arXiv subjects

José Fernando F. Mendes

Publications and source records attributed to José Fernando F. Mendes.

3 recordsLinked to original sources

arXiv2026

Robust q-negative Multifractal Detrended Cross-Correlation Coefficient

The multifractal detrended cross-correlation coefficient $ρ_q(n)$ is widely used to investigate scale-dependent interactions, but its application to negative fluctuation orders is affected by numerical instabilities, unbounded values, and interpretational difficulties. We propose a Signed Multifractal Detrended Cross-Correlation Coefficient, $ρ_{\mathrm{SMFDCCA}}(n,q)$, an amplitude-conditioned correlation observable for multifractal detrended analysis, based on locally normalized detrended correlations and regularized fluctuation amplitudes. The proposed coefficient preserves the sign of local interactions, remains strictly bounded within $[-1,1]$ for both positive and negative values of $q$, and eliminates the corrective procedures required by previous approaches. Validation using independent fractional Gaussian noise confirms the absence of spurious cross-correlations and the numerical stability of the method. Applications demonstrate that the proposed observable resolves how cross-correlations evolve jointly with temporal scale and fluctuation amplitude, revealing scale- and amplitude-dependent correlation structures, including stronger synchronization during large fluctuations in stock-market indices and heterogeneous coupling patterns in temperature records.

cond-mat.stat-mech↗

arXiv2021

Enhanced robustness of single-layer networks with redundant dependencies

Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak variant of this model: nodes with dependency neighbours may continue to function if at least one of their dependency neighbours is active. We show that this relaxation of the dependency rule allows for more robust structures and a rich variety of critical phenomena, as percolation is not determined strictly by finite dependency clusters. We study Erdös-Rényi and random scale-free networks with an underlying Erdös-Rényi network of dependency links. We identify a special "cusp" point above which the system is always stable, irrespective of the density of dependency links. We find continuous and discontinuous hybrid percolation transitions, separated by a tricritical point for Erdös-Rényi networks. For scale-free networks with a finite degree cutoff we observe the appearance of a critical point and corresponding double transitions in a certain range of the degree distribution exponent. We show that at a special point in the parameter space, where the critical point emerges, the giant viable cluster has the unusual critical singularity $S-S_c \propto (p-p_c)^{1/4}$. We study the robustness of networks where connectivity degrees and dependency degrees are correlated and find that scale-free networks are able to retain their high resilience for strong enough positive correlation, i.e., when hubs are protected by greater redundancy.

cond-mat.stat-mech↗

arXiv2016

Scale-free networks with exponent one

A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free equilibrium networks that have the degree distribution exponent $γ= 1$, $P(q) \sim q^{-γ}$. Such degree distributions can be identified in empirical data only if the mean degree of a network is sufficiently high. Our models exploit a rewiring mechanism. They are local in the sense that no knowledge of the network structure, apart from the immediate neighbourhood of the vertices, is required. These models generate uncorrelated networks in the infinite size limit, where they are solved explicitly. We investigate finite size effects by the use of simulations. We find that both models exhibit disassortative degree-degree correlations for finite network sizes. In addition, we observe a markedly degree-dependent clustering in the finite networks. We indicate a real-world network with a similar degree distribution.

physics.soc-ph↗