Related papers: Optimization and self-organized criticality in a m…
We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from…
Conservation principles like conservation of charge or energy provide a natural way to couple and constrain different physical variables. In this letter, we propose a dynamical system model that exploits these constraints for solving…
We present a new dynamic off-equilibrium method for the study of continuous transitions, which represents a dynamic generalization of the usual equilibrium cumulant method. Its main advantage is that critical parameters are derived from…
Mixed-criticality real-time scheduling has been developed to improve resource utilization while guaranteeing safe execution of critical applications. These studies use optimistic resource reservation for all the applications to improve…
We consider Random Hopping Time (RHT) dynamics of the Sherrington - Kirkpatrick (SK) model and p-spin models of spin glasses. For any of these models and for any inverse temperature we prove that, on time scales that are sub-exponential in…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
The probability distribution of the order parameter is exploited in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling…
A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…
In this article, we prove second-order necessary optimality conditions for the so-called time crisis problem that comes up within the context of viability theory. It consists in minimizing the time spent by solutions of a controlled…
The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified to allow grains to disappear on each toppling, it is called…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline.…
Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state.…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
We propose a new approach for solving systems of conservation laws that admit a variational formulation of the time-discretized form, and encompasses the p-system or the system of elastodynamics. The approach consists of using constrained…
We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
A novel mechanism for the generation of self-organized criticality (SOC) is discussed in terms of the coupled-vibration model where the total system is forced under the uniform expansion of the Hubble type. This system shows a robust SOC…