Spatial Congruence Analysis (SCAN): A method for detecting biogeographical patterns based on species range congruences

Species with congruent geographical distributions, potentially caused by common historical and ecological spatial processes, constitute biogeographical units called chorotypes. Nevertheless, the degree of spatial range congruence characterizing these groups of species is rarely used as an explicit parameter. Methods conceived for the identification of patterns of shared ranges often suffer from scale bias associated with the use of grids, or the incapacity to describe the full complexity of patterns, from core areas of high spatial congruence, to long gradients of range distributions expanding from these core areas. Here, we propose a simple analytical method, Spatial Congruence Analysis (SCAN), which identifies chorotypes by mapping direct and indirect spatial relationships among species. Assessments are made under a referential value of congruence as an explicit numerical parameter. A one-layered network connects species (vertices) using pairwise spatial congruence estimates (edges). This network is then analyzed for each species, separately, by an algorithm which searches for spatial relationships to the reference species. The method was applied to two datasets: a simulated gradient of ranges and real distributions of birds. The simulated dataset showed that SCAN can describe gradients of distribution with a high level of detail. The bird dataset showed that only a small portion of range overlaps is biogeographically meaningful, and that there is a large variation in types of patterns that can be found with real distributions. Species analyzed separately may converge on similar or identical groups, may be nested in larger chorotypes, or may even generate overlapped patterns with no species in common. Chorotypes can vary from simple ones, composed by few highly congruent species, to complex, with numerous alternative component species and spatial configurations, which offer insights about possible processes driving these patterns in distinct degrees of spatial congruence. Metrics such as congruence, depth, richness, and ratio between common and total areas can be used to describe chorotypes in detail, allowing comparisons between patterns across regions and taxa.

The forgotten index of complement graph operations and its applications of molecular graph

A topological index of graph \(G\) is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join \(\overline {G_1+G_2}\), tensor product \(\overline {G_1 \otimes G_2}\), Cartesian product \(\overline {G_1\times G_2}\), composition \(\overline {G_1\circ G_2}\), strong product \(\overline {G_1\ast G_2}\), disjunction \(\overline {G_1\vee G_2}\) and symmetric difference \(\overline {G_1\oplus G_2}\) will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.

Towards Highly Efficient Polymer Fiber Laser Sources for Integrated Photonic Sensors

Lab-on-a-Chip (LoC) devices combining microfluidic analyte provision with integrated optical analysis are highly desirable for several applications in biological or medical sciences. While the microfluidic approach is already broadly addressed, some work needs to be done regarding the integrated optics, especially provision of highly integrable laser sources. Polymer optical fiber (POF) lasers represent an alignment-free, rugged, and flexible technology platform. Additionally, POFs are intrinsically compatible to polymer microfluidic devices. Home-made Rhodamine B (RB)-doped POFs were characterized with experimental and numerical parameter studies on their lasing potential. High output energies of 1.65 mJ, high slope efficiencies of 56 % , and 50 % -lifetimes of ≥900 k shots were extracted from RB:POFs. Furthermore, RB:POFs show broad spectral tunability over several tens of nanometers. A route to optimize polymer fiber lasers is revealed, providing functionality for a broad range of LoC devices. Spectral tunability, high efficiencies, and output energies enable a broad field of LoC applications.

EFFECT OF THE SUN ON EARTHʼS SEISMICITY

For the experimental study of the relationship between earthquakes and solar activity, we introduce the idea of the statistical sum Z of earthquake ensemble. A number of numerical parameters of seismicity (average planetary magnitude, entropy, fluctuations of magnitude) are expressed through Z. A severe restriction is, however, imposed on the magnitude during the formation of the ensemble. We propose an alternative method. It does not have this specific restriction, although it allows us to calculate only one numerical parameter, namely the global daily magnitude Mg. Over the 20-year period from 1980 to 1999, 7300 values of Mg have been calculated. The comparison between the Mg values and Wolf numbers W made it possible to determine the effect of the Sun on earthquakes at a statistically significant level.

EFFECT OF THE SUN ON EARTHʼS SEISMICITY

For the experimental study of the relationship between earthquakes and solar activity, we introduce the idea of the statistical sum Z of earthquake ensemble. A number of numerical parameters of seismicity (average planetary magnitude, entropy, fluctuations of magnitude) are expressed through Z. A severe restriction is, however, imposed on the magnitude during the formation of the ensemble. We propose an alternative method. It does not have this specific restriction, although it allows us to calculate only one numerical parameter, namely the global daily magnitude Mg. Over the 20-year period from 1980 to 1999, 7300 values of Mg have been calculated. The comparison between the Mg values and Wolf numbers W made it possible to determine the effect of the Sun on earthquakes at a statistically significant level.

SOME MULTIPLICATIVE NEIGHBORHOOD TOPOLOGICAL INDICES OF NANOCONES AND DENDRIMERS

A topological index is a numerical parameter mathematically derived from the graph structure. In this paper, we introduce the modified multiplicative first and second neighborhood indices, multiplicative F-neighborhood index, general multiplicative neighborhood index, multiplicative inverse sum indeg neighborhood index, multiplicative harmonic neighborhood index and multiplicative symmetric division neighborhood index, first and second multiplicative Gourava neighborhood indices of a graph. We compute these newly defined multiplicative neighborhood indices for nanocones and dendrimers.