arXiv subjects

Gábor Vattay

Publications and source records attributed to Gábor Vattay.

At least 19 recordsLinked to original sources

arXiv2026

Transition from Statistical to Hardware-Limited Scaling in Photonic Quantum State Reconstruction

The theoretical efficiency of classical shadow tomography is predicated on a perfect Haar-random unitary ensemble, yet this mathematical ideal remains physically unattainable in near-term hardware. Here, we report the experimental discovery of a fundamental accuracy bound on integrated photonic processors: a ``Hardware Horizon'' where the reconstruction error undergoes a sharp phase transition. While the error initially obeys the predicted statistical scaling $\mathcal{O}(M^{-1/2})$, it abruptly saturates at a floor determined by the spectral distortions of the realized unitary group. By deriving a phenomenological error model, we decouple the competing mechanisms of static coherent spectral distortion and dynamic decoherence, demonstrating that this intrinsic noise floor imposes a hard bound that statistical accumulation cannot overcome. These findings establish that the utility of shadow tomography on NISQ (noisy intermediate-scale quantum) hardware is defined by a specific scaling law involving hardware parameters, necessitating active compensation strategies to bridge the gap between theoretical purity and the noisy reality of integrated photonics.

quant-ph↗

arXiv2025

Quantum Signatures of Strange Attractors

In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate the quantum Duffing oscillator, a paradigmatic chaotic system, using the Caldirola-Kanai (CK) framework, where dissipation is integrated directly into a time-dependent Hamiltonian. By employing the Husimi distribution to represent the quantum state in phase space, we present the first visualization of a quantum strange attractor within this model. Our simulations demonstrate how an initially simple Gaussian wave packet is stretched, folded, and sculpted by the interplay of chaotic dynamics and energy loss, causing it to localize onto a structure that beautifully mirrors the classical attractor. This quantum "photograph" is inherently smoothed, blurring the infinitely fine fractal details of its classical counterpart as a direct consequence of the uncertainty principle. We supplement this analysis by examining the out-of-time-ordered correlator (OTOC), which shows that stronger dissipation clarifies the exponential growth associated with the classical Lyapunov exponent, thereby confirming the model's semiclassical behavior. This work offers a compelling geometric perspective on open chaotic quantum systems and sheds new light on the quantum-classical transition.

quant-ph↗

arXiv2021

Relaxation of the Ising spin system coupled to a bosonic bath and the time dependent mean field equation

The Ising model doesn't have a strictly defined dynamics, only a spectrum. There are different ways to equip it with a time dependence e.g. the Glauber or the Kawasaki dynamics, which are both stochastic, but it means there is a master equation which can also describes their dynamics. We present a Gluber-type master equation derived from the Redfield equation, where the spin system is coupled to a bosonic bath. We derive a time dependent mean field equation which describes the relaxation of the spin system at finite temperature. Using the fully connected, uniform Ising model the relaxation time will be studied, and the critical behaviour around the critical temperature. The master equation shows the finite size effects, and the mean field equation the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2021

Mean Field Approximation for solving QUBO problems

The Quadratic Unconstrained Binary Optimization (QUBO) problems are NP hard; thus, so far, there are no algorithms to solve them efficiently. There are exact methods like the Branch-and-Bound algorithm for smaller problems, and for larger ones, many good approximations like stochastic simulated annealing for discrete variables or the mean field annealing for continuous variables. This paper will show that the statistical physics approach and the quantum mechanical approach in the mean field annealing give the same result. We examined the Ising problem, which is an alternative formulation of the QUBO problem. Our methods consist of a set of simple gradient-based minimizations with continuous variables, thus easy to simulate. We benchmarked our methods with solving the Maximum Cut problem with the G-sets. In many graphs, we could achieve the best-known Cut Value.

quant-ph↗

arXiv2021

The rich still get richer: Empirical comparison of preferential attachment via linking statistics in Bitcoin and Ethereum

Bitcoin and Ethereum transactions present one of the largest real-world complex networks that are publicly available for study, including a detailed picture of their time evolution. As such, they have received a considerable amount of attention from the network science community, beside analysis from an economic or cryptography perspective. Among these studies, in an analysis on the early instance of the Bitcoin network, we have shown the clear presence of the preferential attachment, or "rich-get-richer" phenomenon. Now, we revisit this question, using a recent version of the Bitcoin network that has grown almost 100-fold since our original analysis. Furthermore, we additionally carry out a comparison with Ethereum, the second most important cryptocurrency. Our results show that preferential attachment continues to be a key factor in the evolution of both the Bitcoin and Ethereum transactoin networks. To facilitate further analysis, we publish a recent version of both transaction networks, and an efficient software implementation that is able to evaluate linking statistics necessary for learn about preferential attachment on networks with several hundred million edges.

physics.soc-ph↗

arXiv2019

A Landauer Formula for Bioelectronic Applications

Recent electronic transport experiments using metallic contacts attached to proteins identified some 'stylized facts' which contradict conventional wisdom that increasing either the spatial distance between the electrodes or the temperature suppresses conductance exponentially. These include nearly temperature independent conductance over the protein in the 30-300K range, distance independent conductance within a single-protein in the 1-10 nm range and an anomalously large conductance in the 0.1-10 nS range. In this paper we develop a generalization of the low temperature Landauer formula which can account for the joint effects of tunneling and decoherence and can explain these new experimental findings. We use novel approximations which greatly simplify the mathematical treatment and allow us to calculate the conductance in terms of a handful macroscopic parameters instead of the myriads of microscopic parameters describing the details of an atomic level quantum chemical computation. The new approach makes it possible to get predictions for the outcomes of new experiments without relying solely on high performance computing and can distinguish important and unimportant details of the protein structures from the point of view of transport properties.

cond-mat.dis-nn↗

arXiv2019

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.

physics.soc-ph↗

arXiv2017

Prediction of employment and unemployment rates from Twitter daily rhythms in the US

By modeling macro-economical indicators using digital traces of human activities on mobile or social networks, we can provide important insights to processes previously assessed via paper-based surveys or polls only. We collected aggregated workday activity timelines of US counties from the normalized number of messages sent in each hour on the online social network Twitter. In this paper, we show how county employment and unemployment statistics are encoded in the daily rhythm of people by decomposing the activity timelines into a linear combination of two dominant patterns. The mixing ratio of these patterns defines a measure for each county, that correlates significantly with employment ($0.46\pm0.02$) and unemployment rates ($-0.34\pm0.02$). Thus, the two dominant activity patterns can be linked to rhythms signaling presence or lack of regular working hours of individuals. The analysis could provide policy makers a better insight into the processes governing employment, where problems could not only be identified based on the number of officially registered unemployed, but also on the basis of the digital footprints people leave on different platforms.

physics.soc-ph↗

arXiv2017

Universal Scaling Laws in Metro Area Election Results

We explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948-2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single parameter only, and one of the parties always shows superlinear scaling and drives the process, while the sublinear exponent of the other party is merely the consequence of probability conservation. Based on the recently developed model of urban scaling, we give a microscopic model of voter behavior in which we replace diversity characterizing humans in creative aspects with social diversity and tolerance. The model can also predict new political developments such as the fragmentation of the left and 'the immigration paradox'.

physics.soc-ph↗

arXiv2017

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.

stat.AP↗

arXiv2016

Race, Religion and the City: Twitter Word Frequency Patterns Reveal Dominant Demographic Dimensions in the United States

Recently, numerous approaches have emerged in the social sciences to exploit the opportunities made possible by the vast amounts of data generated by online social networks (OSNs). Having access to information about users on such a scale opens up a range of possibilities, all without the limitations associated with often slow and expensive paper-based polls. A question that remains to be satisfactorily addressed, however, is how demography is represented in the OSN content? Here, we study language use in the US using a corpus of text compiled from over half a billion geo-tagged messages from the online microblogging platform Twitter. Our intention is to reveal the most important spatial patterns in language use in an unsupervised manner and relate them to demographics. Our approach is based on Latent Semantic Analysis (LSA) augmented with the Robust Principal Component Analysis (RPCA) methodology. We find spatially correlated patterns that can be interpreted based on the words associated with them. The main language features can be related to slang use, urbanization, travel, religion and ethnicity, the patterns of which are shown to correlate plausibly with traditional census data. Our findings thus validate the concept of demography being represented in OSN language use and show that the traits observed are inherently present in the word frequencies without any previous assumptions about the dataset. Thus, they could form the basis of further research focusing on the evaluation of demographic data estimation from other big data sources, or on the dynamical processes that result in the patterns found here.

physics.soc-ph↗

arXiv2014

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.

physics.soc-ph↗

arXiv2014

Efficient classification of billions of points into complex geographic regions using hierarchical triangular mesh

We present a case study about the spatial indexing and regional classification of billions of geographic coordinates from geo-tagged social network data using Hierarchical Triangular Mesh (HTM) implemented for Microsoft SQL Server. Due to the lack of certain features of the HTM library, we use it in conjunction with the GIS functions of SQL Server to significantly increase the efficiency of pre-filtering of spatial filter and join queries. For example, we implemented a new algorithm to compute the HTM tessellation of complex geographic regions and precomputed the intersections of HTM triangles and geographic regions for faster false-positive filtering. With full control over the index structure, HTM-based pre-filtering of simple containment searches outperforms SQL Server spatial indices by a factor of ten and HTM-based spatial joins run about a hundred times faster.

cs.DB↗

arXiv2014

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.

physics.soc-ph↗

arXiv2013

A multi-terabyte relational database for geo-tagged social network data

Despite their relatively low sampling factor, the freely available, randomly sampled status streams of Twitter are very useful sources of geographically embedded social network data. To statistically analyze the information Twitter provides via these streams, we have collected a year's worth of data and built a multi-terabyte relational database from it. The database is designed for fast data loading and to support a wide range of studies focusing on the statistics and geographic features of social networks, as well as on the linguistic analysis of tweets. In this paper we present the method of data collection, the database design, the data loading procedure and special treatment of geo-tagged and multi-lingual data. We also provide some SQL recipes for computing network statistics.

cs.DB↗

arXiv2013

Using Robust PCA to estimate regional characteristics of language use from geo-tagged Twitter messages

Principal component analysis (PCA) and related techniques have been successfully employed in natural language processing. Text mining applications in the age of the online social media (OSM) face new challenges due to properties specific to these use cases (e.g. spelling issues specific to texts posted by users, the presence of spammers and bots, service announcements, etc.). In this paper, we employ a Robust PCA technique to separate typical outliers and highly localized topics from the low-dimensional structure present in language use in online social networks. Our focus is on identifying geospatial features among the messages posted by the users of the Twitter microblogging service. Using a dataset which consists of over 200 million geolocated tweets collected over the course of a year, we investigate whether the information present in word usage frequencies can be used to identify regional features of language use and topics of interest. Using the PCA pursuit method, we are able to identify important low-dimensional features, which constitute smoothly varying functions of the geographic location.

cs.CL↗

arXiv2013

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.

physics.soc-ph↗

arXiv2012

The effect of network structure on phase transitions in queuing networks

Recently, De Martino et al have presented a general framework for the study of transportation phenomena on complex networks. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested to the congested phase at a critical traffic load. In this paper, we also study phase transition in transportation networks using a discrete time random walk model. Our aim is to establish a direct connection between the structure of the graph and the value of the critical traffic load. Applying spectral graph theory, we show that the original results of De Martino et al showing that the critical loading depends only on the degree sequence of the graph -- suggesting that different graphs with the same degree sequence have the same critical loading if all other circumstances are fixed -- is valid only if the graph is dense enough. For sparse graphs, higher order corrections, related to the local structure of the network, appear.

physics.soc-ph↗