相关论文: Jacobi processes with jumps as neuronal models: a …
A classical view of neural coding relies on temporal firing synchrony among functional groups of neurons; however the underlying mechanism remains an enigma. Here we experimentally demonstrate a mechanism where time-lags among neuronal…
We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
We describe, implement and test a novel method for training neural networks to estimate the Jacobian matrix $J$ of an unknown multivariate function $F$. The training set is constructed from finitely many pairs $(x,F(x))$ and it contains no…
We consider a class of Jacobi matrices with unbounded coefficients. This class is known to exhibit a first-order phase transition in the sense that, as a parameter is varied, one has purely discrete spectrum below the transition point and…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
We consider the task of generating draws from a Markov jump process (MJP) between two time-points at which the process is known. Resulting draws are typically termed bridges and the generation of such bridges plays a key role in…
We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process (PDMP) with values in ${\mathbb R}^N, $ where $ N$ is the number of neurons…
We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various…
We study first-passage statistics for one-dimensional random walks $S_n$ with independent and identically distributed jumps starting from the origin. We focus on the joint distribution of the first-passage time $\tau_b$ and first-passage…
Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…
With the goal of understanding the intricate behavior and dynamics of collections of neurons, we present superconducting circuits containing Josephson junctions that model biologically realistic neurons. These "Josephson junction neurons"…
We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results by Jacod (2008) are generalized to the…
We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions,…
This paper presents a transfer learning approach which enables fast and efficient adaptation of Recurrent Neural Network (RNN) models of dynamical systems. A nominal RNN model is first identified using available measurements. The system…
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of…
Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In a first part, we present…