arXiv subjects

Vinko Zlatić

Publications and source records attributed to Vinko Zlatić.

At least 19 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

Robust secret storage in networks

The problem of storing secure information on a network is studied. A formal framework for distributed secret storage is introduced, and possible applications in technological and social systems are discussed. The problem is formulated as the optimization of a robustness functional in which two competing requirements are balanced: survivability under network-degrading processes and resistance to adversarial compromise. An exact representation of survivability is derived in terms of minimal information-carrying subgraphs (MICS), which provide a reduced description of the reconstruction events relevant to the stored information. This representation is then used to construct semi-local optimization methods whose dynamics do not require global knowledge of the network structure. Finally, it is shown that, in a limiting case, the robustness functional can be mapped naturally to an effective spin Hamiltonian.

cond-mat.stat-mech↗

arXiv2026

Exploring the Effect of Basis Rotation on NQS Performance

Neural Quantum States (NQS) are powerful variational representations of quantum many-body wavefunctions, yet their performance depends sensitively on the chosen basis. Using an exactly solvable one-dimensional Ising model, we show that local basis rotations leave the minimization landscape unchanged while relocating the exact ground state in parameter space. This provides a controlled framework to disentangle representational limitations from optimization-induced trainability effects. This geometric displacement, quantified through information-geometric measures, can steer optimization of shallow architectures toward saddle points and high-curvature regions. As a result, low energy errors may coexist with an incorrect wavefunction structure. By comparing energy and infidelity optimization within the same variational architectures, we show that optimization failure can persist even when the rotated target state remains representable. Our results identify a geometric mechanism contributing to basis dependence in NQS and motivate landscape-aware variational design.

quant-ph↗

arXiv2023

Rewiring driven evolution of quenched frustrated signed network

A framework for studying the behavior of a classically frustrated signed network in the process of random rewiring is developed. We describe jump probabilities for change in frustration and formulate a theoretical estimate in terms of the master equation. Stationary thermodynamic distribution and moments are derived from the master equation and compared to numerical simulations. Furthermore, an exact solution of the probability distribution is provided through suitable mapping of rewiring dynamic to birth and death processes with quadratic asymptotically symmetric transition rates.

cond-mat.stat-mech↗

arXiv2023

Credit Valuation Adjustment in Financial Networks

Credit Valuation Adjustment captures the difference in the value of derivative contracts when the counterparty default probability is taken into account. However, in the context of a network of contracts, the default probability of a direct counterparty can depend substantially on the default probabilities of indirect counterparties. We develop a model to clarify when and how these network effects matter for CVA, in particular in the presence of correlation among counterparties defaults. We provide an approximate analytical solution for the default probabilities. This solution allows for identifying conditions on key parameters such as network degree, leverage and correlation, where network effects yield large differences in CVA (e.g. above 50%), and thus relevant for practical applications. Moreover, we find evidence that network effects induce a multi-modal distribution of CVA values.

q-fin.RM↗

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

The Non-Ideal Organic Electrochemical Transistors Impedance

Organic electrochemical transistors offer powerful functionalities for biosensors and neuroinspired electronics, with still much to understand on the time dependent behavior of this electrochemical device. Here, we report on distributed element modeling of the impedance of such microfabricated device, systematically performed under a large concentration variation for KCl(aq) and CaCl2(aq). We propose a new model which takes into account three main deviations to ideality, that were systematically observed, caused by both the materials and the device complexity, over large frequency range (1 Hz to 1 MHz). More than introducing more freedom degree, the introduction of these non redundant parameters and the study of their behaviors as function of the electrolyte concentration and applied voltage give a more detailed picture of the OECT working principles. This optimized model can be further useful for improving OECT performances in many applications (e.g. biosensors, neuroinspired devices) and circuit simulations.

physics.app-ph↗

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↗

arXiv2018

Multicoloring of Graphs to Secure a Secret

Vertex coloring and multicoloring of graphs are a well known subject in graph theory, as well as their applications. In vertex multicoloring, each vertex is assigned some subset of a given set of colors. Here we propose a new kind of vertex multicoloring, motivated by the situation of sharing a secret and securing it from the actions of some number of attackers. We name the multicoloring a highly $a$-resistant vertex $k$-multicoloring, where $a$ is the number of the attackers, and $k$ the number of colors. For small values $a$ we determine what is the minimal number of vertices a graph must have in order to allow such a coloring, and what is the minimal number of colors needed.

math.CO↗

arXiv2018

Bond and site color-avoiding percolation in scale free networks

Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one vulnerability (color), a robust color-avoiding connectivity is possible. However, many infrastructure networks show the problem of vulnerable classes of \textit{edges} instead of vertices. Here we formulate color-avoiding percolation for colored edges as well. Additionally, we allow for random failures of vertices or edges. The interplay of random failures and possible collective failures implies a rich phenomenology. A new form of critical behavior is found for networks with a power law degree distribution independent of the number of the colors, but still dependent on existence of the colors and therefore different from standard percolation. Our percolation framework fills a gap between different multilayer network percolation scenarios.

cond-mat.stat-mech↗

arXiv2016

Color-avoiding percolation

Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these vulnerabilities can greatly improve network robustness. Color-avoiding percolation provides a theoretical framework for analyzing this scenario, focusing on the maximal set of nodes which can be connected via multiple color-avoiding paths. In this paper we extend the basic theory of color-avoiding percolation that was published in [Krause et. al., Phys. Rev. X 6 (2016) 041022]. We explicitly account for the fact that the same particular link can be part of different paths avoiding different colors. This fact was previously accounted for with a heuristic approximation. We compare this approximation with a new, more exact theory and show that the new theory is substantially more accurate for many avoided colors. Further, we formulate our new theory with differentiated node functions, as senders/receivers or as transmitters. In both functions, nodes can be explicitly trusted or avoided. With only one avoided color we obtain standard percolation. With one by one avoiding additional colors, we can understand the critical behavior of color avoiding percolation. For heterogeneous color frequencies, we find that the colors with the largest frequencies control the critical threshold and exponent. Colors of small frequencies have only a minor influence on color avoiding connectivity, thus allowing for approximations.

physics.soc-ph↗

arXiv2015

Optimal redundancy against disjoint vulnerabilities in networks

Redundancy is commonly used to guarantee continued functionality in networked systems. However, often many nodes are vulnerable to the same failure or adversary. A "backup" path is not sufficient if both paths depend on nodes which share a vulnerability.For example, if two nodes of the Internet cannot be connected without using routers belonging to a given untrusted entity, then all of their communication-regardless of the specific paths utilized-will be intercepted by the controlling entity.In this and many other cases, the vulnerabilities affecting the network are disjoint: each node has exactly one vulnerability but the same vulnerability can affect many nodes. To discover optimal redundancy in this scenario, we describe each vulnerability as a color and develop a "color-avoiding percolation" which uncovers a hidden color-avoiding connectivity. We present algorithms for color-avoiding percolation of general networks and an analytic theory for random graphs with uniformly distributed colors including critical phenomena. We demonstrate our theory by uncovering the hidden color-avoiding connectivity of the Internet. We find that less well-connected countries are more likely able to communicate securely through optimally redundant paths than highly connected countries like the US. Our results reveal a new layer of hidden structure in complex systems and can enhance security and robustness through optimal redundancy in a wide range of systems including biological, economic and communications networks.

physics.soc-ph↗

arXiv2014

Reduction of systemic risk by means of Pigouvian taxation

We analyze the possibility of reduction of systemic risk in financial markets through Pigouvian taxation of financial institutions which is used to support the rescue fund. We introduce the concept of the cascade risk with a clear operational definition as a subclass and a network related measure of the systemic risk. Using financial networks constructed from real Italian money market data and using realistic parameters, we show that the cascade risk can be substantially reduced by a small rate of taxation and by means of a simple strategy of the money transfer from the rescue fund to interbanking market subjects. Furthermore, we show that while negative effects on the return on investment ($ROI$) are direct and certain, an overall positive effect on risk adjusted return on investments ($ROI^{RA}$) is visible. Please note that \emph{the taxation} is introduced as a monetary/regulatory, not as a fiscal measure, as the term could suggest. \emph{The rescue fund} is implemented in a form of a common reserve fund.

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↗

arXiv2012

Robustness and Assortativity for Diffusion-like Processes in Scale-free Networks

By analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk.

physics.soc-ph↗

arXiv2012

The Universal Arrow of Time I: Classical mechanics

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker's map.

physics.gen-ph↗