging motor task for FMs. We show that several existing datasets are potentially confounded, and introduce a dataset that more rigorously evaluates models. On this dataset, we find that current FMs, despite showing SOTA performance in multiple MI datasets are outperformed by smaller task-specific models. We also highlight challenges specific to EEG-based handwriting decoding to inform future work. In our 4-letter classification task, we show that (a) Knowledge of movement-onset is crucial to reported decoding performance in prior works, with average performance across subjects dropping from $41.3\%$ to $32.4\%$. (b) Increasing test-time signal quality provides significant performance improvements ($45\%$ to $78\%$ in our best subject) compared to scaling training data with single-trial EEG. (c) While scaling training data steadily improves decoding performance, existing FMs do not outperform specialist models in handwriting decoding. We make our code available at https://anonymous.4open.science/r/EEG-Handwriting-BCI-DFCD/ △ Less

Submitted 15 May, 2026; originally announced May 2026.

COHORT: Hybrid RL for Collaborative Large DNN Inference on Multi-Robot Systems Under Real-Time Constraints

Authors: Mohammad Saeid Anwar, Anuradha Ravi, Indrajeet Ghosh, Gaurav Shinde, Carl Busart, Nirmalya Roy

Abstract: Large deep neural networks (DNNs), especially transformer-based and multimodal architectures, are computationally demanding and challenging to deploy on resource-constrained edge platforms like field robots. These challenges intensify in mission-critical scenarios (e.g., disaster response), where robots must collaborate under tight constraints on bandwidth, latency, and battery life, often without… ▽ More Large deep neural networks (DNNs), especially transformer-based and multimodal architectures, are computationally demanding and challenging to deploy on resource-constrained edge platforms like field robots. These challenges intensify in mission-critical scenarios (e.g., disaster response), where robots must collaborate under tight constraints on bandwidth, latency, and battery life, often without infrastructure or server support. To address these limitations, we present COHORT, a collaborative DNN inference and task-execution framework for multi-robot systems built on the Robotic Operating System (ROS). COHORT employs a hybrid offline-online reinforcement learning (RL) strategy to dynamically schedule and distribute DNN module execution across robots. Our key contributions are threefold: (a) Offline RL policy learning combined with Advantage-Weighted Regression (AWR), trained on auction-based task allocation data from heterogeneous DNN workloads across distributed robots, (b) Online policy adaptation via Multi-Agent PPO (MAPPO), initialized from the offline policy and fine-tuned in real time, and (c) comprehensive evaluation of COHORT on vision-language model (VLM) inference tasks such as CLIP and SAM, analyzing scalability with increasing robot/workload and robustness under . We benchmark COHORT against genetic algorithms and multiple RL baselines. Experimental results demonstrate that COHORT reduces battery consumption by 15.4% and increases GPU utilization by 51.67%, while satisfying frame-rate and deadline constraints 2.55 times of the time. △ Less

Submitted 11 March, 2026; originally announced March 2026.

Comments: Recently accepted at 27th IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks ( IEEE WoWMoM 2026)

Resonant grazing bifurcations revisited

Authors: David J. W. Simpson, Indranil Ghosh

Abstract: In vibro-impact mechanics, the division between an impact and a near miss is a zero-velocity grazing event. Grazing bifurcations of stable periodic motions often produce complicated attractors when grazing generates a square-root term in the Poincaré map. This paper concerns codimension-two scenarios for which the square-root term vanishes in some iterate of the Poincaré map. For forced one-degree… ▽ More In vibro-impact mechanics, the division between an impact and a near miss is a zero-velocity grazing event. Grazing bifurcations of stable periodic motions often produce complicated attractors when grazing generates a square-root term in the Poincaré map. This paper concerns codimension-two scenarios for which the square-root term vanishes in some iterate of the Poincaré map. For forced one-degree-of-freedom oscillators, this occurs when the forcing frequency is a certain rational multiple of the damped natural frequency, i.e., the system is in resonance. In two-parameter bifurcation diagrams, curves of saddle-node and period-doubling bifurcations of single-impact periodic motions emanate from the codimension-two points. In this paper we prove these curves are quadratically tangent to the curve of grazing bifurcations, and derive explicit formulas for their quadratic coefficients. This is achieved by modifying the Poincaré map in a way that circumvents the square-root singularity, enabling us to use the implicit function theorem to demonstrate smoothness and perform asymptotic calculations of the saddle-node and period-doubling bifurcation curves. In doing so we resolve a long-standing conjecture on the admissibility of single-impact periodic motions by supplementing raw asymptotic computations with geometric and topological arguments. We illustrate the results with a linear impact oscillator model, matching the theoretical unfolding to numerically computed bifurcation curves. The results explain why previously reported physical experiments reveal an absence of chaos shortly past the grazing bifurcation. △ Less

Submitted 26 February, 2026; originally announced February 2026.

MSC Class: 37G25; 34A38

Q3R: Quadratic Reweighted Rank Regularizer for Effective Low-Rank Training

Authors: Ipsita Ghosh, Ethan Nguyen, Christian Kümmerle

Abstract: Parameter-efficient training based on low-rank optimization has become a highly successful tool for fine-tuning large deep learning models. However, these methods often fail for low-rank pre-training, where simultaneously maintaining low-rank weight structure and optimizing the task objective remains challenging. We propose the $\textit{Quadratic Reweighted Rank Regularizer}$ ($\texttt{Q3R}$), whi… ▽ More Parameter-efficient training based on low-rank optimization has become a highly successful tool for fine-tuning large deep learning models. However, these methods often fail for low-rank pre-training, where simultaneously maintaining low-rank weight structure and optimizing the task objective remains challenging. We propose the $\textit{Quadratic Reweighted Rank Regularizer}$ ($\texttt{Q3R}$), which leads to a novel low-rank-inducing training strategy inspired by the Iteratively Reweighted Least Squares (IRLS) framework. $\texttt{Q3R}$ is based on a quadratic regularizer term that majorizes a smoothed log-determinant rank surrogate. Unlike other low-rank training techniques, $\texttt{Q3R}$ can train weight matrices to prescribed low target ranks while achieving predictive performance comparable to dense models, with small computational overhead and full compatibility with existing architectures. For example, we demonstrate a $\texttt{Q3R}$-regularized ViT-Tiny experiment where truncating the model to $60\%$ and $80\%$ of its parameters results in only minor absolute accuracy drops of $1.3\%$ and $4\%$, respectively, on CIFAR-10. We confirm the efficacy of $\texttt{Q3R}$ on Transformers across both vision and language tasks, including low-rank fine-tuning. △ Less

Submitted 18 February, 2026; v1 submitted 6 November, 2025; originally announced November 2025.

Journal ref: 39th Conference on Neural Information Processing Systems (NeurIPS 2025)

The VIVID function for numerically continuing periodic orbits arising from grazing bifurcations of hybrid dynamical systems

Authors: Indranil Ghosh, David J. W. Simpson

Abstract: Periodic orbits of systems of ordinary differential equations can be found and continued numerically by following fixed points of Poincaré maps. However, this often fails near grazing bifurcations where a periodic orbit collides tangentially with a boundary of phase space. Failure occurs when the map contains a square-root singularity and the root-finding algorithm searches beyond the domain of vi… ▽ More Periodic orbits of systems of ordinary differential equations can be found and continued numerically by following fixed points of Poincaré maps. However, this often fails near grazing bifurcations where a periodic orbit collides tangentially with a boundary of phase space. Failure occurs when the map contains a square-root singularity and the root-finding algorithm searches beyond the domain of viable values. We show that by instead following the zeros of a function that maps Velocity Into Variation In Displacement (VIVID) this issue is circumvented and there is no such failure. We illustrate this with a prototypical one-degree-of-freedom impact oscillator model by applying Newton's method to the VIVID function to follow periodic orbits collapsing into grazing bifurcations. We also follow curves of saddle-node and period-doubling bifurcations of periodic orbits that issue from a codimension-two resonant grazing bifurcation. The VIVID function provides a simple alternative to the more sophisticated collocation method and enables periodic orbits and their bifurcations to be resolved easily and accurately near grazing bifurcations. △ Less

Submitted 17 October, 2025; originally announced October 2025.

MSC Class: 37M20; 34A38

Assessing Roundabout Safety Perceptions under Heterogeneous Traffic: Socio-Demographic and Geometric Influences in Indian Urban Contexts

Authors: Abhijnan Maji, Indrajit Ghosh

Abstract: Evaluation of the safety perceptions of roundabout users is crucial for improving road safety in mixed-traffic environments. The crash- and conflict-based analyses do not incorporate the socio-demographic characteristics of the roundabout users, which can only be captured through questionnaire surveys on a larger scale. This research evaluated the relationship of roundabout safety perception with… ▽ More Evaluation of the safety perceptions of roundabout users is crucial for improving road safety in mixed-traffic environments. The crash- and conflict-based analyses do not incorporate the socio-demographic characteristics of the roundabout users, which can only be captured through questionnaire surveys on a larger scale. This research evaluated the relationship of roundabout safety perception with demographic factors, driving characteristics, and varying roundabout geometries using multiple correspondence analysis, cluster analysis, factor analysis, and multinomial logistic regression. The study analyzed data from 1,530 respondents across two Indian cities. The study identified three roundabout user clusters. Single-lane roundabouts were perceived as safer during entry and circulation, with a significant prominence among middle-aged users. In contrast, double- and multi-lane roundabouts presented higher perceived risks during exit maneuvers, especially among young, inexperienced, unemployed/self-employed users. Vulnerable road users reported significantly higher perceived risks, especially under suboptimal lighting conditions. Respondents with 10-20 years of driving experience, especially car users, perceived lower risk at single-lane roundabouts but acknowledged the higher risk linked to speed variations and complex maneuvers at multi-lane roundabouts. Driving experience, vehicle type, and geometric configurations were crucial in roundabout safety perception. The study highlighted the need to improve the built environment of roundabouts for vulnerable road users. The roundabout merging area was perceived as the most dangerous spot; however, exits were also perceived as dangerous for double- and multi-lane roundabouts. The findings can benefit policymakers, engineers, and urban planners by enabling them to deploy targeted safety interventions based on issues highlighted in the study. △ Less

Submitted 29 September, 2025; originally announced September 2025.

Report number: IJTST-D-25-00254

Disrupting the scammer lifecycle: A dynamically-consistent numerical analysis of a compartment model for scam-victim dynamics

Authors: Y. O. Tijani, I. Ghosh, S. D. Oloniiju, H. O. Fatoyinbo

Abstract: Online deception and financial scams represent a pervasive threat in the digital age, yet a quantitative analysis and understanding of their propagation is lacking. This study introduces a novel model based on the framework of epidemiological models to describe the interaction between scammers and their victims. We propose a five-compartment deterministic model ($S-V-R-A_s-R_s$) calibrated using l… ▽ More Online deception and financial scams represent a pervasive threat in the digital age, yet a quantitative analysis and understanding of their propagation is lacking. This study introduces a novel model based on the framework of epidemiological models to describe the interaction between scammers and their victims. We propose a five-compartment deterministic model ($S-V-R-A_s-R_s$) calibrated using longitudinal data in fraud reports from the Canadian Anti-Fraud Centre. The model's theoretical properties are established, including the non-negativity of the state variables and the stability threshold defined by the basic reproduction number ($\mathcal{R}_0$). A non-standard finite difference scheme is developed for the numerical simulations to ensure dynamical consistency between the continuous deterministic model and its discrete equivalent. A key finding of the model sensitivity analysis indicates that the proliferation of scams is overwhelmingly driven by the lifecycle of scammers, their recruitment, attrition, and arrest, rather than the susceptibility of the victim population. The results of this study provide strong quantitative evidence that the most effective control strategies are those that directly disrupt the scammers' population. Overall, this study provides a crucial model for designing and evaluating evidence-based policies to combat the scourge of cybercrime. △ Less

Submitted 27 August, 2025; originally announced August 2025.

A mathematical model of HPAI transmission between dairy cattle and wild birds with environmental effects

Authors: H. O. Fatoyinbo, P. Tiwari, P. O. Olanipekun, I. Ghosh

Abstract: Highly pathogenic avian influenza (HPAI), especially the H5N1 strain, remains a major threat to animal health, food security, and public health. Recent spillover events in dairy cattle in the United States, linked to wild birds, highlight the critical importance of understanding transmission pathways at the cattle--wild bird--environment interface. In this work, we formulate and analyze a determin… ▽ More Highly pathogenic avian influenza (HPAI), especially the H5N1 strain, remains a major threat to animal health, food security, and public health. Recent spillover events in dairy cattle in the United States, linked to wild birds, highlight the critical importance of understanding transmission pathways at the cattle--wild bird--environment interface. In this work, we formulate and analyze a deterministic compartmental model that captures the transmission of HPAI between dairy cattle and wild birds, incorporating both direct and indirect (environmental) routes. The model combines an $SEIR$ framework for cattle with an $SIR$ structure for wild birds, coupled through an environmental compartment. We derive the basic reproduction number, $\mathcal{R}_{0}$, using the next-generation matrix approach, decomposing it into cattle-to-cattle, bird-to-bird, and environmental contributions. Qualitative analysis establishes positivity, boundedness, and global stability of equilibria through Lyapunov functions. Numerical simulations confirm the results of the theoretical analyses, illustrating outbreak trajectories, extinction thresholds, and persistence dynamics. A global sensitivity analysis, based on Latin hypercube sampling and partial rank correlation coefficients, identifies key parameters, particularly transmission among cattle, environmental contamination, and recovery rate as critical drivers of epidemic outcomes. Our results show that disease elimination is achievable when $\mathcal{R}_{0} < 1$, while persistence is inevitable for $\mathcal{R}_{0} > 1$. These findings provide a comprehensive mathematical framework for assessing HPAI risks and offer guidance for biosecurity strategies aimed at mitigating spillover and controlling outbreaks in livestock populations. △ Less

Submitted 16 August, 2025; originally announced August 2025.

Comments: 35 pages, 8 figures

Time series analysis of coupled slow-fast neuron models: From Hurst exponent to Granger causality

Authors: Indranil Ghosh, Hammed O. Fatoyinbo, Sishu S. Muni

Abstract: We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a detailed account of how varying their strength drives the dynamics of the small networks. Algorithms for time series analysis range from measuring their persistence (… ▽ More We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a detailed account of how varying their strength drives the dynamics of the small networks. Algorithms for time series analysis range from measuring their persistence (ability to remember past values), irregularity, chaos and quasiperiodicity, to synchronization between time series from every node within a network. Chaos is observed for inhibitory coupling strengths and for temperature higher than a reference temperature when the coupling is thermally sensitive. We observe quasi-periodicity when the coupling is very weak and synchronized bursting for highly excitatory coupling strength. In certain cases we also observe decay oscillations. Finally, a causality test is performed to detect whether the dynamics of one neuron is influencing the dynamics of the other in the coupled system. △ Less

Submitted 17 July, 2025; originally announced July 2025.

Memento: Augmenting Personalized Memory via Practical Multimodal Wearable Sensing in Visual Search and Wayfinding Navigation

Authors: Indrajeet Ghosh, Kasthuri Jayarajah, Nicholas Waytowich, Nirmalya Roy

Abstract: Working memory involves the temporary retention of information over short periods. It is a critical cognitive function that enables humans to perform various online processing tasks, such as dialing a phone number, recalling misplaced items' locations, or navigating through a store. However, inherent limitations in an individual's capacity to retain information often result in forgetting important… ▽ More Working memory involves the temporary retention of information over short periods. It is a critical cognitive function that enables humans to perform various online processing tasks, such as dialing a phone number, recalling misplaced items' locations, or navigating through a store. However, inherent limitations in an individual's capacity to retain information often result in forgetting important details during such tasks. Although previous research has successfully utilized wearable and assistive technologies to enhance long-term memory functions (e.g., episodic memory), their application to supporting short-term recall in daily activities remains underexplored. To address this gap, we present Memento, a framework that uses multimodal wearable sensor data to detect significant changes in cognitive state and provide intelligent in situ cues to enhance recall. Through two user studies involving 15 and 25 participants in visual search navigation tasks, we demonstrate that participants receiving visual cues from Memento achieved significantly better route recall, improving approximately 20-23% compared to free recall. Furthermore, Memento reduced cognitive load and review time by 46% while also substantially reducing computation time (3.86 seconds vs. 15.35 seconds), offering an average of 75% effectiveness compared to computer vision-based cue selection approaches. △ Less

Submitted 28 April, 2025; originally announced April 2025.

Comments: This work has been accepted to the Proceedings of the ACM UMAP 2025

Towards an Optimal Bound for the Interleaving Distance on Mapper Graphs

Authors: Erin Wolf Chambers, Ishika Ghosh, Elizabeth Munch, Sarah Percival, Bei Wang

Abstract: Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a high-dimensional point cloud together with a real-valued function defined on it, a mapper graph summarizes the induced topological structure: each node represents a local neig… ▽ More Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a high-dimensional point cloud together with a real-valued function defined on it, a mapper graph summarizes the induced topological structure: each node represents a local neighborhood, and edges connect nodes whose corresponding neighborhoods overlap. Our focus is the interleaving distance for mapper graphs, arising as a discretized analogue of the interleaving distance for Reeb graphs-a quantity known to be NP-hard to compute. This distance measures how similar two mapper graphs are by quantifying how much they must be ``stretched'' to be made comparable. Recent work introduced a loss function that gives an upper bound on this distance. The loss evaluates how far a given collection of maps, called an assignment, is from being a true interleaving. Importantly, it is computationally tractable, offering a practical way to bound the distance, however the quality of the bound is dependent on the choice of assignment. In this paper, we develop the first framework for bounding the interleaving distance on mapper graphs. We present the bound in two ways: first, by formulating an integer linear program (ILP) that determines whether an $n$-interleaving exists for a given $n$; and second, by constructing an ILP that identifies an assignment with minimal loss for that $n$. We also evaluate the method on small examples where the interleaving distance is known, and on benchmark and simulated datasets, demonstrating the utility of the approach for classification tasks based on mapper graphs. △ Less

Submitted 16 April, 2026; v1 submitted 4 April, 2025; originally announced April 2025.

Comments: Reformulated the problem into both a binary problem and a loss computation problem

MSC Class: 55N31

A Bivariate Poisson-Gamma Distribution: Statistical Properties and Practical Applications

Authors: Indranil Ghosh, Mina Norouzirad, Filipe J. Marques

Abstract: Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate distribution-the bivariate Poisson-Gamma conditional distribution-is introduced, combining both univariate continuous and discrete distributions. This work explores aspects of… ▽ More Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate distribution-the bivariate Poisson-Gamma conditional distribution-is introduced, combining both univariate continuous and discrete distributions. This work explores aspects of this model's structure and statistical inference that have not been studied before. This paper contributes to the field of statistical modeling and distribution theory through the use of maximum likelihood estimation, along with simulations and analyses of real data. △ Less

Submitted 19 March, 2025; originally announced March 2025.

Federated Learning for Secure and Efficient Device Activity Detection in mMTC Networks

Authors: Ali Elkeshawy, Ibrahim Al Ghosh, Haifa Fares, Amor Nafkha

Abstract: Grant-free random access in massive machine-type communications enables low-latency connectivity with minimal signaling. However, sporadic device activation requires efficient device activity detection. We propose a federated learning-based device activity detection approach, leveraging distributed training to enhance security and privacy while maintaining low computational complexity. Compared to… ▽ More Grant-free random access in massive machine-type communications enables low-latency connectivity with minimal signaling. However, sporadic device activation requires efficient device activity detection. We propose a federated learning-based device activity detection approach, leveraging distributed training to enhance security and privacy while maintaining low computational complexity. Compared to existing methods, our solution achieves competitive detection performance, addressing scalability and security challenges in mMTC networks. △ Less

Submitted 14 March, 2025; originally announced March 2025.

Evaluation of CGRA Toolchains

Authors: Dominik Walter, Marita Halm, Daniel Seidel, Indrayudh Ghosh, Christian Heidorn, Frank Hannig, Jürgen Teich

Abstract: Increasing demands for computing power also propel the need for energy-efficient SoC accelerator architectures. One class for such accelerators are so-called processor arrays, which typically integrate a two-dimensional mesh of interconnected processing elements (PEs). Such arrays are specifically designed to accelerate the execution of multidimensional nested loops by exploiting the intrinsic par… ▽ More Increasing demands for computing power also propel the need for energy-efficient SoC accelerator architectures. One class for such accelerators are so-called processor arrays, which typically integrate a two-dimensional mesh of interconnected processing elements (PEs). Such arrays are specifically designed to accelerate the execution of multidimensional nested loops by exploiting the intrinsic parallelism of such loops. Coarse-grained reconfigurable arrays (CGRAs) belong to this class of accelerator architectures. In this work, we analyze four toolchains for mapping loop programs onto CGRAs and compare the resulting mappings wrt. performance, i.e., latency. While most toolchains succeed in simpler kernels like general matrix multiplication, some struggle to find valid mappings for more complex loops like a triangular solver. Furthermore, we observe that the considered CGRA mappers generally tend to underutilize the available PEs. △ Less

Submitted 27 February, 2025; v1 submitted 26 February, 2025; originally announced February 2025.

Comments: OSSMPIC2025, 1st workshop on Open Source Solutions for Massively Parallel Integrated Circuits. arXiv admin note: substantial text overlap with arXiv:2502.12062

Fractional order induced bifurcations in Caputo-type denatured Morris-Lecar neurons

Authors: Indranil Ghosh, Hammed Olawale Fatoyinbo

Abstract: We set up a system of Caputo-type fractional differential equations for a reduced-order model known as the {\em denatured} Morris-Lecar (dML) neurons. This neuron model has a structural similarity to a FitzHugh-Nagumo type system. We explore both a single-cell isolated neuron and a two-coupled dimer that can have two different coupling strategies. The main purpose of this study is to report variou… ▽ More We set up a system of Caputo-type fractional differential equations for a reduced-order model known as the {\em denatured} Morris-Lecar (dML) neurons. This neuron model has a structural similarity to a FitzHugh-Nagumo type system. We explore both a single-cell isolated neuron and a two-coupled dimer that can have two different coupling strategies. The main purpose of this study is to report various oscillatory phenomena (tonic spiking, mixed-mode oscillation) and bifurcations (saddle-node and Hopf) that arise with variation of the order of the fractional operator and the magnitude of the coupling strength for the coupled system. Various closed-form solutions as functions of the system parameters are established that act as the necessary and sufficient conditions for the stability of the equilibrium point. The theoretical analysis are supported by rigorous numerical simulations. △ Less

Submitted 24 February, 2025; originally announced February 2025.

Thermal Conductance Correlations of Static Lubricated Ball Bearings

Authors: Indronil Ghosh, John P. McHale, Yoshimi R. Takeuchi, Peter P. Frantz, Payton J. Batliner, Timothy S. Fisher

Abstract: Ball bearings are commonly used to reduce the friction in rotating mechanical components. The present work reports improved numerical approaches to model bearing thermal conductance in the absence of convection. We start by modeling the thermal pathway across a single ball-to-race pathway for a simplified geometry, an azimuthally symmetric ball in contact with a flat surface (ball-on-flat). A firs… ▽ More Ball bearings are commonly used to reduce the friction in rotating mechanical components. The present work reports improved numerical approaches to model bearing thermal conductance in the absence of convection. We start by modeling the thermal pathway across a single ball-to-race pathway for a simplified geometry, an azimuthally symmetric ball in contact with a flat surface (ball-on-flat). A first-principles approach is used to calculate the static lubricant meniscus shape using a custom-developed Python code. We apply the finite element method (FEM) to extract total thermal conductance of the lubricated ball-on-flat system. Using similar methods, we also present a three-dimensional numerical model of the lubricant meniscus in a static angular contact ball bearing section (ball-on-race). By generating thermal conductance correlations for Yovanovich's classic lubricated model, our two-dimensional multiphysics model, and our three-dimensional multiphysics model, we enable comparison of the results of all three models. To compare them, parametric studies are conducted to illustrate the effect of lubricant volume and applied load on the total thermal conductance for each model. The hierarchical methodology reported here improves both the fidelity of tribo-thermo-mechanical modeling and establishes a reference for the accuracy of commonly used geometric approximations for thermal transport in spacecraft ball bearings. △ Less

Submitted 3 March, 2025; v1 submitted 23 February, 2025; originally announced February 2025.

Comments: 40 pages, 16 figures

Journal ref: ASME J. Heat Mass Transfer. Oct 2026, 148(10): 101401

Mapping and Execution of Nested Loops on Processor Arrays: CGRAs vs. TCPAs

Authors: Dominik Walter, Marita Halm, Daniel Seidel, Indrayudh Ghosh, Christian Heidorn, Frank Hannig, Jürgen Teich

Abstract: Increasing demands for computing power also propel the need for energy-efficient SoC accelerator architectures. One class of such accelerators are so-called processor arrays, which typically integrate a two-dimensional mesh of interconnected processing elements~(PEs). Such arrays are specifically designed to accelerate the execution of multidimensional nested loops by exploiting the intrinsic para… ▽ More Increasing demands for computing power also propel the need for energy-efficient SoC accelerator architectures. One class of such accelerators are so-called processor arrays, which typically integrate a two-dimensional mesh of interconnected processing elements~(PEs). Such arrays are specifically designed to accelerate the execution of multidimensional nested loops by exploiting the intrinsic parallelism of loops. Moreover, for mapping a given loop nest application, two opposed mapping methods have emerged: Operation-centric and iteration-centric. Both differ in the granularity of the mapping. The operation-centric approach maps individual operations to the PEs of the array, while the iteration-centric approach maps entire tiles of iterations to each PE. The operation-centric approach is applied predominantly for processor arrays often referred to as Coarse-Grained Reconfigurable Arrays~(CGRAs), while processor arrays supporting an iteration-centric approach are referred to as Tightly-Coupled Processor Arrays~(TCPAs) in the following. This work provides a comprehensive comparison of both approaches and related architectures by evaluating their respective benefits and trade-offs. ... △ Less

Submitted 17 February, 2025; originally announced February 2025.

Numerical Model of Thermionic- and Photo- emission Electron Heat Spreading

Authors: Indronil Ghosh, Timothy S. Fisher

Abstract: Thermionic emission has been exploited to give rise to the theory of thermionic cooling also known as electron transpiration cooling, which can potentially serve as a powerful and engineerable cooling mode for hypersonic leading edges that can reach temperatures exceeding 2000 °C. However, the contribution to this cooling mode by photoexcited electrons remains relatively unexplored. Here, we prese… ▽ More Thermionic emission has been exploited to give rise to the theory of thermionic cooling also known as electron transpiration cooling, which can potentially serve as a powerful and engineerable cooling mode for hypersonic leading edges that can reach temperatures exceeding 2000 °C. However, the contribution to this cooling mode by photoexcited electrons remains relatively unexplored. Here, we present a numerical model of thermionic emission and photoemission driven cooling and heat spreading, examining the trajectories of electrons emitted based on a random energy model within a prescribed potential space. By simulating surfaces with two different temperature gradients, and imposing potential spaces derived for Cartesian, cylindrical, and spherical coordinate systems, we demonstrate that heat spreading can be significant for temperature gradients on a length scale comparable to the electron spreading distance. Additionally, by testing two different leading edge radii, we find that heat spreading affects a larger percentage of surface area for a smaller leading edge radius. △ Less

Submitted 23 February, 2025; v1 submitted 11 February, 2025; originally announced February 2025.

Comments: 21 pages, 13 figures

New Plasma Sheath Potential Solutions in Cylindrical and Spherical Coordinates

Authors: Indronil Ghosh, Timothy S. Fisher

Abstract: Leading edges of hypersonic vehicles can reach temperatures greater than 2000 °C, and radii of curvature smaller than 1 cm, at which thermionic emission (also known as electron transpiration) can play a significant role in cooling the leading edge alongside other heat transfer modes such as convection and radiation. Existing theoretical analyses of thermionic cooling with space-charge effects at a… ▽ More Leading edges of hypersonic vehicles can reach temperatures greater than 2000 °C, and radii of curvature smaller than 1 cm, at which thermionic emission (also known as electron transpiration) can play a significant role in cooling the leading edge alongside other heat transfer modes such as convection and radiation. Existing theoretical analyses of thermionic cooling with space-charge effects at a leading edge are limited to one-dimensional (1D), analytical and numerical models that do not capture the influences of geometric curvature of the leading edge or temperature gradients along the leading edge. The key to understanding space-charge effects is development of the plasma sheath potential, and to that end we demonstrate a generalized methodology to calculate the sheath potential space in 1D Cartesian, cylindrical, and spherical coordinate systems. We accomplish this by extending Takamura's approach beyond the Cartesian system, and motivate sheath formation conditions for potential sheathes with and without a virtual cathode similar in nature to how Bohm originally presented his criterion of minimum Mach number for a valid 1D Cartesian sheath. By observing for what parameter inputs we satisfy the sheath formation conditions, we illustrate parameter spaces of minimum Mach number, potential derivative at the wall, and net current, for each coordinate system and for two different input work functions; we also show example potential spaces for each coordinate system. With our numerical approach, generalized to multiple coordinate systems, we enable computationally efficient and higher fidelity analysis of thermionic emission with space-charge effects for more realistic system geometries. △ Less

Submitted 23 February, 2025; v1 submitted 11 February, 2025; originally announced February 2025.

Comments: 49 pages, 29 figures

Robust chaos in $\mathbb{R}^n$

Authors: Indranil Ghosh, David J. W. Simpson

Abstract: We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions correspond to an open set within the space of all such maps, allow all $n \ge 2$, and allow all possible values for the unstable eigenvalues in the limit that all s… ▽ More We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions correspond to an open set within the space of all such maps, allow all $n \ge 2$, and allow all possible values for the unstable eigenvalues in the limit that all stable eigenvalues tend to zero. To prove an attractor exists we use the stable manifold of a fixed point to construct a trapping region; to prove the attractor is chaotic we use the unstable directions to construct an invariant expanding cone for the derivatives of the pieces of the map. We also show the chaotic attractor is persistent under nonlinear perturbations, thus when such an attractor is created locally in a border-collision bifurcation of a general piecewise-smooth system, it persists and is chaotic for an interval of parameter values beyond the bifurcation. △ Less

Submitted 29 October, 2024; originally announced October 2024.

MSC Class: 37G35; 39A28

Unsupervised Domain Adaptation for Action Recognition via Self-Ensembling and Conditional Embedding Alignment

Authors: Indrajeet Ghosh, Garvit Chugh, Abu Zaher Md Faridee, Nirmalya Roy

Abstract: Recent advancements in deep learning-based wearable human action recognition (wHAR) have improved the capture and classification of complex motions, but adoption remains limited due to the lack of expert annotations and domain discrepancies from user variations. Limited annotations hinder the model's ability to generalize to out-of-distribution samples. While data augmentation can improve generali… ▽ More Recent advancements in deep learning-based wearable human action recognition (wHAR) have improved the capture and classification of complex motions, but adoption remains limited due to the lack of expert annotations and domain discrepancies from user variations. Limited annotations hinder the model's ability to generalize to out-of-distribution samples. While data augmentation can improve generalizability, unsupervised augmentation techniques must be applied carefully to avoid introducing noise. Unsupervised domain adaptation (UDA) addresses domain discrepancies by aligning conditional distributions with labeled target samples, but vanilla pseudo-labeling can lead to error propagation. To address these challenges, we propose $μ$DAR, a novel joint optimization architecture comprised of three functions: (i) consistency regularizer between augmented samples to improve model classification generalizability, (ii) temporal ensemble for robust pseudo-label generation and (iii) conditional distribution alignment to improve domain generalizability. The temporal ensemble works by aggregating predictions from past epochs to smooth out noisy pseudo-label predictions, which are then used in the conditional distribution alignment module to minimize kernel-based class-wise conditional maximum mean discrepancy ($k$CMMD) between the source and target feature space to learn a domain invariant embedding. The consistency-regularized augmentations ensure that multiple augmentations of the same sample share the same labels; this results in (a) strong generalization with limited source domain samples and (b) consistent pseudo-label generation in target samples. The novel integration of these three modules in $μ$DAR results in a range of $\approx$ 4-12% average macro-F1 score improvement over six state-of-the-art UDA methods in four benchmark wHAR datasets △ Less

Submitted 22 October, 2024; originally announced October 2024.

Comments: This work has been accepted to the Proceedings of the IEEE International Conference on Data Mining, 2024

Sample-Efficient Geometry Reconstruction from Euclidean Distances using Non-Convex Optimization

Authors: Ipsita Ghosh, Abiy Tasissa, Christian Kümmerle

Abstract: The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this paper, we aim to solve this problem given a minimal number of distance samples. To this end, we leverage continuous and non-convex rank minimization formulations of… ▽ More The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this paper, we aim to solve this problem given a minimal number of distance samples. To this end, we leverage continuous and non-convex rank minimization formulations of the problem and establish a local convergence guarantee for a variant of iteratively reweighted least squares (IRLS), which applies if a minimal random set of observed distances is provided. As a technical tool, we establish a restricted isometry property (RIP) restricted to a tangent space of the manifold of symmetric rank-$r$ matrices given random Euclidean distance measurements, which might be of independent interest for the analysis of other non-convex approaches. Furthermore, we assess data efficiency, scalability and generalizability of different reconstruction algorithms through numerical experiments with simulated data as well as real-world data, demonstrating the proposed algorithm's ability to identify the underlying geometry from fewer distance samples compared to the state-of-the-art. △ Less

Submitted 22 October, 2024; originally announced October 2024.

On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings

Authors: Anjana S. Nair, Indranil Ghosh, Hammed O. Fatoyinbo, Sishu S. Muni

Abstract: We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze o… ▽ More We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter. △ Less

Submitted 9 May, 2024; originally announced May 2024.

Comments: 16 pages, 11 figures

Dynamical properties of a small heterogeneous chain network of neurons in discrete time

Authors: Indranil Ghosh, Anjana S. Nair, Hammed Olawale Fatoyinbo, Sishu Shankar Muni

Abstract: We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analy… ▽ More We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy. △ Less

Submitted 12 May, 2024; v1 submitted 9 May, 2024; originally announced May 2024.

Comments: 40 pages, 15 figures

The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps

Authors: Indranil Ghosh, Robert I. McLachlan, David J. W. Simpson

Abstract: We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of this paper is to determine where and how this attractor undergoes bifurcations. We explore the bifurcation structure numerically by using Eckstein's greatest c… ▽ More We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of this paper is to determine where and how this attractor undergoes bifurcations. We explore the bifurcation structure numerically by using Eckstein's greatest common divisor algorithm to estimate from sample orbits the number of connected components in the attractor. Where the map is orientation-preserving the numerical results agree with formal results obtained previously through renormalisation. Where the map is orientation-reversing or non-invertible the same renormalisation scheme appears to generate the bifurcation boundaries, but here we need to account for the possibility of some stable low-period solutions. Also the attractor can be destroyed in novel heteroclinic bifurcations (boundary crises) that do not correspond to simple algebraic constraints on the parameters. Overall the results reveal a broadly similar component-doubling bifurcation structure in the orientation-reversing and non-invertible settings, but with some additional complexities. △ Less

Submitted 7 February, 2024; originally announced February 2024.

On discriminating between Libby-Novick generalized beta and Kumaraswamy distributions: theory and methods

Authors: Indranil Ghosh

Abstract: In fitting a continuous bounded data, the generalized beta (and several variants of this distribution) and the two-parameter Kumaraswamy (KW) distributions are the two most prominent univariate continuous distributions that come to our mind. There are some common features between these two rival probability models and to select one of them in a practical situation can be of great interest. Consequ… ▽ More In fitting a continuous bounded data, the generalized beta (and several variants of this distribution) and the two-parameter Kumaraswamy (KW) distributions are the two most prominent univariate continuous distributions that come to our mind. There are some common features between these two rival probability models and to select one of them in a practical situation can be of great interest. Consequently, in this paper, we discuss various methods of selection between the generalized beta proposed by Libby and Novick (1982) (LNGB) and the KW distributions, such as the criteria based on probability of correct selection which is an improvement over the likelihood ratio statistic approach, and also based on pseudo-distance measures. We obtain an approximation for the probability of correct selection under the hypotheses HLNGB and HKW , and select the model that maximizes it. However, our proposal is more appealing in the sense that we provide the comparison study for the LNGB distribution that subsumes both types of classical beta and exponentiated generators (see, for details, Cordeiro et al. 2014; Libby and Novick 1982) which can be a natural competitor of a two-parameter KW distribution in an appropriate scenario. △ Less

Submitted 29 December, 2023; originally announced January 2024.

Comments: 11 pages

MSC Class: 60 E; 62F

Journal ref: Research in Statistics (2023)

Anticipating dengue outbreaks using a novel hybrid ARIMA-ARNN model with exogenous variables

Authors: I. Ghosh, S. Gupta, S. Rana

Abstract: Dengue incidence forecasting using hybrid models has been surging in the data rich world. Hybridization of statistical time series forecasting models and machine learning models are explored for dengue forecasting with different degrees of success. In this paper, we propose a multivariate expansion of the hybrid ARIMA-ARNN model. The main motivation is to propose a novel hybridization and apply it… ▽ More Dengue incidence forecasting using hybrid models has been surging in the data rich world. Hybridization of statistical time series forecasting models and machine learning models are explored for dengue forecasting with different degrees of success. In this paper, we propose a multivariate expansion of the hybrid ARIMA-ARNN model. The main motivation is to propose a novel hybridization and apply it to dengue outbreak prediction. The asymptotic stationarity of the proposed model has been established. We check the forecasting capability and robustness of the forecasts through numerical experiments. State-of-the-art forecasting models for multivariate time series data are compared with the proposed model using accuracy metrics. Dengue incidence data from San Juan and Iquitos are utilized along with rainfall as an exogenous variable. Results indicate that the proposed model improves the ARIMAX forecasts in some situations and closely follows it otherwise. The theoretical as well as experimental results reinforce that the proposed model has the potential to act as a candidate for early warning of dengue outbreaks. The proposed model can be readily generalized to incorporate more exogenous variables and also applied to other time series forecasting problems wherever exogenous variable(s) are available. △ Less

Submitted 23 December, 2023; originally announced December 2023.

Algebraic aspects and functoriality of the set of affiliated operators

Authors: Indrajit Ghosh, Soumyashant Nayak

Abstract: In this article, we aim to provide a satisfactory algebraic description of the set of affiliated operators for von Neumann algebras. Let $\mathscr{M}$ be a von Neumann algebra acting on a Hilbert space $\mathcal{H}$, and let $\mathscr{M}_{\text{aff}}$ denote the set of unbounded operators of the form $T = AB^{\dagger}$ for $A, B \in \mathscr{M}$ with $\ker(B)\subseteq\ker(A)$ , where… ▽ More In this article, we aim to provide a satisfactory algebraic description of the set of affiliated operators for von Neumann algebras. Let $\mathscr{M}$ be a von Neumann algebra acting on a Hilbert space $\mathcal{H}$, and let $\mathscr{M}_{\text{aff}}$ denote the set of unbounded operators of the form $T = AB^{\dagger}$ for $A, B \in \mathscr{M}$ with $\ker(B)\subseteq\ker(A)$ , where $(\cdot)^{\dagger}$ denotes the Kaufman inverse. We show that $\mathscr{M}_{\text{aff}}$ is closed under product, sum, Kaufman-inverse and adjoint, and has the structure of a right near-semiring; Moreover, the above quotient representation of an operator in $\mathscr{M}_{\text{aff}}$ is essentially unique. The Murray-von Neumann affiliated operators for $\mathscr{M}$ turn out to be precisely the closed operators in $\mathscr{M}_{\text{aff}}$. Let $Φ$ be a unital normal homomorphism between represented von Neumann algebras $(\mathscr{M}; \mathcal{H})$ and $(\mathscr{N}; \mathcal{K})$. With the help of the quotient representation, we obtain a canonical extension of $Φ$ to a mapping $Φ_{\text{aff}} : \mathscr{M}_{\text{aff}} \to \mathscr{N}_{\text{aff}}$ which respects sum, product, Kaufman-inverse, and adjoint. Thus $\mathscr{M}_{\text{aff}}$ is intrinsically associated with $\mathscr{M}$ and transforms functorially as we change representations of $\mathscr{M}$. Furthermore, $Φ_{\text{aff}}$ preserves operator properties such as being symmetric, or positive, or accretive, or sectorial, or self-adjoint, or normal, and also preserves the Friedrichs and Krein-von Neumann extensions of densely-defined closed positive operators. As a proof of concept, we transfer some well-known results about closed unbounded operators to the setting of closed affiliated operators for properly infinite von Neumann algebras, via `abstract nonsense'. △ Less

Submitted 31 August, 2024; v1 submitted 20 November, 2023; originally announced November 2023.

Comments: 39 pages. Accepted for publication in IMRN

Report number: rnae203 MSC Class: 46L10 (Primary) 47C15; 47L60; 46M15; 47B02 (Secondary)

Journal ref: International Mathematics Research Notices, 2024

A Tale of Two Cultures: Comparing Interpersonal Information Disclosure Norms on Twitter

Authors: Mainack Mondal, Anju Punuru, Tyng-Wen Scott Cheng, Kenneth Vargas, Chaz Gundry, Nathan S Driggs, Noah Schill, Nathaniel Carlson, Josh Bedwell, Jaden Q Lorenc, Isha Ghosh, Yao Li, Nancy Fulda, Xinru Page

Abstract: We present an exploration of cultural norms surrounding online disclosure of information about one's interpersonal relationships (such as information about family members, colleagues, friends, or lovers) on Twitter. The literature identifies the cultural dimension of individualism versus collectivism as being a major determinant of offline communication differences in terms of emotion, topic, and… ▽ More We present an exploration of cultural norms surrounding online disclosure of information about one's interpersonal relationships (such as information about family members, colleagues, friends, or lovers) on Twitter. The literature identifies the cultural dimension of individualism versus collectivism as being a major determinant of offline communication differences in terms of emotion, topic, and content disclosed. We decided to study whether such differences also occur online in context of Twitter when comparing tweets posted in an individualistic (U.S.) versus a collectivist (India) society. We collected more than 2 million tweets posted in the U.S. and India over a 3 month period which contain interpersonal relationship keywords. A card-sort study was used to develop this culturally-sensitive saturated taxonomy of keywords that represent interpersonal relationships (e.g., ma, mom, mother). Then we developed a high-accuracy interpersonal disclosure detector based on dependency-parsing (F1-score: 86%) to identify when the words refer to a personal relationship of the poster (e.g., "my mom" as opposed to "a mom"). This allowed us to identify the 400K+ tweets in our data set which actually disclose information about the poster's interpersonal relationships. We used a mixed methods approach to analyze these tweets (e.g., comparing the amount of joy expressed about one's family) and found differences in emotion, topic, and content disclosed between tweets from the U.S. versus India. Our analysis also reveals how a combination of qualitative and quantitative methods are needed to uncover these differences; Using just one or the other can be misleading. This study extends the prior literature on Multi-Party Privacy and provides guidance for researchers and designers of culturally-sensitive systems. △ Less

Submitted 26 September, 2023; originally announced September 2023.

Comments: This work will be presented at the 26th ACM Conference on Computer-Supported Cooperative Work and Social Computing (CSCW 2023). This paper will also be published in The Proceedings of the ACM on Human Computer Interaction

Robust chaos in orientation-reversing and non-invertible two-dimensional piecewise-linear maps

Authors: Indranil Ghosh, Robert I. McLachlan, David J. W. Simpson

Abstract: This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applications. The normal form was recently shown to exhibit a chaotic attractor throughout an open region of parameter space. This was achieved by constructing a trapping region in phase space and an invariant expanding cone i… ▽ More This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applications. The normal form was recently shown to exhibit a chaotic attractor throughout an open region of parameter space. This was achieved by constructing a trapping region in phase space and an invariant expanding cone in tangent space, but only allowed parameter combinations for which the normal form is invertible and orientation-preserving. This paper generalises the construction to include the non-invertible and orientation-reversing cases. This provides a more complete and unified picture of robust chaos by revealing its presence to be disassociated from the global topological properties of the map. We identify a region of parameter space in which the map exhibits robust chaos, and show that part of the boundary of this region consists of bifurcation points at which the chaotic attractor is destroyed. △ Less

Submitted 11 July, 2023; originally announced July 2023.

MSC Class: Primary: 37G35; Secondary: 39A28

HeteroEdge: Addressing Asymmetry in Heterogeneous Collaborative Autonomous Systems

Authors: Mohammad Saeid Anwar, Emon Dey, Maloy Kumar Devnath, Indrajeet Ghosh, Naima Khan, Jade Freeman, Timothy Gregory, Niranjan Suri, Kasthuri Jayaraja, Sreenivasan Ramasamy Ramamurthy, Nirmalya Roy

Abstract: Gathering knowledge about surroundings and generating situational awareness for IoT devices is of utmost importance for systems developed for smart urban and uncontested environments. For example, a large-area surveillance system is typically equipped with multi-modal sensors such as cameras and LIDARs and is required to execute deep learning algorithms for action, face, behavior, and object recog… ▽ More Gathering knowledge about surroundings and generating situational awareness for IoT devices is of utmost importance for systems developed for smart urban and uncontested environments. For example, a large-area surveillance system is typically equipped with multi-modal sensors such as cameras and LIDARs and is required to execute deep learning algorithms for action, face, behavior, and object recognition. However, these systems face power and memory constraints due to their ubiquitous nature, making it crucial to optimize data processing, deep learning algorithm input, and model inference communication. In this paper, we propose a self-adaptive optimization framework for a testbed comprising two Unmanned Ground Vehicles (UGVs) and two NVIDIA Jetson devices. This framework efficiently manages multiple tasks (storage, processing, computation, transmission, inference) on heterogeneous nodes concurrently. It involves compressing and masking input image frames, identifying similar frames, and profiling devices to obtain boundary conditions for optimization.. Finally, we propose and optimize a novel parameter split-ratio, which indicates the proportion of the data required to be offloaded to another device while considering the networking bandwidth, busy factor, memory (CPU, GPU, RAM), and power constraints of the devices in the testbed. Our evaluations captured while executing multiple tasks (e.g., PoseNet, SegNet, ImageNet, DetectNet, DepthNet) simultaneously, reveal that executing 70% (split-ratio=70%) of the data on the auxiliary node minimizes the offloading latency by approx. 33% (18.7 ms/image to 12.5 ms/image) and the total operation time by approx. 47% (69.32s to 36.43s) compared to the baseline configuration (executing on the primary node). △ Less

Submitted 4 May, 2023; originally announced May 2023.

Domain Adaptation for Inertial Measurement Unit-based Human Activity Recognition: A Survey

Authors: Avijoy Chakma, Abu Zaher Md Faridee, Indrajeet Ghosh, Nirmalya Roy

Abstract: Machine learning-based wearable human activity recognition (WHAR) models enable the development of various smart and connected community applications such as sleep pattern monitoring, medication reminders, cognitive health assessment, sports analytics, etc. However, the widespread adoption of these WHAR models is impeded by their degraded performance in the presence of data distribution heterogene… ▽ More Machine learning-based wearable human activity recognition (WHAR) models enable the development of various smart and connected community applications such as sleep pattern monitoring, medication reminders, cognitive health assessment, sports analytics, etc. However, the widespread adoption of these WHAR models is impeded by their degraded performance in the presence of data distribution heterogeneities caused by the sensor placement at different body positions, inherent biases and heterogeneities across devices, and personal and environmental diversities. Various traditional machine learning algorithms and transfer learning techniques have been proposed in the literature to address the underpinning challenges of handling such data heterogeneities. Domain adaptation is one such transfer learning techniques that has gained significant popularity in recent literature. In this paper, we survey the recent progress of domain adaptation techniques in the Inertial Measurement Unit (IMU)-based human activity recognition area, discuss potential future directions. △ Less

Submitted 6 April, 2023; originally announced April 2023.

On classical and Bayesian inference for bivariate Poisson conditionals distributions: Theory, methods and applications

Authors: Barry C. Arnold, Indranil Ghosh

Abstract: Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an important role in modeling such data. In this article, we consider the inferential aspect of a bivariate Poisson conditionals distribution for which both the conditiona… ▽ More Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an important role in modeling such data. In this article, we consider the inferential aspect of a bivariate Poisson conditionals distribution for which both the conditionals are Poisson but the marginals are typically non-Poisson. It has Poisson marginals only in the case of independence. It appears that a simple iterative procedure under the maximum likelihood method performs quite well as compared with other numerical subroutines, as one would expect in such a case where the MLEs are not available in closed form. In the Bayesian paradigm, both conjugate priors and non-conjugate priors have been utilized and a comparison study has been made via a simulation study. For illustrative purposes, a real-life data set is re-analyzed to exhibit the utility of the proposed two methods of estimation, one under the frequentist approach and the other under the Bayesian paradigm. △ Less

Submitted 10 January, 2023; originally announced January 2023.

Comments: 20 pages

MSC Class: 60E; 62F

Bivariate binomial conditionals distributions with positive and negative correlations: A statistical study

Authors: Indranil Ghosh, Filipe Marques, Subrata Chakraborty

Abstract: In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of negative correlation, marginal over-dispersion, distribution… ▽ More In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of negative correlation, marginal over-dispersion, distribution of sum and conditional given the sum are also derived. The distribution is shown to be a member of the multi-parameter exponential family and some natural but useful consequences are also outlined. The proposed distribution tends to a recently investigated conditional Poisson distribution studied by Ghosh et al. (2020). Finally, the distribution is fitted to two bivariate count data sets with an inherent negative correlation to illustrate its suitability. △ Less

Submitted 8 January, 2023; originally announced January 2023.

Comments: 19 pages, 5 figures

MSC Class: 60E; 62F

An ensemble neural network approach to forecast Dengue outbreak based on climatic condition

Authors: Madhurima Panja, Tanujit Chakraborty, Sk Shahid Nadim, Indrajit Ghosh, Uttam Kumar, Nan Liu

Abstract: Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control interven… ▽ More Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control intervention-related decisions. Forecasts routinely provide critical information for dangerous epidemic events. However, the available forecasting models (e.g., weather-driven mechanistic, statistical time series, and machine learning models) lack a clear understanding of different components to improve prediction accuracy and often provide unstable and unreliable forecasts. This study proposes an ensemble wavelet neural network with exogenous factor(s) (XEWNet) model that can produce reliable estimates for dengue outbreak prediction for three geographical regions, namely San Juan, Iquitos, and Ahmedabad. The proposed XEWNet model is flexible and can easily incorporate exogenous climate variable(s) confirmed by statistical causality tests in its scalable framework. The proposed model is an integrated approach that uses wavelet transformation into an ensemble neural network framework that helps in generating more reliable long-term forecasts. The proposed XEWNet allows complex non-linear relationships between the dengue incidence cases and rainfall; however, mathematically interpretable, fast in execution, and easily comprehensible. The proposal's competitiveness is measured using computational experiments based on various statistical metrics and several statistical comparison tests. In comparison with statistical, machine learning, and deep learning methods, our proposed XEWNet performs better in 75% of the cases for short-term and long-term forecasting of dengue incidence. △ Less

Submitted 19 December, 2022; v1 submitted 16 December, 2022; originally announced December 2022.

Towards Practical Explainability with Cluster Descriptors

Authors: Xiaoyuan Liu, Ilya Tyagin, Hayato Ushijima-Mwesigwa, Indradeep Ghosh, Ilya Safro

Abstract: With the rapid development of machine learning, improving its explainability has become a crucial research goal. We study the problem of making the clusters more explainable by investigating the cluster descriptors. Given a set of objects $S$, a clustering of these objects $π$, and a set of tags $T$ that have not participated in the clustering algorithm. Each object in $S$ is associated with a sub… ▽ More With the rapid development of machine learning, improving its explainability has become a crucial research goal. We study the problem of making the clusters more explainable by investigating the cluster descriptors. Given a set of objects $S$, a clustering of these objects $π$, and a set of tags $T$ that have not participated in the clustering algorithm. Each object in $S$ is associated with a subset of $T$. The goal is to find a representative set of tags for each cluster, referred to as the cluster descriptors, with the constraint that these descriptors we find are pairwise disjoint, and the total size of all the descriptors is minimized. In general, this problem is NP-hard. We propose a novel explainability model that reinforces the previous models in such a way that tags that do not contribute to explainability and do not sufficiently distinguish between clusters are not added to the optimal descriptors. The proposed model is formulated as a quadratic unconstrained binary optimization problem which makes it suitable for solving on modern optimization hardware accelerators. We experimentally demonstrate how a proposed explainability model can be solved on specialized hardware for accelerating combinatorial optimization, the Fujitsu Digital Annealer, and use real-life Twitter and PubMed datasets for use cases. △ Less

Submitted 20 October, 2022; v1 submitted 17 October, 2022; originally announced October 2022.

Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds

Authors: Dominique Attali, Hana Dal Poz Kouřimská, Christopher Fillmore, Ishika Ghosh, André Lieutier, Elizabeth Stephenson, Mathijs Wintraecken

Abstract: In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work, Niyogi, Smale, and Weinberger studied samples of $C^2$ manifolds with positive reach embedded in $\mathbb{R}^d$. We extend their results in the following ways: In the first part of our paper we consider both manifolds o… ▽ More In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work, Niyogi, Smale, and Weinberger studied samples of $C^2$ manifolds with positive reach embedded in $\mathbb{R}^d$. We extend their results in the following ways: In the first part of our paper we consider both manifolds of positive reach -- a more general setting than $C^2$ manifolds -- and sets of positive reach embedded in $\mathbb{R}^d$. The sample $P$ of such a set $\mathcal{S}$ does not have to lie directly on it. Instead, we assume that the two one-sided Hausdorff distances -- $\varepsilon$ and $δ$ -- between $P$ and $\mathcal{S}$ are bounded. We provide explicit bounds in terms of $\varepsilon$ and $ δ$, that guarantee that there exists a parameter $r$ such that the union of balls of radius $r$ centred at the sample $P$ deformation-retracts to $\mathcal{S}$. In the second part of our paper we study homotopy learning in a significantly more general setting -- we investigate sets of positive reach and submanifolds of positive reach embedded in a \emph{Riemannian manifold with bounded sectional curvature}. To this end we introduce a new version of the reach in the Riemannian setting inspired by the cut locus. Yet again, we provide tight bounds on $\varepsilon$ and $δ$ for both cases (submanifolds as well as sets of positive reach), exhibiting the tightness by an explicit construction. △ Less

Submitted 29 February, 2024; v1 submitted 21 June, 2022; originally announced June 2022.

Comments: 75 pages, 29 figures

ACM Class: I.3.5

On the analysis of a time varying noise-modulated heterogeneous coupled network of Chialvo neurons under the influence of electromagnetic flux

Authors: Indranil Ghosh, Sishu Shankar Muni, Hammed Olawale Fatoyinbo

Abstract: We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the central-peripheral and the peripheral-peripheral coupling links in the topology that not only vary in space but also in time. The variation in time is understood… ▽ More We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the central-peripheral and the peripheral-peripheral coupling links in the topology that not only vary in space but also in time. The variation in time is understood by two coupling probabilities, one for the central-peripheral connections and the other for the peripheral-peripheral connections respectively, that updates the network topology with each iteration in time. We have further reported the rich spatiotemporal patterns like two-cluster states, chimera states, traveling waves, coherent, and asynchronized states that arise throughout the network dynamics. We have also investigated the appearance of a special kind of asynchronization behavior called "solitary nodes" that have wide range of applications pertaining to real-world nervous systems. In order to characterize the behavior of the nodes under the influence of these heterogeneities, we have studied two different metrics called the "cross-correlation coefficient" and the "synchronization error". Additionally, to capture the statistical property of the network, for example, how complex the system behaves, we have also studied a measure called "sample entropy". Various two-dimensional color-coded plots are presented in the study to exhibit how these metrics/measures behave with the variation of parameters. Finally, how the nodes synchronize or asynchronize is shown via one-dimensional bifurcation diagrams of the last instance of the main dynamical variable, i.e., the state variable associated with the membrane potential, against different network parameters. △ Less

Submitted 8 June, 2022; originally announced June 2022.

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

Authors: Hammed Olawale Fatoyinbo, Sishu Shankar Muni, Indranil Ghosh, Ibrahim Olatunji Sarumi, Afeez Abidemi

Abstract: It is well-known that the electrical activities of neurons are induced by a wide variety of external factors. This work considers the effect of electromagnetic induction on improved denatured Morris-Lecar neuron model. The dependence of dynamical behaviour of the original denatured Morris-Lecar model on parameters is addressed through numerical bifurcation analysis. This allows us to explore the c… ▽ More It is well-known that the electrical activities of neurons are induced by a wide variety of external factors. This work considers the effect of electromagnetic induction on improved denatured Morris-Lecar neuron model. The dependence of dynamical behaviour of the original denatured Morris-Lecar model on parameters is addressed through numerical bifurcation analysis. This allows us to explore the changes in dynamics of the model qualitatively as parameters are varied. Then we investigate the effects of external periodic current and electromagnetic flux on the dynamical properties of the improved denatured Morris-Lecar neuron model. Different types of dynamical behaviour, ranging from regular periodic spiking to complex bursting, are found when the multiple parameters are varied simultaneously. The improved model could be applied to research where simple models are required for physiological and pathophysiological responses in neurons. △ Less

Submitted 26 February, 2022; originally announced February 2022.

MSC Class: 37C10; 37G15

Partitioning Dense Graphs with Hardware Accelerators

Authors: Xiaoyuan Liu, Hayato Ushijima-Mwesigwa, Indradeep Ghosh, Ilya Safro

Abstract: Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose optimization solvers such as Gurobi and CPLEX, a wide range of approaches have been developed. Limitations of these approaches are important to study in order to break t… ▽ More Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose optimization solvers such as Gurobi and CPLEX, a wide range of approaches have been developed. Limitations of these approaches are important to study in order to break the computational optimization barriers of this problem. As we approach the limits of Moore's law, there is now a need to explore ways of solving such problems with special-purpose hardware such as quantum computers or quantum-inspired accelerators. In this work, we experiment with solving the graph partitioning on the Fujitsu Digital Annealer (a special-purpose hardware designed for solving combinatorial optimization problems) and compare it with the existing top solvers. We demonstrate limitations of existing solvers on many dense graphs as well as those of the Digital Annealer on sparse graphs which opens an avenue to hybridize these approaches. △ Less

Submitted 21 February, 2022; v1 submitted 18 February, 2022; originally announced February 2022.

A physics-driven study of dominance space in soccer

Authors: Costas J. Efthimiou, Gregory DeCamillis, Indranil Ghosh

Abstract: In arXiv:2107.05714 the concept of the Voronoi diagram was investigated closely from a theoretical point of view. Then, a physics-driven kinematical method was introduced to produce an improved model for dominance space in soccer. Remaining faithful to the deterministic approach, we extend the original work by the introduction of (a) an asymmetric influence of the players in their surrounding area… ▽ More In arXiv:2107.05714 the concept of the Voronoi diagram was investigated closely from a theoretical point of view. Then, a physics-driven kinematical method was introduced to produce an improved model for dominance space in soccer. Remaining faithful to the deterministic approach, we extend the original work by the introduction of (a) an asymmetric influence of the players in their surrounding area, (b) the frictional forces to the players' motion, and (c) the simultaneous combination of both effects. The asymmetric influence is fairly intuitive; players have more control in the direction they are running than any other direction. The sharper the turn they must make to reach a point on the pitch, the weaker their control of that point will be. From simple kinematical laws, this effect can be quantified explicitly. For the frictional force, a portion comes from air resistance, and so will be proportional to the square of the player's speed, as is well known from fluid dynamics. There are no other external frictional forces, but, at the suggestion of biokinematics, there is an internal frictional force, relating to the consumption of energy by the muscles, which is proportional to the player's speed. Although these additions are intuitively understood, mathematically they introduce many analytical complexities. We establish exact analytical solutions of the dominance areas of the pitch by introducing a few reasonable simplifying assumptions. Given these solutions the new Voronoi diagrams are drawn for the publicly available data by Metrica Sports. In general, it is not necessary anymore for the dominance regions to be convex, they might contain holes, and may be disconnected. The fastest player may dominate points far away from the rest of the players. △ Less

Submitted 1 February, 2022; originally announced February 2022.

Comments: The article contains many computer-generated Voronoi diagrams. We have reduced the file size of the diagrams but there might be a few seconds delay to load some pages

Dynamical effects of electromagnetic flux on Chialvo neuron map: nodal and network behaviors

Authors: Sishu Shankar Muni, Hammed Olawale Fatoyinbo, Indranil Ghosh

Abstract: We consider the dynamical effects of electromagnetic flux on the discrete Chialvo neuron. It is shown that the model can exhibit rich dynamical behaviors such as multistability, firing patterns, antimonotonicity, closed invariant curves, various routes to chaos, fingered chaotic attractors. The system enters chaos via period-doubling cascades, reverse period-doubling route, antimonotonicity, via c… ▽ More We consider the dynamical effects of electromagnetic flux on the discrete Chialvo neuron. It is shown that the model can exhibit rich dynamical behaviors such as multistability, firing patterns, antimonotonicity, closed invariant curves, various routes to chaos, fingered chaotic attractors. The system enters chaos via period-doubling cascades, reverse period-doubling route, antimonotonicity, via closed invariant curve to chaos. The results were confirmed using the techniques of bifurcation diagrams, Lyapunov exponent diagram, phase portraits, basins of attraction and numerical continuation of bifurcations. Different global bifurcations are also shown to exist via numerical continuation. After understanding a single neuron model, a network of Chialvo neuron is explored. A ring-star network of Chialvo neuron is considered and different dynamical regimes such as synchronous, asynchronous, chimera states are revealed. Different continuous and piecewise continuous wavy patterns were also found during the simulations for negative coupling strengths. △ Less

Submitted 11 June, 2022; v1 submitted 10 January, 2022; originally announced January 2022.

Comments: 35 pages, 22 figures

Traffic event description based on Twitter data using Unsupervised Learning Methods for Indian road conditions

Authors: Yasaswi Sri Chandra Gandhi Kilaru, Indrajit Ghosh

Abstract: Non-recurrent and unpredictable traffic events directly influence road traffic conditions. There is a need for dynamic monitoring and prediction of these unpredictable events to improve road network management. The problem with the existing traditional methods (flow or speed studies) is that the coverage of many Indian roads is very sparse and reproducible methods to identify and describe the even… ▽ More Non-recurrent and unpredictable traffic events directly influence road traffic conditions. There is a need for dynamic monitoring and prediction of these unpredictable events to improve road network management. The problem with the existing traditional methods (flow or speed studies) is that the coverage of many Indian roads is very sparse and reproducible methods to identify and describe the events are not available. Addition of some other form of data is essential to help with this problem. This could be real-time speed monitoring data like Google Maps, Waze, etc. or social data like Twitter, Facebook, etc. In this paper, an unsupervised learning model is used to perform effective tweet classification for enhancing Indian traffic data. The model uses word-embeddings to calculate semantic similarity and achieves a test score of 94.7%. △ Less

Submitted 23 December, 2021; originally announced January 2022.

Comments: 13th International (Online) Conference on Transportation Planning and Implementation Methodologies for Developing Countries