Related papers: Source identification via pathwise gradient estima…
The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the…
Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical…
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…
This paper is concerned about a learning algorithm for a probabilistic model of spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a stochastic variational inference algorithm to train SNNs with hidden neurons. The…
We study the worst-case communication complexity of distributed algorithms computing a path problem based on stationary distributions of random walks in a network $G$ with the caveat that $G$ is also the communication network. The problem…
Spike deconvolution is the problem of recovering point sources from their convolution with a known point spread function, playing a fundamental role in many sensing and imaging applications. This paper proposes a novel approach combining…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
Decentralized solutions to finite-sum minimization are of significant importance in many signal processing, control, and machine learning applications. In such settings, the data is distributed over a network of arbitrarily-connected nodes…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long time dynamics for the PDE model. The PDE, originally…
The paper presents an approach to olfactory search for a diffusive emitting source of tracer (e.g. aerosol, gas) in an environment with unknown map of randomly placed and shaped obstacles. The measurements of tracer concentration are…
Consider non-intersecting Brownian motions on the real line, starting from the origin at t=0, with a number of particles forced to reach p distinct target points at time t=1. This work shows that the transition probability, that is the…
Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the…
Stochastic systems are used to model a variety of phenomena in which noise plays an essential role. In these models, one potential goal is to determine if noise can induce transitions between states, and if so, to calculate the most…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…