arXiv subjects

Hrvoje Štefančić

Publications and source records attributed to Hrvoje Štefančić.

11 recordsLinked to original sources

arXiv2026

Variance of the $SIS$ Epidemic on Networks: A Diffusion Approximation

Functional laws of large numbers (FLLNs) describe the mean-field trajectory of epidemics on networks, but say nothing about the fluctuations around it. These fluctuations are governed by moments of the degree distribution not relevant at the level of the mean. A rigorous functional central limit theorem (FCLT) exists for the susceptible--infected ($SI$) process on configuration-model graphs, but no analogue exists for $SIS$, where recovery reintroduces vertices into the susceptible pool with partially known neighborhoods, breaking the clean neighborhood distribution the $SI$ derivation relies on. We develop a tractable variance approximation for Markovian $SIS$ on configuration-model graphs, combining Gleeson's approximate master equation (AME) framework with a van Kampen system-size expansion in the spirit of the $SI$ FCLT. We derive a closed drift and diffusion matrix for a reduced susceptible/$SI$-edge/$SS$-edge count vector and obtain the time-dependent covariance via the associated Langevin/Lyapunov equation. Validation against Gillespie simulation across Poisson, regular, and power-law networks shows close agreement, with deviations near the epidemic threshold and in strongly heterogeneous networks.

cond-mat.stat-mech↗

arXiv2026

Electric potential of insulated conducting objects in presence of electric charges -- some exact and approximate results

Determination of the electric potential of insulated conducting objects is an important problem both theoretically and practically. For an insulated conducting object in the presence of external charges or charges distributed on the object surface, the problem of potential determination is reformulated using a newly introduced $J$ formalism. Using the $J$ formalism, it is shown how the electric potential can be calculated exactly for spherical objects and efficiently approximated for other object geometries using geometrical properties of the insulated conducting object. This approach does not require calculation of the surface charge distribution at the object surface of the calculation of the electric potential in the surrounding space. Properties and the performance of the approach are investigated numerically using the Robin Hood method. Possible applications of the approach based on the $J$ formalism are outlined for calculation of capacitance of conducting objects.

physics.class-ph↗

arXiv2023

Systemic risk measured by systems resiliency to initial shocks

The study of systemic risk is often presented through the analysis of several measures referring to quantities used by practitioners and policy makers. Almost invariably, those measures evaluate the size of the impact that exogenous events can exhibit on a financial system without analysing the nature of initial shock. Here we present a symmetric approach and propose a set of measures that are based on the amount of exogenous shock that can be absorbed by the system before it starts to deteriorate. For this purpose, we use a linearized version of DebtRank that allows to clearly show the onset of financial distress towards a correct systemic risk estimation. We show how we can explicitly compute localized and uniform exogenous shocks and explained their behavior though spectral graph theory. We also extend analysis to heterogeneous shocks that have to be computed by means of Monte Carlo simulations. We believe that our approach is more general and natural and allows to express in a standard way the failure risk in financial systems.

physics.soc-ph↗

arXiv2021

Causal motifs and existence of endogenous cascades in directed networks with application to company defaults

Motivated by the detection of cascades of defaults in economy, we developed a detection framework for an endogenous spreading based on causal motifs we define in this paper. We assume that the change of state of a vertex can be triggered by an endogenous or an exogenous event, that the underlying network is directed and that times when vertices changed their states are available. In addition to the data of company defaults, we also simulate cascades driven by different stochastic processes on different synthetic networks. We show that some of the smallest motifs can robustly detect endogenous spreading events. Finally, we apply the method to the data of defaults of Croatian companies and observe the time window in which an endogenous cascade was likely happening.

physics.soc-ph↗

arXiv2020

Bi-stability of SUDR+K model of epidemics and test kits applied to COVID-19

Motivated with various responses of world governments to COVID-19, here we develop a toy model of the dependence epidemics spreading on the availability of tests for disease. Our model, that we call SUDR+K, is based on usual SIR model, but it splits the total fraction of infected individuals into two components: those that are undetected and those that are detected through tests. Moreover, we assume that available tests increase at a constant rate from the beginning of epidemics but are consumed to detect infected individuals. Strikingly we find a bi-stable behavior between a phase with a giant fraction of infected and a phase with a very small fraction. We show that the separation between these two regimes is governed by a match between the rate of testing and a rate of infection spread at given time. We also show that the existence of two phases does not depend on the mathematical choice of the form of the term describing the rate at which undetected individuals are tested and detected. Presented research implies that a vigorous early testing activity, before the epidemics enters into its giant phase, can potentially keep epidemics under control, and that even a very small change in rate of testing can increase or decrease the size of the whole epidemics of various orders of magnitude. For the real application of realistic model to ongoing epidemics, we would gladly collaborate with field epidemiologists in order to develop quantitative models of testing process.

q-bio.PE↗

arXiv2019

Controlling systemic risk - network structures that minimize it and node properties to calculate it

Evaluation of systemic risk in networks of financial institutions in general requires information of inter-institution financial exposures. In the framework of Debt Rank algorithm, we introduce an approximate method of systemic risk evaluation which requires only node properties, such as total assets and liabilities, as inputs. We demonstrate that this approximation captures a large portion of systemic risk measured by Debt Rank. Furthermore, using Monte Carlo simulations, we investigate network structures that can amplify systemic risk. Indeed, while no topology in general sense is {\em a priori} more stable if the market is liquid [1], a larger complexity is detrimental for the overall stability [2]. Here we find that the measure of scalar assortativity correlates well with level of systemic risk. In particular, network structures with high systemic risk are scalar assortative, meaning that risky banks are mostly exposed to other risky banks. Network structures with low systemic risk are scalar disassortative, with interactions of risky banks with stable banks.

q-fin.RM↗

arXiv2014

Extraction of Temporal Networks from Term Co-occurrences in Online Textual Sources

A stream of unstructured news can be a valuable source of hidden relations between different entities, such as financial institutions, countries, or persons. We present an approach to continuously collect online news, recognize relevant entities in them, and extract time-varying networks. The nodes of the network are the entities, and the links are their co-occurrences. We present a method to estimate the significance of co-occurrences, and a benchmark model against which their robustness is evaluated. The approach is applied to a large set of financial news, collected over a period of two years. The entities we consider are 50 countries which issue sovereign bonds, and which are insured by Credit Default Swaps (CDS) in turn. We compare the country co-occurrence networks to the CDS networks constructed from the correlations between the CDS. The results show relatively small, but significant overlap between the networks extracted from the news and those from the CDS correlations.

physics.soc-ph↗

arXiv2011

Geometric origin of scaling in large traffic networks

Large scale traffic networks are an indispensable part of contemporary human mobility and international trade. Networks of airport travel or cargo ships movements are invaluable for the understanding of human mobility patterns\cite{Guimera2005}, epidemic spreading\cite{Colizza2006}, global trade\cite{Imo2006} and spread of invasive species\cite{Ruiz2000}. Universal features of such networks are necessary ingredients of their description and can point to important mechanisms of their formation. Different studies\cite{Barthelemy2010} point to the universal character of some of the exponents measured in such networks. Here we show that exponents which relate i) the strength of nodes to their degree and ii) weights of links to degrees of nodes that they connect have a geometric origin. We present a simple robust model which exhibits the observed power laws and relates exponents to the dimensionality of 2D space in which traffic networks are embedded. The model is studied both analytically and in simulations and the conditions which result with previously reported exponents are clearly explained. We show that the relation between weight strength and degree is $s(k)\sim k^{3/2}$, the relation between distance strength and degree is $s^d(k)\sim k^{3/2}$ and the relation between weight of link and degrees of linked nodes is $w_{ij}\sim(k_ik_j)^{1/2}$ on the plane 2D surface. We further analyse the influence of spherical geometry, relevant for the whole planet, on exact values of these exponents. Our model predicts that these exponents should be found in future studies of port networks and impose constraints on more refined models of port networks.

physics.soc-ph↗

arXiv2009

Influence of reciprocal arcs on the degree distribution and degree correlations

Reciprocal arcs represent the lowest order cycle possible to find in directed graphs without self-loops. Representing also a measure of feed-back between vertices, it is interesting to understand how reciprocal arcs influence other properties of complex networks. In this paper we focus on influence of reciprocal arcs on vertex degree distribution and degree correlations. We show that there is a fundamental difference between properties observed on the static network compared to the properties of networks which are obtained by simple evolution mechanism driven by reciprocity. We also present a way to statistically infer the portion of reciprocal arcs which can be explained as a consequence of feed-back process on the static network. In the rest of the paper the influence of reciprocal arcs on a model of growing network is also presented. It is shown that our model of growing network nicely interpolates between BA model for undirected and the BA model for directed networks.

cond-mat.stat-mech↗

arXiv2009

Model of Wikipedia growth based on information exchange via reciprocal arcs

We show how reciprocal arcs significantly influence the structural organization of Wikipedias, online encyclopedias. It is shown that random addition of reciprocal arcs in the static network cannot explain the observed reciprocity of Wikipedias. A model of Wikipedia growth based on preferential attachment and on information exchange via reciprocal arcs is presented. An excellent agreement between in-degree distributions of our model and real Wikipedia networks is achieved without fitting the distributions, but by merely extracting a small number of model parameters from the measurement of real networks.

physics.soc-ph↗

arXiv2007

Reciprocity of Networks with Degree Correlations and Arbitrary Degree Sequences

Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with an arbitrary degree sequence and a broad class of degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to $r$ is revealed. Numerical experiments using novel network randomization methods show very good agreement to our analytical estimations.

cond-mat.stat-mech↗