This page has only limited features, please log in for full access.
We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.
R. Aguilar-Sánchez; J. Méndez-Bermúdez; José Rodríguez; José Sigarreta. Normalized Sombor Indices as Complexity Measures of Random Networks. Entropy 2021, 23, 976 .
AMA StyleR. Aguilar-Sánchez, J. Méndez-Bermúdez, José Rodríguez, José Sigarreta. Normalized Sombor Indices as Complexity Measures of Random Networks. Entropy. 2021; 23 (8):976.
Chicago/Turabian StyleR. Aguilar-Sánchez; J. Méndez-Bermúdez; José Rodríguez; José Sigarreta. 2021. "Normalized Sombor Indices as Complexity Measures of Random Networks." Entropy 23, no. 8: 976.
Overcoming the detrimental effect of disorder at the nanoscale is very hard since disorder induces localization and an exponential suppression of transport efficiency. Here we unveil novel and robust quantum transport regimes achievable in nanosystems by exploiting long-range hopping. We demonstrate that in a 1D disordered nanostructure in the presence of long-range hopping, transport efficiency, after decreasing exponentially with disorder at first, is then enhanced by disorder [disorder-enhanced transport (DET) regime] until, counterintuitively, it reaches a disorder-independent transport (DIT) regime, persisting over several orders of disorder magnitude in realistic systems. To enlighten the relevance of our results, we demonstrate that an ensemble of emitters in a cavity can be described by an effective long-range Hamiltonian. The specific case of a disordered molecular wire placed in an optical cavity is discussed, showing that the DIT and DET regimes can be reached with state-of-the-art experimental setups.
Nahum C. Chávez; Francesco Mattiotti; J. A. Méndez-Bermúdez; Fausto Borgonovi; G. Luca Celardo. Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities. Physical Review Letters 2021, 126, 153201 .
AMA StyleNahum C. Chávez, Francesco Mattiotti, J. A. Méndez-Bermúdez, Fausto Borgonovi, G. Luca Celardo. Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities. Physical Review Letters. 2021; 126 (15):153201.
Chicago/Turabian StyleNahum C. Chávez; Francesco Mattiotti; J. A. Méndez-Bermúdez; Fausto Borgonovi; G. Luca Celardo. 2021. "Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities." Physical Review Letters 126, no. 15: 153201.
We introduce a power-law banded random matrix model for the third of the three classical Wigner–Dyson ensembles, i.e., the symplectic ensemble. A detailed analysis of the statistical properties of its eigenvectors and eigenvalues, at criticality, is presented. This ensemble is relevant for time-reversal symmetric systems with strong spin–orbit interaction. For the sake of completeness, we also review the statistical properties of eigenvectors and eigenvalues of the power-law banded random matrix model in the presence and absence of time reversal invariance, previously considered in the literature. Our results show a good agreement with heuristic relations for the eigenstate and eigenenergy statistics at criticality, proposed in previous studies. Therefore, we provide a full picture of the power-law banded random matrix model corresponding to the three classical Wigner–Dyson ensembles.
M. Carrera-Núñez; A.M. Martínez-Argüello; J.A. Méndez-Bermúdez. Multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner–Dyson symmetry classes. Physica A: Statistical Mechanics and its Applications 2021, 573, 125965 .
AMA StyleM. Carrera-Núñez, A.M. Martínez-Argüello, J.A. Méndez-Bermúdez. Multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner–Dyson symmetry classes. Physica A: Statistical Mechanics and its Applications. 2021; 573 ():125965.
Chicago/Turabian StyleM. Carrera-Núñez; A.M. Martínez-Argüello; J.A. Méndez-Bermúdez. 2021. "Multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner–Dyson symmetry classes." Physica A: Statistical Mechanics and its Applications 573, no. : 125965.
R. Aguilar-Sánchez; J. A. Méndez-Bermúdez; José M. Rodríguez; José M. Sigarreta. Analytical and statistical studies of Rodriguez–Velazquez indices. Journal of Mathematical Chemistry 2021, 59, 1246 -1259.
AMA StyleR. Aguilar-Sánchez, J. A. Méndez-Bermúdez, José M. Rodríguez, José M. Sigarreta. Analytical and statistical studies of Rodriguez–Velazquez indices. Journal of Mathematical Chemistry. 2021; 59 (5):1246-1259.
Chicago/Turabian StyleR. Aguilar-Sánchez; J. A. Méndez-Bermúdez; José M. Rodríguez; José M. Sigarreta. 2021. "Analytical and statistical studies of Rodriguez–Velazquez indices." Journal of Mathematical Chemistry 59, no. 5: 1246-1259.
We investigate the escape of particles from the phase space produced by a two-dimensional, nonlinear and discontinuous, area-contracting map. The mapping, given in action-angle variables, is parametrized by K and γ which control the strength of nonlinearity and dissipation, respectively. We focus on two dynamical regimes, K<1 and K≥1, known as slow and quasilinear diffusion regimes, respectively, for the area-preserving version of the map (i.e., when γ=0). When a hole of hight h is introduced in the action axis we find both the histogram of escape times PE(n) and the survival probability PS(n) of particles to be scale invariant, with the typical escape time ntyp=exp〈lnn〉; that is, both PE(n/ntyp) and PS(n/ntyp) define universal functions. Moreover, for γ≪1, we show that ntyp is proportional to h2/D, where D is the diffusion coefficient of the corresponding area-preserving map that in turn is proportional to K5/2 and K2 in the slow and the quasilinear diffusion regimes, respectively.
Juliano A. de Oliveira; Rodrigo M. Perre; J. A. Méndez-Bermúdez; Edson D. Leonel. Leaking of orbits from the phase space of the dissipative discontinuous standard mapping. Physical Review E 2021, 103, 012211 .
AMA StyleJuliano A. de Oliveira, Rodrigo M. Perre, J. A. Méndez-Bermúdez, Edson D. Leonel. Leaking of orbits from the phase space of the dissipative discontinuous standard mapping. Physical Review E. 2021; 103 (1):012211.
Chicago/Turabian StyleJuliano A. de Oliveira; Rodrigo M. Perre; J. A. Méndez-Bermúdez; Edson D. Leonel. 2021. "Leaking of orbits from the phase space of the dissipative discontinuous standard mapping." Physical Review E 103, no. 1: 012211.
Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, especially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed Erdős-Rényi (ER) random networks by means of two adjacency matrix representations, namely, (1) weighted non-Hermitian random matrices and (2) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model 1 and from Poisson to Gaussian unitary ensemble statistics for model 2. Eigenvector delocalization effects of directed networks are also discussed.
Thomas Peron; Bruno Messias F. de Resende; Francisco A. Rodrigues; Luciano Da F. Costa; J. A. Méndez-Bermúdez. Spacing ratio characterization of the spectra of directed random networks. Physical Review E 2020, 102, 062305 .
AMA StyleThomas Peron, Bruno Messias F. de Resende, Francisco A. Rodrigues, Luciano Da F. Costa, J. A. Méndez-Bermúdez. Spacing ratio characterization of the spectra of directed random networks. Physical Review E. 2020; 102 (6):062305.
Chicago/Turabian StyleThomas Peron; Bruno Messias F. de Resende; Francisco A. Rodrigues; Luciano Da F. Costa; J. A. Méndez-Bermúdez. 2020. "Spacing ratio characterization of the spectra of directed random networks." Physical Review E 102, no. 6: 062305.
In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs), a graph model used to study the structure and dynamics of complex systems embedded in a two-dimensional space. RGGs, G(n,ℓ), consist of n vertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidian distance is less than or equal to the connection radius ℓ∈[0,2]. To evaluate the topological properties of RGGs we chose two well-known topological indices, the Randić index R(G) and the harmonic index H(G). We characterize the spectral and eigenvector properties of the corresponding randomly weighted adjacency matrices by the use of random matrix theory measures: the ratio between consecutive eigenvalue spacings, the inverse participation ratios, and the information or Shannon entropies S(G). First, we review the scaling properties of the averaged measures, topological and spectral, on RGGs. Then we show that (i) the averaged-scaled indices, R(G) and H(G), are highly correlated with the average number of nonisolated vertices V×(G); and (ii) surprisingly, the averaged-scaled Shannon entropy S(G) is also highly correlated with V×(G). Therefore, we suggest that very reliable predictions of eigenvector properties of RGGs could be made by computing topological indices.
R. Aguilar-Sánchez; J. A. Méndez-Bermúdez; Francisco A. Rodrigues; José M. Sigarreta. Topological versus spectral properties of random geometric graphs. Physical Review E 2020, 102, 042306 .
AMA StyleR. Aguilar-Sánchez, J. A. Méndez-Bermúdez, Francisco A. Rodrigues, José M. Sigarreta. Topological versus spectral properties of random geometric graphs. Physical Review E. 2020; 102 (4):042306.
Chicago/Turabian StyleR. Aguilar-Sánchez; J. A. Méndez-Bermúdez; Francisco A. Rodrigues; José M. Sigarreta. 2020. "Topological versus spectral properties of random geometric graphs." Physical Review E 102, no. 4: 042306.
We perform a detailed (computational) scaling study of well-known general indices (the first and second variable Zagreb indices, M1α(G) and M2α(G), and the general sum-connectivity index, χα(G)) as well as of general versions of indices of interest: the general inverse sum indeg index ISIα(G) and the general first geometric-arithmetic index GAα(G) (with α∈R). We apply these indices on two models of random networks: Erdös–Rényi (ER) random networks GER(nER,p) and random geometric (RG) graphs GRG(nRG,r). The ER random networks are formed by nER vertices connected independently with probability p∈[0,1]; while the RG graphs consist of nRG vertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidean distance is less or equal than the connection radius r∈[0,2]. Within a statistical random matrix theory approach, we show that the average values of the indices normalized to the network size scale with the average degree k of the corresponding random network models, where kER=(nER−1)p and kRG=(nRG−1)(πr2−8r3/3+r4/2). That is, X(GER)/nER≈X(GRG)/nRG if kER=kRG, with X representing any of the general indices listed above. With this work, we give a step forward in the scaling of topological indices since we have found a scaling law that covers different network models. Moreover, taking into account the symmetries of the topological indices we study here, we propose to establish their statistical analysis as a generic tool for studying average properties of random networks. In addition, we discuss the application of specific topological indices as complexity measures for random networks.
R. Aguilar-Sánchez; I. F. Herrera-González; J. A. Méndez-Bermúdez; José M. Sigarreta. Computational Properties of General Indices on Random Networks. Symmetry 2020, 12, 1341 .
AMA StyleR. Aguilar-Sánchez, I. F. Herrera-González, J. A. Méndez-Bermúdez, José M. Sigarreta. Computational Properties of General Indices on Random Networks. Symmetry. 2020; 12 (8):1341.
Chicago/Turabian StyleR. Aguilar-Sánchez; I. F. Herrera-González; J. A. Méndez-Bermúdez; José M. Sigarreta. 2020. "Computational Properties of General Indices on Random Networks." Symmetry 12, no. 8: 1341.
Mushroom billiards are formed, generically, by a semicircular hat attached to a rectangular stem. The dynamics of mushroom billiards shows a continuous transition from integrability to chaos. However, between those limits the phase space is sharply divided in two components corresponding to regular and chaotic orbits, in contrast to most mixed phase space billiards. In this paper we show that tilting the hat of a mushroom billiard produces a highly non-trivial (i.e. non-KAM) mixed phase space. Moreover, for small tilting, this phase space shows a web-like hierarchical structure.
Diogo Ricardo da Costa; Matheus S. Palmero; J.A. Méndez-Bermúdez; Kelly C. Iarosz; José D. Szezech Jr; Antonio M. Batista. Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space. Communications in Nonlinear Science and Numerical Simulation 2020, 91, 105440 .
AMA StyleDiogo Ricardo da Costa, Matheus S. Palmero, J.A. Méndez-Bermúdez, Kelly C. Iarosz, José D. Szezech Jr, Antonio M. Batista. Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space. Communications in Nonlinear Science and Numerical Simulation. 2020; 91 ():105440.
Chicago/Turabian StyleDiogo Ricardo da Costa; Matheus S. Palmero; J.A. Méndez-Bermúdez; Kelly C. Iarosz; José D. Szezech Jr; Antonio M. Batista. 2020. "Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space." Communications in Nonlinear Science and Numerical Simulation 91, no. : 105440.
Water is a basic natural resource for life and the sustainable development of society. Methods to assess water quality in freshwater ecosystems based on environmental quality bioindicators have proven to be low cost, reliable, and can be adapted to ecosystems with well-defined structures. The objective of this paper is to propose an interdisciplinary approach for the assessment of water quality in freshwater ecosystems through bioindicators. From the presence/absence of bioindicator organisms and their sensitivity/tolerance to environmental stress, we constructed a bipartite network, G. In this direction, we propose a new method that combines two research approaches, Graph Theory and Random Matrix Theory (RMT). Through the topological properties of the graph G, we introduce a topological index, called J P ( G ) , to evaluate the water quality, and we study its properties and relationships with known indices, such as Biological Monitoring Working Party ( B M W P ) and Shannon diversity ( H ′ ). Furthermore, we perform a scaling analysis of random bipartite networks with already specialized parameters for our case study. We validate our proposal for its application in the reservoir of Guájaro, Colombia. The results obtained allow us to infer that the proposed techniques are useful for the study of water quality, since they detect significant changes in the ecosystem.
Jair Pineda-Pineda; Claudia-Teresa Martínez-Martínez; J. Méndez-Bermúdez; Jesús Muñoz-Rojas; José Sigarreta. Application of Bipartite Networks to the Study of Water Quality. Sustainability 2020, 12, 5143 .
AMA StyleJair Pineda-Pineda, Claudia-Teresa Martínez-Martínez, J. Méndez-Bermúdez, Jesús Muñoz-Rojas, José Sigarreta. Application of Bipartite Networks to the Study of Water Quality. Sustainability. 2020; 12 (12):5143.
Chicago/Turabian StyleJair Pineda-Pineda; Claudia-Teresa Martínez-Martínez; J. Méndez-Bermúdez; Jesús Muñoz-Rojas; José Sigarreta. 2020. "Application of Bipartite Networks to the Study of Water Quality." Sustainability 12, no. 12: 5143.
We study spectral and transport properties of one-dimensional (1D) tight-binding PT–symmetric chains with non-equal consecutive couplings, i.e. asymmetric couplings. Based on the transfer matrix method, we obtain analytical expressions for the transmission and reflection coefficients for any values of the model parameters. These expressions, given in a very compact form, separately imbed the generic energy dependence, valid for any periodic structure, as well as specific properties of the dimers composing the 1D scattering chains. Our main interest is in the specific properties of the left/right reflections which are due to the PT–symmetric structure of the model. We have found that for the asymmetric coupling, there is no one-to-one correspondence between the degeneracy of the transfer matrix eigenvalues and PT–symmetric transport properties, such as the unidirectional reflectivity. We show that this correspondence, however, holds in the S−matrix approach, both for symmetric and asymmetric couplings.
L.A. Moreno-Rodríguez; F.M. Izrailev; J.A. Méndez-Bermúdez. PT–symmetric tight-binding model with asymmetric couplings. Physics Letters A 2020, 384, 126495 .
AMA StyleL.A. Moreno-Rodríguez, F.M. Izrailev, J.A. Méndez-Bermúdez. PT–symmetric tight-binding model with asymmetric couplings. Physics Letters A. 2020; 384 (21):126495.
Chicago/Turabian StyleL.A. Moreno-Rodríguez; F.M. Izrailev; J.A. Méndez-Bermúdez. 2020. "PT–symmetric tight-binding model with asymmetric couplings." Physics Letters A 384, no. 21: 126495.
We address the general problem of heat conduction in one dimensional harmonic chains, with correlated isotopic disorder, attached at their ends to white noise or Rubin's model of heat baths. The scaling behavior of the thermal conductivity is independent of the heat reservoirs, but depends on the boundary conditions and the low wave-number μ behavior of the power spectrum W(μ) of the fluctuations of the random masses around their common mean value. Thus, by properly tuning W(μ) we are able to control the scaling of the thermal conductivity κ with the system size N. As an example, we show that if W(μ)∼exp(−1/μ)/μ2, then κ∼N/(logN)3 for fixed boundary conditions and κ∼N/log(N) for free boundary conditions, which represent non-standard scalings of the thermal conductivity. In addition, we obtain the asymptotic dependence of the thermal conductivity on the coupling strength between the harmonic chain and the heat baths.
I.F. Herrera-González; J.A. Méndez-Bermúdez. Controlling the size scaling of the thermal conductivity in harmonic chains with correlated mass disorder. Physics Letters A 2020, 384, 126380 .
AMA StyleI.F. Herrera-González, J.A. Méndez-Bermúdez. Controlling the size scaling of the thermal conductivity in harmonic chains with correlated mass disorder. Physics Letters A. 2020; 384 (18):126380.
Chicago/Turabian StyleI.F. Herrera-González; J.A. Méndez-Bermúdez. 2020. "Controlling the size scaling of the thermal conductivity in harmonic chains with correlated mass disorder." Physics Letters A 384, no. 18: 126380.
In this work we perform computational and analytical studies of the Randić index R(G) in Erdös–Rényi models G(n, p) characterized by n vertices connected independently with probability p ∈ (0, 1). First, from a detailed scaling analysis, we show that 〈R¯(G)〉=〈R(G)〉/(n/2) scales with the product ξ ≈ np, so we can define three regimes: a regime of mostly isolated vertices when ξ < 0.01 (R(G) ≈ 0), a transition regime for 0.01 < ξ < 10 (where 0 < R(G) < n/2), and a regime of almost complete graphs for ξ > 10 (R(G) ≈ n/2). Then, motivated by the scaling of 〈R¯(G)〉, we analytically (i) obtain new relations connecting R(G) with other topological indices and characterize graphs which are extremal with respect to the relations obtained and (ii) apply these results in order to obtain inequalities on R(G) for graphs in Erdös–Rényi models.
C.T. Martínez-Martínez; J.A. Méndez-Bermúdez; José M. Rodríguez; José M. Sigarreta. Computational and analytical studies of the Randić index in Erdös–Rényi models. Applied Mathematics and Computation 2020, 377, 125137 .
AMA StyleC.T. Martínez-Martínez, J.A. Méndez-Bermúdez, José M. Rodríguez, José M. Sigarreta. Computational and analytical studies of the Randić index in Erdös–Rényi models. Applied Mathematics and Computation. 2020; 377 ():125137.
Chicago/Turabian StyleC.T. Martínez-Martínez; J.A. Méndez-Bermúdez; José M. Rodríguez; José M. Sigarreta. 2020. "Computational and analytical studies of the Randić index in Erdös–Rényi models." Applied Mathematics and Computation 377, no. : 125137.
We perform an extensive numerical analysis of β-skeleton graphs, a particular type of proximity graphs. In a β-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter β∈(0,∞), is satisfied. Moreover, for β>1 there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of β, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of random BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at β=1.
L. Alonso; J. A. Méndez-Bermúdez; Ernesto Estrada. Geometrical and spectral study of β -skeleton graphs. Physical Review E 2019, 100, 062309 .
AMA StyleL. Alonso, J. A. Méndez-Bermúdez, Ernesto Estrada. Geometrical and spectral study of β -skeleton graphs. Physical Review E. 2019; 100 (6):062309.
Chicago/Turabian StyleL. Alonso; J. A. Méndez-Bermúdez; Ernesto Estrada. 2019. "Geometrical and spectral study of β -skeleton graphs." Physical Review E 100, no. 6: 062309.
Some dynamical properties for a dissipative two-dimensional discontinuous standard mapping are considered. The mapping, in action-angle variables, is parameterized by two control parameters; namely, k ≥ 0 controlling the intensity of the nonlinearity and γ ∈ [0, 1] representing the dissipation. The case of γ=0 recovers the non-dissipative model while any γ ≠ 0 yields to the breaking of area preservation; hence leading to the existence of attractors, including chaotic ones. We show that when starting from a large initial action, the dynamics converges to chaotic attractors through an exponential decay in time, while the speed of the decay depends on the dissipation intensity. We also investigate the positive Lyapunov exponents and describe their behavior as a function of the control parameters.
Rodrigo M. Perre; Bárbara P. Carneiro; J.A. Méndez-Bermúdez; Edson D. Leonel; Juliano A. De Oliveira. On the dynamics of two-dimensional dissipative discontinuous maps. Chaos, Solitons & Fractals 2019, 131, 109520 .
AMA StyleRodrigo M. Perre, Bárbara P. Carneiro, J.A. Méndez-Bermúdez, Edson D. Leonel, Juliano A. De Oliveira. On the dynamics of two-dimensional dissipative discontinuous maps. Chaos, Solitons & Fractals. 2019; 131 ():109520.
Chicago/Turabian StyleRodrigo M. Perre; Bárbara P. Carneiro; J.A. Méndez-Bermúdez; Edson D. Leonel; Juliano A. De Oliveira. 2019. "On the dynamics of two-dimensional dissipative discontinuous maps." Chaos, Solitons & Fractals 131, no. : 109520.
In this work we present numerical results of classical Li\'{e}nard--type systems in a very general context, since we consider several types of derivatives (integer order and fractional order, global and local). Additionally we made theoretical-methodological observations. En este trabajo presentamos resultados num´ericos de sistemas tipo Li´enard en un contexto muy general ya que consideramos varios tipos dederivadas (de orden entero y fraccionario, globales y locales). Adicionalmente hacemos observaciones te ´oricas y metodol´ogicas.
A. Fleitas; J. A. Mendez-Bermudez; J. E. Napoles Valdes; J. M. Sigarreta Almira. On fractional Liénard--type systems. Revista Mexicana de Física 2019, 65, 618 -625.
AMA StyleA. Fleitas, J. A. Mendez-Bermudez, J. E. Napoles Valdes, J. M. Sigarreta Almira. On fractional Liénard--type systems. Revista Mexicana de Física. 2019; 65 (6 Nov-Dec):618-625.
Chicago/Turabian StyleA. Fleitas; J. A. Mendez-Bermudez; J. E. Napoles Valdes; J. M. Sigarreta Almira. 2019. "On fractional Liénard--type systems." Revista Mexicana de Física 65, no. 6 Nov-Dec: 618-625.
Several spectral fluctuation measures of random matrix theory (RMT) have been applied in the study of spectral properties of networks. However, the calculation of those statistics requires performing an unfolding procedure, which may not be an easy task. In this work, network spectra are interpreted as time series, and we show how their short and long-range correlations can be characterized without implementing any previous unfolding. In particular, we consider three different representations of Erdős–Rényi (ER) random networks: standard ER networks, ER networks with random-weighted self-edges, and fully random-weighted ER networks. In each case, we apply singular value decomposition (SVD) such that the spectra are decomposed in trend and fluctuation normal modes. We obtain that the fluctuation modes exhibit a clear crossover between the Poisson and the Gaussian orthogonal ensemble statistics when the average degree of ER networks changes. Moreover, by using the trend modes, we perform a data-adaptive unfolding to calculate, for comparison purposes, traditional fluctuation measures such as the nearest neighbor spacing distribution, number variance Σ2, as well as Δ3 and δn statistics. The thorough comparison of RMT short and long-range correlation measures make us identify the SVD method as a robust tool for characterizing random network spectra.
G. Torres-Vargas; R. Fossion; J.A. Méndez-Bermúdez. Normal mode analysis of spectra of random networks. Physica A: Statistical Mechanics and its Applications 2019, 545, 123298 .
AMA StyleG. Torres-Vargas, R. Fossion, J.A. Méndez-Bermúdez. Normal mode analysis of spectra of random networks. Physica A: Statistical Mechanics and its Applications. 2019; 545 ():123298.
Chicago/Turabian StyleG. Torres-Vargas; R. Fossion; J.A. Méndez-Bermúdez. 2019. "Normal mode analysis of spectra of random networks." Physica A: Statistical Mechanics and its Applications 545, no. : 123298.
Diogo Ricardo Da Costa; Mario R. Silva; Edson D. Leonel; J.A. Méndez-Bermúdez. Statistical description of multiple collisions in the Fermi-Ulam model. Physics Letters A 2019, 383, 3080 -3087.
AMA StyleDiogo Ricardo Da Costa, Mario R. Silva, Edson D. Leonel, J.A. Méndez-Bermúdez. Statistical description of multiple collisions in the Fermi-Ulam model. Physics Letters A. 2019; 383 (25):3080-3087.
Chicago/Turabian StyleDiogo Ricardo Da Costa; Mario R. Silva; Edson D. Leonel; J.A. Méndez-Bermúdez. 2019. "Statistical description of multiple collisions in the Fermi-Ulam model." Physics Letters A 383, no. 25: 3080-3087.
Bipartite graphs are often found to represent the connectivity between the components of many systems such as ecosystems. A bipartite graph is a set of n nodes that is decomposed into two disjoint subsets, having m and n−m vertices each, such that there are no adjacent vertices within the same set. The connectivity between both sets, which is the relevant quantity in terms of connections, can be quantified by a parameter α ∈ [0, 1] that equals the ratio of existent adjacent pairs over the total number of possible adjacent pairs. Here, we study the spectral and localization properties of such random bipartite graphs. Specifically, within a Random Matrix Theory (RMT) approach, we identify a scaling parameter ξ ≡ ξ(n, m, α) that fixes the localization properties of the eigenvectors of the adjacency matrices of random bipartite graphs. We also show that, when ξ < 1/10 (ξ > 10) the eigenvectors are localized (extended), whereas the localization–to–delocalization transition occurs in the interval 1/10 < ξ < 10. Finally, given the potential applications of our findings, we round off the study by demonstrating that for fixed ξ, the spectral properties of our graph model are also universal.
C.T. Martínez-Martínez; J.A. Méndez-Bermúdez; Yamir Moreno; Jair J. Pineda-Pineda; José M. Sigarreta. Spectral and localization properties of random bipartite graphs. Chaos, Solitons & Fractals: X 2019, 3, 100021 .
AMA StyleC.T. Martínez-Martínez, J.A. Méndez-Bermúdez, Yamir Moreno, Jair J. Pineda-Pineda, José M. Sigarreta. Spectral and localization properties of random bipartite graphs. Chaos, Solitons & Fractals: X. 2019; 3 ():100021.
Chicago/Turabian StyleC.T. Martínez-Martínez; J.A. Méndez-Bermúdez; Yamir Moreno; Jair J. Pineda-Pineda; José M. Sigarreta. 2019. "Spectral and localization properties of random bipartite graphs." Chaos, Solitons & Fractals: X 3, no. : 100021.
We perform an extensive numerical analysis of $\beta$-skeleton graphs, a particular type of proximity graphs. In a $\beta$-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter $\beta\in(0,\infty)$, is satisfied. Moreover, for $\beta>1$ there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of $\beta$, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of randomly weighted BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at $\beta=1$.
L. Alonso; J. A. Méndez-Bermúdez; Ernesto Estrada. Geometrical and spectral study of $β$-skeleton graphs. 2019, 1 .
AMA StyleL. Alonso, J. A. Méndez-Bermúdez, Ernesto Estrada. Geometrical and spectral study of $β$-skeleton graphs. . 2019; ():1.
Chicago/Turabian StyleL. Alonso; J. A. Méndez-Bermúdez; Ernesto Estrada. 2019. "Geometrical and spectral study of $β$-skeleton graphs." , no. : 1.