Related papers: Analytical Investigation of Long-time Diffusion Dy…
Synapses change on multiple timescales, ranging from milliseconds to minutes, due to a combination of both short- and long-term plasticity. Here we develop an extension of the common Generalized Linear Model to infer both short- and…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
Lattice gas automata with collision rules that violate the conditions of semi-detailed-balance exhibit algebraic decay of equal time spatial correlations between fluctuations of conserved densities. This is shown on the basis of a…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…
For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier…
Emulate the gating mechanism of ionic channels in neurons, we present a mathematical model for the time constant of dynamical systems. Our model is an analytical continues function. The analyses give evidence that one can adjust the…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and…
We prove that under certain mild assumptions, the entropy rate of a hidden Markov chain, observed when passing a finite-state stationary Markov chain through a discrete-time continuous-output channel, is jointly analytic as a function of…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
The photoluminescence in amorphous semiconductors decays according to power law $t^{-delta}$ at long times. The photoluminescence is controlled by dispersive transport of electrons. The latter is usually characterized by the power $alpha$…
In this paper we analyze the relaxation to steady-state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both…
A numerical molecular dynamics experiment measuring the two-time correlation function of the transversal velocity field in the homogeneous cooling state of a granular gas is reported. By measuring the decay rate and the amplitude of the…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Aggregation and fragmentation of single molecules in the cell environment lead to a spectrum of diffusivities and to statistical laws of movement very different from typical Brownian motion. Current models of intracellular transport do not…
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an…