4,080 research outputs found
Sparse random matrices: the eigenvalue spectrum revisited
We revisit the derivation of the density of states of sparse random matrices.
We derive a recursion relation that allows one to compute the spectrum of the
matrix of incidence for finite trees that determines completely the low
concentration limit. Using the iterative scheme introduced by Biroli and
Monasson [J. Phys. A 32, L255 (1999)] we find an approximate expression for the
density of states expected to hold exactly in the opposite limit of large but
finite concentration. The combination of the two methods yields a very simple
simple geometric interpretation of the tails of the spectrum. We test the
analytic results with numerical simulations and we suggest an indirect
numerical method to explore the tails of the spectrum.Comment: 18 pages, 7 figures. Accepted version, minor corrections, references
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A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion
We study numerically the magnetic susceptibility of the hierarchical model
with Ising spins () above the critical temperature and for two
values of the epsilon parameter. The integrations are performed exactly, using
recursive methods which exploit the symmetries of the model. Lattices with up
to sites have been used. Surprisingly, the numerical data can be fitted
very well with a simple power law of the form for the {\it whole} temperature range. The numerical values for
agree within a few percent with the values calculated with a high-temperature
expansion but show significant discrepancies with the epsilon-expansion. We
would appreciate comments about these results.Comment: 15 Pages, 12 Figures not included (hard copies available on request),
uses phyzzx.te
Art as a means of alleviating social exclusion : does it really work? A critique of instrumental cultural policies and social impact studies in the UK
Eigenvalue spectra of complex networks
We examine the eigenvalue spectrum, (), of the adjacency matrix of a random scale-free network with an average of p edges per vertex using the replica method. We show how in the dense limit, when p , one can obtain two relatively simple coupled equations whose solution yields () for an arbitrary complex network. For scale-free graphs, with degree distribution exponent , we obtain an exact expression for the eigenvalue spectrum when = 3 and show that () ~ 1/2-1 for large . In the limit we recover known results for the Erdös–Rényi random graph
The Chemical Compositions of the Type II Cepheids -- The BL Her and W Vir Variables
Abundance analyses from high-resolution optical spectra are presented for 19
Type II Cepheids in the Galactic field. The sample includes both short-period
(BL Her) and long-period (W Vir) stars. This is the first extensive abundance
analysis of these variables. The C, N, and O abundances with similar spreads
for the BL Her and W Vir show evidence for an atmosphere contaminated with
-process and CN-cycling products. A notable anomaly of the BL Her
stars is an overabundance of Na by a factor of about five relative to their
presumed initial abundances. This overabundance is not seen in the W Vir stars.
The abundance anomalies running from mild to extreme in W Vir stars but not
seen in the BL Her stars are attributed to dust-gas separation that provides an
atmosphere deficient in elements of high condensation temperature, notably Al,
Ca, Sc, Ti, and -process elements. Such anomalies have previously been seen
among RV Tau stars which represent a long-period extension of the variability
enjoyed by the Type II Cepheids. Comments are offered on how the contrasting
abundance anomalies of BL Her and W Vir stars may be explained in terms of the
stars' evolution from the blue horizontal branch.Comment: 41 pages including 11 figures and 4 tables; Accepted for publication
in Ap
Spectral Statistics of Instantaneous Normal Modes in Liquids and Random Matrices
We study the statistical properties of eigenvalues of the Hessian matrix
(matrix of second derivatives of the potential energy) for a
classical atomic liquid, and compare these properties with predictions for
random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal
Mode or INM spectra) are evaluated numerically for configurations generated by
molecular dynamics simulations. We find that distribution of spacings between
nearest neighbor eigenvalues, s, obeys quite well the Wigner prediction , with the agreement being better for higher densities at fixed
temperature. The deviations display a correlation with the number of localized
eigenstates (normal modes) in the liquid; there are fewer localized states at
higher densities which we quantify by calculating the participation ratios of
the normal modes. We confirm this observation by calculating the spacing
distribution for parts of the INM spectra with high participation ratios,
obtaining greater conformity with the Wigner form. We also calculate the
spectral rigidity and find a substantial dependence on the density of the
liquid.Comment: To appear in Phys. Rev. E; 10 pages, 6 figure
Phenotypes of the ovarian follicular basal lamina predict developmental competence of oocytes
BACKGROUND: The ovarian follicular basal lamina underlies the epithelial membrana granulosa and maintains the avascular intra-follicular compartment. Additional layers of basal lamina occur in a number of pathologies, including pili annulati and diabetes. We previously found additional layers of follicular basal lamina in a significant percentage of healthy bovine follicles. We wished to determine if this phenomenon existed in humans, and if it was related to oocyte function in the bovine. METHODS: AND RESULTS: We examined follicles from human ovaries (n = 18) by electron microscopy and found that many follicles had additional layers of basal lamina. Oocytes (n = 222) from bovine follicles with normal or unusual basal laminas were isolated and their ability to undergo in vitro maturation, fertilization and culture to blastocyst was compared. Healthy bovine follicles with a single layer of basal lamina had oocytes with significantly (P < 0.01) greater developmental competence than healthy follicles with additional layers of follicular basal lamina (65 versus 28). CONCLUSIONS: These findings provide direct evidence that the phenotype of the follicular basal lamina is related to oocyte competence
Norm-dependent Random Matrix Ensembles in External Field and Supersymmetry
The class of norm-dependent Random Matrix Ensembles is studied in the
presence of an external field. The probability density in those ensembles
depends on the trace of the squared random matrices, but is otherwise
arbitrary. An exact mapping to superspace is performed. A transformation
formula is derived which gives the probability density in superspace as a
single integral over the probability density in ordinary space. This is done
for orthogonal, unitary and symplectic symmetry. In the case of unitary
symmetry, some explicit results for the correlation functions are derived.Comment: 19 page
A coarse grained model of granular compaction and relaxation
We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the same collective structure. We rigourously construct the model from first principles and show that numerical solutions compare favourably with a range of experimental results. This includes the logarithmic relaxation towards a statistical steady state, the effect of varying the intensity of vibration resulting in a so-called `annealing' curve, and the power spectrum of density fluctuations in the steady state itself. A mean-field version of the model is introduced which shares many features with the exact model and is open to quantitative analysi
Why does the Engel method work? Food demand, economies of size and household survey methods
Estimates of household size economies are needed for the analysis of poverty and inequality. This paper shows that Engel estimates of size economies are large when household expenditures are obtained by respondent recall but small when expenditures are obtained by daily recording in diaries. Expenditure estimates from recall surveys appear to have measurement errors correlated with household size. As well as demonstrating the fragility of Engel estimates of size economies, these results help resolve a puzzle raised by Deaton and Paxson (1998) about differences between rich and poor countries in the effect of household size on food demand
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