Renormalization Group results for lattice surface models

We study the phase diagram of statistical systems of closed and open interfaces built on a cubic lattice. Interacting closed interfaces can be written as Ising models, while open surfaces as Z(2) gauge systems. When the open surfaces reduce to closed interfaces with few defects, also the gauge model can be written as an Ising spin model. We apply the lower bound renormalization group (LBRG) transformation introduced by Kadanoff (Phys. Rev. Lett. 34, 1005 (1975)) to study the Ising models describing closed and open surfaces with few defects. In particular, we have studied the Ising-like transition of self-avoiding surfaces between the random-isotropic phase and the phase with broken global symmetry at varying values of the mean curvature. Our results are compared with previous numerical work. The limits of the LBRG transformation in describing regions of the phase diagram where not ferromagnetic ground-states are relevant are also discussed.Comment: 24 pages, latex, 5 figures (available upon request to [email protected]

Pricing Step Options under the CEV and other Solvable Diffusion Models

We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elasticity-of-variance (CEV) model as an example. In particular, we derive a general analytically exact expression for the resolvent kernel (i.e. Green's function) of such processes with killing at an exponential stopping time (independent of the process) of occupation above or below a fixed level. Moreover, we succeed in Laplace inverting the resolvent kernel and thereby derive newly closed-form spectral expansion formulae for the transition probability density of such processes with killing. The spectral expansion formulae are rapidly convergent and easy-to-implement as they are based simply on knowledge of a pair of fundamental solutions for an underlying solvable diffusion process. We apply the spectral expansion formulae to the pricing of proportional step options for four specific families of solvable nonlinear diffusion asset price models that include the CEV diffusion model and three other multi-parameter state-dependent local volatility confluent hypergeometric diffusion processes.Comment: 30 pages, 16 figures, submitted to IJTA

Extended d_{x^2 - y^2}-wave superconductivity

Remarkable anisotropic structures have been recently observed in the order parameter Delta_k of the underdoped superconductor Bi-2212. Such findings are strongly suggestive of deviations from a simple d_{x^2 - y^2}-wave picture of high-Tc superconductivity, i.e. Delta_k ~ cos (k_x) - cos (k_y). In particular, flatter nodes in Delta_k are observed along the k_x = (+/-) k_y directions in k-space, than within this simple model for a d-wave gap. We argue that nonlinear corrections in the k-dependence of Delta_k near the nodes introduce new energy scales, which would lead to deviations in the predicted power-law asymptotic behaviour of several measurable quantities, at low or intermediate temperatures. We evaluate such deviations, either analytically or numerically, within the interlayer pair-tunneling model, and within yet another phenomenological model for a d-wave order parameter. We find that such deviations are expected to be of different sign in the two cases. Moreover, the doping dependence of the flatness of the gap near the nodes is also attributable to Fermi surface effects, in addition to possible screening effects modifying the in-plane pairing kernel, as recently proposed.Comment: 7 pages, 4 embedded PostScript figures. Uses svjour, epsfig, amsmath, amssymb, xspace. To be published in Eur. Phys. J.

Homogenization Model for Aberrant Crypt Foci

Several explanations can be found in the literature about the origin of colorectal cancer. There is however some agreement on the fact that the carcinogenic process is a result of several genetic mutations of normal cells. The colon epithelium is characterized by millions of invaginations, very small cavities, called crypts, where most of the cellular activity occurs. It is consensual in the medical community, that a potential first manifestation of the carcinogenic process, observed in conventional colonoscopy images, is the appearance of Aberrant Crypt Foci (ACF). These are clusters of abnormal crypts, morphologically characterized by an atypical behavior of the cells that populate the crypts. In this work an homogenization model is proposed, for representing the cellular dynamics in the colon epithelium. The goal is to simulate and predict, in silico, the spread and evolution of ACF, as it can be observed in colonoscopy images. By assuming that the colon is an heterogeneous media, exhibiting a periodic distribution of crypts, we start this work by describing a periodic model, that represents the ACF cell-dynamics in a two-dimensional setting. Then, homogenization techniques are applied to this periodic model, to find a simpler model, whose solution symbolizes the averaged behavior of ACF at the tissue level. Some theoretical results concerning the existence of solution of the homogenized model are proven, applying a fixed point theorem. Numerical results showing the convergence of the periodic model to the homogenized model are presented.Comment: 26 pages, 4 figure

Evidence from multivariate morphometric study of the quercus pubescens complex in southeast Italy

The name Quercus pubescens s.l. encompasses a complex of deciduous oak taxa with mainly southeastEuropean distribution and a large ecological niche. As the easternmost region of Italy, Apulia is rather isolated from a geographical and physiographical viewpoint and counts the highest number of oak species (10). In the taxonomic and phytosociological literature, the occurrence of several species belonging to the Quercus pubescens collective group is reported for this region. In order to verify if different sets of morphological characters are associated with different taxa, 24 populations of Quercus pubescens s.l. located in different ecological-geographical areas of Apulia were sampled. A total of 367 trees, 4254 leaves and 1120 fruits were collected and morphologically analysed. Overall, 25 morphological characters of oak leaves and fruits were statistically treated using both univariate and multivariate analysis. Nested ANOVA showed that leaves collected from a single tree exhibited a degree of morphological variability higher than that observed when comparing leaves coming from different trees of the same population and from different trees of different populations as well. Almost all the morphological characters analysed exhibited a continuous trend of variation so that none of them can be used as a character to discriminate between populations. Only leaf and fruit “size” and fruit petiole length emerged as slightly discriminating characters. Our results suggest that it is unlikely that more than one species belonging to the Quercus pubescens complex occurs in the Apulia region. Comparison between the Apulian populations and a genetically pure Q. pubescens population coming from a different area (the Molise region) strengthened the assumption as to the existence of a single species that can provisionally be classified under the name of Q. pubescens s.