Related papers: Lecture notes on stochastic models in systems biol…
These lecture notes are derived from a graduate-level course in dynamic optimization, offering an introduction to techniques and models extensively used in management science, economics, operations research, engineering, and computer…
This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as…
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein.…
Stochastic kinetic models of genetic expression are able to describe protein fluctuations. A comparative study of the canonical and a feedback model is given here by using stochastic simulation methods. The feedback model is skeleton model…
These lecture notes introduce key concepts of mathematical population genetics within the most elementary setting and describe a few recent applications to microbial evolution experiments. Pointers to the literature for further reading are…
Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject within the last decade, and the traditional biophysical models of neuronal dynamics such as Hodgkin-Huxley model have been generalized to…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…
These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…
These lecture notes provide an introduction to Langevin processes and briefly discuss some interesting properties and simple applications. They compile material presented at the "School of Physics and Mathematics Without Frontiers"…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…
These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…