Geometric overconvergence of rational functions in unbounded domains

The basic aim of this paper is to study the phenomenon of overconvergence for rational functions converging geometrically on [0, + ∞)

A new approach of analyzing GRB light curves

We estimated the Txx quantiles of the cumulative GRB light curves using our recalculated background. The basic information of the light curves was extracted by multivariate statistical methods. The possible classes of the light curves are also briefly discussed.Comment: 4 pages, 8 figure

On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

We discuss some properties of the generalized entropies, called Renyi entropies and their application to the case of continuous distributions. In particular it is shown that these measures of complexity can be divergent, however, their differences are free from these divergences thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e. to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e. no classical limit can be defined. Numerical simulations on a one dimensional disordered system corroborate our expectations.Comment: 8 pages with 2 embedded eps figures, RevTex4, AmsMath included, submitted to PR

Information Length and Localization in One Dimension

The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical results obtained by assuming an exponential envelope function. A perfect agreement is obtained already for systems of $10^3$--$10^4$ sites over a very wide range of disorder parameter $10^{-4}<W<10^4$. Implications for higher dimensions are also presented.Comment: 11 pages (+3 Figures upon request), Plain TE

A Successful Programme to Help Hungarian Intellectuals Beyond the Border

Collegium Talentum, a support system for Hungarian talent beyond the border, has been operating since 2011 in the Carpathian Basin. The aim of the programme is to train young researchers to become scientifically well-grounded specialists by both national and European standards, to attract fresh blood to academic institutions, and to inspire them to convey national cultural values in addition to having a scientific career. The programme supports the progress of 90 young doctoral students, thus significantly contributing to mitigating the crisis caused by the lack of intellectuals beyond the borders. More than 300 intellectuals from all over the Carpathian Basin have been involved in the programme to date, and a successful network has been organized of professors and researchers committed to national values

Quantum chaos in one dimension?

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.Comment: 7 pages, 10 figures, minor correction, references extende

Divergent estimation error in portfolio optimization and in linear regression

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifestation of an algorithmic phase transition, it is accompanied by a number of critical phenomena, and displays universality. As the structure of a large number of multidimensional regression and modelling problems is very similar to portfolio optimization, the scope of the above observations extends far beyond finance, and covers a large number of problems in operations research, machine learning, bioinformatics, medical science, economics, and technology.Comment: 5 pages, 2 figures, Statphys 23 Conference Proceedin

Spectral Properties of the Chalker-Coddington Network

We numerically investigate the spectral statistics of pseudo-energies for the unitary network operator U of the Chalker--Coddington network. The shape of the level spacing distribution as well the scaling of its moments is compared to known results for quantum Hall systems. We also discuss the influence of multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J. Phys. Soc. Jp

Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition

The distribution of the correlation dimension in a power law band random matrix model having critical, i.e. multifractal, eigenstates is numerically investigated. It is shown that their probability distribution function has a fixed point as the system size is varied exactly at a value obtained from the scaling properties of the typical value of the inverse participation number. Therefore the state-to-state fluctuation of the correlation dimension is tightly linked to the scaling properties of the joint probability distribution of the eigenstates.Comment: 4 pages, 5 figure