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Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We consider the problem of the first passage time to the origin of a spatially non-homogeneous random walk with a position-dependent drift, known as the Gillis random walk, in the presence of resetting. The walk starts from an initial site…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
We consider random walkers searching for a target in a bounded one-dimensional heterogeneous environment, in the interval $[0,L]$, where diffusion is described by a space-dependent diffusion coefficient $D(x)$. Boundary conditions are…
This work examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of…
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of…
Although resetting has widespread applicability, applying it to the dynamics in the presence of spatial quenched disorder, which is essential in many physical problems, is challenging. In this study, we consider a well-known one-dimensional…
Motivated by programmatic advertising optimization, we consider the task of sequentially allocating budget across a set of resources. At every time step, a feasible allocation is chosen and only a corresponding random return is observed.…
We propose a general framework for optimizing noise schedules in diffusion models, applicable to both training and sampling. Our method enforces a constant rate of change in the probability distribution of diffused data throughout the…
This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose…
Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behaviour of a system as exemplified by the emergence of…
We analyze two communication-efficient algorithms for distributed statistical optimization on large-scale data sets. The first algorithm is a standard averaging method that distributes the $N$ data samples evenly to $\nummac$ machines,…
We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t)…
This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states…
This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted…
We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…
The effect of refractory periods in partial resetting processes is studied. Under Poissonian partial resets, a state variable jumps to a value closer to the origin by a fixed fraction at constant rate, $x\to a x$. Following each reset, a…