Eigenvalue correlations in QCD with a chemical potential

We discuss a new Random Matrix Model for QCD with a chemical potential that is based on the symmetries of the Dirac operator and can be solved exactly for all eigenvalue correlations for any number of flavors. In the microscopic limit of small energy levels the results should be an accurate description of QCD. This new model can also be scaled so that all physical observables remain at their $\mu=0$ values until a first order chiral restoration transition is reached. This gives a more realistic model for the QCD phase diagram than previous RMM. We also mention how the model might aid in determining the phase diagram of QCD from future numerical simulations.Comment: 3 pages, 3 figures, Lattice2004(non-zero

Contextual normalization applied to aircraft gas turbine engine diagnosis

Diagnosing faults in aircraft gas turbine engines is a complex problem. It involves several tasks, including rapid and accurate interpretation of patterns in engine sensor data. We have investigated contextual normalization for the development of a software tool to help engine repair technicians with interpretation of sensor data. Contextual normalization is a new strategy for employing machine learning. It handles variation in data that is due to contextual factors, rather than the health of the engine. It does this by normalizing the data in a context-sensitive manner. This learning strategy was developed and tested using 242 observations of an aircraft gas turbine engine in a test cell, where each observation consists of roughly 12,000 numbers, gathered over a 12 second interval. There were eight classes of observations: seven deliberately implanted classes of faults and a healthy class. We compared two approaches to implementing our learning strategy: linear regression and instance-based learning. We have three main results. (1) For the given problem, instance-based learning works better than linear regression. (2) For this problem, contextual normalization works better than other common forms of normalization. (3) The algorithms described here can be the basis for a useful software tool for assisting technicians with the interpretation of sensor data

Universal correlations in spectra of the lattice QCD Dirac operator

Recently, Kalkreuter obtained complete Dirac spectra for $SU(2)$ lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as $12^4$. We performed a statistical analysis of these data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal Ensemble for Wilson fermions. In both cases long range spectral fluctuations are strongly suppressed: the variance of a sequence of levels containing $n$ eigenvalues on average is given by $\Sigma_2(n) \sim 2 (\log n)/\beta\pi^2$ ($\beta$ is equal to 4 and 1, respectively) instead of $\Sigma_2(n) = n$ for a random sequence of levels. Our findings are in agreement with the anti-unitary symmetry of the lattice Dirac operator for $N_c=2$ with staggered fermions which differs from Wilson fermions (with the continuum anti-unitary symmetry). For $N_c = 3$, we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.Comment: Talk present at LATTICE96(chirality in QCD), 3 pages, Late

Quantum chaos in QCD at finite temperature

We study complete eigenvalue spectra of the staggered Dirac matrix in quenched QCD on a $6^3\times 4$ lattice. In particular, we investigate the nearest-neighbor spacing distribution $P(s)$ for various values of $\beta$ both in the confinement and deconfinement phase. In both phases except far into the deconfinement region, the data agree with the Wigner surmise of random matrix theory which is indicative of quantum chaos. No signs of a transition to Poisson regularity are found, and the reasons for this result are discussed.Comment: 3 pages, 6 figures (included), poster presented by R. Pullirsch at "Lattice 97", to appear in the proceeding

QCD critical point and event-by-event fluctuations in heavy ion collisions

A summary of work done in collaboration with K. Rajagopal and E. Shuryak. We show how heavy ion collision experiments, in particular, event-by-event fluctuation measurements, can lead to the discovery of the critical point on the phase diagram of QCD.Comment: 4 pages. Summary of work done in collaboration with K. Rajagopal and E. Shuryak (hep-ph/9903292). To be published in the proceedings of Quark Matter 99, Torino, Italy, May 10-14, 199

Lower Bounds for L1L_1 Discrepancy

We find the best asymptotic lower bounds for the coefficient of the leading term of the $L_1$ norm of the two-dimensional (axis-parallel) discrepancy that can be obtained by K.Roth's orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, complex and harmonic analysis.Comment: a slightly different version of the article is accepted to "Mathematika

EMIGRATIONAL INCLINATION - STAYING OR LEAVING – FREE MIGRATION POSSIBILITIES AND TENDENCIES IN B. A. Z. COUNTY

In this recent study we would like to show how migration affects in Borsod-Abaúj-Zemplén County, which components it has, what differences are there between gross and net emigrational inclination, what measures have been done by the ones who are determined to leave Hungary in expectations of a foreign job. A 375-element-sample was taken and had been appraised in order to measure the net emigration, the emigrational network and so the emigrational shell.migration, motivational factors, emigrational network, Labor and Human Capital,