Invariant probability measures and dynamics of exponential linear type maps

2008 ◽  
Vol 28 (5) ◽  
pp. 1479-1495
Author(s):  
DAVID GAMARNIK ◽  
TOMASZ NOWICKI ◽  
GRZEGORZ ŚWIRSZCZ
Keyword(s):  
Fixed Point ◽  
Probability Measure ◽  
Random Graph ◽  
Statistical Physics ◽  
Positive Linear Operator ◽  
Distribution Functions ◽  
Maximum Weight ◽  
Linear Type ◽  
Maximum Weight Matching ◽  
Attracting Fixed Point

AbstractWe consider the problem of the asymptotic size of the random maximum-weight matching of a sparse random graph, which we translate into dynamics of the operator in the space of distribution functions. A tight condition for the uniqueness of the globally attracting fixed point is provided, which extends the result of Karp and Sipser [Maximum matchings in sparse random graphs. 22nd Ann. Symp. on Foundations of Computer Science (Nashville, TN, 28–30 October, 1981). IEEE, New York, 1981, pp. 364–375] from deterministic weight distributions (Dirac measures μ) to general ones. Given a probability measure μ which corresponds to the weight distribution of a link of a random graph, we form a positive linear operator Φμ (convolution) on distribution functions and then analyze a family of its exponents, with parameter λ, which corresponds to the connectivity of a sparse random graph. The operator 𝕋 relates the distribution F on the subtrees to the distribution 𝕋F on the node of the tree by 𝕋F=exp (−λΦμF). We prove that for every probability measure μ and every λ<e, there exists a unique globally attracting fixed point of the operator; the probability measure corresponding to this fixed point can then be used to compute the expected maximum-weight matching on a sparse random graph. This result is called the e-cutoff phenomenon. For deterministic distributions and λ>e, there is no fixed point attractor. We further establish that the uniqueness of the invariant measure of the underlying operator is not a monotone property of the average connectivity; this parallels similar non-monotonicity results in the statistical physics context.

scholarly journals Validation of Automated Chromosome Recovery in the Reconstruction of Ancestral Gene Order

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 160
Author(s):  
Qiaoji Xu ◽  
Lingling Jin ◽  
James H. Leebens-Mack ◽  
David Sankoff
Keyword(s):  
Phylogenetic Tree ◽  
Gene Order ◽  
Evolutionary Process ◽  
Gene Content ◽  
Ancestral Genome ◽  
Maximum Weight ◽  
Ancestral Gene ◽  
Maximum Weight Matching

The RACCROCHE pipeline reconstructs ancestral gene orders and chromosomal contents of the ancestral genomes at all internal vertices of a phylogenetic tree. The strategy is to accumulate a very large number of generalized adjacencies, phylogenetically justified for each ancestor, to produce long ancestral contigs through maximum weight matching. It constructs chromosomes by counting the frequencies of ancestral contig co-occurrences on the extant genomes, clustering these for each ancestor and ordering them. The main objective of this paper is to closely simulate the evolutionary process giving rise to the gene content and order of a set of extant genomes (six distantly related monocots), and to assess to what extent an updated version of RACCROCHE can recover the artificial ancestral genome at the root of the phylogenetic tree relating to the simulated genomes.

scholarly journals Randomized scheduling algorithm for virtual output queuing switch at the presence of non-uniform traffic

2019 ◽  
Vol 8 (1) ◽  
pp. 50
Author(s):  
Ali Ghiasian ◽  
Majid Jamali
Keyword(s):  
Randomized Algorithms ◽  
High Speed ◽  
Time Slot ◽  
Scheduling Algorithm ◽  
Superior Performance ◽  
High Complexity ◽  
Maximum Weight ◽  
Switch Architecture ◽  
Simulation Results ◽  
Maximum Weight Matching

<span>Virtual Output Queuing (VOQ) is a well-known queuing discipline in data switch architecture that eliminates Head Of Line (HOL) blocking issue. In VOQ scheme, for each output port, a separate FIFO is maintained by each input port. Consequently, a scheduling algorithm is required to determine the order of service to virtual queues at each time slot. Maximum Weight Matching (MWM) is a well-known scheduling algorithm that achieves the entire throughput region. Despite of outstanding attainable throughput, high complexity of MWM makes it an impractical algorithm for implementation in high-speed switches. To overcome this challenge, a number of randomized algorithms have been proposed in the literature. But they commonly perform poorly when input traffic does not uniformly select output ports. In this paper, we propose two randomized algorithms that outperform the well-known formerly proposed solutions. We exploit a method to keep a parametric number of heavy edges from the last time matching and mix it by randomly generated matching to produce a new schedule. Simulation results confirm the superior performance of the proposed algorithms.</span>

scholarly journals Linear-Time Approximation for Maximum Weight Matching

2014 ◽  
Vol 61 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Ran Duan ◽  
Seth Pettie
Keyword(s):  
Linear Time ◽  
Maximum Weight ◽  
Time Approximation ◽  
Maximum Weight Matching

scholarly journals A Solution for Volterra Fractional Integral Equations by Hybrid Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 694 ◽  
Author(s):  
Alqahtani ◽  
Aydi ◽  
Karapınar ◽  
Rakočević
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Linear Type ◽  
Linear And Nonlinear ◽  
Nonlinear Contractions ◽  
Type Contraction

In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions.

scholarly journals The Fréchet transform

1993 ◽  
Vol 16 (1) ◽  
pp. 155-164
Author(s):  
Piotor Mikusiński ◽  
Morgan Phillips ◽  
Howard Sherwood ◽  
Michael D. Taylor
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Measure ◽  
Probability Distribution Function ◽  
Random Variables ◽  
Distribution Functions ◽  
Probability Distribution Functions

LetF1,…,FNbe1-dimensional probability distribution functions andCbe anN-copula. Define anN-dimensional probability distribution functionGbyG(x1,…,xN)=C(F1(x1),…,FN(xN)). Letν, be the probability measure induced onℝNbyGandμbe the probability measure induced on[0,1]NbyC. We construct a certain transformationΦof subsets ofℝNto subsets of[0,1]Nwhich we call the Fréchet transform and prove that it is measure-preserving. It is intended that this transform be used as a tool to study the types of dependence which can exist between pairs orN-tuples of random variables, but no applications are presented in this paper.

Dynamical evolution of the seismic coda wave increments during the 2011-2012 Santorini's caldera unrest. A Non-Extensive Statistical Physics approach.

2020 ◽  
Author(s):  
Theodoros Aspiotis ◽  
Ioannis Koutalonis ◽  
Georgios Michas ◽  
Filippos Valianatos
Keyword(s):  
Statistical Physics ◽  
Distribution Functions ◽  
Coda Waves ◽  
Coda Wave ◽  
Tectonic Activity ◽  
Volcanic Complex ◽  
Dynamical Structure ◽  
Gaussian Shape ◽  
Caldera Unrest ◽  
Seismic Coda

&lt;p&gt;Santorini's caldera being unrest during 2011-2012, led several studies to raise the important question of whether seismicity is associated with an impending and potential volcanic eruption or it solely relieves the accumulated tectonic energy. In the present work we study seismic coda waves generated by local earthquake events prior, during and after the seismic crisis that occurred within the caldera area. Coda waves are interpreted as scattered seismic waves generated by heterogeneities within the Earth, i.e. by faults, fractures, velocity and/or density boundaries and anomalies, etc. In particular, we utilize the three components of the seismograms recorded by three seismological stations on the island of Santorini and estimate the duration of the coda waves by implementing a three step procedure that includes the signal-to-noise ratio, the STA/LTA method and the short time Fourier transform. The final estimation was verified or reestimated manually due to the existent ambient seismic noise. Due to the nature and the path complexity of the coda waves and towards achieving a unified framework for the study of the immerse geo-structural seismotectonic complexity of the Santorini volcanic complex, we use Non-Extensive Statistical Physics (NESP) to study the probability distribution functions (pdfs) of the increments of seismic coda waves. NESP forms a generalization of the Boltzmann-Gibbs statistical mechanics, that has been extensively used for the analysis of semi-chaotic systems that exhibit long-range interactions, memory effects and multi-fractality. The analysis and results demonstrate that the seismic coda waves increments deviate from the Gaussian shape and their respective pdfs could adequately be described and processed by the q-Gaussian distribution. Furthermore and in order to investigate the dynamical structure of the volcanic-tectonic activity, we estimate the q-indices derived from the pdfs of the coda wave time series increments during the period 2009 - 2014 and present their variations as a function of time and as a function of the local magnitude (M&lt;sub&gt;L&lt;/sub&gt;) of the events prior, during and after the caldera unrest.&lt;/p&gt; &lt;p&gt;&amp;#160;&lt;/p&gt; &lt;p&gt;&lt;strong&gt;&amp;#160;Acknowledgments.&amp;#160;&lt;/strong&gt;We acknowledge support by the project &amp;#8220;HELPOS &amp;#8211; Hellenic System for Lithosphere Monitoring&amp;#8221; (MIS 5002697) which is implemented under the Action &amp;#8220;Reinforcement of the Research and Innovation Infrastructure&amp;#8221;, funded by the Operational Programme &quot;Competitiveness, Entrepreneurship and Innovation&quot; (NSRF 2014-2020) and co-financed by Greece &amp; European Union (ERDF)&lt;/p&gt;

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