Emergence of mono-cluster flocking in the thermomechanical Cucker–Smale model under switching topologies

2020 ◽  
pp. 1-38
Author(s):  
Jiu-Gang Dong ◽  
Seung-Yeal Ha ◽  
Doheon Kim
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Dynamical Variable ◽  
Switching Network ◽  
Logarithmic Function ◽  
System Parameters ◽  
Network Topologies ◽  
Isothermal Case ◽  
Uniformly Bounded ◽  
Emergent Dynamics

We study the emergent dynamics of the thermomechanical Cucker–Smale (TCS) model with switching network topologies. The TCS model is a generalized CS model with extra internal dynamical variable called “temperature” in which isothermal case exactly coincides with the CS model for flocking. In previous studies, emergent dynamics of the TCS model has been mostly restricted to some static network topologies such as complete graph, connected graph with positive in and out degrees at each node, and digraphs with spanning trees. In this paper, we consider switching network topologies with a spanning tree in a sequence of time-blocks, and present two sufficient frameworks leading to the asymptotic mono-cluster flocking in terms of initial data and system parameters. In the first framework in which the sizes of time-blocks are uniformly bounded by some positive constant, we show that temperature and velocity diameters tend to zero exponentially fast, and spatial diameter is uniformly bounded. In the second framework, we admit a situation in which the sizes of time-blocks may grow mildly by a logarithmic function. In latter framework, our temperature and velocity diameters tend to zero at least algebraically slow.

Consensus of Conspecific Agents via Collaborative and Antagonistic Interactions

2015 ◽  
Author(s):  
Subhradeep Roy ◽  
Nicole Abaid
Keyword(s):  
Monte Carlo ◽  
Sufficient Conditions ◽  
Switching Network ◽  
Random Networks ◽  
Agent Based ◽  
System Parameters ◽  
Wide Range ◽  
Network Topologies ◽  
Necessary And Sufficient ◽  
Antagonistic Interactions

The vast majority of the existing agent-based models of consensus consider the interactions among the agents to be collaborative. In the present work, we define superimposed stochastically-switching network topologies which capture collaborative and antagonistic interactions among the agents. We consider a general class of agents, so-called conspecifics, which encompasses a wide range of protocols explored in the literature, ranging from Erdos-Renyi random networks to numerosity-constrained networks. We find closed form expressions for necessary and sufficient conditions for consensus. We validate the main results using Monte Carlo simulations and study the consensus conditions for Erdos-Renyi networks. We find that, for certain selections of system parameters, the presence of antagonistic interactions permits consensus in systems that would not reach accordance otherwise.

EVOLUTION OF SHANGHAI STOCK MARKET BASED ON MAXIMAL SPANNING TREES

2012 ◽  
Vol 27 (03) ◽  
pp. 1350022 ◽  
Author(s):  
CHUNXIA YANG ◽  
YING SHEN ◽  
BINGYING XIA
Keyword(s):  
Stock Market ◽  
Stock Prices ◽  
Spanning Tree ◽  
Stock Price ◽  
Spanning Trees ◽  
Turning Points ◽  
Single Step ◽  
P Value ◽  
Power Law Distribution ◽  
Structure Variation

In this paper, using a moving window to scan through every stock price time series over a period from 2 January 2001 to 11 March 2011 and mutual information to measure the statistical interdependence between stock prices, we construct a corresponding weighted network for 501 Shanghai stocks in every given window. Next, we extract its maximal spanning tree and understand the structure variation of Shanghai stock market by analyzing the average path length, the influence of the center node and the p-value for every maximal spanning tree. A further analysis of the structure properties of maximal spanning trees over different periods of Shanghai stock market is carried out. All the obtained results indicate that the periods around 8 August 2005, 17 October 2007 and 25 December 2008 are turning points of Shanghai stock market, at turning points, the topology structure of the maximal spanning tree changes obviously: the degree of separation between nodes increases; the structure becomes looser; the influence of the center node gets smaller, and the degree distribution of the maximal spanning tree is no longer a power-law distribution. Lastly, we give an analysis of the variations of the single-step and multi-step survival ratios for all maximal spanning trees and find that two stocks are closely bonded and hard to be broken in a short term, on the contrary, no pair of stocks remains closely bonded for a long time.

The Causal Tracing Method of Fast Moving Consumer Goods Logistics Quality Based on Extended Spanning Tree

2013 ◽  
Vol 694-697 ◽  
pp. 3480-3483
Author(s):  
Shou Wen Ji ◽  
Zeng Rong Su ◽  
Zhi Hua Zhang
Keyword(s):  
Consumer Goods ◽  
Fast Moving ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Logic Model ◽  
Fast Moving Consumer Goods ◽  
Tracing Algorithm ◽  
Tracing Method ◽  
Logistics Quality

The paper analyzes the extended spanning trees elements corresponding to fast-moving consumer goods (FMCG) logistics quality. According to extended spanning tree, we establish a logic model of FMCGs logistics quality causal tracing. At last, the paper gives out tracing algorithm and specific tracing process of FMCG logistics quality based on extended spanning tree.

On the number of leaves of a euclidean minimal spanning tree

1987 ◽  
Vol 24 (4) ◽  
pp. 809-826 ◽  
Author(s):  
J. Michael Steele ◽  
Lawrence A. Shepp ◽  
William F. Eddy
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Random Variables ◽  
Minimal Spanning Tree ◽  
Absolutely Continuous ◽  
Mean And Variance ◽  
Number Of Leaves ◽  
The Mean ◽  
Vertex Degrees ◽  
Minimal Spanning Trees

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi, , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n–1Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.

scholarly journals Matchings, Cycle Bases, and the Maximum Genus of a Graph

10.37236/2479 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Michal Kotrbčík ◽  
Martin Škoviera
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Perfect Matching ◽  
Intersection Graph ◽  
Matching Number ◽  
Maximum Genus ◽  
Cycle Space ◽  
Intersection Graphs ◽  
Connected Graphs ◽  
Cycle Bases

We study the interplay between the maximum genus of a graph and bases of its cycle space via the corresponding intersection graph. Our main results show that the matching number of the intersection graph is independent of the basis precisely when the graph is upper-embeddable, and completely describe the range of matching numbers when the graph is not upper-embeddable. Particular attention is paid to cycle bases consisting of fundamental cycles with respect to a given spanning tree. For $4$-edge-connected graphs, the intersection graph with respect to any spanning tree (and, in fact, with respect to any basis) has either a perfect matching or a matching missing exactly one vertex. We show that if a graph is not $4$-edge-connected, different spanning trees may lead to intersection graphs with different matching numbers. We also show that there exist $2$-edge connected graphs for which the set of values of matching numbers of their intersection graphs contains arbitrarily large gaps.

scholarly journals A Minimum-Spanning-Tree-Inspired Algorithm for Channel Assignment in 802.11 Networks

2016 ◽  
Vol 62 (4) ◽  
pp. 379-388 ◽  
Author(s):  
Iwona Dolińska ◽  
Mariusz Jakubowski ◽  
Antoni Masiukiewicz ◽  
Grzegorz Rządkowski ◽  
Kamil Piórczyński
Keyword(s):  
Greedy Algorithm ◽  
Channel Assignment ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Minimum Spanning Trees ◽  
Undirected Graphs ◽  
Interference Level ◽  
802.11 Networks ◽  
Crowded Environment

Abstract Channel assignment in 2.4 GHz band of 802.11 standard is still important issue as a lot of 2.4 GHz devices are in use. This band offers only three non-overlapping channels, so in crowded environment users can suffer from high interference level. In this paper, a greedy algorithm inspired by the Prim’s algorithm for finding minimum spanning trees (MSTs) in undirected graphs is considered for channel assignment in this type of networks. The proposed solution tested for example network distributions achieves results close to the exhaustive approach and is, in many cases, several orders of magnitude faster.

scholarly journals Consensus for Multiple Unmanned Surface Vehicle (Musv) Systems with Markov Switching Topologies

2019 ◽  
Vol 26 (1) ◽  
pp. 145-152
Author(s):  
Liyuan Wang ◽  
Wei Yue ◽  
Rubo Zhang
Keyword(s):  
Switching Network ◽  
Linear Matrix ◽  
Sampled Data ◽  
Consensus Control ◽  
Unmanned Surface Vehicle ◽  
Control Scheme ◽  
Random Switching ◽  
Leader Following ◽  
Network Topologies ◽  
Wave Induced

Abstract This paper is concerned with sampled-data leader following consensus of multiple unmanned surface vehicle (MUSV) systems with random switching network topologies and wave-induced disturbance. By modelling the switching of network topologies with the use of a Markov process and considering the effect of wave-induced disturbance, a new sampled-data consensus control protocol is proposed. By employing an appropriate Lyapunov-Krosovskii function method and the weak infinitesimal operation, a novel stability criterion is derived, which ensures that the MUSV system can reach robustly leader-following consensus with H∞ performance satisfied. Based on this criterion, the Markov dependent switching consensus controller gains are obtained by solving a set of linear matrix inequalities. Finally, an illustrative example is given to verify the effectiveness of the proposed control scheme for MUSV systems.

On the number of leaves of a euclidean minimal spanning tree

1987 ◽  
Vol 24 (04) ◽  
pp. 809-826 ◽  
Author(s):  
J. Michael Steele ◽  
Lawrence A. Shepp ◽  
William F. Eddy
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Random Variables ◽  
Minimal Spanning Tree ◽  
Absolutely Continuous ◽  
Mean And Variance ◽  
Number Of Leaves ◽  
The Mean ◽  
Vertex Degrees ◽  
Minimal Spanning Trees

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi , , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n –1 Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.

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