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A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
Experimental neuroscience increasingly requires tractable models for analyzing and predicting the behavior of neurons and networks. The generalized linear model (GLM) is an increasingly popular statistical framework for analyzing neural…
We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially…
This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…
In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article,…
Given that many fundamental questions in neuroscience are still open, it seems pertinent to explore whether the brain might use other physical modalities than the ones that have been discovered so far. In particular it is well established…
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of…
Vascular networks play a key role in the development, function, and survival of many organisms, facilitating transport of nutrients and other critical factors within and between systems. The development of these vessel networks has been…
Disease, opinions, ideas, gossip, etc. all spread on social networks. How these networks are connected (the network structure) influences the dynamics of the spreading processes. By investigating these relationships one gains understanding…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
The paper concerns the multiscale modeling of a myelinated axon. Taking into account the microstructure with alternating myelinated parts and nodes Ranvier, we derive a nonlinear cable equation describing the potential propagation along the…
This study investigates the complex nonlinear coupling of magnetic gears arranged in proximity on a plane. Acknowledging the rich array of geometric and electromagnetic parameters involved, we initiate our exploration with a simplified…
We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review…
In complex systems, many different parts interact in non-obvious ways. Traditional research focuses on a few or a single aspect of the problem so as to analyze it with the tools available. To get a better insight of phenomena that emerge…
In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity…
Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…
Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…