Numerical range for random matrices

We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. In particular, numerical range of complex Ginibre matrix almost surely converges to the disk of radius $\sqrt{2}$. Since the spectrum of non-hermitian random matrices from the Ginibre ensemble lives asymptotically in a neighborhood of the unit disk, it follows that the outer belt of width $\sqrt{2}-1$ containing no eigenvalues can be seen as a quantification the non-normality of the complex Ginibre random matrix. We also show that the numerical range of upper triangular Gaussian matrices converges to the same disk of radius $\sqrt{2}$, while all eigenvalues are equal to zero and we prove that the operator norm of such matrices converges to $\sqrt{2e}$.Comment: 23 pages, 4 figure

Inclusive production of J/ψJ/\psi meson in proton-proton collisions at BNL RHIC

Inclusive cross sections for $J/\psi$ production in proton-proton collisions were calculated in the $k_t$-factorization approach for the RHIC energy. Several mechanisms were considered, including direct color-singlet mechanism, radiative decays of $\chi_c$ mesons, decays of $\psi'$, open-charm associated production of $J/\psi$ as well as weak decays of B mesons. Different unintegrated gluon distributions from the literature were used. We find that radiative $\chi_c$ decays and direct color-singlet contributions constitute the dominant mechanism of $J/\psi$ production. These process cannot be consistently treated within collinear-factorization approach. The results are compared with recent RHIC data. The new precise data at small transverse momenta impose stringent constraints on UGDFs. Some UGDFs are inconsistent with the new data. The Kwieci\'nski UGDFs give the best description of the data. In order to verify the mechanism suggested here we propose $J/\psi$ -- jet correlation measurement and an independent measurement of $\chi_c$ meson production in $\pi^+ \pi^-$ and/or $K^+ K^-$ decay channels. Finally, we address the issue of \J spin alignment.Comment: 26 pages, 20 figures, the text was slightly modified, the title was modified, more discussion was added, one figure was removed, one was adde

Extending scientific computing system with structural quantum programming capabilities

We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave, providing a library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for high-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices

Nonphotonic electrons at RHIC within ktk_t-factorization approach and with experimental semileptonic decay functions

We discuss production of nonphotonic electrons in proton-proton scattering at RHIC. The distributions in rapidity and transverse momentum of charm and bottom quarks/antiquarks are calculated in the $k_t$-factorization approach. We use different unintegrated gluon distributions from the literature. The hadronization of heavy quarks is done by means of Peterson and Braaten et al. fragmentation functions. The semileptonic decay functions are found by fitting recent semileptonic data obtained by the CLEO and BABAR collaborations. We get good description of the data at large transverse momenta of electrons and find a missing strength concentrated at small transverse momenta of electrons. Plausible missing mechanisms are discussed.Comment: 16 pages, 11 figure

Solution of the Kwiecinski evolution equations for unintegrated parton distributions using the Mellin transform

The Kwiecinski equations for the QCD evolution of the unintegrated parton distributions in the transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general case, as well as in a small-b expansion which converges fast for b Lambda_QCD sufficiently small. We also discuss the asymptotic limit of large bQ and show that the distributions generated by the evolution decrease with b according to a power law. Numerical results are presented for the pion distributions with a simple valence-like initial condition at the low scale, following from chiral large-N_c quark models. We use two models: the Spectral Quark Model and the Nambu--Jona-Lasinio model. Formal aspects of the equations, such as the analytic form of the b-dependent anomalous dimensions, their analytic structure, as well as the limits of unintegrated parton densities at x -> 0, x -> 1, and at large b, are discussed in detail. The effect of spreading of the transverse momentum with the increasing scale is confirmed, with growing asymptotically as Q^2 alpha(Q^2). Approximate formulas for for each parton species is given, which may be used in practical applications.Comment: 18 pages, 6 figures, RevTe

kt - factorization and CCFM - the solution for describing the hadronic final states - everywhere ?

The basic ideas of kt-factorization and CCFM parton evolution is discussed. The unintegrated gluon densities, obtained from CCFM fits to the proton structure function data at HERA are used to predict hadronic final state cross sections like jet production at HERA, but also comparisons with recent measurements of heavy quark production at the Tevatron are presented. Finally, the kt-factorization approach is applied to Higgs production at high energy hadron hadron colliders and the transverse momentum spectrum of Higgs production at the LHC is calculated.Comment: to be published in MPLA, replaced with new reference

High-fat-diet-evoked disruption of the rat dorsomedial hypothalamic clock can be prevented by restricted nighttime feeding

Obesity is a growing health problem for modern society; therefore, it has become extremely important to study not only its negative implications but also its developmental mechanism. Its links to disrupted circadian rhythmicity are indisputable but are still not well studied on the cellular level. Circadian food intake and metabolism are controlled by a set of brain structures referred to as the food-entrainable oscillator, among which the dorsomedial hypothalamus (DMH) seems to be especially heavily affected by diet-induced obesity. In this study, we evaluated the effects of a short-term high-fat diet (HFD) on the physiology of the male rat DMH, with special attention to its day/night changes. Using immunofluorescence and electrophysiology we found that both cFos immunoreactivity and electrical activity rhythms become disrupted after as few as 4 weeks of HFD consumption, so before the onset of excessive weight gain. This indicates that the DMH impairment is a possible factor in obesity development. The DMH cellular activity under an HFD became increased during the non-active daytime, which coincides with a disrupted rhythm in food intake. In order to explore the relationship between them, a separate group of rats underwent time-restricted feeding with access to food only during the nighttime. Such an approach completely abolished the disruptive effects of the HFD on the DMH clock, confirming its dependence on the feeding schedule of the animal. The presented data highlight the importance of a temporally regulated feeding pattern on the physiology of the hypothalamic center for food intake and metabolism regulation, and propose time-restricted feeding as a possible prevention of the circadian dysregulation observed under an HFD

Brand Name and Generic Proton Pump Inhibitor Prescriptions in the United States: Insights from the National Ambulatory Medical Care Survey (2006–2010)

Introduction. Proton pump inhibitors (PPI) are one of the most commonly prescribed medication classes with similar efficacy between brand name and generic PPI formulations. Aims. We determined demographic, clinical, and practice characteristics associated with brand name PPI prescriptions at ambulatory care visits in the United States. Methods. Observational cross sectional analysis using the National Ambulatory Medical Care Survey (NAMCS) of all adult (≥18 yrs of age) ambulatory care visits from 2006 to 2010. PPI prescriptions were identified by using the drug entry code as brand name only or generic available formulations. Descriptive statistics were reported in terms of unweighted patient visits and proportions of encounters with brand name PPI prescriptions. Global chi-square tests were used to compare visits with brand name PPI prescriptions versus generic PPI prescriptions for each measure. Poisson regression was used to determine the incidence rate ratio (IRR) for generic versus brand PPI prescribing. Results. A PPI was prescribed at 269.7 million adult ambulatory visits, based on 9,677 unweighted visits, of which 53% were brand name only prescriptions. In 2006, 76.0% of all PPI prescriptions had a brand name only formulation compared to 31.6% of PPI prescriptions in 2010. Visits by patients aged 25–44 years had the greatest proportion of brand name PPI formulations (57.9%). Academic medical centers and physician-owned practices had the greatest proportion of visits with brand name PPI prescriptions (58.9% and 55.6% of visits with a PPI prescription, resp.). There were no significant differences in terms of median income, patient insurance type, or metropolitan status when comparing the proportion of visits with brand name versus generic PPI prescriptions. Poisson regression results showed that practice ownership type was most strongly associated with the likelihood of receiving a brand name PPI over the entire study period. Compared to HMO visits, patient visits at academic medical centers (IRR 4.2, 95% CI 2.2–8.0), physician-owned practices (IRR 3.9, 95% CI 2.1–7.1), and community health centers (IRR 3.6, 95% CI 1.9–6.6) were all more likely to have brand name PPIs. Conclusion. PPI prescriptions with brand name only formulations are most strongly associated with physician practice type