On the high density behavior of Hamming codes with fixed minimum distance

We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the equations describing the liquid up to very large values of the density, but we show that this solution gives a negative entropy for the liquid phase when the density is large enough. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. Finally we discuss the relation between our results and known rigorous bounds on the maximal density of the system.Comment: 15 pages, 6 figure

On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system, we analyze the average link overlap, the probability distribution of window overlaps (among ground states computed with different boundary conditions) and the spatial overlap and link overlap correlation functions. We establish that the picture based on Replica Symmetry Breaking correctly describes the behavior of 3D Spin Glasses.Comment: 25 pages with 11 ps figures include

Imaging the environmental ultraviolet

A technique has been developed to visually represent measured environmental ultraviolet radiation using a digital photograph and measurements of the UV and visible light intensity. The method involves the use of a personal pocket UV meter, an optional lux meter and a simple image processing technique to present visual images that are weighted to the ambient ultraviolet, providing images that highlight regions of high ultraviolet intensity that can be compared with a visible photograph. The technique described, provides a method students can follow to better develop an understanding of the potentially harmful ultraviolet irradiance with respect to visible daylight, indicating that the ambient ultraviolet and visible environment are not directly related, with ultraviolet intensity being dependent on many different factors and not the visual brightness of the location alone

Smooth Muscle Myosin Heavy Chain Isoform Distribution in the Swine Stomach

To evaluate the distribution of smooth muscle myosin heavy chain isoforms (SMB, with head insert), we examined frozen sections from the various regions of swine stomachs using isoform-specific antibodies. We previously reported variable SMB myosin heavy chain (MHC) expression in stomach cells that correlates with unloaded shortening velocities. This is consistent with the generalization of tonic fundic muscle having low expression and phasic antral muscle having high expression of the SMB MHC isoform. Using immunohistochemistry (IHC), we show a progression of the SMB MHC from very low immunoreactivity in the fundus to very intense immunoreactivity in the antrum. In the body, the average level of SMB MHC immunoreactivity lies between that of the antrum and fundus. Intercellular heterogeneity was observed in all stomach regions to a similar extent. However, the intercellular range in SMB MHC immunoreactivity decreases from fundus to antrum. All stomach regions show isolated pockets or clusters of cells with similar SMB MHC immunoreactivity. There is a non-uniform intracellular immunoreactivity in SMB MHC, with many cells showing greater-intensity staining of SMB MHC in their cell peripheries. This information may prove useful in helping to elucidate possible unique physiological roles of SMB MHC

On kk-Core Percolation in Four Dimensions

The $k$-core percolation on the Bethe lattice has been proposed as a simple model of the jamming transition because of its hybrid first-order/second-order nature. We investigate numerically $k$-core percolation on the four-dimensional regular lattice. For $k=4$ the presence of a discontinuous transition is clearly established but its nature is strictly first order. In particular, the $k$-core density displays no singular behavior before the jump and its correlation length remains finite. For $k=3$ the transition is continuous

On the Four-Dimensional Diluted Ising Model

In this letter we show strong numerical evidence that the four dimensional Diluted Ising Model for a large dilution is not described by the Mean Field exponents. These results suggest the existence of a new fixed point with non-gaussian exponents.Comment: 9 pages. compressed ps-file (uufiles

1-loop contribution to the dynamical exponents in spin glasses

We evaluate the corrections to the mean field values of the $x$ and the $z$ exponents at the first order in the $\epsilon$-expansion, for $T=T_c$. We find that both $x$ and $z$ are decreasing when the space dimension decreases.Comment: 12 pages 3 Postscript figure

Replica Symmetry Breaking in the Random Replicant Model

We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica symmetry breaking and we compare our findings with accurate numerical simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request, submitted to Journal of Physics A: Mathematical and Genera

Scaling above the upper critical dimension in Ising Models

We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our numerical data are in a good agreement with the Mean Field theoretical predictions, in particular, with the finite size exponent of the connected susceptibility and with the value of the Binder cumulant.Comment: 9 pages and 3 figures, available at http://chimera.roma1.infn.it/index_papers_complex.htm

Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition

An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This corresponds to the approach made by Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin glasses. Taking into account the fact that in the Hopfield model there exist correlations between different elements of the interaction matrix, we obtain its TAP free energy explicitly, which consists of a series of terms exhibiting the cluster effect. Nature of the spin-glass transition in the model is also examined and compared with those given by the replica method as well as the cavity method.Comment: 12 pages, LaTex, 1 PostScript figur