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In the interchange process on a graph $G=(V,E)$, distinguished particles are placed on the vertices of $G$ with independent Poisson clocks on the edges. When the clock of an edge rings, the two particles on the two sides of the edge…
Game dynamics theory, as a field of science, the consistency of theory and experiment is essential. In the past 10 years, important progress has been made in the merging of the theory and experiment in this field, in which dynamics cycle is…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Imitation learning practitioners have often noted that conditioning policies on previous actions leads to a dramatic divergence between "held out" error and performance of the learner in situ. Interactive approaches can provably address…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
Continual Learning (CL) methods usually learn from all available data. However, this is not the case in human cognition which efficiently focuses on key experiences while disregarding the redundant information. Similarly, not all data…
Modern recommender systems operate in uniquely dynamic settings: user interests, item pools, and popularity trends shift continuously, and models must adapt in real time without forgetting past preferences. While existing tutorials on…
In this study, we rederive the fluctuation theorems in presence of feedback, by assuming the known Jarzynski equality and detailed fluctuation theorems. We first reproduce the already known work theorems for a classical system, and then…
This paper addresses the question of the fluctuations of the empirical entropy of a chain of infinite order. We assume that the chain takes values on a finite alphabet and loses memory exponentially fast. We consider two possible…
We obtain self-similar solutions that describe the dynamics of a self-gravitating, rotating, viscous system. We use simplifying assumptions; but explicitly include viscosity and the cooling due to the dissipation of energy. By assuming that…
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a…
We investigate the conditions under which periodically driven quantum systems subject to dissipation exhibit a stable subharmonic response. Noting that coupling to a bath introduces not only cooling but also noise, we point out that a…
The spin echo approach is extended to include bio-complexes for which the interaction with dynamical noise is strong. Significant restoration of the free induction decay signal due to homogeneous (decoherence) and inhomogeneous (dephasing)…
Simulation can enable the study of recommender system (RS) evolution while circumventing many of the issues of empirical longitudinal studies; simulations are comparatively easier to implement, are highly controlled, and pose no ethical…
We study reinforcement learning in settings where sampling an action from the policy must be done concurrently with the time evolution of the controlled system, such as when a robot must decide on the next action while still performing the…
In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by concrete examples in signaling and gene regulation, a body of work has focused…
While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…