Related papers: Log-normal distribution in growing systems with we…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We…
Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal…
Study of the characteristic properties of charged particle production in hadron-nucleus collisions at high energies, by utilising the approaches from different statistical models is performed.~Predictions from different approaches using the…
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…
Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0…
Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance…
We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy…
Explaining empirically observed wealth and income distributions, featuring power-law tails alongside gamma or log-normal bulk shapes, challenges models that focus on either pairwise competition or individual investment mechanisms. This…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
Considering the interactions of two arbitrary particles, we obtain an internal energy expression of the complex system having long-range interactions. Based on the postulate of "equal-probability principle" for all microstates, the…
Since some realistic networks are influenced not only by increment behavior but also by tunable clustering mechanism with new nodes to be added to networks, it is interesting to characterize the model for those actual networks. In this…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
We study the long-term behavior of two piecewise-deterministic Markov processes used to model stochastic gene regulatory networks with bursting dynamics. Under regularity assumptions on the jump rate, we prove the existence and uniqueness…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
Face-to-face interactions reveal recurring patterns, suggesting the possibility of shared underlying mechanisms. More specifically, inter-contact durations, contact durations and number of contacts per edge share similar heavy-tail…
The slow dynamics for a colloidal suspension of particles interacting with a hard-core repulsion complemented by a short-ranged attraction is discussed within the frame of mode-coupling theory for ideal glass transitions for parameter…
We investigate the kinetics of particle aggregation within the framework of the Smoluchowski coagulation equation, extending it to account for electrostatic interactions among charged clusters. Using a stochastic Monte Carlo implementation,…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
In this manuscript we introduce a generalisation of the log-Normal distribution that is inspired by a modification of the Kaypten multiplicative process using the $q$-product of Borges [Physica A \textbf{340}, 95 (2004)]. Depending on the…