324 research outputs found
Mixed Correlation Functions of the Two-Matrix Model
We compute the correlation functions mixing the powers of two non-commuting
random matrices within the same trace. The angular part of the integration was
partially known in the literature: we pursue the calculation and carry out the
eigenvalue integration reducing the problem to the construction of the
associated biorthogonal polynomials. The generating function of these
correlations becomes then a determinant involving the recursion coefficients of
the biorthogonal polynomials.Comment: 16 page
Large deviations of the maximal eigenvalue of random matrices
We present detailed computations of the 'at least finite' terms (three
dominant orders) of the free energy in a one-cut matrix model with a hard edge
a, in beta-ensembles, with any polynomial potential. beta is a positive number,
so not restricted to the standard values beta = 1 (hermitian matrices), beta =
1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This
model allows to study the statistic of the maximum eigenvalue of random
matrices. We compute the large deviation function to the left of the expected
maximum. We specialize our results to the gaussian beta-ensembles and check
them numerically. Our method is based on general results and procedures already
developed in the literature to solve the Pastur equations (also called "loop
equations"). It allows to compute the left tail of the analog of Tracy-Widom
laws for any beta, including the constant term.Comment: 62 pages, 4 figures, pdflatex ; v2 bibliography corrected ; v3 typos
corrected and preprint added ; v4 few more numbers adde
An integrated approach to discover tag semantics
Tag-based systems have become very common for online classification thanks to their intrinsic advantages such as self-organization and rapid evolution. However, they are still affected by some issues that limit their utility, mainly due to the inherent ambiguity in the semantics of tags. Synonyms, homonyms, and polysemous words, while not harmful for the casual user, strongly affect the quality of search results and the performances of tag-based recommendation systems. In this paper we rely on the concept of tag relatedness in order to study small groups of similar tags and detect relationships between them. This approach is grounded on a model that builds upon an edge-colored multigraph of users, tags, and resources. To put our thoughts in practice, we present a modular and extensible framework of analysis for discovering synonyms, homonyms and hierarchical relationships amongst sets of tags. Some initial results of its application to the delicious database are presented, showing that such an approach could be useful to solve some of the well known problems of folksonomies
Large N expansion of the 2-matrix model
We present a method, based on loop equations, to compute recursively all the
terms in the large topological expansion of the free energy for the
2-hermitian matrix model. We illustrate the method by computing the first
subleading term, i.e. the free energy of a statistical physics model on a
discretized torus.Comment: 41 pages, 9 figures eps
Genus one contribution to free energy in hermitian two-matrix model
We compute an the genus 1 correction to free energy of Hermitian two-matrix
model in terms of theta-functions associated to spectral curve arising in large
N limit. We discuss the relationship of this expression to isomonodromic
tau-function, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius
manifolds and determinant of Laplacian in a singular metric over spectral
curve.Comment: 25 pages, detailed version of hep-th/040116
Correlation Functions of Complex Matrix Models
For a restricted class of potentials (harmonic+Gaussian potentials), we
express the resolvent integral for the correlation functions of simple traces
of powers of complex matrices of size , in term of a determinant; this
determinant is function of four kernels constructed from the orthogonal
polynomials corresponding to the potential and from their Cauchy transform. The
correlation functions are a sum of expressions attached to a set of fully
packed oriented loops configurations; for rotational invariant systems,
explicit expressions can be written for each configuration and more
specifically for the Gaussian potential, we obtain the large expansion ('t
Hooft expansion) and the so-called BMN limit.Comment: latex BMN.tex, 7 files, 6 figures, 30 pages (v2 for spelling mistake
and added reference) [http://www-spht.cea.fr/articles/T05/174
Universality of Nonperturbative Effects in c<1 Noncritical String Theory
Nonperturbative effects in c<1 noncritical string theory are studied using
the two-matrix model. Such effects are known to have the form fixed by the
string equations but the numerical coefficients have not been known so far.
Using the method proposed recently, we show that it is possible to determine
the coefficients for (p,q) string theory. We find that they are indeed finite
in the double scaling limit and universal in the sense that they do not depend
on the detailed structure of the potential of the two-matrix model.Comment: 17 page
Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
We generalize the topological recursion of Eynard-Orantin (2007) to the
family of spectral curves of Hitchin fibrations. A spectral curve in the
topological recursion, which is defined to be a complex plane curve, is
replaced with a generic curve in the cotangent bundle of an arbitrary
smooth base curve . We then prove that these spectral curves are
quantizable, using the new formalism. More precisely, we construct the
canonical generators of the formal -deformation family of -modules
over an arbitrary projective algebraic curve of genus greater than ,
from the geometry of a prescribed family of smooth Hitchin spectral curves
associated with the -character variety of the fundamental
group . We show that the semi-classical limit through the WKB
approximation of these -deformed -modules recovers the initial family
of Hitchin spectral curves.Comment: 34 page
Effects of dietary lipids on cell proliferation of murine oral mucosa.
Background: The lack of certain essential polyunsaturated fatty acids (PUFAs) induces
perturbation in cell proliferation, apoptosis and dedifferentiation that could be linked to an
increased protumorigenic trend. Contrarily, n-3 essential fatty acids (EFAs) arrest cell proliferation
in several tumor models. According to the concept of field cancerization, multiple patches of
abnormal epithelial proliferation may coexist in the vicinity of oropharyngeal neoplasms.
The purpose of the present study is to determine whether certain dietary PUFAs differentially
modulate the patterns of cell proliferation and apoptosis at non-tumoral sites of the oral mucosa
in mice bearing DMBA induced salivary tumors.
After weaning, BALB/c mice were assigned to four diets: Control (C), Corn Oil (CO), Fish (FO)
and Olein (O). Two weeks later, DMBA was injected into the submandibular area. The animals
were sacrificed between 94 and 184 days at 4–6 PM. Fixed samples of lip, tongue and palate were
stained using H-E and a silver technique. A quantification of AgNORs in the basal (BS) and
suprabasal stratum (SBS) of the covering squamous epithelia as well as of mitosis and apoptosis was
performed.
Results: Analysis of Variance showed greater proliferation in tongue than in palate or lip.
According to the diet, a significant difference was found in the Fish Oil, in which palate exhibited
fewer AgNOR particles than that of the control group, both for BS and SBS (p < 0.05 and 0.152,
respectively), indicating a reduced cell proliferation.
Conclusions: These results corroborate and reaffirm that the patterns of cell proliferation,
apoptosis and differentiation of the oral stratified squamous epithelium may be differentially
modulated by dietary lipids, and arrested by n-3 fatty acids, as shown in several other cell
populations.publishedVersio
correction to free energy in hermitian two-matrix model
Using the loop equations we find an explicit expression for genus 1
correction in hermitian two-matrix model in terms of holomorphic objects
associated to spectral curve arising in large N limit. Our result generalises
known expression for in hermitian one-matrix model. We discuss the
relationship between , Bergmann tau-function on Hurwitz spaces, G-function
of Frobenius manifolds and determinant of Laplacian over spectral curve
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