The present article contains a short introduction to Modular Theory for von Neumann algebras with a cyclic and separating vector. It includes the formulation of the central result in this area, the Tomita-Takesaki theorem, and several of its consequences. We illustrate this theory through several elementary examples. We also present more elaborate examples and compute modular objects for a disc...

{ Using a computer vision system to supervise a construction task requires the reliable recognition of assembled objects. A particularly reliable object recognition is possible if a comprehensive representation of knowledge about assembled objects is provided. In this paper we present a cyclic semantic network which models all possible assemblies of objects from a wooden construction-kit for ch...

A novel representation of the linear birth process with immigration is analysed. The state space of the process is the collection of permutations of the integers, written in a particular cyclic form. The stochastic structure of the model is particularly simple to describe. The results serve to explain the combinatorial structure of some sampling formulae that arise in the study of neutral mutat...

Representation and analysis of complex biological and engineered systems as directed networks is useful for understanding their global structure/function organization. Enrichment of network motifs, which are over-represented subgraphs in real networks, can be used for topological analysis. Because counting network motifs is computationally expensive, only characterization of 3- to 5-node motifs...

In this paper we extend several results about classical knot invariants derived from the infinite cyclic cover to the twisted case. Let X be a finite complex with fundamental group n, let o :nPG ̧(») be a linear representation where » is a finite dimensional vector space over a field F, and let e : nPZ be a homomorphism. Finally let X = be the infinite cyclic cover of X corresponding to e. The r...

Long-lasting interference effects in picture naming are induced when objects are presented in categorically related contexts in both continuous and blocked cyclic paradigms. Less consistent context effects have been reported when the task is changed to semantic classification. Experiment 1 confirmed the recent finding of cumulative facilitation in the continuous paradigm with living/non-living ...

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

Let $G$ be a reductive group over number field $F$, which is split at finite place $\mathfrak{p}$ of and let $\pi$ cuspidal automorphic representation $G$, cohomological with respect to the trivial coefficient system Steinberg $\mathfrak{p}$. We use cohomology $\mathfrak{p}$-arithmetic subgroups attach $\mathcal{L}$-invariants $\pi$. This generalizes construction Darmon (respectively Spie\ss), ...

This paper explores the asymptotic spectral decomposition of periodically Toeplitz matrices with finite summable elements. As an alternative to polyphase and other approaches based on Gladyshev representation, proposed route exploits structure cyclic autocorrelation matrices, thus leveraging known results providing a more direct link spectrum coherence. concrete application, problem linear pred...