The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions

Path Integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in (2+1) dimensions on anisotropic lattices. We extractthe static quark potential, the string tension and the low-lying "glueball" spectrum.The Euclidean string tension and mass gap decrease exponentially at weakcoupling in excellent agreement with the predictions of Polyakov and G{\" o}pfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.Comment: 12 pages, 16 figure

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Charged rotating dilaton black branes in AdS universe

We present the metric for the $(n+1)$-dimensional charged rotating dilaton black branes with cylindrical or toroidal horizons in the background of anti-de Sitter spacetime. We find the suitable counterterm which removes the divergences of the action in the presence of the dilaton potential in all higher dimensions. We plot the Penrose diagrams of the spacetime and reveal that the spacetime geometry crucially modifies in the presence of the dilaton field. The conserved and thermodynamic quantities of the black branes are also computed.Comment: 13 pages, 3 figures, to appear in Gen. Relat. Gravi

The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices

The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory. It is particularly important to take into account the renormalization of both the anisotropy, and the Euclidean coupling $\beta_E$, in obtaining these results.Comment: 10 pages, 11 figure

RQM description of the charge form factor of the pion and its asymptotic behavior

The pion charge and scalar form factors, $F_1(Q^2)$ and $F_0(Q^2)$, are first calculated in different forms of relativistic quantum mechanics. This is done using the solution of a mass operator that contains both confinement and one-gluon-exchange interactions. Results of calculations, based on a one-body current, are compared to experiment for the first one. As it could be expected, those point-form, and instant and front-form ones in a parallel momentum configuration fail to reproduce experiment. The other results corresponding to a perpendicular momentum configuration (instant form in the Breit frame and front form with $q^+=0$) do much better. The comparison of charge and scalar form factors shows that the spin-1/2 nature of the constituents plays an important role. Taking into account that only the last set of results represents a reasonable basis for improving the description of the charge form factor, this one is then discussed with regard to the asymptotic QCD-power-law behavior $Q^{-2}$. The contribution of two-body currents in achieving the right power law is considered while the scalar form factor, $F_0(Q^2)$, is shown to have the right power-law behavior in any case. The low-$Q^2$ behavior of the charge form factor and the pion-decay constant are also discussed.}Comment: 30 pages, 10 figure

The role of secreted aspartyl proteinases in Candida tropicalis invasion and damage of oral mucosa

Candida virulence attributes include the ability to colonize and invade host tissues, and the secretion of hydrolytic enzymes. Although Candida albicans is regarded as the principal fungi causing infections in humans, other species, particularly Candida tropicalis, are increasingly being recognized as human pathogens. Relatively little is known, however, about the virulence attributes associated with C. tropicalis. The present study aimed to investigate epithelial infection by C. tropicalis using a reconstituted human oral epithelium (RHOE) together with confocal laser scanning microscopy and real-time PCR. A comparison of clinical strains was made in terms of tissue colonization, invasion and C. tropicalis secreted aspartyl proteinase (SAPT) gene expression. All C. tropicalis strains were able to colonize RHOE in a strain-dependent manner. After 12 h of infection, C. tropicalis was found to be highly invasive, with extensive tissue damage occurring after 24 h. Real-time PCR of C. tropicalis SAPT1-4 genes showed that expression was strain-dependent, with SAPT2-4 transcripts being frequently detected and SAPT1 rarely detected. Tissue invasion and damage was not inhibited by the presence of pepstatin A. Accordingly, and given that an increase in infection time was not accompanied with an increase in SAPT gene expression, it can be suggested that the proteinases are not involved in invasion and damage of RHOE by C. tropicalis. In summary, C. tropicalis can be considered as highly invasive with the ability to induce significant tissue damage. These features, however, do not appear to be related to specific SAPT gene expression.We would like to thank Mrs Kath Allsopp for processing and sectioning the tissue samples. This work was supported by grant SFRH/BD/28341/2006 from 'Fundacao para a Ciencia e Tecnologia' (FCT), Portugal

Light-cone QCD Sum Rules for the Λ\Lambda Baryon Electromagnetic Form Factors and its magnetic moment

We present the light-cone QCD sum rules up to twist 6 for the electromagnetic form factors of the $\Lambda$ baryon. To estimate the magnetic moment of the baryon, the magnetic form factor is fitted by the dipole formula. The numerical value of our estimation is $\mu_\Lambda=-(0.64\pm0.04)\mu_N$, which is in accordance with the experimental data and the existing theoretical results. We find that it is twist 4 but not the leading twist distribution amplitudes that dominate the results.Comment: 13 page, 7 figures, accepted for publication in Euro. Phys. J.

Deep exclusive π+\pi^+ electroproduction off the proton at CLAS

The exclusive electroproduction of $\pi^+$ above the resonance region was studied using the $\rm{CEBAF}$ Large Acceptance Spectrometer ($\rm{CLAS}$) at Jefferson Laboratory by scattering a 6 GeV continuous electron beam off a hydrogen target. The large acceptance and good resolution of $\rm{CLAS}$, together with the high luminosity, allowed us to measure the cross section for the $\gamma^* p \to n \pi^+$ process in 140 ($Q^2$, $x_B$, $t$) bins: $0.16<x_B<0.58$, 1.6 GeV$^2<$$Q^2$$<4.5$ GeV$^2$ and 0.1 GeV$^2<$$-t$$<5.3$ GeV$^2$. For most bins, the statistical accuracy is on the order of a few percent. Differential cross sections are compared to two theoretical models, based either on hadronic (Regge phenomenology) or on partonic (handbag diagram) degrees of freedom. Both can describe the gross features of the data reasonably well, but differ strongly in their ingredients. If the handbag approach can be validated in this kinematical region, our data contain the interesting potential to experimentally access transversity Generalized Parton Distributions.Comment: 18pages, 21figures,2table