Related papers: Fiber entropy and algorithmic complexity of random…
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…
G. Edelman, O. Sporns, and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural…
Given a surface $M$ and a Borel probability measure $\nu$ on the group of $C^2$-diffeomorphisms of $M$, we study $\nu$-stationary probability measures on $M$. Assuming the positivity of a certain entropy, the following dichotomy is proved:…
We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…
Real-world computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are ``periodic'', iteratively undergoing the same physical process; and ``local", in that…
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…
We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS are matrix-valued random variables whose…
Complex systems often exhibit highly structured network topologies that reflect functional constraints. In this work, we investigate how, under varying combinations of system-wide selection rules and special agents, different classes of…
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, including specific examples over reals, complex numbers,…
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `$r$' of a discrete time Markov chain with `$\mu_{\pi}$' as invariant ergodic measure, possibly having support on an unbounded state space. The…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
For each $n, d \in \mathbb{N}$ and $0 < \alpha < 1$, we define a random subset of $\mathcal{A}^{\{1, 2, \dots, n\}^d}$ by independently including each element with probability $\alpha$ and excluding it with probability $1-\alpha$, and…
This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…
We consider a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been…
This work contains two single-letter upper bounds on the entropy rate of a discrete-valued stationary stochastic process, which only depend on second-order statistics, and are primarily suitable for models which consist of relatively large…
Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering…
In this paper we carry out an information-theoretic analysis of the $D$-dimensional rigid rotator by studying the entropy and complexity measures of its wavefunctions, which are controlled by the hyperspherical harmonics. These measures…
Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…