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Вальба Ольга Владимировна

Московский институт электроники и математики им. А.Н. Тихонова

Профиль на hse.ru ↗ тел.: 8 (495) 916-8876 | +7 (495) 772-9590 доб. 15129 | 8 925 548 97 29
Публикаций
28
Языков
2
Наград
7
Конференций
0
Профиль Публикации (28) Курсы (7)

Должности

  • Доцент — Московский институт электроники и математики им. А.Н. Тихонова, Департамент прикладной математики
  • Ведущий научный сотрудник — Факультет математики

Био

  • · Начала работать в НИУ ВШЭ в 2014 году.
  • · Научно-педагогический стаж: 11 лет.

Образование

  • 2014 · Кандидат физико-математических наук: Институт химической физики им. Н.Н. Семенова Российской академии наук
  • 2010 · Магистратура: Московский физико-технический институт, специальность «Прикладная математика и физика», квалификация «Магистр»
  • — · Doctor of Philosophy in Theoretical Physics, 2013 Université Paris XI - Paris-Sud

Опыт работы

  • · 2011-2014: Институт химической физики им. Н.Н. Семенова РАН (инженер научный сотрудник 2014-наст.вр.)
  • · Université Paris XI - Paris-Sud (researcher 2010-2013)

Награды и поощрения

  • · Благодарность МИЭМ НИУ ВШЭ (февраль 2021)
  • · Надбавка за публикацию в международном рецензируемом научном издании (2022–2023, 2021–2022, 2019–2021, 2017–2019)
  • · Надбавка за регулярные публикации в международных рецензируемых научных изданиях (2023–2028)
  • · Надбавка за статью в зарубежном рецензируемом журнале (2014–2016)
  • · Надбавка за статью в зарубежном рецензируемом научном издании (2016–2017)
  • · Лучший преподаватель — 2024, 2019–2022
  • · Группа высокого профессионального потенциала (кадровый резерв НИУ ВШЭ)Категория "Будущие профессора" (2017–2018)

Идентификаторы исследователя

Публикации (28)

Spectral peculiarity and criticality of a human connectome

2019 · ARTICLE · en

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.

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Localization and non-ergodicity in clustered random networks

2019 · ARTICLE · en

We consider clustering in rewired Erdős–Rényi networks with conserved vertex degree and in random regular graphs from the localization perspective. It has been found in Avetisov et al. (2016, Phys. Rev. E, 94, 062313) that at some critical value of chemical potential μcrμcr of closed triad of bonds, the evolving networks decay into the maximally possible number of dense subgraphs. The adjacency matrix acquires above μcrμcr the two-zonal support with the triangle-shaped main (perturbative) zone separated by a wide gap from the side (non-perturbative) zone. Studying the distribution of gaps between neighbouring eigenvalues (the level spacing), we demonstrate that in the main zone the level spacing matches the Wigner–Dyson law and is delocalized, however it shares the Poisson statistics in the side zone, which is the signature of localization. In parallel with the evolutionary designed networks, we consider ‘instantly’ ad hoc prepared networks with in- and cross-cluster probabilities exactly as at the final stage of the evolutionary designed network. For such ‘instant’ networks the eigenvalues are delocalized in both zones. We speculate about the difference in eigenvalue statistics between ‘evolutionary’ and ‘instant’ networks from the perspective of a possible phase transition between ergodic and non-ergodic network patterns with a strong ‘memory dependence’, thus advocating possible existence of non-ergodic delocalized states in the clustered random networks at least at finite network sizes.

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Phase transitions in social networks inspired by the Schelling model

2018 · ARTICLE · en

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 μ favors/disfavors connected “monochromatic triads,” i.e., connected groups of three individuals within the same social category, while the parameter ν controls the preference of interactions between two individuals from different social categories. The polychromatic model has several distinct regimes in (μ,ν)-parameter space. In ν-dominated region, the phase diagram is characterized by the plateau in the number of the intercolor connections, where the network is bipartite, while in μ-dominated region, the network looks as two weakly connected unicolor clusters. At μ>μcrit and ν>νcrit two phases are separated by a critical line, while at small values of μ and ν, a gradual crossover between the two phases occurs. The second “colorless” model describes a society in which the advantage or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a parameter γ. We analyze the topological structure of a social network in this model and demonstrate that above a critical threshold, γ+>0, the entire network splits into a set of weakly connected clusters, while below another threshold, γ−

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Path counting on simple graphs: from escape to localization

2017 · ARTICLE · en

We study the asymptotic behavior of the number of paths of length N on several classes of infinite graphs with a single special vertex. This vertex can work as an ‘entropic trap’ for the path, i.e. under certain conditions the dominant part of long paths becomes localized in the vicinity of the special point instead of spreading to infinity. We study the conditions for such localization on decorated star graphs, regular trees and regular hyperbolic graphs as a function of the functionality of the special vertex. In all cases the localization occurs for large enough functionality. The particular value of the transition point depends on the large-scale topology of the graph. The emergence of localization is supported by analysis of the spectra of the adjacency matrices of corresponding finite graphs.

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

2017 · ARTICLE · en

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 an 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.

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Finite plateau in spectral gap of polychromatic constrained random networks

2017 · ARTICLE · en

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, µ, 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 µ 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, λ2). We claim that at the plateau the restoring of the spontaneously broken Z2 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.

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Spontaneous symmetry breaking and phase coexistence in two-color networks

2016 · ARTICLE · en

We consider an equilibrium ensemble of large Erdos-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 μ. Minimizing the system energy, we see for some positive μ the formation of two predominantly unicolor clusters, linked by a string of Nbw black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the Nbw(μ) curve, which is relevant to a spinodal decomposition in first-order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby universes in two-dimensional gravity. We conjecture that the observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

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Eigenvalue tunneling and decay of quenched random network

2016 · ARTICLE · en

We consider the canonical ensemble of vertex ErdősRényi (ER) random topological graphs with quenched vertex degree, and with fugacity 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 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 a multizonal support for \mu>\mu_c. Eigenvalue tunneling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a blockdiagonal form, where the number of vertices in blocks fluctuates around the mean value N_p. 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.

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On predicting regulatory genes by analysis of functional networks in C. elegans

2015 · ARTICLE · en

Background: Connectivity networks, which reflect multiple interactions between genes and proteins, possess not only a descriptive but also a predictive value, as new connections can be extrapolated and tested by means of computational analysis. Integration of different types of connectivity data (such as co-expression and genetic interactions) in one network has proven to benefit ‘guilt by association’ analysis. However predictive values of connectives of different types, that had their specific functional meaning and topological characteristics were not obvious, and have been addressed in this analysis. Methods: eQTL data for 3 experimental C.elegans age groups were retrieved from WormQTL. WormNet has been used to obtain pair-wise gene interactions. The Shortest Path Function (SPF) has been adopted for statistical validation of the co-expressed gene clusters and for computational prediction of their potential gene expression regulators from a network context. A new SPF-based algorithm has been applied to genetic interactions sub-networks adjacent to the clusters of co-expressed genes for ranking the most likely gene expression regulators causal to eQTLs. Results: We have demonstrated that known co-expression and genetic interactions between C. elegans genes can be complementary in predicting gene expression regulators. Several algorithms were compared in respect to their predictive potential in different network connectivity contexts. We found that genes associated with eQTLs are highly clustered in a C. elegans co-expression sub-network, and their adjacent genetic interactions provide the optimal functional connectivity environment for application of the new SPF-based algorithm. It was successfully tested in the reverse-prediction analysis on groups of genes with known regulators and applied to co-expressed genes and experimentally observed expression quantitative trait loci (eQTLs). Conclusions: This analysis demonstrates differences in topology and connectivity of co-expression and genetic interactions sub-networks in WormNet. The modularity of less continuous genetic interaction network does not correspond to modularity of the dense network comprised by gene co-expression interactions. However the genetic interaction network can be used much more efficiently with the SPF method in prediction of potential regulators of gene expression. The developed method can be used for validation of functional significance of suggested eQTLs and a discovery of new regulatory modules.

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Islands of Stability in Motif Distributions of Random Networks

2014 · ARTICLE · en

We consider random nondirected networks subject to dynamics conserving vertex degrees and study, analytically and numerically, equilibrium three-vertex motif distributions in the presence of an external field h coupled to one of the motifs. For small h, the numerics is well described by the “chemical kinetics” for the concentrations of motifs based on the law of mass action. For larger h, a transition into some trapped motif state occurs in Erdős-Rényi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a nonzero cubic term. A localization transition should always occur if the entropy function is nonconvex. We conjecture that this phenomenon is the origin of the motifs’ pattern formation in real evolutionary networks.

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Курсы (7)