scholarly journals Strongly Connected Multivariate Digraphs

10.37236/6539 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Yaokun Wu ◽  
Zeying Xu ◽  
Yinfeng Zhu
Keyword(s):  
Matrix Multiplication ◽  
Combinatorial Designs ◽  
Linear Map ◽  
Nonnegative Tensors ◽  
Strongly Connected ◽  
Tensor Multiplication ◽  
Special Case

Generalizing the idea of viewing a digraph as a model of a linear map, we suggest a multi-variable analogue of a digraph, called a hydra, as  a model of a multi-linear map. Walks in digraphs correspond to usual matrix multiplication while walks in hydras correspond to the tensor multiplication introduced by Robert Grone in 1987.  By viewing matrix multiplication as a special case of this tensor multiplication, many concepts on strongly connected digraphs are generalized to corresponding  ones for hydras, including strongly connectedness, periods and primitiveness, etc. We explore the structure of all possible periods of strongly connected hydras, which turns out to be related to the existence of certain kind of  combinatorial designs. We also provide estimates of largest primitive exponents and largest diameters of relevant hydras. Much  existing research  on tensors are based on some other definitions of multiplications of tensors and so our work here  supplies new perspectives for understanding irreducible and primitive  nonnegative tensors.

scholarly journals Tight paths in convex geometric hypergraphs

2020 ◽  
Author(s):  
Dhruv Mubayi ◽  
Zoltán Füredi ◽  
Jacques Verstraëte ◽  
Alexandr Kostochka ◽  
Tao Jiang
Keyword(s):  
Graph Theory ◽  
Upper Bound ◽  
Geometric Structure ◽  
Related Problem ◽  
Combinatorial Designs ◽  
Uniform Hypergraph ◽  
Single Edge ◽  
Vertex Graph ◽  
Geometric Hypergraphs ◽  
Special Case

One of the most intruguing conjectures in extremal graph theory is the conjecture of Erdős and Sós from 1962, which asserts that every $n$-vertex graph with more than $\frac{k-1}{2}n$ edges contains any $k$-edge tree as a subgraph. Kalai proposed a generalization of this conjecture to hypergraphs. To explain the generalization, we need to define the concept of a tight tree in an $r$-uniform hypergraph, i.e., a hypergraph where each edge contains $r$ vertices. A tight tree is an $r$-uniform hypergraph such that there is an ordering $v_1,\ldots,v_n$ of its its vertices with the following property: the vertices $v_1,\ldots,v_r$ form an edge and for every $i>r$, there is a single edge $e$ containing the vertex $v_i$ and $r-1$ of the vertices $v_1,\ldots,v_{i-1}$, and $e\setminus\{v_i\}$ is a subset of one of the edges consisting only of vertices from $v_1,\ldots,v_{i-1}$. The conjecture of Kalai asserts that every $n$-vertex $r$-uniform hypergraph with more than $\frac{k-1}{r}\binom{n}{r-1}$ edges contains every $k$-edge tight tree as a subhypergraph. The recent breakthrough results on the existence of combinatorial designs by Keevash and by Glock, Kühn, Lo and Osthus show that this conjecture, if true, would be tight for infinitely many values of $n$ for every $r$ and $k$. The article deals with the special case of the conjecture when the sought tight tree is a path, i.e., the edges are the $r$-tuples of consecutive vertices in the above ordering. The case $r=2$ is the famous Erdős-Gallai theorem on the existence of paths in graphs. The case $r=3$ and $k=4$ follows from an earlier work of the authors on the conjecture of Kalai. The main result of the article is the first non-trivial upper bound valid for all $r$ and $k$. The proof is based on techniques developed for a closely related problem where a hypergraph comes with a geometric structure: the vertices are points in the plane in a strictly convex position and the sought path has to zigzag beetwen the vertices.

THE TRANSITIVE CLOSURE AND RELATED ALGORITHMS OF DIGRAPH ON THE RECONFIGURABLE ARCHITECTURE

2011 ◽  
Vol 21 (01) ◽  
pp. 27-43 ◽  
Author(s):  
TIEN-TAI PAN ◽  
SHUN-SHII LIN
Keyword(s):  
Transitive Closure ◽  
Matrix Multiplication ◽  
Three Dimensional ◽  
Reconfigurable Architecture ◽  
Processor Arrays ◽  
Tree Construction ◽  
The Matrix ◽  
Strongly Connected ◽  
Reconfigurable Mesh ◽  
Closure Algorithm

The reconfigurable architecture is a parallel computation model that consists of many processor elements (PEs) and a reconfigurable bus system. There are many variant proposed reconfigurable architectures, for example, reconfigurable mesh (R-Mesh), directional reconfigurable mesh (DR-Mesh), processor arrays with reconfigurable bus systems (PARBS), complete directional processor arrays with reconfigurable bus systems (CD-PARBS), reconfigurable multiple bus machine (RMBM), directional reconfigurable multiple bus machine (directional RMBM), and etc. In this paper, a transitive closure (TC) algorithm of digraph is proposed on the models without the directional capability (non-directional). Some related digraph problems, such as strongly connected digraph, strongly connected component (SCC), cyclic checking, and tree construction, can also be resolved by modifying our transitive closure algorithm. All the proposed algorithms are designed on a three-dimensional (3-D) n×n×n non-directional reconfigurable mesh, n is the number of vertices in a digraph D, and can resolve the respective problems in O(log d(D)) time, d(D) is the diameter of the digraph D. The cyclic checking problem can be further reduced to O(log c(D)) time, c(D) is the minimum distance of cycles in the digraph D. There exist two different approaches: the matrix multiplication approach on the non-directional models for algebraic path problems (APP) and s-t connectivity approach on the directional models. In this paper, we will use the tree construction algorithm to prove those two approaches are insufficient to resolve all digraph problems and demonstrate why our approach is so important and innovative for digraph problems on the reconfigurable models.

Approximately Periodic Functionals on C*-Algebras and von Neumann Algebras

1985 ◽  
Vol 37 (5) ◽  
pp. 769-784 ◽  
Author(s):  
John C. Quigg
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Related Question ◽  
Compact Groups ◽  
Von Neumann ◽  
Linear Map ◽  
C Algebras ◽  
Preceding Question ◽  
Special Case ◽  
Algebraic Tensor Product

In the duality for locally compact groups, much use is made of a version of the Hopf algebra technique in the context of von Neumann algebras, culminating in the theory of Kac algebras [6], [14]. It seems natural to ask whether something like a Hopf algebraic structure can be defined on the pre-dual of a Kac algebra. This leads to the question of whether the multiplication on a von Neumann algebra M, viewed as a linear map m from M ⊙ M (the algebraic tensor product) to M, can be pre-transposed to give a co-multiplication on the pre-dual M*, i.e., a linear map m* from M* to the completion of M* ⊙ M* with respect to some cross-norm. A related question is whether the multiplication on a C*-algebra A can be transposed to give a co-multiplication on the dual A*. Of course, this can be regarded as a special case of the preceding question by taking M = A**, where the double dual A** is identified with the enveloping von Neumann algebra of A.

scholarly journals KMS states on the C*-algebras of Fell bundles over groupoids

2019 ◽  
pp. 1-25
Author(s):  
ZAHRA AFSAR ◽  
AIDAN SIMS
Keyword(s):  
Equilibrium States ◽  
Cross Sectional ◽  
Kms States ◽  
C Algebras ◽  
Trace Space ◽  
Strongly Connected ◽  
The Cross ◽  
Natural Dynamics ◽  
Special Case

Abstract We consider fibrewise singly generated Fell bundles over étale groupoids. Given a continuous real-valued 1-cocycle on the groupoid, there is a natural dynamics on the cross-sectional algebra of the Fell bundle. We study the Kubo–Martin–Schwinger equilibrium states for this dynamics. Following work of Neshveyev on equilibrium states on groupoid C*-algebras, we describe the equilibrium states of the cross-sectional algebra in terms of measurable fields of states on the C*-algebras of the restrictions of the Fell bundle to the isotropy subgroups of the groupoid. As a special case, we obtain a description of the trace space of the cross-sectional algebra. We apply our result to generalise Neshveyev’s main theorem to twisted groupoid C*-algebras, and then apply this to twisted C*-algebras of strongly connected finite k-graphs.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

Impact of Digitalization on Service Work in Knowledge-Intensive Business Services: An Empirical Study in Tax Consultancies

2019 ◽  
Vol 3 (4) ◽  
pp. 209-222
Author(s):  
Philipp K. Görs ◽  
Henning Hummert ◽  
Anne Traum ◽  
Friedemann W. Nerdinger
Keyword(s):  
Work Engagement ◽  
Service Work ◽  
Psychological Consequences ◽  
Business Services ◽  
Knowledge Intensive Business Services ◽  
Positive Effects ◽  
Knowledge Intensive ◽  
The Impact ◽  
Positive Effect ◽  
Special Case

Digitalization is a megatrend, but there is relatively little knowledge about its consequences for service work in general and specifically in knowledge-intensive business services (KIBS). We studied the impact of digitalization on psychological consequences for employees in tax consultancies as a special case of KIBS. We compare two tax consulting jobs with very different job demands, those of tax consultants (TCs) and assistant tax consultants (ATCs). The results show that the extent of digitalization at the workplace level for ATCs correlates significantly positively with their job satisfaction. For TCs, the same variable correlates positively with their work engagement. These positive effects of digitalization are mediated in the case of ATCs by the impact on important job characteristics. In the case of TCs, which already have very good working conditions, the impact is mediated by the positive effect on self-efficacy. Theoretical and practical consequences of these results are discussed.

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