Related papers: A Type System for a Stochastic CLS
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
In the present paper, we introduce so-called operator-stable-like processes. Roughly speaking, they behave locally like operator-stable processes, but they need not to be homogenous in space. Having shown existence for this class of…
This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. Well-known…
Microbiome-based stratification of healthy individuals into compositional categories, referred to as "community types", holds promise for drastically improving personalized medicine. Despite this potential, the existence of community types…
We introduce a natural language interface for building stochastic pi calculus models of biological systems. In this language, complex constructs describing biochemical events are built from basic primitives of association, dissociation and…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
By analogue of [1,2] we define a cubic stochastic process and study evolution (dynamics) of a system $E$ which contains at least three elements.
Biological cells are the prototypical example of active matter. Cells sense and respond to mechanical, chemical and electrical environmental stimuli with a range of behaviors, including dynamic changes in morphology and mechanical…
Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which…
These notes are inspired by the theory of cellular automata. A linear cellular automaton on a lattice of finite rank or on a toric grid is a discrete dinamical system generated by a convolution operator with kernel concentrated in the…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
We examine microscopic mechanisms for coupling stochastic oscillators so that they display similar and correlated temporal variations. Unlike oscillatory motion in deterministic dynamical systems, complete synchronization of stochastic…
Process algebra and temporal logic are two popular paradigms for the specification, verification and systematic development of reactive and concurrent systems. These two approaches take different standpoint for looking at specifications and…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
In the realm of big data, discerning patterns in nonlinear systems affected by external control inputs is increasingly challenging. Our approach blends the coarse-graining strengths of centroid-based unsupervised clustering with the clarity…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…
Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…
The past decade has seen a revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the finite copy number of the participating species. That is, rather than modeling regulatory networks in…