We give a simple necessary and sufficient condition for the dynamical equivalence of two coupled cell networks with different network architectures. The results are applicable to both continuous and discrete dynamical systems and are framed in terms of what we term input and output equivalence. We also give an algorithm that allows explicit construction of the cells in a system with a given net...

L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete classification up to isometry, and also their isometry groups. The key tool is the so-called canonical decomposition of hyperbolic manifolds.

Recently some results have been presented which show that certain kinds of deterministic descriptions and indeterministic descriptions are observationally equivalent (Werndl 2009a, Werndl 2011). These results prompt interesting philosophical questions, such as what exactly they show or whether the deterministic or indeterministic description is preferable. There is hardly any philosophical disc...

In this paper we introduce the concept of a behavior homomorphisms and isomorphisms and use it to present a uni.ed approach to the study of equivalence of di/erent behavior representations concentrating on a special representation we call normalized ARMA (NARMA) representation. c © 2001 Elsevier Science B.V. All rights reserved.

According to a previous result by S. V. Avgustinovich and the author, each factorial language admits a unique canonical decomposition to a catenation of factorial languages. In this paper, we analyze the appearance of the canonical decomposition of a catenation of two factorial languages whose canonical decompositions are given.

In this paper we discuss the relationship between two of the fundamental examples of restricted orbit equivalence: even Kakutani equivalence and α equivalence. Both equivalence relations arise in the context of representations of ergodic and measure preserving Rd actions. The first is related to the Ambrose-Kakutani Theorem [1]: every free, measure preserving and ergodic R action can be represe...

Equivalence testing is of emerging importance in genomics studies but has hitherto been little studied in this content. In this paper, we define the notion of equivalence of gene expression and determine a ‘strength of evidence’ measure for gene equivalence. It is common practice in genome-wide studies to rank genes according to observed gene-specific P -values or adjusted P -values, which are ...