Related papers: The arcsine law as a universal aging scheme for tr…
Network science provides an indispensable theoretical framework for studying the structure and function of real complex systems. Different network models are often used for finding the rules that govern their evolution, whereby the correct…
We establish three tractable, jointly sufficient conditions for the control landscapes of non-linear control systems to be trap free comparable to those now well known in quantum control. In particular, our results encompass end-point…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Aging in a two dimensional suspension containing rods was studied by means of kinetic Monte Carlo simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state was…
There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…
We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display non-local entanglement. To this end, we introduce and study a…
Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…
The continuous time random walk model has been widely applied in various fields, including physics, biology, chemistry, finance, social phenomena, etc. In this work, we present an algorithm that utilizes a subordinate formula to generate…
Here we propose a generic mechanism - networked buffering - for generating robust traits in complex systems that requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role…
The gradual accumulation of damage and dysregulation during the aging of living organisms can be quantified. Even so, the aging process is complex and has multiple interacting physiological scales -- from the molecular to cellular to whole…
Physical aging is one of the non-equilibrium phenomena where physical properties change over time due to structural relaxation. Aging in spin glass systems has been explained by a trap model on the temperature-independent energy landscape.…
Based on their earlier studies of the arcsine law, Pitman and Yor in \cite{PY97} constructed a widely adopted PD($\alpha, \theta)$ family of random mass-partitions with parameters $\alpha \in [0,1),\ \theta+\alpha>0$. We propose an…
We prove a martingale triangular array generalization of the Chow-Birnbaum-Marshall's inequality. The result is used to derive a strong law of large numbers for martingale triangular arrays whose rows are asymptotically stable in a certain…
In this paper, we propose a general framework for the trapping problem on a weighted network with a perfect trap fixed at an arbitrary node. By utilizing the spectral graph theory, we provide an exact formula for mean first-passage time…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
We formulate time series tasks as input-output mappings under varying objectives, where the same input may yield different outputs. This challenges a model's generalization and adaptability. To study this, we construct a synthetic dataset…
Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of direction constraints between the points is equivalent to the…
The arc-routing problems are known to be notoriously hard. We study here a natural arc-routing problem on trees and more generally on bounded tree-width graphs and surprisingly show that it can be solved in a polynomial time. This implies a…