Models of discretized moduli spaces, cohomological field theories, and Gaussian means

We prove combinatorially the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM). The latter is the generating function for volumes of discretized (open) moduli spaces $M_{g,s}^{\mathrm{disc}}$ given by $N_{g,s}(P_1,\dots,P_s)$ for $(P_1,\dots,P_s)\in{\mathbb Z}_+^s$. This generating function therefore enjoys the topological recursion, and we prove that it is simultaneously the generating function for ancestor invariants of a cohomological field theory thus enjoying the Givental decomposition. We use another Givental-type decomposition obtained for this model by the second authors in 1995 in terms of special times related to the discretisation of moduli spaces thus representing its asymptotic expansion terms (and therefore those of the Gaussian means) as finite sums over graphs weighted by lower-order monomials in times thus giving another proof of (quasi)polynomiality of the discrete volumes. As an application, we find the coefficients in the first subleading order for ${\mathcal M}_{g,1}$ in two ways: using the refined Harer--Zagier recursion and by exploiting the above Givental-type transformation. We put forward the conjecture that the above graph expansions can be used for probing the reduction structure of the Delgne--Mumford compactification $\overline{\mathcal M}_{g,s}$ of moduli spaces of punctured Riemann surfaces.Comment: 36 pages in LaTex, 6 LaTex figure

Topological recursion for Gaussian means and cohomological field theories

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M_(g,s)^(disc) (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M_(g,1) for all g in three ways: using the refined Harer–Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly

Haematologic and Clinical Chemical values in 3 and 6 months old Göttingen minipigs

Blood samples were collected from sixty healthy Göttingen minipigs. fifteen males and fifteen females at the age of three months and fifteen males and fifteen females at the age of six months. The samples were taken at the breeder’s facilities. The samples were analysed for nineteen haematological and twenty~six clinical chemical parameters. Means, standard deviations and lowest and highest values are presented. In general the parameters were comparable with those reponed for other breeds of miniature and domestic swine. The white blood cell count, the percentages of neutrophils and monocytes and serum globulin levels were lower in these microbiologically defined minipigs compared with conventionally rearedpigs and minipigs. Three litter mates had a complex of abnormally high serum creatine kinase, lactate dehydrogenase, uspartate aminotransterase and alanine aminotmnsferase levels

Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos we consider elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors. Based on that we derive the correlation functions for amplitudes and intensities of elastic displacements. Comparison to numerics in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure

Energy level statistics of the two-dimensional Hubbard model at low filling

The energy level statistics of the Hubbard model for $L \times L$ square lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for a wide range of the coupling strength. All known symmetries of the model (space, spin and pseudospin symmetry) have been taken into account explicitly from the beginning of the calculation by projecting into symmetry invariant subspaces. The details of this group theoretical treatment are presented with special attention to the nongeneric case of L=4, where a particular complicated space group appears. For all the lattices studied, a significant amount of levels within each symmetry invariant subspaces remains degenerated, but except for L=4 the ground state is nondegenerate. We explain the remaining degeneracies, which occur only for very specific interaction independent states, and we disregard these states in the statistical spectral analysis. The intricate structure of the Hubbard spectra necessitates a careful unfolding procedure, which is thoroughly discussed. Finally, we present our results for the level spacing distribution, the number variance $\Sigma^2$, and the spectral rigidity $\Delta_3$, which essentially all are close to the corresponding statistics for random matrices of the Gaussian ensemble independent of the lattice size and the coupling strength. Even very small coupling strengths approaching the integrable zero coupling limit lead to the Gaussian ensemble statistics stressing the nonperturbative nature of the Hubbard model.Comment: 31 pages (1 Revtex file and 10 postscript figures

Morphological Instabilities in a growing Yeast Colony: Experiment and Theory

We study the growth of colonies of the yeast Pichia membranaefaciens on agarose film. The growth conditions are controlled in a setup where nutrients are supplied through an agarose film suspended over a solution of nutrients. As the thickness of the agarose film is varied, the morphology of the front of the colony changes. The growth of the front is modeled by coupling it to a diffusive field of inhibitory metabolites. Qualitative agreement with experiments suggests that such a coupling is responsible for the observed instability of the front.Comment: RevTex, 4 pages and 3 figure

Coherent pion production in neutrino nucleus collision in the 1 GeV region

We calculate cross sections for coherent pion production in nuclei induced by neutrinos and antineutrinos of the electron and muon type. The analogies and differences between this process and the related ones of coherent pion production induced by photons, or the (p,n) and $(^3 He, t)$ reactions are discussed. The process is one of the several ones occurring for intermediate energy neutrinos, to be considered when detecting atmospheric neutrinos. For this purpose the results shown here can be easily extrapolated to other energies and other nuclei.Comment: 13 pages, LaTex, 8 post-script figures available at [email protected]