Kemeny's Constant And An Analogue Of Braess' Paradox For Trees

2016 ◽  
Vol 31 ◽  
pp. 444-464 ◽  
Author(s):  
Steve Kirkland ◽  
Ze Zeng
Keyword(s):  
Random Walk ◽  
Transition Matrix ◽  
Undirected Graph ◽  
Stochastic Matrix ◽  
Simple Expression ◽  
Initial State ◽  
Final State ◽  
Expected Time ◽  
Almost All ◽  
Special Case

Given an irreducible stochastic matrix M, Kemeny’s constant K(M) measures the expected time for the corresponding Markov chain to transition from any given initial state to a randomly chosen final state. A combinatorially based expression for K(M) is provided in terms of the weights of certain directed forests in a directed graph associated with M, yielding a particularly simple expression in the special case that M is the transition matrix for a random walk on a tree. An analogue of Braess’ paradox is investigated, whereby inserting an edge into an undirected graph can increase the value of Kemeny’s constant for the corresponding random walk. It is shown in particular that for almost all trees, there is an edge whose insertion increases the corresponding value of Kemeny’s constant. Finally, it is proven that for any m ∈ N, almost every tree T has the property that there are at least m trees, none of which are isomorphic to T , such that the values of Kemeny’s constant for the corresponding random walks coincide with the value of Kemeny’s constant for the random walk on T . Several illustrative examples are included.

scholarly journals Capturing the Drunk Robber on a Graph

10.37236/3398 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Natasha Komarov ◽  
Peter Winkler
Keyword(s):  
Random Walk ◽  
Undirected Graph ◽  
Simple Random Walk ◽  
Adjacent Vertex ◽  
Expected Time ◽  
Capture Time ◽  
Vertex Graph

We show that the expected time for a smart "cop"' to catch a drunk "robber" on an $n$-vertex graph is at most $n + {\rm o}(n)$. More precisely, let $G$ be a simple, connected, undirected graph with distinguished points $u$ and $v$ among its $n$ vertices. A cop begins at $u$ and a robber at $v$; they move alternately from vertex to adjacent vertex. The robber moves randomly, according to a simple random walk on $G$; the cop sees all and moves as she wishes, with the object of "capturing" the robber—that is, occupying the same vertex—in least expected time. We show that the cop succeeds in expected time no more than $n {+} {\rm o}(n)$. Since there are graphs in which capture time is at least $n {-} o(n)$, this is roughly best possible. We note also that no function of the diameter can be a bound on capture time.

scholarly journals A Band and Bound Technique for Simple Random Algorithms

1990 ◽  
Vol 4 (3) ◽  
pp. 333-344 ◽  
Author(s):  
Vernon Rego
Keyword(s):  
Markov Chain ◽  
Time Complexity ◽  
Transition Matrix ◽  
Standard Approach ◽  
Initial State ◽  
First Order ◽  
Expected Time ◽  
Order Markov Chain ◽  
Probability Transition Matrix ◽  
Random Algorithm

A simple random algorithm (SRA) is an algorithm whose behavior is governed by a first-order Markov chain. The expected time complexity of an SRA, given its initial state, is essentially the time to absorption of the underlying chain. The standard approach in computing the expected runtime is numerical. Under certain conditions on the probability transition matrix of an SRA, bounds on its expected runtime can be obtained using simple probabilistic arguments. In particular, one can obtain upper and lower (average time) logarithmic bounds for certain algorithms based on SRAs.

Nonwovens: Global Trends in World Economy, European Foreign Trade, and Selected Case Studies from Poland and Asian Brics Countries

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zofia Wysokińska ◽  
Tomasz Czajkowski ◽  
Katarzyna Grabowska
Keyword(s):  
Case Studies ◽  
World Economy ◽  
World Market ◽  
Global Trends ◽  
Textile Materials ◽  
Brics Countries ◽  
Recent Trends ◽  
Almost All ◽  
Special Case

AbstractNonwovens are one of the most versatile textile materials and have become increasingly popular in almost all sectors of the economy due to their low manufacturing costs and unique properties. In the next few years, the world market of nonwovens is predicted to grow by 7%–8% annually (International Nonwovens & Disposables Association [INDA], European Disposables and Nonwovens Association [EDANA], and Markets and Markets). This article aims to analyze the most recent trends in the global export and import of nonwovens, to present two case studies of Polish companies that produce them, and to present one special case study of the market of nonwoven geotextiles in China and India, which are the Asian transition economies among the BRICS countries (Brazil, Russia, India, China, and South Africa).

scholarly journals Dual subtractions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Renato Maria Prisco ◽  
Francesco Tramontano
Keyword(s):  
Field Theory ◽  
Quantum Field ◽  
Matrix Elements ◽  
Leading Order ◽  
Initial State ◽  
Final State ◽  
Dual Representation ◽  
Subtraction Scheme ◽  
Theoretical Predictions ◽  
Perturbative Quantum

Abstract We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.

A NOTE ON THE NORMS OF TRANSITION OPERATORS ON LAMPLIGHTER GRAPHS AND GROUPS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1261-1272 ◽  
Author(s):  
WOLFGANG WOESS
Keyword(s):  
Random Walk ◽  
Wreath Products ◽  
Locally Compact Group ◽  
Operator Matrix ◽  
Locally Compact ◽  
Finitely Generated Groups ◽  
Group Of Isometries ◽  
Transition Operators ◽  
Special Case ◽  
Product Of Groups

Let L≀X be a lamplighter graph, i.e., the graph-analogue of a wreath product of groups, and let P be the transition operator (matrix) of a random walk on that structure. We explain how methods developed by Saloff-Coste and the author can be applied for determining the ℓp-norms and spectral radii of P, if one has an amenable (not necessarily discrete or unimodular) locally compact group of isometries that acts transitively on L. This applies, in particular, to wreath products K≀G of finitely-generated groups, where K is amenable. As a special case, this comprises a result of Żuk regarding the ℓ2-spectral radius of symmetric random walks on such groups.

Intermittency and related issues in 16O-Ag/Br collision at 200A GeV/c

2010 ◽  
Vol 88 (8) ◽  
pp. 575-584 ◽  
Author(s):  
M. K. Ghosh ◽  
P. K. Haldar ◽  
S. K. Manna ◽  
A. Mukhopadhyay ◽  
G. Singh
Keyword(s):  
Particle Density ◽  
Simulated Data ◽  
Space Distribution ◽  
Monte Carlo Code ◽  
Final State ◽  
Data Set ◽  
Fractal Properties ◽  
Self Similar ◽  
Singly Charged ◽  
Almost All

In this paper we present some results on the nonstatistical fluctuation in the 1-dimensional (1-d) density distribution of singly charged produced particles in the framework of the intermittency phenomenon. A set of nuclear emulsion data on 16O-Ag/Br interactions at an incident momentum of 200A GeV/c, was analyzed in terms of different statistical methods that are related to the self-similar fractal properties of the particle density function. A comparison of the present experiment with a similar experiment induced by the 32S nuclei and also with a set of results simulated by the Lund Monte Carlo code FRITIOF is presented. A similar comparison between this experiment and a pseudo-random number generated simulated data set is also made. The analysis reveals the presence of a weak intermittency in the 1-d phase space distribution of the produced particles. The results also indicate the occurrence of a nonthermal phase transition during emission of final-state hadrons. Our results on factorial correlators suggests that short-range correlations are present in the angular distribution of charged hadrons, whereas those on oscillatory moments show that such correlations are not restricted only to a few particles. In almost all cases, the simulated results fail to replicate their experimental counterparts.

scholarly journals Development and testing of a community flood resilience measurement tool

2016 ◽  
Author(s):  
Adriana Keating ◽  
Karen Campbell ◽  
Michael Szoenyi ◽  
Colin McQuistan ◽  
David Nash ◽  
...  
Keyword(s):  
Sustainable Livelihoods ◽  
Development Work ◽  
Measurement Tool ◽  
Disaster Resilience ◽  
Initial State ◽  
Final State ◽  
Sustainable Livelihoods Framework ◽  
Flood Characteristics ◽  
Over Time ◽  
Livelihoods Framework

Abstract. Given the increased attention on resilience-strengthening in international humanitarian and development work, there is a growing need to invest in its measurement and the overall accountability of "resilience strengthening" initiatives. We present a framework and tool for measuring community level resilience to flooding, built around the five capitals (5Cs) of the Sustainable Livelihoods Framework. At the time of writing the tool is being tested in 75 communities across 10 countries. Currently 88 potential sources of resilience are measured at the baseline (initial state) and endline (final state) approximately two years later. If a flood occurs in the community during the study period, resilience outcome measures are recorded. By comparing pre-flood characteristics to post flood outcomes, we aim to empirically verify sources of resilience, something which has never been done in this field. There is an urgent need for the continued development of theoretically anchored, empirically verified and practically applicable disaster resilience measurement frameworks and tools so that the field may: a) deepen understanding of the key components of "disaster resilience" in order to better target resilience enhancing initiatives, and b) enhance our ability to benchmark and measure disaster resilience over time, and compare how resilience changes as a result of different capacities, actions and hazards.

UML-BASED MODELING AND ANALYSIS OF SECURITY THREATS

2010 ◽  
Vol 20 (06) ◽  
pp. 875-897 ◽  
Author(s):  
JUN KONG ◽  
DIANXIANG XU ◽  
XIAOQIN ZENG
Keyword(s):  
Formal Method ◽  
Graph Transformation ◽  
State Transitions ◽  
Security Threats ◽  
Sequence Diagrams ◽  
Security Threat ◽  
Initial State ◽  
Final State ◽  
Modeling And Analysis ◽  
Software Application

Poor design has been a major source of software security problems. Rigorous and designer-friendly methodologies for modeling and analyzing secure software are highly desirable. A formal method for software development, however, often suffers from a gap between the rigidity of the method and the informal nature of system requirements. To narrow this gap, this paper presents a UML-based framework for modeling and analyzing security threats (i.e. potential security attacks) rigorously and visually. We model the intended functions of a software application with UML statechart diagrams and the security threats with sequence diagrams, respectively. Statechart diagrams are automatically converted into a graph transformation system, which has a well-established theoretical foundation. Method invocations in a sequence diagram of a security threat are interpreted as a sequence of paired graph transformations. Therefore, the analysis of a security threat is conducted through simulating the state transitions from an initial state to a final state triggered by method invocations. In our approach, designers directly work with UML diagrams to visually model system behaviors and security threats while threats can still be rigorously analyzed based on graph transformation.

scholarly journals Study of the influence of initial-state fluctuations on hydrodynamic simulations

2020 ◽  
Vol 245 ◽  
pp. 06005
Author(s):  
Marcin Słodkowski ◽  
Patryk Gawryszewski ◽  
Dominik Setniewski
Keyword(s):  
Initial Conditions ◽  
Graphics Processing Unit ◽  
Heavy Ion ◽  
Processing Unit ◽  
Initial State ◽  
Final State ◽  
Hydrodynamic Simulation ◽  
Hydrodynamic Simulations ◽  
Cartesian Coordinate ◽  
Ion Collision

In this work, we are focusing on assessing the contribution of the initial-state fluctuations of heavy ion collision in the hydrodynamic simulations. We are trying to answer the question of whether the hydrodynamic simulation retains the same level of fluctuation in the final-state as for the initial stage. In another scenario, the hydrodynamic simulations of the fluctuation drowns in the final distribution of expanding matter. For this purpose, we prepared sufficient relativistic hydrodynamic program to study A+A interaction which allows analysing initial-state fluctuations in the bulk nuclear matter. For such an assumption, it is better to use high spatial resolution. Therefore, we applied the (3+1) dimensional Cartesian coordinate system. We implemented our program using parallel computing on graphics cards processors - Graphics Processing Unit (GPU). Simulations were carried out with various levels of fluctuation in initial conditions using the average method of events coming from UrQMD models. Energy density distributions were analysed and the contribution of fluctuations in initial conditions was assessed in the hydrodynamic simulation.

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