Synchronization of a Generalized High-dimensional Kuramoto Model With Directed Graphs

Initial State ◽

Theoretical Results

Abstract In this paper, a generalized high-dimensional Kuramoto model with directed graphs is investigated. A necessary and sufficient condition for equilibria is given and the synchronization is proved under weaker directed graph conditions and more general initial state constrains. Finally, an example is given to validate the theoretical results.

On the Divisibility of Homogeneous Directed Graphs

Canadian Journal of Mathematics ◽

10.4153/cjm-1993-014-0 ◽

1993 ◽

Vol 45 (2) ◽

pp. 284-294 ◽

Cited By ~ 6

Author(s):

M. El-Zahar ◽

N. W. Sauer

Keyword(s):

Directed Graph ◽

Directed Graphs ◽

Isomorphic Copy ◽

Sufficient Condition ◽

Finite Set ◽

AbstractLet be a finite set of finite tournaments. We will give a necessary and sufficient condition for the -free homogeneous directed graph to be divisible. That is, that there is a partition of into two classes such that neither of them contains an isomorphic copy of .

Quantum walks on directed graphs

Quantum Information and Computation ◽

10.26421/qic7.1-2-5 ◽

2007 ◽

Vol 7 (1&2) ◽

pp. 93-102

Author(s):

A. Montanaro

Keyword(s):

Directed Graph ◽

Discrete Time ◽

Directed Graphs ◽

Quantum Walk ◽

Quantum Walks ◽

Sufficient Condition ◽

Time Quantum ◽

Definition Of ◽

We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices $(v_i, v_j)$, if $v_i$ is connected to $v_j$ then there is a path from $v_j$ to $v_i$. We show that reversibility is a necessary and sufficient condition for a directed graph to allow the notion of a discrete-time quantum walk, and discuss some implications of this condition. We present a method for defining a "partially quantum'' walk on directed graphs that are not reversible.

A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2016.141 ◽

2017 ◽

Vol 38 (7) ◽

pp. 2401-2421 ◽

Cited By ~ 3

Author(s):

SARA E. ARKLINT ◽

SØREN EILERS ◽

EFREN RUIZ

Keyword(s):

Directed Graphs ◽

Sufficient Condition ◽

Orbit Equivalence ◽

Graph Algebras ◽

Boundary Path ◽

We characterize when there exists a diagonal-preserving $\ast$-isomorphism between two graph $C^{\ast }$-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of ‘orbit equivalence’ between the boundary path spaces of the directed graphs $E$ and $F$ and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving $\ast$-isomorphism between the graph $C^{\ast }$-algebras $C^{\ast }(E)$ and $C^{\ast }(F)$.

Sifat-Sifat Representasi Indekomposabel The Properties of Indecomposable Representations

Natural Science Journal of Science and Technology ◽

10.22487/25411969.2019.v8.i3.14598 ◽

2019 ◽

Vol 8 (3) ◽

Author(s):

Vika Yugi Kurniawan

Keyword(s):

Vector Space ◽

Directed Graph ◽

Linear Mapping ◽

Sufficient Condition ◽

Paper Study ◽

Direct Sum ◽

Indecomposable Representations ◽

Finite Set ◽

A directed graph is also called as a quiver where is a finite set of vertices, is a set of arrows, and are two maps from to . A representation of a quiver is an assignment of a vector space to each vertex of and a linear mapping to each arrow. We denote by the direct sum of representasions and of a quiver . A representation is called indecomposable if is not ishomorphic to a direct sum of non-zero representations. This paper study about the properties of indecomposable representations. These properties will be used to investigate the necessary and sufficient condition of indecomposable representations.

Initial state estimation from limited observations of the heat equation in metric graphs

Inverse Problems ◽

10.1088/1361-6420/ac4afc ◽

2022 ◽

Author(s):

Satoru Iwasaki

Keyword(s):

Heat Equation ◽

State Estimation ◽

Observation Data ◽

Sufficient Condition ◽

Transition Matrices ◽

Metric Graphs ◽

Initial State ◽

Estimation Problems ◽

Abstract This paper deals with initial state estimation problems of the heat equation in equilateral metric graphs being admitted to have cycles. Particularly, we are concerned with suitable placements of observation points in order to uniquely determine the initial state from observation data. We give a necessary and sufficient condition for suitable placements of observation points, and such suitable placements are determined from transition matrices of metric graphs. From numerical simulations, we confirm effectiveness of a necessary and sufficient condition.

Stochastic monotonicity of birth–death processes

Advances in Applied Probability ◽

10.1017/s0001867800033383 ◽

1980 ◽

Vol 12 (01) ◽

pp. 59-80 ◽

Cited By ~ 3

Author(s):

Erik A. Van Doorn

Keyword(s):

Initial Distribution ◽

Unit Vector ◽

Death Process ◽

Sufficient Condition ◽

Stochastic Monotonicity ◽

Initial State ◽

Distribution Vector ◽

Birth Death

A birth–death process {x(t): t ≥ 0} with state space the set of non-negative integers is said to be stochastically increasing (decreasing) on the interval (t 1, t 2) if Pr {x(t) > i} is increasing (decreasing) with t on (t 1, t 2) for all i = 0, 1, 2, ···. We study the problem of finding a necessary and sufficient condition for a birth–death process with general initial state probabilities to be stochastically monotone on an interval. Concrete results are obtained when the initial distribution vector of the process is a unit vector. Fundamental in the analysis, and of independent interest, is the concept of dual birth–death processes.

Study of “Sticking and Restarting Phenomenon” in Electropneumatic Positioning Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1858443 ◽

2005 ◽

Vol 127 (1) ◽

pp. 173-184 ◽

Cited By ~ 8

Author(s):

Xavier Brun ◽

Sylvie Sesmat ◽

Daniel Thomasset ◽

Serge Scavarda

Keyword(s):

Dry Friction ◽

Partial Equilibrium ◽

Experimental Result ◽

Sufficient Condition ◽

Pressure Force ◽

Friction Forces ◽

Positioning Systems ◽

Theoretical Results

This paper explains the possible occurrence of the “sticking and restarting phenomenon” observed with electropneumatic positioning systems. This is carried out from the notion of partial equilibrium, with the analysis of the model which incorporates two parallel phenomena which are used to generate a pressure force subjected to dry friction forces. Also, an experimental result has been studied in a particular pressure force plane which shows the origin of the problem more explicitly. The theoretical results give a necessary and sufficient condition for the restarting phenomenon not to occur and, if this condition is not validated, there is an estimation of the restarting time. Understanding this undesirable phenomenon will be the basis for further work which will attempt to find solutions to avoid its occurrence.

On Invertibility of an Interconnected System Composed of Two Dynamic Subsystems

Applied Sciences ◽

10.3390/app11020596 ◽

2021 ◽

Vol 11 (2) ◽

pp. 596

Author(s):

Mei Zhang ◽

Boutaïeb Dahhou ◽

Ze-tao Li

Keyword(s):

Local Level ◽

Sufficient Condition ◽

Global Level ◽

Initial State ◽

Interconnected System ◽

Global System ◽

System A ◽

Local Input

In this paper, the invertibility of an interconnected system that consists of two dynamic subsystems was studied. It can be viewed as the distinguishability of the impacts of local input on the final global output, that is to say, whether the input at the local level can be recovered uniquely under a given output at the global level and initial state. The interconnected system constitutes two dynamic subsystems connected in a cascade manner. In order to guarantee the invertibility of the studied system, a necessary and sufficient condition was established. On the condition that both individual subsystems are invertible, the invertibility of the global system can be guaranteed. In order to recover the local input which generates a given global output, an algorithm was proposed for the studied interconnected system. Numerical examples were considered to confirm the effectiveness and robustness of the proposed algorithm.

Automorphism Groups of Wreath Product Digraphs

The Electronic Journal of Combinatorics ◽

10.37236/106 ◽

2009 ◽

Vol 16 (1) ◽

Cited By ~ 5

Author(s):

Edward Dobson ◽

Joy Morris

Keyword(s):

Wreath Product ◽

Directed Graph ◽

Classical Result ◽

Automorphism Groups ◽

Sufficient Condition ◽

Vertex Transitive ◽

Vertex Transitive Graphs ◽

Transitive Graphs

We generalize a classical result of Sabidussi that was improved by Hemminger, to the case of directed color graphs. The original results give a necessary and sufficient condition on two graphs, $C$ and $D$, for the automorphsim group of the wreath product of the graphs, ${\rm Aut}(C\wr D)$ to be the wreath product of the automorphism groups ${\rm Aut}(C)\wr {\rm Aut}(D)$. Their characterization generalizes directly to the case of color graphs, but we show that there are additional exceptional cases in which either $C$ or $D$ is an infinite directed graph. Also, we determine what ${\rm Aut}(C \wr D)$ is if ${\rm Aut}(C \wr D) \neq {\rm Aut} (C) \wr {\rm Aut} (D)$, and in particular, show that in this case there exist vertex-transitive graphs $C'$ and $D'$ such that $C' \wr D' = C \wr D$ and ${\rm Aut} (C\wr D) = {\rm Aut} (C') \wr {\rm Aut}(D')$.

Stochastic monotonicity of birth–death processes

Advances in Applied Probability ◽

10.2307/1426494 ◽

1980 ◽

Vol 12 (1) ◽

pp. 59-80 ◽

Cited By ~ 12

Author(s):

Erik A. Van Doorn

Keyword(s):

Initial Distribution ◽

Unit Vector ◽

Death Process ◽

Sufficient Condition ◽

Stochastic Monotonicity ◽

Initial State ◽

Distribution Vector ◽

Birth Death

A birth–death process {x(t): t ≥ 0} with state space the set of non-negative integers is said to be stochastically increasing (decreasing) on the interval (t1, t2) if Pr {x(t) > i} is increasing (decreasing) with t on (t1, t2) for all i = 0, 1, 2, ···. We study the problem of finding a necessary and sufficient condition for a birth–death process with general initial state probabilities to be stochastically monotone on an interval. Concrete results are obtained when the initial distribution vector of the process is a unit vector. Fundamental in the analysis, and of independent interest, is the concept of dual birth–death processes.