Abstract:
a case-control study was carried out in order to analyze the association between diet and risk of non melanoma skin cancer -basal cell carcinoma (bcc) and squamous cell carcinoma (scc), with adjustments for demographic, anthropometric and phenotypic characteristics, sunburns history, skin cancerfamily history, sun-exposure history and skin sensitivity to sun exposure. a full-body skin examination was performed. dietary data were obtained applying a standardized semi-quantitative questionnaire of consumption frequency. cases (n=27; age: 65,5+15,1 years) and controls (n=37; age: 63,9+12,3 years) were attended at the same facilities. a decreased risk ofbcc and scc tumors (adjusted odd ratio=0.10; ic 95%= 0.02-0.63; p=0.01) was found for high intakes of green leafy vegetables (more than 40 gr/day). however, results obtained for fruits, cruciferous, vitamin a and carotene-rich vegetables and other vegetables were not statistically significant.

Abstract:
Mediante un dise o de casos y controles se evaluó si la dieta habitual modifica el riesgo de desarrollar cáncer de piel no melanoma: carcinomas basocelulares y carcinomas espinocelulares. En la consulta se consignaron datos demográficos, características fenotípicas y antropométricas, antecedentes de quemadura solar, antecedentes familiares de cáncer de piel y hábitos de exposición solar, y se realizó un exhaustivo examen físico cutáneo. La dieta fue evaluada por cuestionarios semi-cuantitativos de frecuencia de consumo. Se estudiaron 27 casos (edad: 65,5±15,1 a os) y 37 controles (63,9±12,3) que asistieron a las mismas instituciones por otras patologías. La ingesta alta de vegetales de hojas verdes (más de 40 g/d) actuaría como factor protector (Odd Ratio ajustado= 0,10; IC 95%= 0,02-0,63; p=0,01), modificando el efecto negativo de la exposición solar. En cambio, los resultados obtenidos para frutas, crucíferas, vegetales ricos en vitamina A y carotenos y otros vegetales no resultaron estadísticamente significativos. A case-control study was carried out in order to analyze the association between diet and risk of non melanoma skin cancer -basal cell carcinoma (BCC) and squamous cell carcinoma (SCC), with adjustments for demographic, anthropometric and phenotypic characteristics, sunburns history, skin cancerfamily history, sun-exposure history and skin sensitivity to sun exposure. A full-body skin examination was performed. Dietary data were obtained applying a standardized semi-quantitative questionnaire of consumption frequency. Cases (n=27; age: 65,5+15,1 years) and controls (n=37; age: 63,9+12,3 years) were attended at the same facilities. A decreased risk ofBCC and SCC tumors (Adjusted Odd Ratio=0.10; IC 95%= 0.02-0.63; p=0.01) was found for high intakes of green leafy vegetables (more than 40 gr/day). However, results obtained for fruits, cruciferous, vitamin A and carotene-rich vegetables and other vegetables were not statistically significant.

Abstract:
We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann-Hilbert problem associated to certain classes of (multiple) orthogonal polynomials. The determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants appear also as partition functions of random matrix models, including an instance of a two-matrix model.

Abstract:
The isomonodromic tau function defined by Jimbo-Miwa-Ueno vanishes on the Malgrange's divisor of generalized monodromy data for which a vector bundle is nontrivial, or, which is the same, a certain Riemann-Hilbert problem has no solution. In their original work, Jimbo, Miwa, Ueno did not derive the dependence on the (generalized) monodromy data (i.e. monodromy representation and Stokes' parameters). We fill the gap by providing a (simpler and more general) description in which all the parameters of the problem (monodromy-changing and monodromy-preserving) are dealt with at the same level. We thus provide variational formulae for the isomonodromic tau function with respect to the (generalized) monodromy data. The construction applies more generally: given any (sufficiently well-behaved) family of Riemann-Hilbert problems (RHP) where the jump matrices depend arbitrarily on deformation parameters, we can construct a one-form Omega (not necessarily closed) on the deformation space (Malgrange's differential), defined off Malgrange's divisor. We then introduce the notion of discrete Schlesinger transformation: it means that we allow the solution of the RHP to have poles (or zeros) at prescribed point(s). Even if Omega is not closed, its difference evaluated along the original solution and the transformed one, is shown to be the logarithmic differential (on the deformation space) of a function. As a function of the position of the points of the Schlesinger transformation, yields a natural generalization of Sato formula for the Baker-Akhiezer vector even in the absence of a tau function, and it realizes the solution of the RHP as such BA vector. Some exemples (Painleve' II and finite Toplitz/Hankel determinants) are provided.

Abstract:
The nonlinear steepest descent method for rank-two systems relies on the notion of g-function. The applicability of the method ranges from orthogonal polynomials (and generalizations) to Painleve transcendents, and integrable wave equations (KdV, NonLinear Schroedinger, etc.). For the case of asymptotics of generalized orthogonal polynomials with respect to varying complex weights we can recast the requirements for the Cauchy-transform of the equilibrium measure into a problem of algebraic geometry and harmonic analysis and completely solve the existence and uniqueness issue without relying on the minimization of a functional. This addresses and solves also the issue of the ``free boundary problem'', determining implicitly the curves where the zeroes of the orthogonal polynomials accumulate in the limit of large degrees and the support of the measure. The relevance to the quasi--linear Stokes phenomenon for Painleve equations is indicated. A numerical algorithm to find these curves in some cases is also explained. Technical note: the animations included in the file can be viewed using Acrobat Reader 7 or higher. Mac users should also install a QuickTime plugin called Flip4Mac. Linux users can extract the embedded animations and play them with an external program like VLC or MPlayer. All trademarks are owned by the respective companies.

Abstract:
In this paper we complement our recent result on the explicit formula for the planar limit of the free energy of the two-matrix model by computing the second and third order observables of the model in terms of canonical structures of the underlying genus g spectral curve. In particular we provide explicit formulas for any three-loop correlator of the model. Some explicit examples are worked out.

Abstract:
Using a simple operator-norm estimate we show that the solution to the second Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well defined region of the complex plane of the independent variable. The result is illustrated with several numerical examples.

Abstract:
We consider the biorthogonal polynomials associated to the two-matrix model where the eigenvalue distribution has potentials V_1,V_2 with arbitrary rational derivative and whose supports are constrained on an arbitrary union of intervals (hard-edges). We show that these polynomials satisfy certain recurrence relations with a number of terms d_i depending on the number of hard-edges and on the degree of the rational functions V_i'. Using these relations we derive Christoffel-Darboux identities satisfied by the biorthogonal polynomials: this enables us to give explicit formulae for the differential equation satisfied by d_i+1 consecutive polynomials, We also define certain integral transforms of the polynomials and use them to formulate a Riemann-Hilbert problem for (d_i+1) x (d_i+1) matrices constructed out of the polynomials and these transforms. Moreover we prove that the Christoffel-Darboux pairing can be interpreted as a pairing between two dual Riemann-Hilbert problems.

Abstract:
We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the tau-function of the dispersionless two--dimensional Toda hierarchy. The formula generalizes the case studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan in the case of conformal maps of Jordan curves. Finally we generalize the formula found in genus zero to the case of spectral curves of arbitrary genus with certain fixed data.

Abstract:
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization of the corresponding notion for moment functionals and motivated by the applications to multi-matrix random models. Integral representations of such functionals are derived and shown to be linearly independent.