arXiv subjects

O. Valba

Publications and source records attributed to O. Valba.

11 recordsLinked to original sources

arXiv2022

Interaction of functional brain networks is formed by k-clique percolation in the human structural connectome

The human structural connectome has a complex internal community organization, characterized by a high degree of overlap and related to functional and cognitive phenomena. We explored connectivity properties in connectome networks and showed that $k$-clique percolation of an anomalously high order is characteristic of the human structural connectome. The resulting structural organization maintains a high local density of connectivity distributed throughout the connectome while preserving the overall sparsity of the network. To analyze these findings, we proposed a novel model for the emergence of high-order clique percolation during network formation with a phase transition dynamic under constraints on connection length. Investigating the structural basis of functional brain subnetworks, we identified a direct relationship between their interaction and the formation of clique clusters within their structural connections. Based on these findings, we hypothesize that the percolating clique cluster serves as a distributed boundary between interacting functional subnetworks, showing the complex, complementary nature of their structural connections. We also examined the difference between individual-specific and common structural connections and found that the latter plays a sustaining role in the connectivity of structural communities. At the same time, the superiority of individual connections, in contrast to common ones, creates variability in the interaction of functional brain subnetworks.

cond-mat.dis-nn↗

arXiv2021

Mobility Edge in the Anderson model on partially disordered random regular graphs

In this Letter we study numerically the Anderson model on partially disordered random regular graphs (RRG) considered as the toy model for a Hilbert space of interacting disordered many-body system. The protected subsector of zero-energy states in a many-body system corresponds to clean nodes in RRG ensemble. Using adjacent gap ratio statistics and IPR we find the sharp mobility edge in the spectrum of one-particle Anderson model above some critical density of clean nodes. Its position in the spectrum is almost independent on the disorder strength. The possible application of our result for the controversial issue of mobility edge in the many-body localized (MBL) phase is discussed.

cond-mat.dis-nn↗

arXiv2020

Self-isolation or borders closing: what prevents epidemic spreading better?

Pandemic distribution of COVID-19 in the world has motivated us to discuss combined effects of network clustering and adaptivity on epidemic spreading. We address the question concerning the choice of optimal mechanism for most effective prohibiting disease propagation in a connected network: adaptive clustering, which mimics self-isolation (SI) in local communities, or sharp instant clustering, which looks like frontiers closing (FC) between cities and countries. SI-networks are "adaptively grown" under condition of maximization of small cliques in the entire network, while FC-networks are "instantly created". Running the standard SIR model on clustered SI- and FC-networks, we demonstrate that the adaptive network clustering prohibits the epidemic spreading better than the instant clustering in the network with similar parameters. We found that SI model has scale-free property for degree distribution $P(k)\sim k^{\eta}$ with small critical exponent $-2<\eta<-1$ and argue that scale-free behavior emerges due to the randomness in the initial degree distributions and is absent for random regular graphs.

physics.soc-ph↗

arXiv2019

Finite-size effects in exponential random graphs and cluster evaporation

In this Letter we find numerically the strong finite-size effects in the critical behavior of Erd\H{o}s-R\'enyi (ER) networks supplemented with chemical potentials for some motifs, in particular 2-stars and triangles. For the 2-star model above the critical value of the chemical potential a ground state looks as star-like graph with the finite set of hubs at ER parameter $p<0.5$ or as the single cluster at $p>0.5$. It is found that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover and at $N>N^{*}(p)$ the network flows via a cluster evaporation to the state involving the small star in the ER environment. The similar evaporation of the cluster takes place at $N>N^{*}(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime. The possible analogies concerning the strong entropic finite-size effects in the holographic description of matrix black hole (BH) formation and evaporation are mentioned.

cond-mat.dis-nn↗

arXiv2018

Spectral peculiarity and criticality of the human connectome

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our analysis indicates several new peculiar features of the human connectome. We found that the spectral density of human connectome has the maximal deviation from the spectral density of the randomized network compared to all other organisms. For many animals except human structural peculiarities of connectomes are well reproduced in the network evolution induced by the preference of 3-cycles formation. To get the reliable fit , we discovered the crucial role of the conservation of local clusterization in human connectome evolution. We investigated for the first time the level spacing distribution in the spectrum of human connectome graph Laplacian. It turns out that the spectral statistics of human connectome corresponds exactly to the critical regime familiar in the condensed matter physics which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides the strong support for the much debated statement of the brain criticality.

q-bio.NC↗

arXiv2018

Phase transitions in social networks inspired by the Schelling model

We propose two models of social segregation inspired by the Schelling model. Agents in our models are nodes of evolving social networks. The total number of social connections of each node remains constant in time, though may vary from one node to the other. The first model describes a "polychromatic" society, in which colors designate different social categories of agents. The parameter $\mu$ favors/disfavors connected "monochromatic triads", i.e. connected groups of three individuals \emph{within the same social category}, while the parameter $\nu$ controls the preference of interactions between two individuals \emph{from different social categories}. The polychromatic model has several distinct regimes in $(\mu,\nu)$-parameter space. In $\nu$-dominated region, the phase diagram is characterized by the plateau in the number of the inter-color connections, where the network is bipartite, while in $\mu$-dominated region, the network looks as two weakly connected unicolor clusters. At $\mu>\mu_{crit}$ and $\nu >\nu_{crit}$ two phases are separated by a critical line, while at small values of $\mu$ and $\nu$, a gradual crossover between the two phases occurs. The second "colorless" model describes a society in which the advantage/disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a parameter $\gamma$. We analyze the topological structure of a social network in this model and demonstrate that above a critical threshold, $\gamma^+>0$, the entire network splits into a set of weakly connected clusters, while below another threshold, $\gamma^-<0$, the network acquires a bipartite graph structure. Our results propose mechanisms of formation of self-organized communities in international communication between countries, as well as in crime clans and prehistoric societies.

physics.soc-ph↗

arXiv2017

Finite plateau in spectral gap of polychromatic constrained random networks

We consider the canonical ensemble of multilayered constrained Erdos-Renyi networks (CERN) and regular random graphs (RRG), where each layer represents graph vertices painted in a specific color. We study the critical behavior in such networks under changing the fugacity, $\mu$, which controls the number of monochromatic triads of nodes. The behavior of considered systems is investigated via the spectral properties of the adjacency and Laplacian matrices of corresponding networks. For some wide region of $\mu$ we find the formation of a finite plateau in the number of the intercolor links, which exactly matches the finite plateau for the algebraic connectivity of the network (the value of the first non-vanishing eigenvalue of the Laplacian matrix, $\lambda_2$). We claim that at the plateau the restoring of the spontaneously broken $Z_2$ symmetry by the mechanism of modes collectivization in clusters of different colors occurs. The phenomena of a finite plateau formation holds for the polychromatic (multilayer) networks with $M>2$ colors.

cond-mat.stat-mech↗

arXiv2016

Peculiar spectral statistics of ensembles of trees and star-like graphs

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and $p$-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the "Lifshitz singularity" emerging in the one-dimensional localization, while the spectral statistics of $p$-branching star-like graphs is less universal, being strongly dependent on $p$. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However, the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, reflecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.

cond-mat.stat-mech↗

arXiv2016

Many-body localization and new critical phenomena in regular random graphs and constrained Erd\H{o}s-Renyi networks

We consider from the localization perspective the new critical phenomena discovered recently for perturbed random regular graphs (RRG) and constrained Erd\H{o}s-R\'enyi networks (CERN) \cite{crit2}. At some critical value of the chemical potential of 3-cycles, $\mu$, the network decays into the maximally possible number of almost full subgraphs, and the spectrum of the Laplacian matrix acquires the two-zonal structure with a large gap. We find that the Laplacian eigenvalue statistics corresponds to delocalized states in one zone, and to the localized states in the second one. We interpret this behavior in terms of the many-body localization problem where the structure of the Fock space of some interacting many-body system is approximated by the RGG and/or by the CERN. We associate 3-cycles in RRGs and CERNs as resonant triples in the Fock space. We show that the scenario of the "localization without disorder", discussed previously in physical space, can be realized in the Fock space as well. We argue that it is natural to identify clusters in a RRG with particles in a many-body system above the phase transition. We discuss the controversial issue of an additional phase transition between ergodic and non-ergodic regimes in the delocalized phase in the Fock space and find a strong "memory dependence" of the states in the delocalized phase, thus advocating existence of non-ergodic delocalized states.

cond-mat.dis-nn↗

arXiv2016

Eigenvalue tunnelling and decay of quenched random networks

We consider the canonical ensemble of $N$-vertex Erd\H{o}s-R\'enyi (ER) random topological graphs with quenched vertex degree, and with fugacity $\mu$ for each closed triple of bonds. We claim complete defragmentation of large-$N$ graphs into the collection of $[p^{-1}]$ almost full subgraphs (cliques) above critical fugacity, $\mu_c$, where $p$ is the ER bond formation probability. Evolution of the spectral density, $\rho(\lambda)$, of the adjacency matrix with increasing $\mu$ leads to the formation of two-zonal support for $\mu>\mu_c$. Eigenvalue tunneling from one (central) zone to the other means formation of a new clique in the defragmentation process. The adjacency matrix of the ground state of a network has the block-diagonal form where number of vertices in blocks fluctuate around the mean value $Np$. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.

cond-mat.stat-mech↗

arXiv2015

Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks

We have considered an equilibrium ensemble of large Erd\H{o}s-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability, $p$. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples, $\mu$. Minimizing the system energy, we see for some positive $\mu$ formation of two predominantly unicolor clusters, linked by a "string" of $N_{bw}$ black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in emergence of a wide plateau on the $N_{bw}(\mu)$-curve, which is relevant to a spinodal decomposition in 1st order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby-universes in 2D gravity. We have conjectured that observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

cond-mat.stat-mech↗