Lobby index in networks

We propose a new node centrality measure in networks, the lobby index, which is inspired by Hirsch’s h-index. It is shown that in scale-free networks with exponent α the distribution of the l-index has power tail with exponent α(α+1). Properties of the l-index and extensions are discussed.     

A centrality measure for communication ability in weighted network

This paper proposes a new node centrality measurement in a weighted network, the communication centrality, which is inspired by Hirsch’s h$h$-index. We investigated the properties of the communication centrality, and proved that the distribution of the communication centrality has the power-law upper tail in weighted scale-free networks. Relevant measures for node and network are discussed as extensions. A case study of a scientific collaboration network indicates that the communication centrality is different from other common centrality measures and other h$h$-type indexes. Communication centrality displays moderate correlation with other indexes, and contains a well-balanced mix of other centrality measures and cannot be replaced by any of them.     

Vertex centrality as a measure of information flow in Italian Corporate Board Networks

The aim of this article is to investigate the governance models of companies listed on the Italian Stock Exchange by using a network approach, which describes the interlinks between boards of directors. Following mainstream literature, I construct a weighted graph representing the listed companies (vertices) and their relationships (weighted edges), the Corporate Board Network; I then apply three different vertex centrality measures: degree, betweenness and flow betweenness. What emerges from the network construction and by applying the degree centrality is a structure with a large number of connections but not particularly dense, where the presence of a small number of highly connected nodes (hubs) is evident.Then I focus on betweenness and flow betweenness; indeed I expect that these centrality measures may give a representation of the intensity of the relationship between companies, capturing the volume of information flowing from one vertex to another. Finally, I investigate the possible scale-free structure of the network.     

A vibrational approach to node centrality and vulnerability in complex networks

We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.     

Twenty Hirsch index variants and other indicators giving more or less preference to highly cited papers

The Hirsch index or h‐index is widely used to quantify the impact of an individual's scientific research output, determining the highest number h of a scientist's papers that received at least h citations. Several variants of the index have been proposed in order to give more or less preference to highly cited papers. I analyse the citation records of 26 physicists discussing various suggestions, in particular A, e, f, g, h(2), h_w, hT, ?, m, π, R, s, t, w, and maxprod. The total number of all and of all cited publications as well as the highest and the average number of citations are also compared. Advantages and disadvantages of these indices and indicators are discussed. Correlation coefficients are determined quantifying which indices and indicators yield similar and which yield more deviating rankings of the 26 datasets. For 6 datasets the determination of the indices and indicators is visualized.     

A case study of the Hirsch index for 26 non‐prominent physicists

The h index was introduced by Hirsch to quantify an individual's scientific research output. It has been widely used in different fields to show the relevance of the research work of prominent scientists. I have worked out 26 practical cases of physicists which are not so prominent. Therefore this case study should be more relevant to discuss various features of the Hirsch index which are interesting or disturbing or both for the more average situation. In particular, I investigate quantitatively some pitfalls in the evaluation and the influence of self‐citations.     

The topology of a causal network for the Chinese financial system

The paper builds a causal network for the Chinese financial system based on the Granger causality of company risks, studies its different topologies in crisis and bull period, and applies the centrality to explain individual risk and prevent systemic risk. The results show that this causal network possesses both small-world phenomenon and scale-free property, and has a little different average distance, clustering coefficient, and degree distribution in different periods, and financial institutions with high centrality not only have large individual risk, but also are important for systemic risk immunization.     

A theorem on refractive index as a function of wavelength

A theorem upon refractive index as a function of wavelength is derived starting from the Taylor expansion around the origin of this function. Our result involves the above index, the group index, and the coefficient of material dispersion all extrapolated to zero wavelength.     

Degree and wealth distribution in a network induced by wealth

A network induced by wealth is a social network model in which wealth induces individuals to participate as nodes, and every node in the network produces and accumulates wealth utilizing its links. More specifically, at every time step a new node is added to the network, and a link is created between one of the existing nodes and the new node. Innate wealth-producing ability is randomly assigned to every new node, and the node to be connected to the new node is chosen randomly, with odds proportional to the accumulated wealth of each existing node. Analyzing this network using the mean value and continuous flow approaches, we derive a relation between the conditional expectations of the degree and the accumulated wealth of each node. From this relation, we show that the degree distribution of the network induced by wealth is scale-free. We also show that the wealth distribution has a power-law tail and satisfies the 80/20 rule. We also show that, over the whole range, the cumulative wealth distribution exhibits the same topological characteristics as the wealth distributions of several networks based on the Bouchaud-Mèzard model, even though the mechanism for producing wealth is quite different in our model. Further, we show that the cumulative wealth distribution for the poor and middle class seems likely to follow by a log-normal distribution, while for the richest, the cumulative wealth distribution has a power-law behavior.     

Refractive index of standard oils as a function of wavelength and temperature

The refractive indices (n) of eight standard oils from Physikalisch Technische Bundesanstalt, Germany were determined with an accuracy of ±1×10⁻⁴ by using Abbe Refractometer. The measurements were performed at temperature 20°C in the spectral range 0.4–0.7 μm. The experimental data were fitted to the simple Cauchy dispersion formula and the results were found to be consistent within the limits of experimental error. In all cases, the refractive index decreased monotonically with increasing wavelength. The refractive indices (n) of these oils have been measured as a function of the temperature t (20°C up to 50°C) at λ=0.589 μm and were found to have linear temperature dependencies. The refractive indices of the studied oils and the uncertainty in their values are calculated at λ=0.589. The Lorentz–Lorenz (L–L) formula has been tested and it was found to be valid with a maximum deviation of 0.4% and was used to calculate the molecular polarizability θ.     

用M-Z干涉仪对空气折射率的定量测量与理论探讨

用自行组建的M-Z干涉仪测量空气在不同压强下的折射率,得到恒定温度下折射率随压强变化的具体关系,并从理论上对空气折射率的成因进行了分析,较好地解释了实验结果.     

Entropy as a measure of diffusion

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.     

基于彩虹光学原理测量介质材料折射率的新方法

基于彩虹的光学原理,获得测量介质材料折射率的一种新方法,且在此基础上设计了一套适应该方法的实验测量装置.通过该装置,可以在实验室中简便地模拟彩虹中的光学现象,深刻地理解彩虹现象的光学本质,同时能够测量介质材料的折射率.     

Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics

We report a study of the determination of polymer cross‐linking, namely the degree of conversion and refractive index of the microstructures created by two‐photon polymerization (TPP). The influence of TPP processing parameters such as laser intensity and scanning velocity is investigated. The degree of conversion is analyzed via Raman microspectroscopy and the refractive index is measured with the interferometric technique employing a Michelson interferometer. Moreover, the relationship between these two properties is revealed and details are discussed. The largest refractive index change that we have obtained is of the order of 10⁻². Finally, we propose and demonstrate experimentally the realization of the gradient‐index (GRIN) structure, resulting from a laser‐induced local refractive index modification due to monomer cross‐linking, i.e. degree of conversion. This work implies that the TPP technique is a valuable tool for the fabrication of GRIN microoptics for (in)homogeneous molding of light flow at the micrometer scale.

     

Sum of characteristic polynomial coefficients of cycloparaphenylene graphs as topological index

ABSTRACT

Algorithm for obtaining characteristic polynomial (CP) coefficients of an alternant edge-weighted cycle is used to arrive at the algorithm for that of the cycloparaphenylene (CPP) graphs in matrix product form. The algorithm gives a recursive relation in expressing the sum of the CP coefficients of a CPP in terms of that of its two immediately preceding analogues which ultimately ends up with the use of transfer matrix in an analytical form. The sum of CP coefficients, being combinatorial in nature, is found to be used as a topological index showing much similarity with Hosoya index (sum all matching polynomial coefficients), cardinality and number of Kekulé valence structures of CPP graphs compared to the Wiener index which is the distance sum of all pairs of vertices in the graph. The sum of CP coefficients has been found to model the physical properties like strain energy and diameter of CPPs that are verified by the respective excellent correlations.     

共振光的大折射率

揭示了在多能级原子介质中的一种新现象:利用原子相干可使共振光获得明显大于1的折射率.     

Thermodynamic characteristics of a biological organism: Information value of a gene and of a protein as a measure of the efficiency and as an index of selective pressure

Summary For the treatment of the information exchanged by the biological system and the external world, the concept of information amount is not sufficient because of their remoteness from equilibrium states. Further explanations are, in fact, necessary about the effects of the reception of the message,i.e. its information value that is then necessary to define for each case. We have, therefore, defined the information value of a gene and of a protein and analysed a sample of about hundred genes looking for some significative regularity in the frequency of usage of codons and amino acids allowing us to individualize the salient characteristics of a translated sequence of codons. We have found that the most used amino acids have, on the average, a low information value and, for each amino acid type, the most used codons have a lower information value. Moreover, we can say that the composition in amino acids or in codons of a sequence useful for the biological systems is such that more frequent mutations cause the smaller variation in the phenotype. All that shows that our definitions well describe the system of transmission and reception of the information value in a biological organism and that they can be considered as an index of its efficiency,i.e. of its ability to minimize the effects of the mutation of the genotype on the phenotype. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

利用泄漏波导测量低折射率薄膜的折射率和厚度

根据泄漏波导原理对K_9玻璃基板上的冰晶石薄膜进行折射率测量,达到的精度为1×10~(-4),与真实波导的情况相似。文中讨论了利用添加高折射率薄层减小待测薄膜的最小厚度的可能性。文中还利用光电方法观察反射光中暗条纹的方法判别波导的激发,并测出了冰晶石薄膜在4500到6500范围内的折射率。     

Study and investigation of long period grating as refractive index sensor

In this paper, we have investigated the response of long period grating (LPG) as refractive index sensor. The response has been studied for refractive index variation ranging from 1 to 1.45. In this work, we found that the sensing mechanism is based on two different aspects. First is the change of coupling power from the guided core mode to other co-propagating cladding modes and second is the wavelength shift of the peak resonant wavelengths from their original positions due the change of refractive index of the environmental (external) medium surrounding the cladding of the grating.