Entire Fredholm determinants for Evaluation of Semi-classical and Thermodynamical Spectra

Proofs that Fredholm determinants of transfer operators for hyperbolic flows are entire can be extended to a large new class of multiplicative evolution operators. We construct such operators both for the Gutzwiller semi-classical quantum mechanics and for classical thermodynamic formalism, and introduce a new functional determinant which is expected to be entire for Axiom A flows, and whose zeros coincide with the zeros of the Gutzwiler-Voros zeta function.Comment: 4 pages, Revtex + one PS figure attached to the end of the text cut before you run revtex

Komplex viselkedés klasszikus és kvantum hálózatokban = Complex behavior in classical and Quantum Networks

A pályázat keretében komplex hálózatok statisztikus fizikai tulajdonságait vizsgáltuk. Elsősorban az Internet mint komplex hálózat topológián túlmenő vizsgálatára koncentráltunk, de az ad-hoc kommunikációs hálózatok összeköttetési tulajdonságait valamint a kvantum hálózatok eszköztárának felhasználhatóságát is vizsgáltuk. A kutatások eredményeit 1 könyvben és 20 egyéb publikációban foglaltuk össze. Az eredmények közül kiemelkedik az Internet ''univerzális'' lognormális késleltetés eloszlásának kimutatása, az Interneten kialakuló torlódási hullámok kvantitatív vizsgálata, a hosszútávon korrelált hálózati forgalom különböző új aspektusainak feltárása, a skála független fák terén elért egzakt eredmények, és az Erdős-Rényi gráfok szint statisztikájának kapcsolatba hozása a perkolációs átalakulással. | In this project the statistical properties of complex networks has been investigated. Wr concentrated mostly on the properties of Internet as a complex system especially beyond the topological properties. We investigated some aspects of ad-hoc communication networks and we also used the tools developed in the theory of quantum graphs. We published 1 book and 20 other publicatios. Our most important results are the discovery of ""universal"" delay distribution in the Internet, the quantitative analysis of congestion waves in the Internet, various new aspects of the propagation of long range dependence, some exact results on tree graphs and the identification of the percolation transition in the level spacing distribution of the eigenvalue spectrum of adjacency matrices of Erdos-Renyi graphs

Scaling in Words on Twitter

Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the Metropolitan and Micropolitan Statistical Areas of the United States. We observe a slightly superlinear urban scaling with the city population for the total volume of the tweets and words created in a city. We then find that a certain core vocabulary follows the scaling relationship of that of the bulk text, but most words are sensitive to city size, exhibiting a super- or a sublinear urban scaling. For both regimes we can offer a plausible explanation based on the meaning of the words. We also show that the parameters for Zipf's law and Heaps law differ on Twitter from that of other texts, and that the exponent of Zipf's law changes with city size

Measuring the dimension of partially embedded networks

Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In this paper we propose a new dimension measurement method for networks, which does not require global knowledge on the embedding of the nodes, instead it exploits link-wise information (link lengths, link delays or other physical quantities). Our method can be regarded as a generalization of the spectral dimension, that grasps the network's large-scale structure through local observations made by a random walker while traversing the links. We apply the presented method to synthetic and real-world networks, including road maps, the Internet infrastructure and the Gowalla geosocial network. We analyze the theoretically and empirically designated case when the length distribution of the links has the form P(r) ~ 1/r. We show that while previous dimension concepts are not applicable in this case, the new dimension measure still exhibits scaling with two distinct scaling regimes. Our observations suggest that the link length distribution is not sufficient in itself to entirely control the dimensionality of complex networks, and we show that the proposed measure provides information that complements other known measures

Do the rich get richer? An empirical analysis of the BitCoin transaction network

The possibility to analyze everyday monetary transactions is limited by the scarcity of available data, as this kind of information is usually considered highly sensitive. Present econophysics models are usually employed on presumed random networks of interacting agents, and only macroscopic properties (e.g. the resulting wealth distribution) are compared to real-world data. In this paper, we analyze BitCoin, which is a novel digital currency system, where the complete list of transactions is publicly available. Using this dataset, we reconstruct the network of transactions, and extract the time and amount of each payment. We analyze the structure of the transaction network by measuring network characteristics over time, such as the degree distribution, degree correlations and clustering. We find that linear preferential attachment drives the growth of the network. We also study the dynamics taking place on the transaction network, i.e. the flow of money. We measure temporal patterns and the wealth accumulation. Investigating the microscopic statistics of money movement, we find that sublinear preferential attachment governs the evolution of the wealth distribution. We report a scaling relation between the degree and wealth associated to individual nodes.Comment: Project website: http://www.vo.elte.hu/bitcoin/; updated after publicatio

A Bayesian Approach to Identify Bitcoin Users

Bitcoin is a digital currency and electronic payment system operating over a peer-to-peer network on the Internet. One of its most important properties is the high level of anonymity it provides for its users. The users are identified by their Bitcoin addresses, which are random strings in the public records of transactions, the blockchain. When a user initiates a Bitcoin-transaction, his Bitcoin client program relays messages to other clients through the Bitcoin network. Monitoring the propagation of these messages and analyzing them carefully reveal hidden relations. In this paper, we develop a mathematical model using a probabilistic approach to link Bitcoin addresses and transactions to the originator IP address. To utilize our model, we carried out experiments by installing more than a hundred modified Bitcoin clients distributed in the network to observe as many messages as possible. During a two month observation period we were able to identify several thousand Bitcoin clients and bind their transactions to geographical locations

Inferring the interplay of network structure and market effects in Bitcoin

A main focus in economics research is understanding the time series of prices of goods and assets. While statistical models using only the properties of the time series itself have been successful in many aspects, we expect to gain a better understanding of the phenomena involved if we can model the underlying system of interacting agents. In this article, we consider the history of Bitcoin, a novel digital currency system, for which the complete list of transactions is available for analysis. Using this dataset, we reconstruct the transaction network between users and analyze changes in the structure of the subgraph induced by the most active users. Our approach is based on the unsupervised identification of important features of the time variation of the network. Applying the widely used method of Principal Component Analysis to the matrix constructed from snapshots of the network at different times, we are able to show how structural changes in the network accompany significant changes in the exchange price of bitcoins.Comment: project website: http://www.vo.elte.hu/bitcoi

A Fredholm Determinant for Semi-classical Quantization

We investigate a new type of approximation to quantum determinants, the ``\qFd", and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the \qS s derived from the \Gt. The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-$d$ map.Comment: Revtex, Ask for figures from [email protected]