Related papers: Compartmental-reaction diffusion framework for mic…
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
Understanding how adult humans learn non-native speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions…
Cortical neurons exhibit a hierarchy of timescales across brain regions in response to input stimuli, which is thought to be crucial for information processing of different temporal scales. Modeling studies suggest that both intra-regional…
The paper treats a reaction-diffusion equation with hysteretic nonlinearity on a one-dimensional lattice. It arises as a result of the spatial discretization of the corresponding continuous model with so-called nontransverse initial data…
Neural variability plays a central role in neural coding and neuronal network dynamics. Unreliability of synaptic transmission is a major source of neural variability: synaptic neurotransmitter vesicles are released probabilistically in…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrodinger equation. Two main interaction…
The difference diffusion model with two equilibrium states is given by a stochastic equation with two components: the predicted one, which is determined by the regression function of increments with two equilibriums, and the stochastic one,…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
The spatial distribution of neuronal cells is an important requirement for achieving proper neuronal function in several parts of the nervous system of most animals. For instance, specific distribution of photoreceptors and related neuronal…
Hidden interactions and components in complex systems-ranging from covert actors in terrorist networks to unobserved brain regions and molecular regulators-often manifest only through indirect behavioral signals. Inferring the underlying…
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…
Neuron models have attracted a lot of attention recently, both in mathematics and neuroscience. We are interested in studying long-time and large-population emerging properties in a simplified toy model. From a mathematical perspective,…
During the first years of life, the human brain undergoes dynamic spatially-heterogeneous changes, involving differentiation of neuronal types, dendritic arborization, axonal ingrowth, outgrowth and retraction, synaptogenesis, and…
In general, many dynamic processes are involved with interacting variables, from physical systems to sociological analysis. The interplay of components in the system can give rise to confounding dynamic behavior. Many approaches model…
The spatiotemporal stochastic dynamics of the voltage as well as the upcrossing rate are derived for a model neuron comprising a long dendrite with uniformly distributed filtered excitatory and inhibitory synaptic drive. A cascade of…
The temporal and spatial development of Parkinson's disease has been characterised as the progressive formation of {\alpha}-synuclein aggregations through susceptible neuronal pathways. This article describes a new model for this…