arXiv subjects

Anastasiya Salova

Publications and source records attributed to Anastasiya Salova.

6 recordsLinked to original sources

arXiv2026

Preferential Attachment with Local Flexibility

From the formation of social ties to the budding quantum internet, growing networks often exhibit local flexibility upon new nodes attaching to an existing network. In our proposed model, a new node connects uniformly at random to a node within the proximity of the intended target, including, but not restricted to, the target itself. Through numerical simulations and rigorous stochastic analysis, we find this local flexibility to qualitatively change the global network behavior of nonlinear preferential attachment. Depending on whether the preferential attachment is superlinear or (sub)linear, two distinct classes of complex network architectures emerge. The superlinear phase leads to a layered hierarchy, with no stationary degree distribution. Although there is a stationary degree distribution in the linear and sublinear cases, it decays strictly faster than for the Barabási--Albert model. We interpret our results within a two-dimensional phase diagram of network growth models incorporating redirection, with broad implications.

quant-ph↗

arXiv2024

Combined topological and spatial constraints are required to capture the structure of neural connectomes

Volumetric brain reconstructions provide an unprecedented opportunity to gain insights into the complex connectivity patterns of neurons in an increasing number of organisms. Here, we model and quantify the complexity of the resulting neural connectomes in the fruit fly, mouse, and human and unveil a simple set of shared organizing principles across these organisms. To put the connectomes in a physical context, we also construct contactomes, the network of neurons in physical contact in each organism. With these, we establish that physical constraints -- either given by pairwise distances or the contactome -- play a crucial role in shaping the network structure. For example, neuron positions are highly optimal in terms of distance from their neighbors. However, spatial constraints alone cannot capture the network topology, including the broad degree distribution. Conversely, the degree sequence alone is insufficient to recover the spatial structure. We resolve this apparent conflict by formulating scalable maximum entropy models, incorporating both types of constraints. The resulting generative models have predictive power beyond the input data, as they capture several additional biological and network characteristics, like synaptic weights and graphlet statistics.

q-bio.NC↗

arXiv2022

Cluster synchronization on hypergraphs

Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster synchronization. Here we develop the necessary formalism. We introduce the notion of edge clusters and show how node and edge partitions allow us to verify admissible states and simplify their linear stability calculations. This provides a principled way to track dynamics on hypergraphs, and the projected Laplacian matrices based on each edge cluster are essential to linear stability analysis and its dimensionality reduction. This work goes beyond full synchronization and beyond dyadic interactions.

nlin.AO↗

arXiv2021

Analyzing states beyond full synchronization on hypergraphs requires methods beyond projected networks

A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure and is not universally applicable for studying dynamical processes on hypergraphs, which we demonstrate through the framework of cluster synchronization. Specifically, we show that the projected network does not always correspond to a unique hypergraph structure. This means the projection does not always properly predict the true dynamics unfolding on the hypergraph. Additionally, we show that the symmetry group consisting of permutations that preserve the hypergraph structure can be distinct from the symmetry group of its projected matrix. Thus, considering the full hypergraph is required for analyzing the most general types of dynamics on hypergraphs. We show that a formulation based on node clusters and the corresponding edge clusters induced by the node partitioning, enables the analysis of admissible patterns of cluster synchronization and their effective dynamics. Additionally, we show that the coupling matrix projections corresponding to each edge cluster synchronization pattern, and not just to each order of interactions, are necessary for understanding the structure of the Jacobian matrix and performing the linear stability calculations efficiently.

nlin.AO↗

arXiv2020

Decoupled synchronized states in networks of linearly coupled limit cycle oscillators

Networks of limit cycle oscillators can show intricate patterns of synchronization such as splay states and cluster synchronization. Here we analyze dynamical states that display a continuum of seemingly independent splay clusters. Each splay cluster is a block splay state consisting of sub-clusters of fully synchronized nodes with uniform amplitudes. Phases of nodes within a splay cluster are equally spaced, but nodes in different splay clusters have an arbitrary phase difference that can be fixed or evolve linearly in time. Such coexisting splay clusters form a decoupled state in that the dynamical equations become effectively decoupled between oscillators that can be physically coupled. We provide the conditions that allow the existence of particular decoupled states by using the eigendecomposition of the coupling matrix. Additionally, we provide an algorithm to search for admissible decoupled states using the external equitable partition and orbital partition considerations combined with symmetry groupoid formalism. Unlike previous studies, our approach is applicable when existence does not follow from symmetries alone and also illustrates the differences between adjacency and Laplacian coupling. We show that the decoupled state can be linearly stable for a substantial range of parameters using a simple eight-node cube network and its modifications as an example. We also demonstrate how the linear stability analysis of decoupled states can be simplified by taking into account the symmetries of the Jacobian matrix. Some network structures can support multiple decoupled patterns. To illustrate that, we show the variety of qualitatively different decoupled states that can arise on two-dimensional square and hexagonal lattices.

nlin.AO↗

arXiv2019

Koopman Operator and its Approximations for Systems with Symmetries

Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and to simplify their analysis. The Koopman operator is an infinite dimensional linear operator that fully captures a system's nonlinear dynamics through the linear evolution of functions of the state space. Importantly, in contrast with local linearization, it preserves a system's global nonlinear features. We demonstrate how the presence of symmetries affects the Koopman operator structure and its spectral properties. In fact, we show that symmetry considerations can also simplify finding the Koopman operator approximations using the extended and kernel dynamic mode decomposition methods (EDMD and kernel DMD). Specifically, representation theory allows us to demonstrate that an isotypic component basis induces block diagonal structure in operator approximations, revealing hidden organization. Practically, if the data is symmetric, the EDMD and kernel DMD methods can be modified to give more efficient computation of the Koopman operator approximation and its eigenvalues, eigenfunctions, and eigenmodes. Rounding out the development, we discuss the effect of measurement noise.

math.DS↗