A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems

We perform a detailed numerical study of the conductance $G$ through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies $\epsilon$ of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large $\epsilon$, $P(\epsilon)\sim 1/\epsilon^{1+\alpha}$ with $\alpha\in(0,2)$. Our model serves as a generalization of 1D Lloyd's model, which corresponds to $\alpha=1$. First, we verify that the ensemble average $\left\langle -\ln G\right\rangle$ is proportional to the length of the wire $L$ for all values of $\alpha$, providing the localization length $\xi$ from $\left\langle-\ln G\right\rangle=2L/\xi$. Then, we show that the probability distribution function $P(G)$ is fully determined by the exponent $\alpha$ and $\left\langle-\ln G\right\rangle$. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at $G=0$ and $1$. In addition, we show that $P(\ln G)$ is proportional to $G^\beta$, for $G\to 0$, with $\beta\le\alpha/2$, in agreement to previous studies.Comment: 5 pages, 5 figure

Stability mapping of bipartite tight-binding graphs with losses and gain: PT−{\cal PT}-symmetry and beyond

We consider bipartite tight-binding graphs composed by $N$ nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability $p$. We give a rationale for the relevance of such "throttle/brake" coupled systems (physically open systems) to grasp the stability issues of complex networks in areas such as biochemistry, neurons or economy, for which their modelling in terms of non-hermitian Hamiltonians is still in infancy. Specifically, we measure the connectivity between the two sets with the parameter $\alpha$, which is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. For general undirected-graph setups, the non-hermitian Hamiltonian $H(\gamma,\alpha,N)$ of this model presents pseudo-Hermiticity, where $\gamma$ is the loss/gain strength. However, we show that for a given graph setup $H(\gamma,\alpha,N)$ becomes ${\cal PT}-$symmetric. In both scenarios (pseudo-Hermiticity and ${\cal PT}-$symmetric), depending on the parameter combination, the spectra of $H(\gamma,\alpha,N)$ can be real even when it is non-hermitian. Thus, we numerically characterize the average fractions of real and imaginary eigenvalues of $H(\gamma,\alpha,N)$ as a function of the parameter set $\{\gamma,\alpha,N\}$. We demonstrate, for both setups, that there is a well defined sector of the $\gamma\alpha-$plane (which grows with $N$) where the spectrum of $H(\gamma,\alpha,N)$ is predominantly real.Comment: 10 pages, 9 figure

Computational and analytical studies of the harmonic index on Erdös-Rényi models

A main topic in the study of topological indices is to find bounds of the indices involving several parameters and/or other indices. In this paper we perform statistical (numerical) and analytical studies of the harmonic index H(G), and other topological indices of interest, on Erdos-Rényi (ER) graphs G(n, p) characterized by n vertices connected independently with probability p ∈ (0, 1). Particularly, in addition to H(G), we study here the (−2) sum-connectivity index χ−2(G), the modified Zagreb index MZ(G), the inverse degree index ID(G) and the Randic index R(G). First, to perform the statistical study of these indices, we define the averages of the normalized indices to their maximum value: {H(G)}, {χ−2(G)}, {MZ(G)}, {ID(G)}, {R(G)}. Then, from a detailed scaling analysis, we show that the averages of the normalized indices scale with the product ξ ≈ np. Moreover, we find two different behaviors. On the one hand, hH(G)i and hR(G)i, as a function of the probability p, show a smooth transition from zero to n/2 as p increases from zero to one. Indeed, after scaling, it is possible to define three regimes: a regime of mostly isolated vertices when ξ 10 (H(G), R(G) ≈ n/2). On the other hand, hχ−2(G)i, hMZ(G)i and hID(G)i increase with p until approaching their maximum value, then they decrease by further increasing p. Thus, after scaling the curves corresponding to these indices display bell-like shapes in log scale, which are symmetric around ξ ≈ 1; i.e. the percolation transition point of ER graphs. Therefore, motivated by the scaling analysis, we analytically (i) obtain new relations connecting the topological indices H, χ−2, MZ, ID and R that characterize graphs which are extremal with respect to the obtained relations and (ii) apply these results in order to obtain inequalities on H, χ−2, MZ, ID and R for graphs in ER models.J.A.M.-B. acknowledges financial support from FAPESP (Grant No. 2019/ 06931-2), Brazil, CONACyT (Grant No. 2019-000009-01EXTV-00067) and PRODEP-SEP (Grant No. 511-6/2019.-11821), Mexico. J.M.R. and J.M.S. acknowledge financial support from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/ 10.13039/501100011033), Spain

Spectral and localization properties of random bipartite graphs

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 $\alpha\in[0,1]$ 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 $\xi\equiv\xi(n,m,\alpha)$ that fixes the localization properties of the eigenvectors of the adjacency matrices of random bipartite graphs. We also show that, when $\xi10$) the eigenvectors are localized (extended), whereas the localization--to--delocalization transition occurs in the interval $1/10<\xi<10$. Finally, given the potential applications of our findings, we round off the study by demonstrating that for fixed $\xi$, the spectral properties of our graph model are also universal.Comment: 17 pages, 10 figure

Avifauna en un area perturbada del bosque andino en el parque nacional natural Farallones de Cali, corregimiento de Pance, Valle del Cauca (Colombia)

El presente conjunto de datos en el formato de archivo Darwin Core incluye información del monitoreo de la avifauna en un área perturbada del Parque Nacional Natural Farallones de Cali. Con el objetivo de caracterizar y determinar la composición y estructura de la avifauna, se llevaron a cabo censos visuales desde agosto 2008 hasta julio 2009 en las localidades de El Topacio y El Pato en recorridos de 2 km de longitud, a elevaciones entre 1550 y 1800 m s.n.m. En total se hicieron 2363 registros de 157 especies de aves, pertenecientes a 41 familias y 19 órdenes. Se observaron 12 especies nuevas para el área, 10 de las cuales son aves propias de áreas abiertas. Nueve especies que habían sido registradas en El Topacio en 1978, no lo fueron en el presente estudio y en consecuencia se consideran extintas y vulnerables localmente, lo cual ilustra y ratifica cómo el reemplazo de los hábitats naturales por potreros, la fragmentación y el efecto de borde afectan negativamente las comunidades de aves en áreas protegidas.This dataset in Darwin Core Archive format includes monitoring information about bird life in a disturbed area of the Farallones de Cali National Natural Park. Aiming to characterize and determine the composition and structure of bird life, visual censuses were carried out from August 2008 to July 2009 at both the El Pato and the El Topacio localities along line census of 2 km and from elevations between1550 to 1800 m a.s.l. A total of 2363 records were obtained of 157 species of 41 families and 19 orders. Twelve were new records for the area, 10 of which are common in open areas. Nine species previously recorded in 1978 at El Topacio were absent and considered locally extinct and vulnerable. This illustrates how the replacement of natural habitats with pasturelands, as well as fragmentation and border effect affect negatively bird communities in protected areas.Fil: Bermudez Vera, Julio Cesar . Universidad del Valle. Departamento de Biología; ColombiaFil: Duque Lopez, Juan Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte. Centro de Investigación Esquel de Montaña y Estepa Patagónicas; ArgentinaFil: Sanchez Martinez, Manuel A. . Universidad del Valle. Departamento de Biología; ColombiaFil: Tenorio, Elkin . Calima - Fundación para la Investigación de la Biodiversidad y Conservación en el Trópico; Colombi

In vitro Validation of Quantitative Light-Induced Fluorescence for the Diagnosis of Enamel Fluorosis in Permanent Teeth

This study aimed to validate quantitative light-induced fluorescence (QLF) as a diagnostic tool for mild and moderate enamel fluorosis in permanent teeth, comparing it to visual diagnosis and histological assessment completed using polarized light microscopy (PLM). The buccal surfaces of 139 teeth were visually classified using the Thylstrup and Fejerskov Index (TFI) into sound (TFI 0; n = 17), mild (TFI 1-2; n = 69), and moderate (TFI 3-4; n = 43) fluorosis. Fluorosis was then assessed with QLF (variables ΔF, A, and ΔQ at 5-, 15-, and 30-radiance thresholds) using as reference areas the entire surface and a region of interest (ROI), identified as the most representative region of a fluorosis lesion. PLM images of longitudinal thin sections including the ROI were assessed for histological changes. Correlations among TFI, PLM, and QLF were determined. A receiver-operating characteristic curve was conducted to determine QLF's diagnostic accuracy when compared to the TFI and PLM assessments. This was used to assess the probability that the images were correctly ranked according to severity as determined by PLM and TFI. A positive correlation was found between QLF and PLM, and between QLF and TFI. QLF showed the highest sensitivity and specificity for the diagnosis of mild fluorosis. There was also a strong agreement between TFI and PLM. The selection of a ROI resulted in a stronger correlation with TFI and PLM than when the entire surface was used. The study results indicate that defining an ROI for QLF assessments is a valid method for the diagnosis of mild and moderate enamel fluorosis