1,721,028 research outputs found
Two problems concerning interacting systems: 1. On the purity of the free boundary condition Potts measure on Galton-Watson trees 2. Uniform propagation of chaos in some spin-flip models
No full textAbstract: A rigorous approach to Statistical Physics issues often produces interesting mathematical questions. This Ph.D. thesis is composed of two different parts.
One does not intersect the other, but both research topics lie at the interface between Probability Theory and Statistical Mechanics.
• In the first part we deal with reconstruction of a tree-indexedMarkov chain on Galton-Watson trees, improving previous bound byMossel and Peres, both for symmetric and strongly asymmetric chains. Moreover, we give some numerical estimates to compare our bound with those of other authors. We provide a sufficient condition of the form Q(d)c(M) < 1 for the non-reconstructability of tree-indexed q-stateMarkov chains obtained by broadcasting a signal from the root with a given transition matrix M. Here c(M) is a constant depending on the transition matrixM and Q(d) is the expected number of offspring on the Galton-Watson tree. This result is equivalent to proving
the extremality of the free boundary condition Gibbs measure within the corresponding Gibbs-simplex. When considering the Potts model case we take this point of view too. Our theorem holds for possibly non-reversible M. In the case of the symmetric Ising model the method produces the correct reconstruction threshold, in the case of the (strongly) asymmetric Ising modelwhere the Kesten-Stigum bound is known to be not sharp the method provides improved numerical bounds.
• In the second part of the thesis we give sharp estimates for time uniformpropagation of chaos in some specialsmean field spin-flipmodels exhibiting phase transition. The first model is the dynamical Curie-Weiss model, that can be considered as the most basic mean field model. The second example is a model proposed recently in the context of credit risk in Finance; it describes the time evolution of finantial indicators for a network of interacting firms. Although we have chosen to deal with two specific models, the method we use appear to be rather general, and should work for other classes of models. A substantial limitation of our results is that they are limited to the subcritical case or, in StatisticalMechanical terms, to the high temperature regime.Sommario: Un approccio rigoroso a questioni di Fisica Statistica spesso produce interessanti problemi matematici. Questa tesi di dottorato è composta da due parti.
La prima non interseca la seconda, ma entrambe stanno sul confine tra Teoria della Probabilità e Meccanica Statistica.
• La prima parte tratta il problema della ricostruzione per catene di Markov su alberi di tipo Galton-Watson. Miglioriamoi risultati precedentemente ottenuti da Mossel e Peres, sia per catene simmetriche che fortemente asimmetriche.
Dimostriamo una condizione sufficiente della forma Q(d)c(M) < 1 per la non ricostruzione di catene diMarkov a q-stati sull’albero. Qui c(M) è una costante che dipende dalla matrice di transizione M e Q(d) è la media del numero di figli per vertice nell’albero di Galton-Watson. Questo risultato è equivalente alla purezza della misura libera di Gibbs. Quando consideriamo il caso del modello di Potts assumiamo anche questo punto di vista. Il teorema è valido anche per catene non reversibili. Nel caso del modello di Ising il nostro risultato produce la correta soglia di ricostruzione, nel caso di catene (fortemente) asimmetriche dove si sa che il bound di Kesten-Stigum non è esatto il metodo usato dà risultati numerici migliori.
• Nella seconda parte diamo delle stime uniformi nel tempo per la propagazione del caos in alcuni modelli di spin con interazione a campo medio che presentano transizione di fase. Il primo è il modello dinamico di Curie-Weiss, che può essere considerato come il più semplice esempio di sistema con interazione a campo medio. Il secondo è un modello recentemente impiegato per spiegare i meccanismi del rischio di credito; esso descrive l’evoluzione temporale di
indicatori finaziari per un gruppo di aziende interagenti quotate sul mercato.
Anche se abbiamo trattato modelli specifici, crediamo che il metodo funzioni piuttosto in generale e che sia applicabile anche ad altre classi di modelli. Una limitazione sostanziale dei nostri risultati è che valgono solo nel caso sottocritico, che corrisponde, nel linguaggio della Meccanica Statistica, al regime di alta temperatura
The limiting shape of a full mailbox
Full text linkWe study a model for email communication due to Gabrielli and Cal- darelli, where someone receives and answers emails at the times of independent Poisson processes with intensities λin > λout. The receiver assigns i.i.d. priorities to incoming emails according to some atomless law and always answers the email in the mailbox with the highest priority. Since the frequency of incoming emails is higher than the frequency of answering, below a critical priority, the mailbox fills up ad infinitum. We prove a theorem about the limiting shape of the mailbox just above the critical point, linking it to the convex hull of Brownian motion. We con- jecture that this limiting shape is universal in a class of similar models, including a model for the evolution of an order book due to Stigler and Luckock
Collective periodicity in mean-field models of cooperative behavior
No full textWe propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromag- netic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit
Optimal entropic properties of SARS-CoV-2 RNA sequences
Full text linkThe reaction of the scientific community against the COVID-19 pandemic has generated a huge (approx. 106 entries) dataset of genome sequences collected worldwide and spanning a relatively short time window. These unprecedented conditions together with the certain identification of the reference viral genome sequence allow for an original statistical study of mutations in the virus genome. In this paper, we compute the Shannon entropy of every sequence in the dataset as well as the relative entropy and the mutual information between the reference sequence and the mutated ones. These functions, originally developed in information theory, measure the information content of a sequence and allows us to study the random character of mutation mechanism in terms of its entropy and information gain or loss. We show that this approach allows us to set in new format known features of the SARS-CoV-2 mutation mechanism like the CT bias, but also to discover new optimal entropic properties of the mutation process in the sense that the virus mutation mechanism track closely theoretically computable lower bounds for the entropy decrease and the information transfer
Optimal entropic properties of SARS-CoV-2 RNA sequences
Full text link: The reaction of the scientific community against the COVID-19 pandemic has generated a huge (approx. 106 entries) dataset of genome sequences collected worldwide and spanning a relatively short time window. These unprecedented conditions together with the certain identification of the reference viral genome sequence allow for an original statistical study of mutations in the virus genome. In this paper, we compute the Shannon entropy of every sequence in the dataset as well as the relative entropy and the mutual information between the reference sequence and the mutated ones. These functions, originally developed in information theory, measure the information content of a sequence and allows us to study the random character of mutation mechanism in terms of its entropy and information gain or loss. We show that this approach allows us to set in new format known features of the SARS-CoV-2 mutation mechanism like the CT bias, but also to discover new optimal entropic properties of the mutation process in the sense that the virus mutation mechanism track closely theoretically computable lower bounds for the entropy decrease and the information transfer
New activity pattern in human interactive dynamics
No full textWe investigate the response function of human agents as demonstrated by written correspondence, uncovering a new pattern for how the reactive dynamics of individuals is distributed across the set of each agent's contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to each different correspondent of a given writer, generate a family of heavy-tailed distributions, which have largely the same features for all agents, and whose characteristic times grow exponentially with the rank of each correspondent. We furthermore show that this new behavioral pattern emerges robustly by considering weighted moving averages of the priority-conditioned response-time probabilities generated by a basic prioritization model. Our findings clarify how the range of priorities in the inputs from one's environment underpin and shape the dynamics of agents embedded in a net of reactive relations. These newly revealed activity patterns might be universal, being present in other general interactive environments, and constrain future models of communication and interaction networks, affecting their architecture and evolution
Application of optimal data-based binning method to spatial analysis of ecological datasets
No full textIn this paper we investigate a method proposed recently by K.H. Knuth to find the optimal bin size of an histogram as a tool for statistical analysis of spatial point processes. We test it through numerical simulations on various spatial processes which are of interest in ecology. We show that Knuth optimal bin size rule reducing noisy fluctuations performs better than standard kernel methods to infer the intensity of the underlying process
Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model
Full text linkWe consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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