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Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…

Quantitative Methods · Quantitative Biology 2018-09-07 Walter de Back , Thomas Zerjatke , Ingo Roeder

Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…

Signal Processing · Electrical Eng. & Systems 2023-06-08 Nir Shlezinger , Yonina C. Eldar

General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…

Pattern Formation and Solitons · Physics 2025-08-26 Edgardo Villar-Sepúlveda , Alan R. Champneys , Andrew L. Krause

A method for classifying $n$-species reaction-diffusion models, admitting shock solutions is presented. The most general one-dimensional two-species reaction-diffusion model with nearest neighbor interactions admitting uniform product…

Statistical Mechanics · Physics 2011-01-04 S. Masoomeh Hashemi , Amir Aghamohammadi

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…

Methodology · Statistics 2023-10-11 Michelle Carey , James O. Ramsay

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…

Machine Learning · Computer Science 2018-11-28 Fernando Gama , Alejandro Ribeiro , Joan Bruna

This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…

Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…

Analysis of PDEs · Mathematics 2026-03-24 Brocchieri Elisabetta , Soresina Cinzia

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…

Molecular Networks · Quantitative Biology 2023-06-28 Federico Bocci , Dongya Jia , Qing Nie , Mohit Kumar Jolly , Jose Onuchic

We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop…

Optimization and Control · Mathematics 2014-01-09 R. M. Jungers , A. D'Innocenzo , M. D. Di Benedetto

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…

Statistical Mechanics · Physics 2007-05-23 V. Colizza , R. Pastor-Satorras , A. Vespignani

Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…

Populations and Evolution · Quantitative Biology 2018-05-24 Andrea Cangiani , Emmanuil H. Georgoulis , Andrew Yu. Morozov , Oliver J. Sutton

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…

In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…

Molecular Networks · Quantitative Biology 2007-05-23 Kanchan Thadani , Ashutosh

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…

Computational Physics · Physics 2016-03-02 Fabian Spill , Pilar Guerrero , Tomas Alarcon , Philip K. Maini , Helen Byrne

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…

Analysis of PDEs · Mathematics 2010-03-12 Wei Wang , A. J. Roberts

This paper presents a Markov-based system model for microfluidic molecular communication (MC) channels. By discretizing the advection-diffusion dynamics, the proposed model establishes a physically consistent state-space formulation. The…

Emerging Technologies · Computer Science 2025-11-11 Ruifeng Zheng , Pengjie Zhou , Pit Hofmann , Fatima Rani , Juan A. Cabrera , Frank H. P. Fitzek

This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the…

Molecular Networks · Quantitative Biology 2019-09-02 Elisenda Feliu

Parameter sensitivity analysis is a powerful tool in the building and analysis of biochemical network models. For stochastic simulations, parameter sensitivity analysis can be computationally expensive, requiring multiple simulations for…

Computational Physics · Physics 2015-06-04 Patrick B. Warren , Rosalind J. Allen