Related papers: Sensitivity to initial conditions in coherent nois…
Recent progress in diverse intelligence has shown simple learning capacities below the organism level - single cells and even molecular networks. However, there are still many knowledge gaps around learning capacity above the organism…
Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains…
Shared and correlated Gamma frailty models are widely used in the literature to model the association in multivariate current status data. In this paper, we have proposed two other new Gamma frailty models, namely shared cause-specific and…
An active dissipative process organizes auditory frequency analysis in the mammalian cochlea. A minimal active beam model reveals that a spatially varying viscous coupling operator, $\partial_{xx}\kappa\partial_{xx}$, generates dissipative…
Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…
We elucidate how the strong coupling phases of a coupled driven model, originally proposed in S. Mukherjee, Phys. Rev. E 108, 024219 (2023), are affected by noise cross correlations in general dimensions $d$. This model has two dynamical…
An exact formula for the distribution of lifetimes in coherent-noise models and related models is derived. For certain stress distributions, this formula can be analytically evaluated and yields simple closed expressions. For those types of…
The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm [Inst. Hautes \'{E}tudes Sci. Publ. Math. 90 (1999) 5-43],…
In this work we focus on how noise propagates in biochemical reaction networks and affects sensitivities of the system. We discover that the stochastic fluctuations can enhance sensitivities in one region of the value of control parameters…
We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of toy model used for climate studies. The system is subjected to both temporal and spatiotemporal perturbations.…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of…
Natural Language Inference is a challenging task that has received substantial attention, and state-of-the-art models now achieve impressive test set performance in the form of accuracy scores. Here, we go beyond this single evaluation…
We use the perturbative renormalization group to study classical stochastic processes with memory. We focus on the generalized Langevin dynamics of the \phi^4 Ginzburg-Landau model with additive noise, the correlations of which are local in…
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…
We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
We introduce highly optimized tolerance (HOT), a mechanism that connects evolving structure and power laws in interconnected systems. HOT systems arise, e.g., in biology and engineering, where design and evolution create complex systems…
We theoretically evaluate the impact of drift-free noise on the dynamics of $\mathcal{PT}$-symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as…