arXiv subjects

Piotr Fronczak

Publications and source records attributed to Piotr Fronczak.

At least 37 records · Page 2Linked to original sources

arXiv2017

Exact combinatorial approach to finite coagulating systems

The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, the exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then, this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

cond-mat.stat-mech↗

arXiv2016

How transfer flights shape structure of the airline network

In this paper we analyze the gravity model in the world passenger air-transport network. We show that in the standard form the model is inadequate to correctly describe the relationship between passenger flows and typical geo-economic variables that characterize connected countries. We propose a model of transfer flights which allows to exploit these discrepancies to discover hidden subflows in the network. We illustrate its usefulness by retrieving the distance coefficient in the gravity model which is one of the determinants of the globalization process. Finally, we discuss the correctness of the presented approach by comparing the distance coefficient to several well known economical events.

physics.soc-ph↗

arXiv2016

Day of the week effect in paper submission/acceptance/rejection to/in/by peer review journals. II. An ARCH econometric-like modeling

This paper aims at providing a statistical model for the preferred behavior of authors submitting a paper to a scientific journal. The electronic submission of (about 600) papers to the Journal of the Serbian Chemical Society has been recorded for every day from Jan. 01, 2013 till Dec. 31, 2014, together with the acceptance or rejection paper fate. Seasonal effects and editor roles (through desk rejection and subfield editors) are examined. An ARCH-like econometric model is derived stressing the main determinants of the favorite day-of-week process.

cs.DL↗

arXiv2016

A new fast algorithm for reproducing complex networks with community structure

In this paper, we introduce a new algorithm allowing for generation of networks with heterogeneity of both node degrees and community sizes. The quality and efficiency of the algorithm is analyzed and compared to the other, so far the most popular algorithm which was proposed by Lancichinetti et al. We discuss the advantages and shortcomings of both algorithms indicating the areas of their potential application.

physics.soc-ph↗

arXiv2016

Exact solution of the isotropic majority-vote model on complete graphs

The isotropic majority-vote (MV) model which, apart from the one-dimensional case, is thought to be non-equilibrium and violating the detailed balance condition. We show that this is not true, when the model is defined on a complete graph. In the stationary regime, the MV model on a fully connected graph fulfills the detailed balance. We derive the exact expression for the probability distribution of finding the system in a given spin configuration. We show that it only depends on the absolute value of magnetization. Our theoretical predictions are validated by numerical simulations.

cond-mat.stat-mech↗

arXiv2016

Mixed-order phase transition in a minimal, diffusion based spin model

In this paper, we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model "diffusion-based" because its hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.

cond-mat.stat-mech↗

arXiv2015

A minimal exactly solved model with the extreme Thouless effect

We present and analyze a minimal exactly solved model that exhibits a mixed-order phase transition known in the literature as the Thouless effect. Such hybrid transitions do not fit into the modest classification of thermodynamic transitions and as such, they used to be overlooked or incorrectly identified in the past. The recent series of observations of such transitions in many diverse systems suggest that a new taxonomy of phase transitions is needed. The spin model we present due to its simplicity and possible experimental designs could bring us to this goal. We find the Hamiltonian of the model from which partition function is easily calculated. Thermodynamic properties of the model, i.e. discontinuous magnetization and diverging susceptibility, are discussed. Finally, its generalizations and further research directions are proposed.

cond-mat.stat-mech↗

arXiv2015

Quantifying the quality of peer reviewers through Zipf's law

This paper introduces a statistical and other analysis of peer reviewers in order to approach their "quality" through some quantification measure, thereby leading to some quality metrics. Peer reviewer reports for the Journal of the Serbian Chemical Society are examined. The text of each report has first to be adapted to word counting software in order to avoid jargon inducing confusion when searching for the word frequency: e.g. C must be distinguished, depending if it means Carbon or Celsius, etc. Thus, every report has to be carefully "rewritten". Thereafter, the quantity, variety and distribution of words are examined in each report and compared to the whole set. Two separate months, according when reports came in, are distinguished to observe any possible hidden spurious effects. Coherence is found. An empirical distribution is searched for through a Zipf-Pareto rank-size law. It is observed that peer review reports are very far from usual texts in this respect. Deviations from the usual (first) Zipf's law are discussed. A theoretical suggestion for the "best (or worst) report" and by extension "good (or bad) reviewer", within this context, is provided from an entropy argument, through the concept of "distance to average" behavior. Another entropy-based measure also allows to measure the journal reviews (whence reviewers) for further comparison with other journals through their own reviewer reports.

physics.soc-ph↗

arXiv2015

Review times in peer review: quantitative analysis of editorial workflows

We examine selected aspects of peer review and suggest possible improvements. To this end, we analyse a dataset containing information about 300 papers submitted to the Biochemistry and Biotechnology section of the Journal of the Serbian Chemical Society. After separating the peer review process into stages that each review has to go through, we use a weighted directed graph to describe it in a probabilistic manner and test the impact of some modifications of the editorial policy on the efficiency of the whole process.

physics.soc-ph↗

arXiv2015

Exact low-temperature series expansion for the partition function of the two-dimensional zero-field s=1/2 Ising model on the infinite square lattice

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic--to--paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

math-ph↗

arXiv2014

Spanning trees of the World Trade Web: real-world data and the gravity model of trade

In this paper, we investigate the statistical features of the weighted international-trade network. By finding the maximum weight spanning trees for this network we make the extraction of the truly relevant connections forming the network's backbone. We discuss the role of large-sized countries (strongest economies) in the tree. Finally, we compare the topological properties of this backbone to the maximum weight spanning trees obtained from the gravity model of trade. We show that the model correctly reproduces the backbone of the real-world economy.

physics.soc-ph↗

arXiv2014

International trade network: fractal properties and globalization puzzle

Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue, that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

physics.soc-ph↗

arXiv2014

Percolation in the classical blockmodel

Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation transition in the classical blockmodel has not been examined so far, although the phenomenon has been studied in a variety of much more complicated models of interconnected and multiplex networks. In this paper we derive the self-consistent equation for the size the global percolation cluster in the classical blockmodel. We also find the condition for percolation threshold which characterizes the emergence of the giant component. We show that the discussed percolation phenomenon may cause unexpected problems in a simple optimization process of the multilevel network construction. Numerical simulations confirm the correctness of our theoretical derivations.

cond-mat.dis-nn↗

arXiv2014

Polish and English wordnets -- statistical analysis of interconnected networks

Wordnets are semantic networks containing nouns, verbs, adjectives, and adverbs organized according to linguistic principles, by means of semantic relations. In this work, we adopt a complex network perspective to perform a comparative analysis of the English and Polish wordnets. We determine their similarities and show that the networks exhibit some of the typical characteristics observed in other real-world networks. We analyse interlingual relations between both wordnets and deliberate over the problem of mapping the Polish lexicon onto the English one.

cs.CL↗

arXiv2013

Exponential random graph models for networks with community structure

Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both, the classical blockmodel and its degree-corrected counterpart, and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. The scaling feature comes as a surprise, especially that in this study, contrary to what is suggested in the literature, the scaling property is not attributed to any specific network construction procedure. It is an intrinsic feature of the degree-corrected blockmodel. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.

physics.soc-ph↗

arXiv2013

Exact expression for the number of states in lattice models

We derive a closed-form combinatorial expression for the number of states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach provides interesting insights into basis of statistical mechanics. In particular, it is shown that in some cases the logarithm of the partition function may be considered the generating function for the number of internal states of energy clusters, which characterize system's microscopic configurations. Apart from elementary examples including the Poisson, geometric and negative binomial probability distributions for the energy, the framework is also validated against the one-dimensional Ising model.

cond-mat.stat-mech↗

arXiv2012

Theoretical approach and impact of correlations on the critical packet generation rate in traffic dynamics on complex networks

Using the formalism of the biased random walk in random uncorrelated networks with arbitrary degree distributions, we develop theoretical approach to the critical packet generation rate in traffic based on routing strategy with local information. We explain microscopic origins of the transition from the flow to the jammed phase and discuss how the node neighbourhood topology affects the transport capacity in uncorrelated and correlated networks.

physics.soc-ph↗

arXiv2012

Statistical mechanics of the international trade network

Analyzing real data on international trade covering the time interval 1950-2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of the trading countries' GDPs. It means that time evolution of this network may be considered as a continuous sequence of equilibrium states, i.e. quasi-static process. This, in turn, allows one to apply the linear response theory to make (and also verify) simple predictions about the network. In particular, we show that bilateral trade fulfills fluctuation-response theorem, which states that the average relative change in import (export) between two countries is a sum of relative changes in their GDPs. Yearly changes in trade volumes prove that the theorem is valid.

q-fin.GN↗