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Output-sensitive enumeration of maximal cliques in temporal graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-03-06 DOI: 10.1016/j.dam.2025.02.025

Filippo Brunelli , Alessio Conte , Roberto Grossi , Andrea Marino

Community detection is one of the fundamental tasks in graph analysis, and cliques, representing a fully interconnected subset of nodes, are one of the archetypal models of community, typically focusing on those that are maximal under inclusion. Recent years witnessed an increase in prominence of temporal graphs, i.e., graphs where edges may freely appear and disappear. This scenario caused a wave of research devoted to understand the temporal structure, and how to adapt classical graph methods to this more complex model. Several adaptations have been proposed for cliques, as well as algorithms for finding maximal cliques. These, however, do not have output-sensitive guarantees, meaning considerable time could be spent to find a small number of solutions.

In this paper, we show how two different proposed models of temporal graphs, and the corresponding definitions of clique, are essentially equivalent, allowing us to consider a single model of clique without losing generality; furthermore, we develop an output-sensitive algorithm for finding all maximal cliques in the restricted scenario where each edge is present for a continuous interval: the algorithm runs in polynomial total time using polynomial space, or in incremental polynomial time if we allow exponential space usage.

While the restricted scenario limits the generality of the result, no output-sensitive algorithm for the problem exists as of yet, making this the first such result, and a first step into output-sensitive community detection in temporal graphs.

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引用次数: 0

Partial Regularity for Navier-Stokes Equations 纳维-斯托克斯方程的部分正则性

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics

Pub Date : 2025-03-06 DOI: 10.1007/s00021-025-00929-z

Lihe Wang

Using a more geometric approach, we demonstrate that the solutions to the Navier–Stokes equations remain regular except on a set with a null Hausdorff measure of dimension 1. The proof primarily relies on a new compactness lemma and the monotonicity property of harmonic functions. The combination of linear and nonlinear approximation schemes makes the proof clear and transparent.

引用次数: 0

Asymptotic stability of Plasma-Sheaths to the full Euler–Poisson system

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-03-06 DOI: 10.1016/j.nonrwa.2025.104342

Lei Yao , Haiyan Yin , Mengmeng Zhu

The main concern of this paper is to study large-time behavior of the sheath to the full Euler–Poisson system. As is well known, the monotone stationary solution under the Bohm criterion can be referred to as the sheath which is formed by interactions of plasma with wall. So far, the existence and asymptotic stability of stationary solutions in one-dimensional half space to the full Euler–Poisson system have been proved in Duan et al. (2021). In the present paper, we extend the results in Duan et al. (2021) to

N

-dimensional (

N

=1,2,3) half space. By assuming that the velocity of the positive ion satisfies the Bohm criterion at the far field, we establish the global unique existence and the large time asymptotic stability of the sheath in some weighted Sobolev spaces by weighted energy method. Moreover, the time-decay rates are also obtained. A key different point from Duan et al. (2021) is to derive some boundary estimates on the derivative of the potential in the

x_{1}

-direction.

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引用次数: 0

Tame deformations of highly singular function germs

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-03-06 DOI: 10.1016/j.geomphys.2025.105471

Cezar Joiţa , Matteo Stockinger , Mihai Tibăr

We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus is a deformation with fibre constancy.

引用次数: 0

Non-parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence

IF 3 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics

Pub Date : 2025-03-06 DOI: 10.1007/s10208-025-09705-x

Riccardo Bonalli, Alessandro Rudi

We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker–Planck equation to such observations, yielding theoretical estimates of non-asymptotic learning rates which, unlike previous works, become increasingly tighter when the regularity of the unknown drift and diffusion coefficients becomes higher. Our method being kernel-based, offline pre-processing may be profitably leveraged to enable efficient numerical implementation, offering excellent balance between precision and computational complexity.

引用次数: 0

David J. Kaup and Boson Stars

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-03-06 DOI: 10.1111/sapm.70041

Stoytcho Yazadjiev

David Kaup's 1968 paper, “Klein–Gordon Geon”, introduced one of the first detailed studies of self-gravitating configurations of a complex scalar field, known as boson stars. These objects, formed by a massive complex scalar field interacting with gravity, provide a compelling theoretical model for understanding various phenomena in astrophysics and cosmology, particularly in the context of dark matter. Kaup's pioneering work, which considered the Einstein–Klein–Gordon equations, remains foundational in the study of nontopological solitons and self-gravitating systems in general.

引用次数: 0

Observer-based dynamic event-triggered second-level MPC for nonlinear time-delay CPSs under joint hybrid attacks

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-03-06 DOI: 10.1016/j.amc.2025.129391

Hongchao Song , Zhenlei Wang , Xin Wang

This study investigates observer-based dynamic event-triggered (DET) second-level model predictive control (MPC) for a specific class of nonlinear time-delay cyber-physical systems (CPSs) under hybrid attacks on the sensor-controller (S-C) channel and controller-actuator (C-A) channel. A dynamic event-triggered mechanism with adaptive bias components is developed to reduce trigger frequency, uphold system performance, and conserve communication resources. Additionally, the observer gain is determined using the nominal observation model and linear matrix inequalities. A novel model predictive control approach is devised based on the identified model to enhance system performance. Theoretical analysis demonstrates that the proposed method effectively guarantees that the closed-loop system satisfies the input-to-state practical stability criterion. Finally, a numerical simulation case study is presented to validate the effectiveness of the proposed algorithm.

引用次数: 0

Double Categories of Relations Relative to Factorisation Systems 与因式分解系统有关的双重关系类别

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures

Pub Date : 2025-03-06 DOI: 10.1007/s10485-025-09799-y

Keisuke Hoshino, Hayato Nasu

We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension scheme, and the second focuses on a specific class of vertical arrows defined solely double-categorically. We organise diverse classes of double categories of relations and correlate them with significant classes of factorisation systems. Our framework embraces double categories of spans and double categories of relations on regular categories, which we meticulously compare to existing work on the characterisations of bicategories and double categories of spans and relations.

引用次数: 0

Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters 演化系统中的粗略数据泛化了随温度变化的参数的一维热可塑性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization

Pub Date : 2025-03-06 DOI: 10.1007/s00245-025-10243-9

Michael Winkler

A Neumann-type initial-boundary value problem for

$$begin{aligned} left{ begin{array}{l} u_{tt} = nabla cdot (gamma (Theta ) nabla u_t) + a nabla cdot (gamma (Theta ) nabla u) + nabla cdot f(Theta ), Theta _t = DDelta Theta + Gamma (Theta ) |nabla u_t|^2 + F(Theta )cdot nabla u_t, end{array} right. end{aligned}$$

is considered in a smoothly bounded domain (Omega subset mathbb {R}^n), (nge 1). In the case when (n=1), (gamma equiv Gamma ) and (fequiv F), this system coincides with the standard model for heat generation in a viscoelastic material of Kelvin-Voigt type, well-understood in situations in which (gamma =const). Covering scenarios in which all key ingredients (gamma ,Gamma ,f) and F may depend on the temperature (Theta ) here, for initial data which merely satisfy (u_0in W^{1,p+2}(Omega )), (u_{0t}in W^{1,p}(Omega )) and (Theta _0in W^{1,p}(Omega )) with some (pge 2) such that (p>n), a result on local-in-time existence and uniqueness is derived in a natural framework of weak solvability.

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引用次数: 0

Besov Regularity Estimates for a Class of Obstacle Problems with Variable Exponents

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae

Pub Date : 2025-03-06 DOI: 10.1007/s10440-025-00718-w

Rumeng Ma, Fengping Yao

In this paper we obtain the local regularity estimates in Besov spaces of weak solutions for a class of elliptic obstacle problems with variable exponents (p(x)). We deal with the case in which the solutions to the obstacle problems satisfy a variational inequality in the following form

$$begin{aligned} int _{Omega } langle Aleft (x, Du right ),~D left (varphi -u right )rangle {mathrm{d}}xgeq int _{Omega } langle F,~D left ( varphi -u right )rangle {mathrm{d}}x end{aligned}$$

under some proper assumptions on the function (p(x)), (A), (varphi ) and (F). Moreover, we would like to point out that our results improve the known results for such problems.

引用次数: 0

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