arXiv subjects

Souvik Roy

Publications and source records attributed to Souvik Roy.

At least 55 records · Page 3Linked to original sources

arXiv2023

Ergodicity of a generalized probabilistic cellular automaton with parity-based neighbourhoods

We study a one-dimensional generalized probabilistic cellular automaton $E_{p, q}$ with universe $\mathbb Z$, alphabet $\mathcal A = \{0, 1\}$, parameters $p$ and $q$ such that $0 < p+q \leq 1$ and two neighbourhoods $\mathcal N_0 = \{0, 1\}$ and $\mathcal N = \{1, 2\}$. The state $E_{p, q} η(x)$ of any $x \in \mathbb Z$ under the application of $E_{p, q}$ is a random variable whose probability distribution depends on the states $η(x + y)$ for $y \in \mathcal N_i$ where $i$ has the same parity as $x$. We establish ergodicity of this GPCA for various ranges of values of $p$ and $q$ via its connection with a suitable percolation game on a two-dimensional lattice. For these same ranges of values of $p$ and $q$, we show that the above-mentioned game has probability $0$ of resulting in a draw.

math.PR↗

arXiv2023

Learning end-to-end inversion of circular Radon transforms in the partial radial setup

We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value decomposition-based method, which is the only traditional algorithm available to solve this problem, leads to severe artifacts which renders the reconstructed field as unusable. With the objective of overcoming this computational bottleneck, we train a ResBlock based U-Net to recover the inferred field that directly operates on the measured data. Numerical results with augmented Shepp-Logan phantoms, in the presence of noisy full and limited view data, demonstrate the superiority of the proposed algorithm.

cs.LG↗

arXiv2023

A Time-Efficient, Data Driven Modelling Approach For Predicting The Geomagnetic Impact of Coronal Mass Ejections

To understand the global-scale physical processes behind coronal mass ejection (CME)-driven geomagnetic storms and predict their intensity as a space weather forecasting measure, we develop an interplanetary CME flux rope-magnetosphere interaction module using 3D magnetohydrodynamics. The simulations adequately describe ICME-forced dynamics of the magnetosphere including the imposed magnetotail torsion. These interactions also result in induced currents which is used to calculate the geomagnetic perturbation. Through a suitable calibration, we estimate a proxy of geoeffectiveness -- the Storm Intensity index (STORMI) -- that compares well with the Dst/SYM-H Index. Simulated impacts of two contrasting coronal mass ejections quantified by the STORMI index exhibit a high linear correlation with the corresponding Dst and SYM-H indices. Our approach is relatively simple, has fewer parameters to be fine-tuned, is time-efficient compared to complex fluid-kinetic methods. Furthermore, we demonstrate that flux rope erosion does not significantly affect our results. Thus our method has the potential to significantly extend the time window for predictability -- an outstanding challenge in geospace environment forecasting -- if early predictions of near-Earth CME flux rope structures based on near-Sun observations are available as inputs. This study paves the way for early warnings based on operational predictions of CME-driven geomagnetic storms.

astro-ph.SR↗

arXiv2023

Phase transition in percolation games on rooted Galton-Watson trees

We study the bond percolation game and the site percolation game on the rooted Galton-Watson tree $T_χ$ with offspring distribution $χ$. We obtain the probabilities of win, loss and draw for each player in terms of the fixed points of functions that involve the probability generating function $G$ of $χ$, and the parameters $p$ and $q$. Here, $p$ is the probability with which each edge (respectively vertex) of $T_χ$ is labeled a trap in the bond (respectively site) percolation game, and $q$ is the probability with which each edge (respectively vertex) of $T_χ$ is labeled a target in the bond (respectively site) percolation game. We obtain a necessary and sufficient condition for the probability of draw to be $0$ in each game, and we examine how this condition simplifies to yield very precise phase transition results when $χ$ is Binomial$(d,π)$, Poisson$(λ)$, or Negative Binomial$(r,π)$, or when $χ$ is supported on $\{0,d\}$ for some $d \in \mathbb{N}$, $d \geqslant 2$. It is fascinating to note that, while all other specific classes of offspring distributions we consider in this paper exhibit phase transition phenomena as the parameter-pair $(p,q)$ varies, the probability that the bond percolation game results in a draw remains $0$ for all values of $(p,q)$ when $χ$ is Geometric$(π)$, for all $0 < π\leqslant 1$. By establishing a connection between these games and certain finite state probabilistic tree automata on rooted $d$-regular trees, we obtain a precise description of the regime (in terms of $p$, $q$ and $d$) in which these automata exhibit ergodicity or weak spatial mixing.

math.PR↗

arXiv2023

The spread of an epidemic: a game-theoretic approach

We introduce and study a model stemming from game theory for the spread of an epidemic throughout a given population. Each agent is allowed to choose an action whose value dictates to what extent they limit their social interactions, if at all. Each of them is endowed with a certain amount of immunity such that if the viral risk/exposure is more than that they get infected. We consider a discrete-time stochastic process where, at the beginning of each epoch, a randomly chosen agent is allowed to update their action, which they do with the aim of maximizing a utility function that is a function of the state in which the process is currently in. The state itself is determined by the subset of infected agents at the beginning of that epoch, and the most recent action profile of all the agents. Our main results are concerned with the limiting distributions of both the cardinality of the subset of infected agents and the action profile as time approaches infinity, considered under various settings (such as the initial action profile we begin with, the value of each agent's immunity etc.). We also provide some simulations to show that the final asymptotic distributions for the cardinality of infected set are almost always achieved within the first few epochs.

math.PR↗

arXiv2023

Regularized Bayesian best response learning in finite games

We introduce the notion of regularized Bayesian best response (RBBR) learning dynamic in heterogeneous population games. We obtain such a dynamic via perturbation by an arbitrary lower semicontinuous, strongly convex regularizer in Bayesian population games with finitely many strategies. We provide a sufficient condition for the existence of rest points of the RBBR learning dynamic, and hence the existence of regularized Bayesian equilibrium in Bayesian population games. These equilibria are shown to approximate the original Bayesian equilibria for vanishingly small perturbations. We also explore the fundamental properties of the RBBR learning dynamic, which includes the existence of unique continuous solutions from arbitrary initial conditions, as well as the continuity of the solution trajectories thus obtained with respect to the initial conditions. Finally, as application the the theory we introduce the notions of Bayesian potential and Bayesian negative semidefinite games and provide convergence results for such games.

math.OC↗

arXiv2022

Optimal personalized therapies in colon-cancer induced immune response using a Fokker-Planck framework

In this paper, a new stochastic framework to determine optimal combination therapies in colon cancer-induced immune response is presented. The dynamics of colon cancer is described through an Itö stochastic process, whose probability density function evolution is governed by the Fokker-Planck equation. An open-loop control optimization problem is proposed to determine the optimal combination therapies. Numerical results with combination therapies comprising of the chemotherapy drug \ind{Doxorubicin} and immunotherapy drug IL-2 validate the proposed framework.

math.OC↗

arXiv2022

On a class of probabilistic cellular automata with size-$3$ neighbourhood and their applications in percolation games

Different versions of percolation games on $\mathbb{Z}^{2}$, with parameters $p$ and $q$ that indicate, respectively, the probability with which a site in $\mathbb{Z}^{2}$ is labeled a trap and the probability with which it is labeled a target, are shown to have probability $0$ of culminating in draws when $p+q > 0$. We show that, for fixed $p$ and $q$, the probability of draw in each of these games is $0$ if and only if a certain $1$-dimensional probabilistic cellular automaton (PCA) $F_{p,q}$ with a size-$3$ neighbourhood is ergodic. This allows us to conclude that $F_{p,q}$ is ergodic whenever $p+q > 0$, thereby rigorously establishing ergodicity for a considerable class of PCAs.

math.PR↗

arXiv2022

Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences

We study fairness in social choice settings under single-peaked preferences. Construction and characterization of social choice rules in the single-peaked domain has been extensively studied in prior works. In fact, in the single-peaked domain, it is known that unanimous and strategy-proof deterministic rules have to be min-max rules and those that also satisfy anonymity have to be median rules. Further, random social choice rules satisfying these properties have been shown to be convex combinations of respective deterministic rules. We non-trivially add to this body of results by including fairness considerations in social choice. Our study directly addresses fairness for groups of agents. To study group-fairness, we consider an existing partition of the agents into logical groups, based on natural attributes such as gender, race, and location. To capture fairness within each group, we introduce the notion of group-wise anonymity. To capture fairness across the groups, we propose a weak notion as well as a strong notion of fairness. The proposed fairness notions turn out to be natural generalizations of existing individual-fairness notions and moreover provide non-trivial outcomes for strict ordinal preferences, unlike the existing group-fairness notions. We provide two separate characterizations of random social choice rules that satisfy group-fairness: (i) direct characterization (ii) extreme point characterization (as convex combinations of fair deterministic social choice rules). We also explore the special case where there are no groups and provide sharper characterizations of rules that achieve individual-fairness.

cs.GT↗

arXiv2022

Transport characteristics of a $\mathcal{PT}$-symmetric non-Hermitian system: Effect of environmental interaction

The environmental influence is inevitable but often ignored in the study of electronic transport properties of small-scale systems. Such an environment-mediated interaction can generally be described by a parity-time symmetric non-Hermitian system with a balanced distribution of physical gain and loss. It is quite known in the literature that along with the conventional junction current, another current called bias-driven circular current can be established in a loop geometry depending upon the junction configuration. This current, further, induces a strong magnetic field that can even reach to few Tesla. What will happen to these quantities when the system interacts with its surrounding environment? Would it exhibit a detrimental response? We address such issues considering a two-terminal ring geometry where the junction setup is described within a tight-binding framework. All the transport quantities are evaluated using the standard Green's function formalism based on the Landauer-Büttiker approach.

cond-mat.mes-hall↗

arXiv2022

Probabilistic Fixed Ballot Rules and Hybrid Domains

We study a class of preference domains that satisfies the familiar properties of minimal richness, diversity and no-restoration. We show that a specific preference restriction, hybridness, has been embedded in these domains so that the preferences are single-peaked at the "extremes" and unrestricted in the "middle". We also study the structure of strategy-proof and unanimous Random Social Choice Functions on these domains. We show them to be special cases of probabilistic fixed ballot rules (introduced by Ehlers, Peters, and Storcken (2002)).

econ.TH↗

arXiv2021

A Fokker-Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis

In this paper, a new framework for obtaining personalized optimal treatment strategies in colon cancer-induced angiogenesis is presented. The dynamics of colon cancer is given by a Itó stochastic process, which helps in modeling the randomness present in the system. The stochastic dynamics is then represented by the Fokker-Planck (FP) partial differential equation (PDE) that governs the evolution of the associated probability density function. The optimal therapies are obtained using a three step procedure. First, a finite dimensional FP-constrained optimization problem is formulated that takes input individual noisy patient data, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Next, a sensitivity analysis of the optimal parameter set is used to determine the parameters to be controlled, thus, helping in assessing the types of treatment therapies. Finally, a feedback FP control problem is solved to determine the optimal combination therapies. Numerical results with the combination drug, comprising of Bevacizumab and Capecitabine, demonstrate the efficiency of the proposed framework.

q-bio.QM↗

arXiv2021

On percolation in a generalized backbend process

We have generalized the idea of backbend in a nearest-neighbor oriented bond percolation process by considering a backbend sequence $β: \mathbb{Z}_+ \to \mathbb{Z}_+ \cup \{\infty\}$, and defining a $β$-backbend path from the origin as a path that never retreats further than $β(h)$ levels back from its record level $h$. We study the relationship between the critical probabilities of different percolation processes based on different backbend sequences on half-space, full-space, and half-slabs of the $d$-dimensional ($d \geq 2$) body-centered cubic (BCC) lattice. We also give sufficient conditions on the backbend sequences such that there will be no percolation at the critical probabilities of the corresponding percolation processes on half-space and full-space of the BCC lattice.

math.PR↗

arXiv2021

Exploring the dynamics of protest against National Register of Citizens & Citizenship Amendment Act through online social media: the Indian experience

The generic fluidity observed in the nature of political protest movements across the world during the last decade weigh heavily with the presence of social media. As such, there is a possibility to study the contemporary movements with an interdisciplinary approach combining computational analytics with social science perspectives. The present study has put efforts to understand such dynamics in the context of the ongoing nationwide movement in India opposing the NRC-CAA enactment. The transformative nature of individual discontent into collective mobilization, especially with a reflective intervention in social media across a sensitive region of the nation state, is presented here with a combination of qualitative (fieldwork) and quantitative (computing) techniques. The study is augmented further by the primary data generation coupled with real-time application of analytical approaches.

cs.CY↗

arXiv2020

A New Non-Linear Conjugate Gradient Algorithm for Destructive Cure Rate Model and a Simulation Study: Illustration with Negative Binomial Competing Risks

In this paper, we propose a new estimation methodology based on a projected non-linear conjugate gradient (PNCG) algorithm with an efficient line search technique. We develop a general PNCG algorithm for a survival model incorporating a proportion cure under a competing risks setup, where the initial number of competing risks are exposed to elimination after an initial treatment (known as destruction). In the literature, expectation maximization (EM) algorithm has been widely used for such a model to estimate the model parameters. Through an extensive Monte Carlo simulation study, we compare the performance of our proposed PNCG with that of the EM algorithm and show the advantages of our proposed method. Through simulation, we also show the advantages of our proposed methodology over other optimization algorithms (including other conjugate gradient type methods) readily available as R software packages. To show these we assume the initial number of competing risks to follow a negative binomial distribution although our general algorithm allows one to work with any competing risks distribution. Finally, we apply our proposed algorithm to analyze a well-known melanoma data.

math.ST↗

arXiv2020

Sparse reconstruction of log-conductivity in current density impedance tomography

A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the interior electric field data corresponding to two boundary voltage measurements, where the conductivity and the electric potential are related through an elliptic PDE arising in electrical impedance tomography. Further, the objective functional consists of a $L^1$ regularization term that promotes sparsity patterns in the conductivity and a Perona-Malik anisotropic diffusion term that enhances the edges to facilitate high contrast and resolution. This framework is motivated by a similar recent approach to solve an inverse problem in acousto-electric tomography. Several numerical experiments and comparison with an existing method demonstrate the effectiveness of the proposed method for superior image reconstructions of a wide-variety of log-conductivity patterns.

math.OC↗

arXiv2020

A sparsity-based nonlinear reconstruction method for two-photon photoacoustic tomography

We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in photoacoustic tomography (PAT). This framework comprises of minimizing an objective functional involving a least squares fit of the interior pressure field data corresponding to two boundary source functions, where the absorption coefficients and the photon density are related through a semi-linear elliptic partial differential equation (PDE) arising in PAT. Further, the objective functional consists of an $L^1$ regularization term that promotes sparsity patterns in absorption coefficients. The motivation for this framework primarily comes from some recent works related to solving inverse problems in acousto-electric tomography and current density impedance tomography. We provide a new proof of existence and uniqueness of a solution to the semi-linear PDE. Further, a proximal method, involving a Picard solver for the semi-linear PDE and its adjoint, is used to solve the optimization problem. Several numerical experiments are presented to demonstrate the effectiveness of the proposed framework.

math.OC↗

arXiv2020

Elementary Cellular Automata along with delay sensitivity can model communal riot dynamics

This work explores the potential of elementary cellular automata to model the dynamics of riot. Here, to model such dynamics, we introduce probabilistic loss of information and delay perturbation in the updating scheme of automata to capture sociological parameters - presence of anti-riot population and organizational presence of communal forces in the rioting society respectively. Moreover, delay has also been incorporated in the model to capture the non-local interaction of neighbours. Finally, the model is verified by a recent event of riot that occurred in Baduria of West Bengal, India.

nlin.CG↗