arXiv subjects

Neeraja Sahasrabudhe

Publications and source records attributed to Neeraja Sahasrabudhe.

10 recordsLinked to original sources

arXiv2026

Opinion Dynamics with Memory Loss and Communication Delays

We propose a novel framework for modeling binary opinions (0 or 1) of individuals connected through a weighted directed network, where edge weights quantify interpersonal influence. Unlike classical models that assume complete access to previously expressed opinions, our framework allows individuals to update their biases using structured memory sets that capture limited and delayed information exchange. To analyze these opinion differences, we introduce a mathematically tractable notion of relative bias between pairs of individuals. The relative biases evolve according to a linear update rule involving past expressed opinions specified by the memory sets. We define the belief of an individual as the probability of expressing opinion 1 and derive a time-delayed dynamical system governing the evolution of network beliefs. We establish its asymptotic behavior and characterize its properties. The framework is further extended to networks containing bots, which maintain fixed biases while influencing neighboring individuals. We quantify the effect of bots by comparing the fixed points of the dynamics in their presence and absence. Finally, simulations illustrate the influence of memory, network structure, and bot interactions on the resulting opinion dynamics.

math.PR↗

arXiv2026

Tampered Memory Elephant Random Walk on One-Dimensional Integer Lattice

One of the outstanding questions in the theory of elephant random walks as observed by Gut and Stadtmüller (2023), is to determine how much memory is needed for a phase transition between the diffusive, critical and superdiffusive regimes to persist. To investigate this memory breakpoint, we introduce the tampered memory elephant random walk, in which the memory is partitioned into two disjoint sets $D_n$ and $D_n^c$, which may be deterministic or random. On $D_n^c$ the dynamics is the same as an elephant random walk, while on $D_n$ the increments are replaced by independent innovations. The resulting walk is thus driven by two competing components: elephant random walk and an independent simple random walk corresponding to the innovations. We first establish a law of large numbers when the increasing collections $\{D_n\}_{n \ge 1}$ and $\{D^c_n\}_{n \ge 1}$ have a renewal structure with exponential moments. We then identify a sharp threshold that governs the persistence of the phase transition for deterministic memory partitions. We show that if $\{D_n\}_{n \ge 1}$ is non-random increasing collection with increasing complement $\{D^c_n\}_{n \ge 1}$ such that $\lim_{n \to \infty} \frac{\lvert D^c_n\rvert}{n} >1/2$, then a phase transition into diffusive, critical and superdiffusive regimes persists, whereas for $\lim_{n \to \infty} \frac{\lvert D^c_n \rvert}{n}<1/2$, there is only the diffusive regime with $\mathcal{O}(\sqrt{n})$. The case of $\lim_{n\to \infty}\frac{\lvert D^c_n \rvert}{n}=1/2$ is also characterised. Thus, one-half emerges as the sharp breakpoint for the persistence of anomalous diffusion in this competitive setting. We conjecture that the same threshold governs the case when $\{D_n\}_{n \ge 1}$ is random. Our proofs rely on stochastic approximation applied to the two dependent competing components of the walk, representing the retained memory and the innovations.

math.PR↗

arXiv2025

Interacting Urns on Directed Networks with Node-Dependent Sampling and Reinforcement

We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We classify the sampling and reinforcement schemes, as well as the networks on which the proportion of balls of either colour in each urn converges almost surely to a deterministic limit. We also investigate conditions for achieving synchronisation of the colour proportions across the urns and analyse fluctuations under specific conditions on the reinforcement scheme and network structure.

math.PR↗

arXiv2024

Urns with Multiple Drawings and Graph-Based Interaction

Consider a finite undirected graph and place an urn with balls of two colours at each vertex. At every discrete time step, for each urn, a fixed number of balls are drawn from that same urn with probability $p$, and from a randomly chosen neighbour of that urn with probability $1-p$. Based on what is drawn, the urns then reinforce themselves or their neighbours. For every ball of a given colour in the sample, in case of Pólya-type reinforcement, a constant multiple of balls of that colour is added while in case of Friedman-type reinforcement, balls of the other colour are reinforced. These different choices for reinforcement give rise to multiple models. In this paper, we study the convergence of the fraction of balls of either colour across urns for all of these models. We show that in most cases the urns synchronize, that is, the fraction of balls of either colour in each urn converges to the same limit almost surely. A different kind of asymptotic behaviour is observed on bipartite graphs. We also prove similar results for the case of finite directed graphs.

math.PR↗

arXiv2021

Interacting Urns on a Finite Directed Graph

We introduce a general two colour interacting urn model on a finite directed graph, where each urn at a node, reinforces all the urns in its out-neighbours according to a fixed, non-negative and balanced reinforcement matrix. We show that the fraction of balls of either colour converges almost surely to a deterministic limit if either the reinforcement is not of Pólya type or if the graph is such that every vertex with non-zero in-degree can be reached from some vertex with zero in-degree. We also obtain joint central limit theorems, with appropriate scaling, around the vector of limiting proportion. Further, in the remaining case when there are no vertices with zero in-degree and the reinforcement is of Pólya type, we restrict our analysis to a regular graph and show that the fraction of balls of either colour converges almost surely to a finite random limit, which is the same across all the urns.

math.PR↗

arXiv2020

Influencing Opinions of Heterogeneous Populations over Finite Time Horizons

In this work, we focus on strategies to influence the opinion dynamics of a well-connected society. We propose a generalization of the popular voter model. This variant of the voter model can capture a wide range of individuals including strong-willed individuals whose opinion evolution is independent of their neighbors as well as conformist/rebel individuals who tend to adopt the opinion of the majority/minority. Motivated by political campaigns which aim to influence opinion dynamics by the end of a fixed deadline, we focus on influencing strategies for finite time horizons. We characterize the nature of optimal influencing strategies as a function of the nature of individuals forming the society. Using this, we show that for a society consisting of predominantly strong-willed/rebel individuals, the optimal strategy is to influence towards the end of the finite time horizon, whereas, for a society predominantly consisting of conformist individuals who try to adopt the opinion of the majority, it could be optimal to influence in the initial phase of the finite time horizon.

cs.SI↗

arXiv2020

Influencing Opinion Dynamics in Networks with Limited Interaction

The focus of this work is on designing influencing strategies to shape the collective opinion of a network of individuals. We consider a variant of the voter model where opinions evolve in one of two ways. In the absence of external influence, opinions evolve via interactions between individuals in the network, while, in the presence of external influence, opinions shift in the direction preferred by the influencer. We focus on a finite time-horizon and an influencing strategy is characterized by when it exerts influence in this time-horizon given its budget constraints. Prior work on this opinion dynamics model assumes that individuals take into account the opinion of all individuals in the network. We generalize this and consider the setting where the opinion evolution of an individual depends on a limited collection of opinions from the network. We characterize the nature of optimal influencing strategies as a function of the way in which this collection of opinions is formed.

cs.SI↗

arXiv2020

S.L.L.N. and C.L.T. for Random Walks in I.I.D. Random Environment on Cayley Trees

We consider the random walk in an independent and identically distributed (i.i.d.) random environment on a Cayley graph of a finite free product of copies of $\mathbb{Z}$ and $\mathbb{Z}_2$. Such a Cayley graph is readily seen to be a regular tree. Under a uniform elipticity assumption on the i.i.d. environment we show that the walk has positive speed and establish the annealed central limit theorem for the graph distance of the walker from the starting point.

math.PR↗

arXiv2016

Gradient Estimation with Simultaneous Perturbation and Compressive Sensing

This paper aims at achieving a "good" estimator for the gradient of a function on a high-dimensional space. Often such functions are not sensitive in all coordinates and the gradient of the function is almost sparse. We propose a method for gradient estimation that combines ideas from Spall's Simultaneous Perturbation Stochastic Approximation with compressive sensing. The aim is to obtain "good" estimator without too many function evaluations. Application to estimating gradient outer product matrix as well as standard optimization problems are illustrated via simulations.

stat.ML↗

arXiv2013

A note on the geometric interpretation of Bell's inequalities

Using results of Pitowsky and Gupta, we show in a direct, elementary fashion that, in the case of three spins, Bell's inequalities indeed provide a representation of the tetrahedron of all spin correlation matrices as intersection of half-spaces.

quant-ph↗