arXiv subjects

Augusto Almeida Santos

Publications and source records attributed to Augusto Almeida Santos.

4 recordsLinked to original sources

arXiv2026

Preorder Construct on Simple Undirected Graphs

We construct a novel preorder on the set of nodes of a simple undirected graph. We prove that the preorder (induced by the topology of the graph) is preserved, e.g., by the logistic dynamical system (both in discrete and continuous time). Moreover, the underlying equivalence relation of the preorder corresponds to the coarsest equitable partition (CEP). This will further imply that the logistic dynamical system on a graph preserves its coarsest equitable partition. The results provide a nontrivial invariant set for the logistic and the like dynamical systems, as we show. We note that our construct provides a functional characterization for the CEP as an alternative to the pure set theoretical iterated degree sequences characterization. The construct and results presented might have independent interest for analysis on graphs or qualitative analysis of dynamical systems over networks.

math.CO↗

arXiv2017

Early Signals from Volumetric DDoS Attacks: An Empirical Study

Distributed Denial of Service (DDoS) is a common type of Cybercrime. It can strongly damage a company reputation and increase its costs. Attackers improve continuously their strategies. They doubled the amount of unleashed communication requests in volume, size, and frequency in the last few years. This occurs against different hosts, causing resource exhaustion. Previous studies focused on detecting or mitigating ongoing DDoS attacks. Yet, addressing DDoS attacks when they are already in place may be too late. In this article, we consider network resilience by early prediction of attack trends. We show empirically the advantage of using non-parametric leading indicators for early prediction of volumetric DDoS attacks. We report promising results over a real dataset from CAIDA. Our results raise new questions and opportunities for further research in early predicting trends of DDoS attacks.

cs.NI↗

arXiv2017

Thermodynamic Limit of Interacting Particle Systems over Time-varying Sparse Random Networks

We establish a functional weak law of large numbers for observable macroscopic state variables of interacting particle systems (e.g., voter and contact processes) over fast time-varying sparse random networks of interactions. We show that, as the number of agents $N$ grows large, the proportion of agents $\left(\overline{Y}_{k}^{N}(t)\right)$ at a certain state $k$ converges in distribution -- or, more precisely, weakly with respect to the uniform topology on the space of \emph{càdlàg} sample paths -- to the solution of an ordinary differential equation over any compact interval $\left[0,T\right]$. Although the limiting process is Markov, the prelimit processes, i.e., the normalized macrostate vector processes $\left(\mathbf{\overline{Y}}^{N}(t)\right)=\left(\overline{Y}_{1}^{N}(t),\ldots,\overline{Y}_{K}^{N}(t)\right)$, are non-Markov as they are tied to the \emph{high-dimensional} microscopic state of the system, which precludes the direct application of standard arguments for establishing weak convergence. The techniques developed in the paper for establishing weak convergence might be of independent interest.

math.PR↗

arXiv2016

Strong Attractors in Stochastic Adaptive Networks: Emergence and Characterization

We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical systems, on the edges of a graph, exhibits \emph{good} convergence properties, in particular, we prove a strong-stability result: a subset of binary matrices or graphs -- characterized by certain compatibility properties -- is a global almost sure attractor of the family of stochastic dynamical systems. To illustrate finer properties of the corresponding strong attractor, we present some simulation results that capture, e.g., the conspicuous phenomenon of emergence and downfall of leaders in social networks.

physics.soc-ph↗