Eigenvalue density of empirical covariance matrix for correlated samples

We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for uncorrelated samples. The method allows for exact determination of the experimental spectrum for a given covariance matrix and given correlations between samples in the limit of large N and N/T=r=const with N being the number of degrees of freedom and T being the number of samples. We discuss the effect of correlations on several examples.Comment: 12 pages, 5 figures, to appear in Acta Phys. Pol. B (Proceedings of the conference on `Applications of Random Matrix Theory to Economy and Other Complex Systems', May 25-28, 2005, Cracow, Polan

Perturbing General Uncorrelated Networks

This paper is a direct continuation of an earlier work, where we studied Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring the formation of short cycles. Here, we generalize these results. We keep the same interaction Hamiltonian but let it act on general graphs with uncorrelated nodes and an arbitrary given degree distribution. It is shown that the results obtained for Erd\"os-R\'enyi graphs are generic, at the qualitative level. However, scale-free graphs are an exception to this general rule and exhibit a singular behaviour, studied thoroughly in this paper, both analytically and numerically.Comment: 7 pages, 7 eps figures, 2-column revtex format, references adde

Czynniki wpływające na funkcjonowanie chorych po zabiegu wszczepienia pomostów aortalno-wieńcowych

Wstęp. W ostatnich latach obserwuje się dynamiczny rozwój kardiologii inwazyjnej i innych metod leczenia choroby niedokrwiennej serca, w tym pomostowania aortalno-wieńcowego (ang. Coronary artery bypass graft, CABG). CABG jest obecnie najczęściej przeprowadzanym zabiegiem kardiochirurgicznym w Polsce, jednak liczba aktualnych doniesień na te-mat codziennego funkcjonowania osób po przebytej rewaskularyzacji mięśnia sercowego jest niewielka. Celem pracy była ocena czynników wpływających na funkcjonowanie chorych po CABG. Materiał i metody. Grupę badaną stanowiło 61 chorych (70,5% mężczyzn) w przedziale wiekowym 48-81 lat (śr. 65,3 ± 7,8) w okresie 2-6 miesięcy po CABG. W badaniach zastosowano kwestionariusz wywiadu własnego autorstwa oraz skalę jakości życia WHOQOL-BREF. Wyniki. Wraz z wiekiem obniżały się wyniki w dziedzinie somatycznej i psychologicznej (p<0,001). Chorzy pozostający w związkach małżeńskich osiągali znacznie lepsze wyniki niż osoby żyjące samotnie w zakresie ogólnej percepcji jakości życia oraz w poszczególnych jej dziedzinach (p<0,05). Im wyższy był poziom wykształcenia badanych, tym lepiej postrzegali oni własne zdrowie (F=7,872; p=0,001) oraz uzyskiwali wyższe wyniki w dziedzinie somatycznej (F=6,119; p=0,004). Osoby aktywne zawodowo znacznie lepiej oceniały jakość swojego życia i zdrowia oraz wszystkie dziedziny funkcjonowania (p<0,05). Wnioski. Funkcjonowanie pacjentów po operacji było zależne od: wieku, stanu cywilnego, statusu rodzinnego, wykształcenia, aktywności zawodowej, współistnienia innych schorzeń z chorobą wieńcową, czasu od operacji oraz aktywności fizycznej.Introduction. In recent years, there has been rapid development of invasive cardiology and other methods of treat-ment of coronary heart disease, including coronary artery bypass grafting (CABG). CABG is currently the most frequently per-formed cardiac surgery in Poland; however, there are few up-to-date reports on the daily functioning of persons with a history of myocardial revascularization. The aim of the study was to assess the factors affecting the func-tioning of patients after CABG. Materials and methods. The study group consisted of 61 patients (70.5% were men) aged 48-81 (av. 65.3 ± 7.8) in a period of 2-6 months after CABG. The study used a questionnaire developed by the authors and the WHOQOL-BREF scale for the quality of life. Results. The results in the somatic and psychological field de-creased with age (p<0.001). Married patients achieved signifi-cantly better results than the persons living alone in the overall perception of the quality of life and in each of its fields (p<0.05). The higher the level of education of the respondents was, the better they perceived their health (F=7.872; p=0.001) and the higher scores they obtained in the somatic field (F=6.119; p=0.004). Active persons assessed the quality of their life and health better in all the areas of functioning (p<0.05). Conclusions. The functioning of the patients after the surgery was dependent on age, marital status, family status, education, profes-sional activity, the coexistence of other diseases with coronary artery disease, the duration of the surgery, and physical activity

Signal from noise retrieval from one and two-point Green's function - comparison

We compare two methods of eigen-inference from large sets of data, based on the analysis of one-point and two-point Green's functions, respectively. Our analysis points at the superiority of eigen-inference based on one-point Green's function. First, the applied by us method based on Pad?e approximants is orders of magnitude faster comparing to the eigen-inference based on uctuations (two-point Green's functions). Second, we have identified the source of potential instability of the two-point Green's function method, as arising from the spurious zero and negative modes of the estimator for a variance operator of the certain multidimensional Gaussian distribution, inherent for the two-point Green's function eigen-inference method. Third, we have presented the cases of eigen-inference based on negative spectral moments, for strictly positive spectra. Finally, we have compared the cases of eigen-inference of real-valued and complex-valued correlated Wishart distributions, reinforcing our conclusions on an advantage of the one-point Green's function method.Comment: 14 pages, 8 figures, 3 table

Numerical Study of c>1 Matter Coupled to Quantum Gravity

We present the results of a numerical simulation aimed at understanding the nature of the `c = 1 barrier' in two dimensional quantum gravity. We study multiple Ising models living on dynamical $\phi^3$ graphs and analyse the behaviour of moments of the graph loop distribution. We notice a universality at work as the average properties of typical graphs from the ensemble are determined only by the central charge. We further argue that the qualitative nature of these results can be understood from considering the effect of fluctuations about a mean field solution in the Ising sector.Comment: 12 page

Search for Scaling Dimensions for Random Surfaces with c=1

We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled to matter fields with $c=1$. Using baby universe surgery it was possible to simulate randomly triangulated surfaces made of 260.000 triangles. Our results are consistent with the theoretical prediction $d_H = 2+\sqrt{2}$ for the intrinsic Hausdorff dimension.Comment: 10 pages, (csh will uudecode and uncompress ps-file), NBI-HE-94-3

Wealth Condensation in Pareto Macro-Economies

We discuss a Pareto macro-economy (a) in a closed system with fixed total wealth and (b) in an open system with average mean wealth and compare our results to a similar analysis in a super-open system (c) with unbounded wealth. Wealth condensation takes place in the social phase for closed and open economies, while it occurs in the liberal phase for super-open economies. In the first two cases, the condensation is related to a mechanism known from the balls-in-boxes model, while in the last case to the non-integrable tails of the Pareto distribution. For a closed macro-economy in the social phase, we point to the emergence of a ``corruption'' phenomenon: a sizeable fraction of the total wealth is always amassed by a single individual.Comment: 4 pages, 1 figur

Research on the threaded connection system from AlMgSi alloy for electrical power cables under various clamping loads

This article presents strain gauge tests showing the force loads in the connection system of power cables, with AlMgSi sheer bolts. Among others, the analysis of the influence of the tightening torque of the clamping unit on the distribution of forces and the evaluation of the strain in the entire system was carried out. The knowledge of the force conditions and loads in the threaded connection system allowed to develop, with the use of Finite Element Method (FEM) modelling, the optimal geometry and material of elements for the power cable connection system

New generation of cable screw connectors for electrical power engineering systems

The article presents a material analysis for a new generation of cable screw connectors with shear bolts designed for not only 1st and 2nd class of cables but also 5tth class of aluminium and copper conductors that have not been previously supported. The set of properties of aluminium series 6xxx designated for screw connectors production has been determined. Finite Element Method (FEM) simulation of the controlled shear of the bolt at the body of the screw connector has been carried out. The repeatability of the bolt shear in the actual conditions was also conducted in order to verify the prototypes of the new generation of cable screw connectors