Related papers: Order from Randomness
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
In this paper, we study the dynamics of a system of $n$ coupled, self-propelled particles: $\ddot r_k = (\alpha-\beta |\dot r_k|^2)\dot r_k - \frac{\gamma}{n}\sum_{m=1}^n(r_k-r_m)$, $r_k\in \mathbb R^2.$ Numerical experiments indicate that,…
Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for…
How can we understand the origins of highly symmetrical objects? One way is to characterize them as the solutions of natural optimization problems from discrete geometry or physics. In this paper, we explore how to prove that exceptional…
We consider infinite harmonic chain on the real line with deterministic dynamics (no stochasticity). We indicate classes of uniformly bounded initial conditions when the trajectories of particles stay uniformly bounded.
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
We tackle the problem of consciousness by taking the naturally selected, embodied organism as our starting point. We provide a formalism describing how biological systems such as human bodies self-organize to hierarchically interpret…
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta…
We show that extremely simple systems of a not too large number of particles can be simultane- ously thermally stable and complex. To such an end, we extend the statistical complexity's notion to simple configurations of non-interacting…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
Properties of systems with majority voting rules have been exhaustingly studied. In this work we focus on the randomized case - where the system is initialized by randomized initial set of seeds. Our main aim is to give an asymptotic…