We address the excess entropy, which is a measure of complexity for stationary time series, from the ordinal point of view. We show that the permutation excess entropy is equal to the mutual information between two adjacent semi-infinite blocks in the space of orderings for finite-state stationary ergodic Markov processes. This result may shed a new light on the relationship between complexity ...

Following works of Furstenberg and Nevo and Zimmer we present an outline of a theory of stationary (or m-stationary) dynamical systems for a general acting group G equipped with a probability measure m. Our purpose is two-fold: First to suggest a more abstract line of development, including a simple structure theory. Second, to point out some interesting applications; one of these is a Szemeréd...

Driven diffusive systems are models from non-equilibrium statistical mechanics where discrete and identical particles move on a fixed lattice. These systems conserve the number of particles and are used to model traffic dynamics, granular systems and various biological processes. Often these systems exhibit a condensation transition, [1]. This means there exists some critical density such that ...

We analyze a jump processes Z with a jump measure determined by a “memory” process S. The state space of (Z, S) is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of (Z, S) is the product of the uniform probability measure and a Gaussian distribution.

BACKGROUND There is a need for valid population level measures of physical activity in young children. The aim of this paper is to report the development, and the reliability and validity, of the Preschool-age Children's Physical Activity Questionnaire (Pre-PAQ) which was designed to measure activity of preschool-age children in the home environment in population studies. METHODS Pre-PAQ was ...

The purpose of present study was to examine the effects of short time static and dynamic stretching of muscles on kinematics variability of lower extremity in healthy active males during cycling. 15 physical education and sport sciences male students from Kharazmi University voluntarily participated in this study. Subjects referred to the laboratory during two days, with 48 hours intervals betw...

We consider a stationary source emitting letters from a finite al­ phabet A. The source is described by a stationary probability measure a on the space 0 := AlN of sequences of letters. Denote by On the set of words of length n and by an the probability measure induced on On by a. \Ve consider sequences {rneOn : n E IN} having special properties. Call {rneOn: n E IN} a sup­ porting sequence for...

This paper presents the first generalization bounds for time series prediction with a non-stationary mixing stochastic process. We prove Rademacher complexity learning bounds for both average-path generalization with non-stationary β-mixing processes and path-dependent generalization with non-stationary φ-mixing processes. Our guarantees are expressed in terms of βor φ-mixing coefficients and a...

T he fin al pu bl ic at io n is av ai la bl e at Sp ri ng er vi a ht tp :// dx .d oi .o rg /1 0. 10 07 /9 78 -3 -6 42 -3 68 44 -8 5 Abstract Completing their initial phase of rapid growth social networks are expected to reach a plateau from where on they are in a statistically stationary state. Such stationary conditions may have different dynamical properties. For example, if each message in a...