Related papers: Efficiency of random search with space-dependent d…
The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…
We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then,…
We present a theory of chemokinetic search agents that regulate directional fluctuations according to distance from a target. A dynamic scattering effect reduces the probability to penetrate regions with high fluctuations and thus search…
In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
Search processes are a fundamental part of natural and artificial systems. In such settings, the number of searchers is rarely constant: new agents may be recruited while others can abandon the search. Despite the ubiquity of these…
We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial…
We consider a drift-diffusion model, with an unknown function depending on the spatial variable and an additional structural variable, the amount of ingested lipid. The diffusion coefficient depends on this additional variable. The drift…
Classical search algorithms have long underpinned modern artificial intelligence. In this work, we tackle the challenge of inference-time control in diffusion models -- adapting generated outputs to meet diverse test-time objectives --…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
The dynamics of a subdiffusive continuous time random walker in an inhomogeneous environment is analyzed. In each microscopic jump, a random time is drawn from a waiting time probability density function (WT-PDF) that decays as a power law:…
A variety of systems in physics, chemistry, biology, and psychology are modeled in terms of diffusing "searchers" looking for "targets." Examples range from gene regulation, to cell sensing, to human decision-making. A commonly studied…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we…
We study the diffusion of a particle with a time-dependent diffusion constant $D(t)$ that switches between random values drawn from a distribution $W(D)$ at a fixed rate $r$. Using a renewal approach, we compute exactly the moments of the…
Intelligent dispatching is crucial to obtaining low response times in large-scale systems. One common scalable dispatching paradigm is the ``power-of-$d$,'' in which the dispatcher queries $d$ servers at random and assigns the job to a…
Classical paradigms for distributed learning, such as federated or decentralized gradient descent, employ consensus mechanisms to enforce homogeneity among agents. While these strategies have proven effective in i.i.d. scenarios, they can…