Patent citation network in nanotechnology (1976–2004)

The patent citation networks are described using critical node, core network, and network topological analysis. The main objective is understanding of the knowledge transfer processes between technical fields, institutions and countries. This includes identifying key influential players and subfields, the knowledge transfer patterns among them, and the overall knowledge transfer efficiency. The proposed framework is applied to the field of nanoscale science and engineering (NSE), including the citation networks of patent documents, submitting institutions, technology fields, and countries. The NSE patents were identified by keywords “full-text” searching of patents at the United States Patent and Trademark Office (USPTO). The analysis shows that the United States is the most important citation center in NSE research. The institution citation network illustrates a more efficient knowledge transfer between institutions than a random network. The country citation network displays a knowledge transfer capability as efficient as a random network. The technology field citation network and the patent document citation network exhibit a␣less efficient knowledge diffusion capability than a random network. All four citation networks show a tendency to form local citation clusters.     

PageRank model of opinion formation on social networks

We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of the Universities of Cambridge and Oxford, LiveJournal, and Twitter. In this model, the opinion formation of linked electors is weighted with their PageRank probability. Such a probability is used by the Google search engine for ranking of web pages. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion on a significant fraction of the society. However, for a homogeneous distribution of two opinions, there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We find that the LiveJournal and Twitter networks have a stronger tendency to a totalitarian opinion formation than the university networks. We also analyze the Sznajd model generalized for scale-free networks with the weighted PageRank vote of electors.     

Modeling innovation by a kinetic description of the patent citation system

This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From patent data we extract an attractiveness function, A(k,l)$A(k,l)$, which determines the likelihood that a patent will be cited. A(k,l)$A(k,l)$ shows power law aging and preferential attachment. The exponent of the latter is increasing since 1993, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. In particular, our results appear consistent with an increasing patent “thicket”, in which more and more patents are issued on minor technical advances.     

Worldwide nanotechnology development: a comparative study of USPTO,EPO, and JPO patents (1976–2004)

To assess worldwide development of nanotechnology, this paper compares the numbers and contents of nanotechnology patents in the United States Patent and Trademark Office (USPTO), European Patent Office (EPO), and Japan Patent Office (JPO). It uses the patent databases as indicators of nanotechnology trends via bibliographic analysis, content map analysis, and citation network analysis on nanotechnology patents per country, institution, and technology field. The numbers of nanotechnology patents published in USPTO and EPO have continued to increase quasi-exponentially since 1980, while those published in JPO stabilized after 1993. Institutions and individuals located in the same region as a repository’s patent office have a higher contribution to the nanotechnology patent publication in that repository (“home advantage” effect). The USPTO and EPO databases had similar high-productivity contributing countries and technology fields with large number of patents, but quite different high-impact countries and technology fields after the average number of received cites. Bibliographic analysis on USPTO and EPO patents shows that researchers in the United States and Japan published larger numbers of patents than other countries, and that their patents were more frequently cited by other patents. Nanotechnology patents covered physics research topics in all three repositories. In addition, USPTO showed the broadest representation in coverage in biomedical and electronics areas. The analysis of citations by technology field indicates that USPTO had a clear pattern of knowledge diffusion from highly cited fields to less cited fields, while EPO showed knowledge exchange mainly occurred among highly cited fields.     

Relativity of Pure States Entanglement

Entanglement of any pure state of an N×N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N≥3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the “Future,” the “Past,” and the set of noncomparable states.     

Google matrix of Bitcoin network

We construct and study the Google matrix of Bitcoin transactions during the time period from the very beginning in 2009 till April 2013. The Bitcoin network has up to a few millions of bitcoin users and we present its main characteristics including the PageRank and CheiRank probability distributions, the spectrum of eigenvalues of Google matrix and related eigenvectors. We find that the spectrum has an unusual circle-type structure which we attribute to existing hidden communities of nodes linked between their members. We show that the Gini coefficient of the transactions for the whole period is close to unity showing that the main part of wealth of the network is captured by a small fraction of users. In global the Google matrix analysis of bitcoin network gives a new understanding of the bitcoin transactions with PageRank and CheiRank characterization of sellers and buyers which are dominant not simply due to the sold/bought volume but also by taking into account if bitcoins are sold to (bought by) other important sellers (buyers).     

Weighted networks of scientific communication: the measurement and topological role of weight

In order to take the weight of connection into consideration and to find a natural measurement of weight, we have collected papers in Econophysics and constructed a network of scientific communication to integrate idea transportation among econophysicists by collaboration, citation and personal discussion. Some basic statistics such as weight per degree are discussed in Fan et al. J. Mod. Phys. B (17–19) (2004) 2505. In this paper, by including the papers published recently, further statistical results for the network are reported. Clustering coefficient of weighted networks is introduced and empirically studied in this network. We also compare the typical statistics on this network under different weight assignments, including random and inverse weight. The conclusion from weight-redistributed network is helpful to the investigation of the topological role of weight.     

Community detection based on the “clumpiness” matrix in complex networks

The “clumpiness” matrix of a network is used to develop a method to identify its community structure. A “projection space” is constructed from the eigenvectors of the clumpiness matrix and a border line is defined using some kind of angular distance in this space. The community structure of the network is identified using this borderline and/or hierarchical clustering methods. The performance of our algorithm is tested on some computer-generated and real-world networks. The accuracy of the results is checked using normalized mutual information. The effect of community size heterogeneity on the accuracy of the method is also discussed.     

Measuring science–technology interactions using patent citations and author-inventor links: an exploration analysis from Chinese nanotechnology

This article contributes to the growing study on the interactions between science and technology with China’s evidence in the field of nanotechnology, based on the database of United States Patent and Trademark Office. The analysis is focused during the period of 1991–2008, a rapid increasing period for the development of nanotechnology. Using the non-patent references cited by patents, we first investigate the science–technology connections in the context of Chinese nanotechnology, especially in institutional sectors and its application fields. Those patents, produced by academic researchers and directed towards basic scientific knowledge, generally cite more scientific references with a higher proportion of self-citations. It is interesting to find that patents contributed by collaborations between public organizations and corporations seldom contain scientific references. Following an interesting path on matching the data of publications and patents, we establish the author-inventor links in this emerging field. Author-inventors, who are co-active in publishing and patenting, are at the very top of the most prolific and highly cited researchers. Finally, we employ social network analysis to explore the characteristics of scientific and technological networks generated by co-authorship and co-invention data, to investigate the position and the role of patenting–publishing scientists in these research networks.     

Complex propagation on directed small world networks

The effect of directionality on the information propagation in a contagion model with complex propagation, i.e., that takes into account the need for simultaneous exposure to multiple activation sources, is studied. While it is known that complex propagation is blocked with increasing network randomness, here it is shown that network directionality affects such a result, leading to several different behaviors depending on the preservation of the in-degree or out-degree. The critical points for the occurrence of complex propagation in 1D directed small world networks are determined. It is shown that these points only depend on the number of outgoing links.     

Runaway events dominate the heavy tail of citation distributions

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have unproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether citation distribution follows the log-normal or power-law fit. The goal of our study is to solve this debate by measuring citation distribution for a very large and homogeneous data. We measured citation distribution for 418, 438 Physics papers published in 1980–1989 and cited by 2008. While the log-normal fit deviates too strong from the data, the discrete power-law function with the exponent γ = 3.15 does better and fits 99.955% of the data. However, the extreme tail of the distribution deviates upward even from the power-law fit and exhibits a dramatic “runaway” behavior. The onset of the runaway regime is revealed macroscopically as the paper garners 1000-1500 citations, however the microscopic measurements of autocorrelation in citation rates are able to predict this behavior in advance.     

High-temperature B2 ordering in Fe50Co50 alloy

High-temperature (above 1200 °C) B2 ordering was experimentally found in the Fe₅₀Co₅₀ alloy with the help of the electron diffraction. Using the X-ray photoelectron spectroscopy method the “ordering-phase separation” transition was shown to lead to changes both in the 3d-electron spectra of the valence band (3d-valence electron localization on Fe atoms increases at phase separation and it decreases at ordering). The investigation of multiplet splitting of the 3s-electron spectra of core-level electrons reveals that magnetic moments on Fe and Co atoms in the Fe₅₀Co₅₀ alloy are larger, when there is the tendency toward ordering, and they are smaller in the case of the tendency toward phase separation. A number of examples are presented, which are indicative of the fact that chemical ordering can influence magnetic ordering by the formation of the respective microstructures and magnetic ordering has no influence on chemical ordering. It can be concluded that the phase transition “ordering-phase separation” takes place both at 730 °C and at the temperature somewhat higher that 1200 °C.     

A directed network of Greek and Roman mythology

We construct a directed network using a dictionary of Greek and Roman mythology in which the nodes represent the entries listed in the dictionary and we make directional links from an entry to other entries that appear in its explanatory part. We find that this network is clearly not a random network but a directed scale-free network in which the distributions of out-degree and in-degree follow a power-law with exponents γ_out≈3.0 and γ_in≈2.5, respectively. Also we measure several quantities which describe the topological properties of the network and compare it to that of other real networks.     

Network analysis to detect common strategies in Italian foreign direct investment

In this paper we reconstruct and discuss the network of Italian firms investing abroad, exploiting information from complex network analysis. This method, detecting the key nodes of the system (both in terms of firms and countries of destination), allows us to single out the linkages among firms without ex-ante priors. Moreover, through the examination of affiliates’ economic activity, it allows us to highlight different internationalization strategies of “leaders” in different manufacturing sectors.     

Reprint of: Two-dimensional planar photonic crystals: Calculation of coherent transmittance and reflectance at normal illumination under the quasicrystalline approximation

The technique to calculate coherent transmission and reflection coefficients of two-dimensional (2D) planar photonic crystal (PC) at the normal to layer plane illumination is proposed. It is based on the quasicrystalline approximation of the theory of multiple scattering of waves. At this approximation spatial particle correlations are characterized by the radial distribution function. We propose the method of the 2D planar PC radial distribution function simulation. It consists in the calculation of coordination circles of ideal crystal lattice and following blurring them into the “rings” with fuzzy edges to describe the crystal lattice of an actual crystal. The width of the “rings” depends on the distance from coordinate origin. The blurring technique is proposed and discussed. The method allows simulation of the PCs lattices with various ordering degrees and spatial particle correlations. The results of numerical calculations of coherent transmittance and reflectance of monolayers with different orderings and refractive indices of spherical monodisperse particles are displayed.     

Formal versus self-organised knowledge systems: A network approach

In this work, we consider the topological analysis of symbolic formal systems in the framework of network theory. In particular, we analyse the network extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the vertices are the statements and two statements are connected with a directed link if one statement is used to demonstrate the other one. We compare the obtained network with other directed acyclic graphs, such as a scientific citation network and a stochastic model. We also introduce a novel topological ordering for directed acyclic graphs and we discuss its properties with respect to the classical one. The main result is the observation that formal systems of knowledge topologically behave similarly to self-organised systems.     

Two-dimensional planar photonic crystals: Calculation of coherent transmittance and reflectance at normal illumination under the quasicrystalline approximation

The technique to calculate coherent transmission and reflection coefficients of two-dimensional (2D) planar photonic crystal (PC) at the normal to layer plane illumination is proposed. It is based on the quasicrystalline approximation of the theory of multiple scattering of waves. At this approximation spatial particle correlations are characterized by the radial distribution function. We propose the method of the 2D planar PC radial distribution function simulation. It consists in the calculation of coordination circles of ideal crystal lattice and following blurring them into the “rings” with fuzzy edges to describe the crystal lattice of an actual crystal. The width of the “rings” depends on the distance from coordinate origin. The blurring technique is proposed and discussed. The method allows simulation of the PCs lattices with various ordering degrees and spatial particle correlations. The results of numerical calculations of coherent transmittance and reflectance of monolayers with different orderings and refractive indices of spherical monodisperse particles are displayed.     

Routing and wavelength assignment algorithms for multiclass WDM optical networks

In this paper dynamic routing and wavelength assignment strategies have been proposed for multiclass WDM optical networks. Multiclass optical networks provide multiple classes of services to the subscriber according to the requirement, which in turn increase operational profitability. Each class of service could be characterized by parameters like number of wavelengths, expected call holding time and average arrival rate of request. The proposed strategies have been analyzed and compared with existing strategies on the basis of blocking probabilities for multiclass traffic scenarios. Simulation results on different network topologies demonstrate that the performance of proposed strategies “Fixed shortest/alternate shortest path routing with wavelength reservation (FSASWR)” and “Fixed alternate shortest path routing with least priority wavelength assignment (FASPL)” are much better as compared to existing strategies. Proposed strategies minimize blocking probability of the multiclass network using limited number of wavelengths.     

Complex networks and banking systems supervision

Comprehensive and thorough supervision of all banking institutions under a Central Bank’s regulatory control has become necessary as recent banking crises show. Promptly identifying bank distress and contagion issues is of great importance to the regulators. This paper proposes a methodology that can be used additionally to the standard methods of bank supervision or the new ones proposed to be implemented. By this, one can reveal the degree of banks’ connectedness and thus identify “core” instead of just “big” banks. Core banks are central in the network in the sense that they are shown to be crucial for network supervision. Core banks can be used as gauges of bank distress over a sub-network and promptly raise a red flag so that the central bank can effectively and swiftly focus on the corresponding neighborhood of financial institutions. In this paper we demonstrate the proposed scheme using as an example the asset returns variable. The method may and should be used with alternative variables as well.