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Many events in the vertebrate immune system are influenced by some element of chance. The objective of the present work is to describe affinity maturation of B lymphocytes (in which random events are perhaps the most characteristic), and to…
Stochastic finite-state generators are compressed descriptions of infinite time series. Alternatively, compressed descriptions are given by quantum finite- state generators [K. Wiesner and J. P. Crutchfield, Physica D 237, 1173 (2008)].…
Processing long temporal sequences is a key challenge in deep learning. In recent years, Transformers have become state-of-the-art for this task, but suffer from excessive memory requirements due to the need to explicitly store the…
Scientific inference involves obtaining the unknown properties or behavior of a system in the light of what is known, typically, without changing the system. Here we propose an alternative to this approach: a system can be modified in a…
We prove the stochastic domination for determinantal processes associated with finite rank projection kernels. The result was first proved by Lyons in discrete setting. We avoid the machinery of matroids in order to obtain a proof that…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomogeneous highly degenerate diffusion for…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
This paper considers a stochastic control framework, in which the residual model uncertainty of the dynamical system is learned using a Gaussian Process (GP). In the proposed formulation, the residual model uncertainty consists of a…
We study a one-dimensional anisotropic exclusion model describing particles moving deterministically on a ring with a single defect across which they move with probability 0 < q < 1. We show that the stationary state of this model can be…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
We explore two notions of stationary processes. The first is called a random-step Markov process in which the stationary process of states, $(X_i)_{i \in \mathbb{Z}}$ has a stationary coupling with an independent process on the positive…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest…
Stochastic network-dynamics are typically assumed to be memory-less. Involving prolonged dwells interrupted by instantaneous transitions between nodes such Markov networks stand as a coarse-graining paradigm for chemical reactions, gene…
Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
We establish sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. The new assumption, localized continuity, is formalized with the help of the notion of context trees, and includes the…
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…