In this article we propose a generalization of two known invariants of real networks: degree and ksi-centrality. More precisely, we found a series of centralities based on Laplacian matrix, that have exponential distributions (power-law for the case $j = 0$) for real networks and different distributions for artificial ones.
Alkali metals of rubidium and cesium are studied through doping in lithium, sodium or potassium ion batteries. A vast study on H-capture by LiRb (Ge–Si)O2, LiCs(Ge–Si)O2, NaRb(Ge–Si)O2, NaCs(Ge–Si)O2, KRb(Ge–Si)O2, KCs(Ge–Si)O2, was carried out including using density functional theory (DFT) computations at the Coulomb-attenuating method–Becke, 3-parameter, Lee-Yang-Parr with Dispersion–corrected (CAM–B3LYP–D3/6–311+G (d,p))/6–311+G (d,p) level of theory. The hypothesis of the hydrogen adsorption phenomenon was figured out by density distributions of charge density differences (CDD), total density of states (TDOS) and electron localization function (ELF) for nanoclusters of "LiRb(Ge–Si)O2–2H2, LiCs(Ge–Si)O2–2H2, NaRb(Ge–Si)O2–2H2, NaCs(Ge–Si)O2–2H2, KRb(Ge–Si)O2–2H2, KCs(Ge–Si)O2–2H2. The differences of charge density for these structures are measured as: ΔQLiRb(Ge–Si)O2 = –0.002 , ΔQLiCs(Ge–Si)O2 = –0.005, ΔQNaRb(Ge–Si)O2 = –0.001 , ΔQNaCs(Ge–Si)O2 = –0.004 , ΔQKRb(Ge–Si)O2 = –0.001, ΔQKCs(Ge–Si)O2 = –0.007 coulomb. Therefore, the results have shown that the cluster of KCs(Ge–Si)O2, LiCs(Ge–Si)O2 and NaCs(Ge–Si)O2 may have the most tensity for electron accepting owing to hydrogen grabbing. A small portion of Rb or Cs entered the Ge–Si layer to replace the Li, Na or K sites might improve the structural stability of the electrode material at high multiplicity, thereby improving the capacity retention rate. Among these, potassium-ion batteries seem to show the most promise in terms of Rb or Cs doping. The general tendency that the gap values of these ionic semiconductors are increased as their ionicities are increased and alkali metal incorporation into (Ge–Si)O2 heterocluster will be hopeful to broaden its band-gap.
The SI unit of length, the Metre, is presently defined by taking the fixed numerical value of the fundamental constant `c', the invariant speed of light in vacuum. This definition has the same physical basis as the previous definition, as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. With the atomic standard second defined in terms of the ground state hyperfine transition in Caesium-133, this definition is supposed to provide a universally reproducible standard of length. However, this relies on Einstein's singular postulate that the relative velocity of light in vacuum is an invariant constant that is independent of any inertial motion of the reference laboratory. I argue that the basis of the definition of the standard metre should be changed to the specific form, "the length of the path equal to the two-way propagation of light in vacuum during a time interval of 1/299 792 458 of a second", to be compatible and consistent with the fact that it is only the two-way relative velocity that is consistent with being an invariant. The null result in the Michelson-Morley two-way experiment, and in all such experiments to date, is consistent with a Galilean one-way propagation of light (relative velocity $c'=c\pm v$) as well as an invariant relative velocity of light. All practical methods and protocols related to the implementation of length standard involve also a two-way propagation, not conforming to the present definition. Besides, this redefinition is absolutely necessary because the relative velocity of light in one-way propagation is indeed Galilean, and not an invariant, as proved here in multiple ways including a direct experiment.
In this article, we try to find the best routes during the pandemic so that the probability of contracting the disease is the lowest. According to the results of this article, we can design software to find the best route.
In previous work, we introduced the notion of an impact bundle, showing how e.g., the h-index and the g-index can lead to such a bundle. Here we extend the set of impact bundles by a new impact bundle, based on the Zhang e-index. It is, moreover, shown that some other plausible definitions do not lead to an impact bundle.
We provided quantitative data supporting significant changes between the time Twitter acceptance the offer on April 25 and the time the agreement was finalized on October 27. Republican politicians saw significant increases in their follower counts, while Democrat politicians saw significant decreases.
It has been experimentally shown that communities in social networks tend to have a core-periphery topology. However, there is still a limited understanding of the precise structure of core-periphery communities in social networks including the connectivity structure and interaction rates between agents. In this paper, we use a game-theoretic approach to derive a more precise characterization of the structure of core-periphery communities.
In this note I derive simple formulas based on the adjacency matrix of a network to compute measures associated with Ronald S. Burt's structural holes (effective size, redundancy, local constraint and constraint). This can help to interpret these measures and also to define naive algorithms for their computation based on matrix operations.
In this paper we devise a generative random network model with core-periphery properties whose core nodes act as sublinear dominators, that is, if the network has $n$ nodes, the core has size $o(n)$ and dominates the entire network. We show that instances generated by this model exhibit power law degree distributions, and incorporates small-world phenomena. We also fit our model in a variety of real-world networks.
In this paper, some main eigenvalues and eigenvectors of the politics matrix are investigated. The number of upper-class families in a society is the number of eigenvalues which are very close to 1. An algorithm to identify all the upper-class families from the right and left eigenvectors of those eigenvalues is developed.
Bots, software-controlled accounts that operate on social media, have been used to manipulate and deceive. We studied the characteristics and activity of bots around major political events, including elections in various countries. In this chapter, we summarize our findings of bot operations in the context of the 2016 and 2018 US Presidential and Midterm elections and the 2017 French Presidential election.
In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman's normalization of networks. We propose some alternatives for fractional bibliographic coupling measures.
Spectral clustering and Singular Value Decomposition (SVD) are both widely used technique for analyzing graph data. In this note, I will present their connections using simple linear algebra, aiming to provide some in-depth understanding for future research.
To address "bad actors" online, I argue for more specific definitions of acceptable and unacceptable behaviors and explicit attention to the social structures in which behaviors occur.