abstract

We study collective behavior of Brodmann regions of human cerebral cortex using functional Magnetic Resonance Imaging (fMRI) and Random Matrix Theory (RMT). The raw fMRI data is mapped onto the cortex regions corresponding to the Brodmann areas with the aid of the Talairach coordinates. Principal Component Analysis (PCA) of the Pearson correlation matrix for 41 different Brodmann regions is carried out to determine their collective activity in the idle state and in the active state stimulated by tapping. The collective brain activity is identified through the statistical analysis of the eigenvectors to the largest eigenvalues of the Pearson correlation matrix. The leading eigenvectors have a large participation ratio. This indicates that several Broadmann regions collectively give rise to the brain activity associated with these eigenvectors. We apply Random Matrix Theory to interpret the underlying multivariate data.

abstract

In this paper, we discuss three methods to calculate energy splitting in cosine potential on a circle, Bloch waves, semi-classical approximation and restricted basis approach. While the Bloch wave method gives only a qualitative result, with the WKB method we are able to determine its unknown coefficients. The numerical approach is most exact and enables us to extract further corrections to previous results.

abstract

In this work, two different methods for extracting the mass of a new quark from the (pseudo) data are compared: the classical cut-based method and the Matrix Element Method. As a concrete example, a fourth family up type quark is searched in \(p\)–\(p\) collisions of 7 TeV center-of-mass energy. We have shown that even with a very small number of events, Matrix Element Method gives better estimations for the mass value and its error. Especially, for event samples in which Signal-to-Background ratio is greater than 0.2, Matrix Element Method reduces the statistical error approximately ten times.

abstract

We study the contribution of the antisymmetric tensor unparticle mediation to the diphoton production rate of the Higgs boson and try to explain the discrepancy between the measured value of the decay width of the discovered new resonance and that of the Standard Model Higgs boson. We observe that tree level contribution of the antisymmetric unparticle mediation is a possible candidate to explain the measured value of the diphoton decay rate.

abstract

Three-dimensional electrodynamics in the spinor (i.e. two-component) version is considered. With the use of the so-called Salam’s vertex, the infinite hierarchy of Dyson–Schwinger equations is turned into a set of four self-consistent equations for four parameters describing the infrared behavior of fermion and boson propagators. It is shown numerically, that this set of equations has solutions, at least for certain values of gauge parameter. For weak coupling (i.e. for heavy fermions), the values of all these quantities are found analytically. In the case of massless bare fermion, masses of both particles are generated leading thereby to parity breaking.

abstract

We calculate the coupling constants \(g_{SV\gamma }\), where \(S\) and \(V\) denote scalar, \(a_{0}(980)\) and \(f_{0}(980)\), mesons and vector, \(\rho \) and \(\omega \), mesons in QCD sum rules. A comparison of our estimates on the coupling constants with the results existing in the literature is also presented.

abstract

A Reggeometric (Regge+Geometry) model, based on the observed proportionality between the forward slope of the differential cross section and the interaction radius, the latter depending on virtuality \(Q^2\) of the incoming virtual photon and on the mass \(M^2\) of the produced particle, is constructed. The objective of this study is the dependence of the Regge-pole amplitude on the virtuality \(Q^2\) and masses of the external particles, which remains an open problem for the theory. The present analysis is based on the HERA data on Deeply Virtual Compton Scattering (DVCS) and exclusive diffractive Vector Meson Production (VMP). We treat each class of reactions separately, anticipating a further study that will include both a soft and a hard component of the unique Pomeron.