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An analytical solution of the QCD evolution equations for the singlet and gluon distribution is presented. We decouple DGLAP evolution equations into the initial conditions by using a Laplace transform method at $N^{n}LO$ analysis. The…
We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition…
Theories including a collapse mechanism have been presented various years ago. They are based on a modification of standard quantum mechanics in which nonlinear and stochastic terms are added to the evolution equation. Their principal…
Sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the response produced by the sensor is adapted to the overall amplitude of the signal; reducing the sensitivity in the presence of strong…
Models that adapt their predictions based on some given contexts, also known as in-context learning, have become ubiquitous in recent years. We propose to study the behavior of such models when data is contaminated by noise. Towards this…
People make strategic decisions many times a day - during negotiations, when coordinating actions with others, or when choosing partners for cooperation. The resulting dynamics can be studied with learning theory and evolutionary game…
Learning from noisy data has attracted much attention, where most methods focus on closed-set label noise. However, a more common scenario in the real world is the presence of both open-set and closed-set noise. Existing methods typically…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
We study damage spreading among the opinions of a system of agents, subjected to the dynamics of the Krause-Hegselmann consensus model. The damage consists in a sharp change of the opinion of one or more agents in the initial random opinion…
A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously…
The dynamics of living systems often serves the purpose of reaching functionally important target states. We previously proposed a theory to analyze stochastic biological dynamics evolving towards target states in reverse time. However, a…
In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of weakly-related or independent components. However, a theory may represent knowledge that is subject to…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
A scientific model need not be a passive and static descriptor of its subject. If the subject is affected by the model, the model must be updated to explain its affected subject. In this study, two models regarding the dynamics of model…
How the very first nervous systems evolved remains a fundamental open question. Molecular and genomic techniques have revolutionized our knowledge of the molecular ingredients behind this transition but not yet provided a clear picture of…
In this paper we obtain uniform propagation estimates for systems of interacting diffusions. We adopt a general model, satisfying various conditions which ensure that the decay resulting from the internal dynamics term dominates the…
We study the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior…
We derive a general formula for the early time dependence of a phase space distribution evolving according to the kinetic Boltzmann equation. Assuming that the early evolution of the system created in high-energy nuclear collisions can be…
Seismic data noise processing is an important part of seismic exploration data processing, and the effect of noise elimination is directly related to the follow-up processing of data. In response to this problem, many authors have proposed…
Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…