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We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring…
Spatio-temporal dynamics of singly resonant optical parametric oscillators with external seeding displays hexagonal, roll and honeycomb patterns, optical turbulence, rogue waves and cavity solitons. We derive appropriate mean-field…
In silico, cell based approaches for modeling biological morphogenesis are used to test and validate our understanding of the biological and mechanical process that are at work during the growth and the organization of multi-cell tissues.…
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
Successful biological development via spatial regulation of cell differentiation relies on action of multiple signaling molecules that are known as morphogens. It is now well established that signaling molecules create non-uniform…
The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning the main topics of the fruitful…
Sperm are propelled by bending waves travelling along the flagellum. During steering in gradients of sensory cues, sperm adjust the flagellar beat waveform. Symmetric and asymmetric beat waveforms produce straight and curved swimming paths,…
In this paper we present a thorough study on the existence of traveling waves in a mathematical model of dispersal in a partially sedentary age-structured population. This type of model was first proposed by Veit and Lewis in [{\it Am.…
We discuss a two-dimensional model for the dynamics of axonemal deformations driven by internally generated forces of molecular motors. Our model consists of an elastic filament pair connected by active elements. We derive the dynamic…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
Some mechanisms of cardiac arrhythmias can be presented as a composition of elementary acts of block and reflection on the contacts of homogeneous areas of the conducting tissue. For study this phenomena we use an axiomatic one-dimensional…
In this report, we introduce a novel self-supervised learning method for extracting latent embeddings from behaviors of larval zebrafish. Drawing inspiration from Masked Modeling techniquesutilized in image processing with Masked…
The time evolution of wave packets in a harmonic oscillator potential is studied. Some new results for the most general case are obtained. A natural number, called ``degree of rigidity'', is introduced to describe qualitatively how much the…
The dynamics of phase-separated interfaces shape the behavior of both passive and active condensates. While surface tension in equilibrium systems minimizes interface length, non-equilibrium fluxes can destabilize flat or constantly curved…
Organogenesis is a tightly regulated process that has been studied experimentally for decades. We are developing mechanistic models for the morphogenesis of limbs, lungs, and kidneys with a view to integrate available knowledge and to…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions;…
The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
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.…