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One of the most intriguing questions in evolution is how organisms exhibit suitable phenotypic variation to rapidly adapt in novel selective environments which is crucial for evolvability. Recent work showed that when selective environments…
In this paper, we study the behavior of systems of individuals in confined environments that are driven by laws of self-organization. We propose that, under certain conditions, the long-term behavior of such systems will be global…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…
We consider a finite element approximation for a system consisting of the evolution of a curve evolving by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The curve evolves inside a given domain…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
Self-organized criticality (SOC) is widely proposed as a fundamental mechanism for collective behavior, yet its role in objective-driven, heterogeneous adaptive systems underpinning real complex systems remains less understood. We introduce…
We introduce Evolutionary Ensemble (EvE), a decentralized framework that organizes existing, highly capable coding agents into a live, co-evolving system for algorithmic discovery. Rather than reinventing the wheel within the "LLMs as…
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…
Optimal processes in stochastic thermodynamics are a frontier for understanding the control and design of non-equilibrium systems, with broad practical applications in biology, chemistry, and nanoscale/mesoscale systems. Optimal mass…
We prove a strong law of large numbers for directed last passage times in an independent but inhomogeneous exponential environment. Rates for the exponential random variables are obtained from a discretisation of a speed function that may…
With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the…
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
In this paper, we consider the problem of steering a family of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by using an…
Institutions and cultures evolve adaptively in response to the current environmental incentives, usually. But sometimes institutional change is due to stochastic drives beyond current fitness, including drift, path dependency, blind…