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Grzegorz Siudem

Publications and source records attributed to Grzegorz Siudem.

16 recordsLinked to original sources

Generating Synthetic Citation Networks with Communities

Generating realistic synthetic citation, patent, or component dependency networks is essential for benchmarking community detection, graph visualisation, and network data mining algorithms. We present a systematic comparison of generators of directed graphs that are nearly acyclic and have a ground-truth community structure. We evaluate 12 methods across 7 real citation networks and 26 metrics. We propose the practice of reversing the directions of edges in static generators to break cycles and induce a citation-like flow, which markedly improves the performance of a degree-corrected Stochastic Block Model. Our methodological approach to evaluating community detection benchmarks distinguishes between endogenous and exogenous mesoscopic similarities, with the latter proving more important. This distinction reveals that high-parameter models gain much of their advantage by memorising planted community statistics, which limits their fidelity when the evaluation is blind to those labels. Finally, we introduce the Citation Seeder (CS) algorithm, an iterative generator grounded in the Price-Pareto model of citation networks, with interpretable parameters and O(N+E) generation. CS achieves competitive results against the best-performing baselines while using up to four orders of magnitude fewer parameters, providing an interpretable account of a network's structure and, on a temporal hold-out, extrapolating its future in-degree distribution more faithfully than descriptive baselines.

cs.SI↗

Equivalence of inequality indices in the three-dimensional model of informetric impact

Inequality is an inherent part of our lives: we see it in the distribution of incomes, talents, citations, to name a few. However, its intensity varies across environments: there are systems where the available resources are relatively evenly distributed but also where a small group of items or agents controls the majority of assets. Numerous indices for quantifying the degree of inequality have been proposed but in general, they work quite differently. We recently observed (Siudem et al., 2020) that many rank-size distributions might be approximated by a time-dependent agent-based model involving a mixture of preferential (rich-get-richer) and accidental (sheer chance) attachment. In this paper, we point out its relationship to an iterative process that generates rank distributions of any length and a predefined level of inequality, as measured by the Gini index. We prove that, under our model, the Gini, Bonferroni, De Vergottini, and Hoover indices are equivalent for samples of similar sizes. Given one of them, we can recreate the value of another measure. Thanks to the obtained formulae, we can also understand how they depend on the sample size. An empirical analysis of a large database of citation records in economics (RePEc) yields a good match with our theoretical derivations.

physics.soc-ph↗

The Price-Pareto growth model of networks with community structure

We introduce a new analytical framework for modelling degree sequences in individual communities of real-world networks, e.g., citations to papers in different fields. Our work is inspired by a recent modification of the Price's model, which assumes that citations are gained partly accidentally, and to some extent preferentially. Our work addresses the need to represent the heterogeneity of various scientific domains, as standard homogeneous models fail to capture the distinct growth ratios and citing cultures of different fields. Extending the model to networks with a community structure allows us to devise the analytical formulae for, amongst others, citation counts in each cluster and their inequality as described by the Gini index. We also show that a citation count distribution in each community tends to a Pareto type II distribution. Thanks to the derived model parameter estimators, the new model can be fitted to real citation and similar networks.

physics.soc-ph↗

Gini-stable Lorenz curves and their relation to the generalised Pareto distribution

We introduce an iterative discrete information production process where we can extend ordered normalised vectors by new elements based on a simple affine transformation, while preserving the predefined level of inequality, G, as measured by the Gini index. Then, we derive the family of empirical Lorenz curves of the corresponding vectors and prove that it is stochastically ordered with respect to both the sample size and G which plays the role of the uncertainty parameter. We prove that asymptotically, we obtain all, and only, Lorenz curves generated by a new, intuitive parametrisation of the finite-mean Pickands' Generalised Pareto Distribution (GPD) that unifies three other families, namely: the Pareto Type II, exponential, and scaled beta distributions. The family is not only totally ordered with respect to the parameter G, but also, thanks to our derivations, has a nice underlying interpretation. Our result may thus shed a new light on the genesis of this family of distributions. Our model fits bibliometric, informetric, socioeconomic, and environmental data reasonably well. It is quite user-friendly for it only depends on the sample size and its Gini index.

physics.soc-ph↗

Community detection in complex networks via node similarity, graph representation learning, and hierarchical clustering

Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this task. The introduced approach supports various linkage-based clustering algorithms, vertex proximity matrices, and graph representation learning models. We compare over a hundred module combinations on the Stochastic Block Model graphs and real-life datasets. We observe that our best pipelines (Wasserman-Faust and the mutual information-based PPMI proximity, as well as the deep learning-based DNGR representations) perform competitively to the state-of-the-art Leiden and Louvain algorithms. At the same time, unlike the latter, they remain hierarchical. Thus, they output a series of nested partitions of all possible cardinalities which are compatible with each other. This feature is crucial when the number of correct partitions is unknown in advance.

cs.SI↗

Power Laws, the Price Model, and the Pareto type-2 Distribution

We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and preferential (rich-get-richer) rules. Instead of relying on the typical master equation approach, we formulate and solve this problem in terms of the rank-size distribution. We show that, asymptotically, such a process leads to a Pareto-type 2 distribution with an appealingly interpretable parametrisation. We prove that the solution to the Price model expressed in terms of the rank-size distribution coincides with the expected values of order statistics in an independent Paretian sample. We study the bias and the mean squared error of three well-behaving estimators of the underlying model parameters. An empirical analysis of a large repository of academic papers yields a good fit not only in the tail of the distribution (as it is usually the case in the power law-like framework), but also across the whole domain. Interestingly, the estimated models indicate higher degree of preferentially attached citations and smaller share of randomness than previous studies.

physics.soc-ph↗

Modelling railway delay propagation as diffusion-like spreading

Railway systems form an important means of transport across the world. However, congestions or disruptions may significantly decrease these systems' efficiencies, making predicting and understanding the resulting train delays a priority for railway organisations. Delays are studied in a wide variety of models, which usually simulate trains as discrete agents carrying delays. In contrast, in this paper, we define a novel model for studying delays, where they spread across the railway network via a diffusion-like process. This type of modelling has various advantages such as quick computation and ease of applying various statistical tools like spectral methods, but it also comes with limitations related to the directional and discrete nature of delays and the trains carrying them. We apply the model to the Belgian railways and study its performance in simulating the delay propagation in severely disrupted railway situations. In particular, we discuss the role of spatial aggregation by proposing to cluster the Belgian railway system into sets of stations and adapt the model accordingly. We find that such aggregation significantly increases the model's performance. For some particular situations, a non-trivial optimal level of spatial resolution is found on which the model performs best. Our results show the potential of this type of delay modelling to understand large-scale properties of railway systems.

physics.soc-ph↗

Combinatorial origins of the canonical ensemble

The Darwin-Fowler method in combination with the steepest descent approach is a common tool in the asymptotic description of many models arising from statistical physics. In this work, we focus rather on the non-asymptotic behavior of the Darwin-Fowler procedure. By using a combinatorial approach based on Bell polynomials, we solve it exactly. Due to that approach, we also show relationships of typical models with combinatorial Lah and Stirling numbers.

math-ph↗

Bell polynomials in the series expansions of the Ising model

Through applying Bell polynomials to the integral representation of the free energy of the Ising model for the triangular and hexagonal lattices we obtain the exact combinatorial formulas for the number of spin configurations at a given energy (i.e. low-temperature series expansion of the partition function or, alternatively, the number of states). We also generalize this approach to the wider class of the (chequered) Utiyama graphs. Apart from the presented exact formulas, our technique allows one to establish the correspondence between the perfect gas of clusters and the Ising model on the lattices which have positive coefficients in the low-temperature expansion (e.g. square lattice, hexagonal lattice). However it is not always the case -- we present that for the triangular lattice the coefficients could be negative and the perfect gas of clusters interpretation is problematic.

math-ph↗

Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions

In this paper, we draw attention to the problem of phase transitions in systems with locally affine microcanonical entropy, in which partial equivalence of (microcanonical and canonical) ensembles is observed. We focus on a very simple spin model, that was shown to be an equilibrium statistical mechanics representation of the biased random walk. The model exhibits interesting discontinuous phase transitions that are simultaneously observed in the microcanonical, canonical, and grand canonical ensemble, although in each of these ensembles the transition occurs in a slightly different way. The differences are related to fluctuations accompanying the discontinuous change of the number of positive spins. In the microcanonical ensemble, there is no fluctuation at all. In the canonical ensemble, one observes power-law fluctuations, which are, however, size-dependent and disappear in the thermodynamic limit. Finally, in the grand canonical ensemble, the discontinuous transition is of mixed-order (hybrid) kind with diverging (critical-like) fluctuations. In general, this paper consists of many small results, which together make up an interesting example of phase transitions that are not covered by the known classifications of these phenomena.

cond-mat.stat-mech↗

Diffusion on hierarchical systems of weakly-coupled networks

We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and derived a transport equation that is analogous to Fick's First Law and includes a driving force. Entropy production is a sum of microscopic entropy transport, which results from the particle's migration between networks of different topologies and macroscopic entropy production of the Markov chain. Equilibrium particles partition between different sub-networks depends only on internal sub-network parameters. Our framework, confirmed by numerical simulations, is also useful for considering diffusion in nested systems corresponding to hierarchical networks with several different time scales thus it can serve to uncover hidden hierarchy levels from observations of diffusion processes.

nlin.CD↗

Area-width scaling in generalised Motzkin paths

We consider a generalised version of Motzkin paths, where horizontal steps have length $\ell$, with $\ell$ being a fixed positive integer. We first give the general functional equation for the area-length generating function of this model. Using a heuristic ansatz, we derive the area-length scaling behaviour in terms of a scaling function in one variable for the special cases of Dyck, (standard) Motzkin and Schröder paths, before generalising our approach to arbitrary $\ell$. We then derive an expression for the generating function of Schröder paths and analyse the scaling behaviour of this function rigorously in the vicinity of the tri-critical point of the model by applying the method of steepest descents for the case of two coalescing saddle points. Our results show that for Dyck and Schröder paths, the heuristic scaling ansatz reproduces the rigorous results.

cond-mat.stat-mech↗

Agent-based model for the h-index - Exact solution

The Hirsch's $h$-index is perhaps the most popular citation-based measure of the scientific excellence. In 2013 G. Ionescu and B. Chopard proposed an agent-based model for this index to describe a publications and citations generation process in an abstract scientific community. With such an approach one can simulate a single scientist's activity, and by extension investigate the whole community of researchers. Even though this approach predicts quite well the $h$-index from bibliometric data, only a solution based on simulations was given. In this paper, we complete their results with exact, analytic formulas. What is more, due to our exact solution we are able to simplify the Ionescu-Chopard model which allows us to obtain a compact formula for $h$-index. Moreover, a simulation study designed to compare both, approximated and exact, solutions is included. The last part of this paper presents evaluation of the obtained results on a real-word data set.

physics.soc-ph↗

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↗

Analytical approach to model of scientific revolutions

The model of scientific paradigms spreading throughout the community of agents with memory is analyzed using the master equation. The case of two competing ideas is considered for various networks of interactions, including agents placed at Erdős-Rényi graphs or complete graphs. The pace of adopting a new idea by a community is analyzed, along with the distribution of periods after which a new idea replaces the old one. The approach is extended for the chain topology onto the more general case when more than two ideas compete. Our analytical results are in agreement with numerical simulations.

physics.soc-ph↗

External bias in the model of isolation of communities

We extend a model of community isolation in the d-dimensional lattice onto the case with an imposed imbalance between birth rates of competing communities. We give analytical and numerical evidences that in the asymmetric two-specie model there exists a well defined value of the asymmetry parameter when the emergence of the isolated (blocked) subgroups is the fastest, i.e. the characteristic time tc is minimal. This critical value of the parameter depends only on the lattice dimensionality and is independent from the system size. Similar phenomenon was observed in the multi-specie case with a geometric distribution of the birth rates. We also show that blocked subgroups in the multi-specie case are absent or very rare when either there is a strictly dominant specie that outnumbers the others or when there is a large diversity of species. The number of blocked species of different kinds decreases with the dimension of the multi-specie system.

physics.soc-ph↗