arXiv subjects

Nikita Deniskin

Publications and source records attributed to Nikita Deniskin.

5 recordsLinked to original sources

arXiv2026

Convergence and acceleration of a nonlinear fixed-point iteration for computing the Fitness Centrality of general graphs

We establish the global convergence of the (non-homogeneous) Fitness Centrality algorithm for general graphs, deriving an explicit convergence bound for the corresponding fixed-point iteration. Furthermore, we show how the convergence can be dramatically improved by Anderson acceleration and by switching to Newton's method once a sufficiently good approximation to the fixed point has been found. The efficacy of this strategy is illustrated by numerical experiments on different types of graphs.

math.NA↗

arXiv2026

Fractional Diffusion on Graphs: Superposition of Laplacian Semigroups and Memory

Subdiffusion on graphs is often modeled by time-fractional diffusion equations, yet its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random time change that compresses operational time, produces long-tailed waiting times, and breaks Markovianity while preserving linearity and mass conservation. We prove that Mittag-Leffler graph dynamics admit an exact convex, mass-preserving representation as a superposition of classical heat semigroups evaluated at rescaled times, revealing fractional diffusion as ordinary diffusion acting across multiple intrinsic time scales. This framework uncovers heterogeneous, vertex-dependent memory effects and induces transport biases absent in classical diffusion, including algebraic relaxation, degree-dependent waiting times, and early-time asymmetries between sources and neighbors. These features define a subdiffusive geometry on graphs enabling particles to locally discover global shortest paths while favoring high-degree regions. Finally, we show that time-fractional diffusion arises as a singular limit of multi-rate diffusion.

cs.SI↗

arXiv2025

Error analysis of Abate--Whitt methods for Inverse Laplace Transforms and a new algorithm for queuing theory applications

We study the accuracy of a class of methods to compute the Inverse Laplace Transform, the so-called \emph{Abate--Whitt methods} [Abate, Whitt 2006], which are based on a linear combination of evaluations of $\widehat{f}$ in a few points. We provide error bounds which relate the accuracy of a method to the rational approximation of the exponential function. We specialize our analysis to applications in queuing theory, a field in which Abate--Whitt methods are often used; in particular, we study phase-type distributions and Markov-modulated fluid models (or \emph{fluid queues}). We use a recently developed algorithm for rational approximation, the AAA algorithm [Nakatsukasa, Sète, Trefethen 2018], to produce a new family of methods, which we call TAME. The parameters of these methods are constructed depending on a function-specific domain $Ω$; we provide a quasi-optimal choice for certain families of functions. We discuss numerical issues related to floating-point computation, and we validate our results through numerical experiments which show that the new methods require significantly fewer function evaluations to achieve an accuracy that is comparable (or better) to that of the classical methods.

math.NA↗

arXiv2022

New results and open problems on subgraph centrality

Subgraph centrality, introduced by Estrada and Rodríguez-Velázquez in [12], has become a widely used centrality measure in the analysis of networks, with applications in biology, neuroscience, economics and many other fields. It is also worthy of study from a strictly mathematical point of view, in view of its connections to topics in spectral graph theory, number theory, analytic matrix functions, and combinatorics. In this paper we present some new results and a list of open questions about subgraph centrality and other node centrality measures based on graph walks.

math.CO↗

arXiv2021

Vertex distinction with subgraph centrality: a proof of Estrada's conjecture and some generalizations

Centrality measures are used in network science to identify the most important vertices for transmission of information and dynamics on a graph. One of these measures, introduced by Estrada and collaborators, is the $β$-subgraph centrality, which is based on the exponential of the matrix $βA$, where $A$ is the adjacency matrix of the graph and $β$ is a real parameter ("inverse temperature"). We prove that for algebraic $β$, two vertices with equal $β$-subgraph centrality are necessarily cospectral. We further show that two such vertices must have the same degree and eigenvector centralities. Our results settle a conjecture of Estrada and a generalization of it due to Kloster, Král and Sullivan. We also discuss possible extensions of our results.

math.CO↗