Вальба Ольга Владимировна
Московский институт электроники и математики им. А.Н. Тихонова
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
- ORCID:
0000-0003-0830-0166 - ResearcherID:
J-8939-2013 - SPIN РИНЦ:
4028-1717 - Google Scholar: https://scholar.google.com/citations?view_op=list_works&hl=en&user=0YkBv7sAAAAJ
- Scopus AuthorID:
37100734000
Публикации (28)
Metric structural human connectomes: Localization and multifractality of eigenmodes
2025 · ARTICLE · en
We explore the fundamental principles underlying the architecture of the human brain’s structural connectome through the lens of spectral analysis of Laplacian and adjacency matrices. Building on the idea that the brain balances efficient information processing with minimizing wiring costs, our goal is to understand how the metric properties of the connectome relate to the presence of an inherent scale. We demonstrate that a simple generative model combining nonlinear preferential attachment with an exponential penalty for spatial distance between nodes can effectively reproduce several key features of the human connectome. These include spectral density, edge length distribution, eigenmode localization, local clustering, and topological properties. Additionally, we examine the finer spectral characteristics of human structural connectomes by evaluating the inverse participation ratios (IPRq) across various parts of the spectrum. Our analysis shows that the level statistics in the soft cluster region of the Laplacian spectrum (where eigenvalues are small) deviate from a purely Poisson distribution due to interactions between clusters. Furthermore, we identify localized modes with large IPR values in the continuous spectrum. Multiple fractal eigenmodes are found across different parts of the spectrum, and we evaluate their fractal dimensions. We also find a power-law behavior in the return probability—a hallmark of critical behavior—and conclude by discussing how our findings are related to previous conjectures that the brain operates in an extended critical phase that supports multifractality.
Robust extended states in Anderson model on partially disordered random regular graphs
2024 · ARTICLE · en
In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction ββ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in a certain range of parameters (d,ββ) at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.
Fiber-Optic Telecommunication Network Wells Monitoring by Phase-Sensitive Optical Time-Domain Reflectometer with Disturbance Recognition
2023 · ARTICLE · en
The paper presents the application of a phase-sensitive optical time-domain reflectometer (phi-OTDR) in the field of urban infrastructure monitoring. In particular, the branched structure of the urban network of telecommunication wells. The encountered tasks and difficulties are described. The possibilities of usage are substantiated, and the numerical values of the event quality classification algorithms applied to experimental data are calculated using machine learning methods. Among the considered methods, the best results were shown by convolutional neural networks, with a probability of correct classification as high as 98.55%.
Anatomy of the fragmented Hilbert space: Eigenvalue tunneling, quantum scars, and localization in the perturbed random regular graph
2023 · ARTICLE · en
We consider the properties of the random regular graph with node degree d perturbed by chemical potentials μk for a number of short k-cycles. We analyze both numerically and analytically the phase diagram of the model in the (μk,d) plane. The critical curve separating the homogeneous and clusterized phases is found and it is demonstrated that the clusterized phase itself generically is separated as the function of d into the phase with ideal clusters and phase with coupled ones when the continuous spectrum gets formed. The eigenstate spatial structure of the model is investigated and it is found that there are localized scarlike states in the delocalized part of the spectrum, that are related to the topologically equivalent nodes in the graph. We also reconsider the localization of the states in the nonperturbative band formed by eigenvalue instantons and find the semi-Poisson level spacing distribution. The Anderson transition for the case of combined (k-cycle) structural and diagonal (Anderson) disorders is investigated. It is found that the critical diagonal disorder gets reduced sharply at the clusterization phase transition but does it unevenly in nonperturbative and mid-spectrum bands, due to the scars, present in the latter. The applications of our findings to 2d quantum gravity are discussed.
K-clique percolation in free association networks and the possible mechanism behind the 7±2 law
2022 · ARTICLE · en
It is important to reveal the mechanisms of propagation in diferent cognitive networks. In this study, we discuss the k-clique percolation phenomenon as related to the free association networks including the English Small World of Words project (SWOW-EN). We compared diferent semantic networks and networks of free associations for various languages. Surprisingly, k-clique percolation for all k
Mobility Edge in the Anderson Model on Partially Disordered Random Regular Graphs
2022 · ARTICLE · en
We study numerically the Anderson model on partially disordered random regular graphs 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 random regular graphs ensemble. Using adjacent gap ratio statistics and inverse participation ratio 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 phase is discussed.
Analysis of English free association network reveals mechanisms of efficient solution of Remote Association Tests
2021 · ARTICLE · en
We study correlations between the structure and properties of a free association network of the English language, and solutions of psycholinguistic Remote Association Tests (RATs). We show that average hardness of individual RATs is largely determined by relative positions of test words (stimuli and response) on the free association network. We argue that the solution of RATs can be interpreted as a first passage search problem on a network whose vertices are words and links are associations between words. We propose different heuristic search algorithms and demonstrate that in “easily-solving” RATs (those that are solved in 15 seconds by more than 64% subjects) the solution is governed by “strong” network links (i.e. strong associations) directly connecting stimuli and response, and thus the efficient strategy consist in activating such strong links. In turn, the most efficient mechanism of solving medium and hard RATs consists of preferentially following sequence of “moderately weak” associations.
Interacting thermofield doubles and critical behavior in random regular graphs
2021 · ARTICLE · en
We discuss numerically the nonperturbative effects in exponential random graphs which are analogue of eigenvalue instantons in matrix models. The phase structure of exponential random graphs with chemical potential for C4 μ4 and degree preserving constraint is clarified. The first order phase transition at critical value of chemical potential for C4 μRRG 4 into bipartite phase with a formation of fixed number of bipartite clusters is found for ensemble of random regular graphs (RRG). We consider the similar phase transition in mean field version of combinatorial quantum gravity based of the Ollivier graph curvature for RRG supplemented with hard-core constraint and show that a order of a phase transition at μCRRG 4 and the structure of emerging phase depend on a vertex degree d in RRG. For d ¼ 3 the bipartite closed ribbon emerges at μ4 > μCRRG 4 while for d > 3 the ensemble of isolated or weakly interacting hypercubes supplemented with the bipartite closed ribbon gets emerged at the first order phase transition with a clearcut hysteresis. If the additional connectedness condition is imposed the phase at μ4 > μCRRG 4 gets identified as the closed chain of weakly coupled hypercubes. Since the ground state of isolated hypercube is the thermofield double we suggest that the dual holographic picture involves multiboundary wormholes. Treating RRG as a model of a Hilbert space for a interacting many-body system we discuss the patterns of the Hilbert space fragmentation at the phase transition. We also briefly comment on a possible relation of the found phase transition to the problem of holographic interpretation of a partial deconfinement transition in the gauge theories.
Finite-size effects in exponential random graphs
2020 · ARTICLE · en
In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density p0.5p>0.5. We find that there exists the critical value of number of nodes N∗(p)N∗(p) when the ground state undergoes clear-cut crossover. At N>N∗(p),N>N∗(p), the network flows via a cluster evaporation to the state involving the small star in the Erdős–Rényi environment. The similar evaporation of the cluster takes place at N>N∗(p)N>N∗(p) in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.
Self-isolation or borders closing: What prevents the spread of the epidemic better?
2020 · ARTICLE · en
Pandemic propagation of COVID-19 motivated us to discuss the impact of the human network clustering on epidemic spreading. Today, there are two clustering mechanisms which prevent of uncontrolled disease propagation in a connected network: an “internal” clustering, which mimics self-isolation (SI) in local naturally arranged communities, and an “external” clustering, which looks like a sharp frontiers closing (FC) between cities and countries, and which does not care about the natural connections of network agents. SI networks are “evolutionarily grown” under the 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 evolutionary grown clustered network prevents the spread of an epidemic better than the instantly clustered network with similar parameters. We find that SI networks have the scale-free property for the degree distribution P(k)∼kη, with a small critical exponent −2
Курсы (7)
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Математические методы и компьютерные технологии (семинар наставника)
2025/2026 · семинар наставника · рус
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Машинное обучение
2025/2026 · Специалитет · рус
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Проектный семинар
2025/2026 · Магистратура · рус
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Статистический анализ и моделирование сложных систем · 4 раза
2025/2026, 2024/2025, 2023/2024, 2022/2023 · Дисциплина общефакультетского пула · рус
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Моделирование сетей · 3 раза
2024/2025, 2023/2024, 2022/2023 · Магистратура / Маго-лего · рус
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01.04.02. Прикладная математика и информатика · 3 раза
2023/2024, 2022/2023, 2021/2022 · Магистратура · рус
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Анализ данных и машинное обучение · 2 раза
2023/2024, 2022/2023 · Маго-лего · рус