Related papers: Anomalous diffusion and long-range memory in the s…
We analyze \emph{fractional Brownian motion} and \emph{scaled Brownian motion} on the two-dimensional sphere $\mathbb{S}^{2}$. We find that the intrinsic long time correlations that characterize fractional Brownian motion collude with the…
Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic…
In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…
Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this…
The idea that memory behavior relies on a gradually-changing internal state has a long history in mathematical psychology. This chapter traces this line of thought from statistical learning theory in the 1950s, through distributed memory…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
We study the effect of latency on binary-choice opinion formation models. Latency is introduced into the models as an additional dynamic rule: after a voter changes its opinion, it enters a waiting period of stochastic length where no…
We study noise sensitivity of the consensus opinion of the voter model on finite graphs, with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small…
We study the ordering dynamics of nonlinear voter models with multiple states, also providing a discussion of the two-state model. The rate with which an individual adopts an opinion scales as the $q$-th power of the number of the…
We examine parliamentary presence data of the 2008-2012 and the 2012-2016 legislatures of Lithuanian parliament. We consider cumulative presence series of each individual representative in the data set. These series exhibit superdiffusive…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…
Single-file diffusion behaves as normal diffusion at small time and as anomalous subdiffusion at large time. These properties can be described by fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We…
Stochastic time-varying optimization is an integral part of learning in which the shape of the function changes over time in a non-deterministic manner. This paper considers multiple models of stochastic time variation and analyzes the…
We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of $N$ particles is studied and it is described by use of the…
Slow Feature Analysis is a unsupervised representation learning method that extracts slowly varying features from temporal data and can be used as a basis for subsequent reinforcement learning. Often, the behavior that generates the data on…
We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or…
The voter model consists of a set of agents whose opinion is a binary variable. At each time step, an agent along with a social neighbor is selected and the agent imitates the social neighbor at the next time step. In this paper, we study a…
A new model for the dynamics of opinion formation is proposed and analysed at the mean-field level. It can be regarded as a generalization of the noisy voter model in which agents update their binary states by copying others and by an…
Choice models, which capture popular preferences over objects of interest, play a key role in making decisions whose eventual outcome is impacted by human choice behavior. In most scenarios, the choice model, which can effectively be viewed…