Pareto law and Pareto index in the income distribution of Japanese companies

In order to study the phenomenon in detail that income distribution follows Pareto law, we analyze the database of high income companies in Japan. We find a quantitative relation between the average capital of the companies and the Pareto index. The larger the average capital becomes, the smaller the Pareto index becomes. From this relation, we can possibly explain that the Pareto index of company income distribution hardly changes, while the Pareto index of personal income distribution changes sharply, from a viewpoint of capital (or means). We also find a quantitative relation between the lower bound of capital and the typical scale at which Pareto law breaks. The larger the lower bound of capital becomes, the larger the typical scale becomes. From this result, the reason there is a (no) typical scale at which Pareto law breaks in the income distribution can be understood through (no) constraint, such as the lower bound of capital or means of companies, in the financial system.Comment: 12 pages, 8 figure

Relations between a typical scale and averages in the breaking of fractal distribution

We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law in the large scale region and deviate further from the power law in the smaller scale region, we employ 2-dim quantum gravity modified by the $R^2$ term. As examples of distributions in the real world which have similar property to this model, we consider those of personal income in Japan over latest twenty fiscal years. We find relations between the typical scale and several kinds of averages in this model, and observe that these relations are also valid in recent personal income distributions in Japan with sufficient accuracy. We show the existence of the fiscal years so called bubble term in which the gap has arisen in power law, by observing that the data are away from one of these relations. We confirm, therefore, that the distribution of this model has close similarity to those of personal income. In addition, we can estimate the value of Pareto index and whether a big gap exists in power law by using only these relations. As a result, we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions.Comment: 17 pages, latex, 13 eps figure

Analytic Structure of Three-Mass Triangle Coefficients

``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised unitarity techniques to produce compact expressions for three-mass triangle coefficients. We present formulae for the N=1 contributions to the n-point NMHV amplitude.Comment: 22 pages; v3: NMHV n=point expression added. 7 point expression remove

Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited

We show the David-Jerison construction of big pieces of Lipschitz graphs inside a corkscrew domain does not require its surface measure be upper Ahlfors regular. Thus we can study absolute continuity of harmonic measure and surface measure on NTA domains of locally finite perimeter using Lipschitz approximations. A partial analogue of the F. and M. Riesz Theorem for simply connected planar domains is obtained for NTA domains in space. As a consequence every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure

Effects of film criticism on audience interest, attendance, and evaluation

The influence of arts critics has been debated for centuries, but there is little scientific evidence on the subject. This research brings a variety of data to the issue via a laboratory experiment with both attitudinal and behavioral measures. In April 1985, 318 Middle Tennessee State University students were randomly assigned to four treatment conditions, in which they read either a positive, mixed, or negative review, or a non-evaluative description (non-review) of the motion picture Butley. Before exposure to treatments, subjects reported interest in seeing the movie; after exposure, they rated the reviews for appeal, credibility, and informativeness and again reported interest in seeing the movie. These self-report measures were supplemented with behavioral measures. Subjects were provided with opportunities to take a free pass for a subsequent screening of Butley. to attend the screening, and to bring a guest. Subjects and guests who attended screenings also evaluated the film. The results showed review condition significantly affects audience interest, with interest increasing most in the positive condition, least in the negative condition, and in between in mixed and non-review conditions. Factor analysis of subjects\u27 evaluations of reviews revealed two underlying dimensions: appeal and credibility-informativeness. Review condition was significantly related to appeal, with positive and non-reviews more appealing than mixed and negative reviews. However, condition was not related to credibility-informativeness. Review condition did not significantly affect the taking of a free pass; however, trends were in the expected direction, with subjects exposed to the positive review most likely to take a pass, and those exposed to the negative review least likely. Because only 12 subjects attended screenings, inferential statistics were not applied to attendance or post-viewing film evaluation. However, 6 of the 12 who attended were from the positive review condition and only 1 from the negative

Recursive Calculation of One-Loop QCD Integral Coefficients

We present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including bubbles and triangles, can be determined without resorting to integration. We give criteria for avoiding spurious singularities and boundary terms that would invalidate the recursion. As an example where the criteria are satisfied, we obtain all cut-constructible contributions to the one-loop n-gluon scattering amplitude, A_n^{oneloop}(...--+++...), with split-helicity from an N=1 chiral multiplet and from a complex scalar. Using the supersymmetric decomposition, these are ingredients in the construction of QCD amplitudes with the same helicities. This method requires prior knowledge of amplitudes with sufficiently large numbers of legs as input. In many cases, these are already known in compact forms from the unitarity method.Comment: 36 pages; v2 clarification added and typos fixed, v3 typos fixe

All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory

We compute the non-MHV one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (- - - + + + +), (- - + - + + +), (- - + + -+ +) and (- + - + - + +). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and n-3 positive-helicity gluons, and the color ordering (- - - + + ... + +); we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.Comment: 54 pages, v3 minor correction

MHV-Vertices for Gravity Amplitudes

We obtain a CSW-style formalism for calculating graviton scattering amplitudes and prove its validity through the use of a special type of BCFW-like parameter shift. The procedure is illustrated with explicit examples.Comment: 21 pages, minor typos corrected, proof added in section

Hauntings – A nodalist study

Since Deleuze and Guattari first described the concept of the rhizome as a model of cultural transmission in A Thousand Plateaus (1980), a new way of processing information in the Arts and Social Sciences has emerged – ‘Nodalism’. Philip Gochenour has convincingly argued that units of culture can now be thought of as ‘nodes’ existing in a nonhierarchical, web-like network. Information transfer between nodes in the network is horizontal, omni-directional and not necessarily teleological, a way of viewing the world which has been paralleled and actualized in the last twenty years by the emergence, growth and ubiquity of the internet and the World Wide Web. The author – a developing audiovisual artist – here offers four videomusic pieces and one virtual sound-synthesis tool. At first glance, the pieces may appear to have little in common. However, the commentary will attempt to show that they are subtly linked together, immersed in a cocoon of rhizomatic, pluralistic, thread-like connections. The strongest ‘thread’ holding them together appears to be the trope of being ‘haunted’ in some way – either by influence, genre, or overarching concept. However, this thesis will attempt to show how a detailed consideration of each piece results in a highly complex final picture in which the pieces can be thought of as individual cultural nodes suspended in a dense rhizomatic mass of lateral cultural threads. For the sake of completion, however, the project has received the name Hauntings in reference to one of the strongest shared tropes running throughout all five works