Fully Packed O(n=1) Model on Random Eulerian Triangulations

We introduce a matrix model describing the fully-packed O(n) model on random Eulerian triangulations (i.e. triangulations with all vertices of even valency). For n=1 the model is mapped onto a particular gravitational 6-vertex model with central charge c=1, hence displaying the expected shift c -> c+1 when going from ordinary random triangulations to Eulerian ones. The case of arbitrary n is also discussed.Comment: 12 pages, 3 figures, tex, harvmac, eps

Hamiltonian Cycles on Random Eulerian Triangulations

A random Eulerian triangulation is a random triangulation where an even number of triangles meet at any given vertex. We argue that the central charge increases by one if the fully packed O(n) model is defined on a random Eulerian triangulation instead of an ordinary random triangulation. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case one should see a change in the entropy exponent from the value gamma=-1 to the irrational value gamma=(-1-\sqrt{13})/6=-0.76759... when going from a usual random triangulation to an Eulerian one. A direct enumeration of configurations confirms this change in gamma.Comment: 22 pages, 9 figures, references and a comment adde

Inhomogeneous loop models with open boundaries

We consider the crossing and non-crossing O(1) dense loop models on a semi-infinite strip, with inhomogeneities (spectral parameters) that preserve the integrability. We compute the components of the ground state vector and obtain a closed expression for their sum, in the form of Pfaffian and determinantal formulas.Comment: 42 pages, 31 figures, minor corrections, references correcte

Folding of the Triangular Lattice in the FCC Lattice with Quenched Random Spontaneous Curvature

We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face Centered Cubic lattice, in the presence of quenched random spontaneous curvature. We consider two types of quenched randomness: (1) a ``physical'' randomness arising from a prior random folding of the lattice, creating a prefered spontaneous curvature on the bonds; (2) a simple randomness where the spontaneous curvature is chosen at random independently on each bond. We study the folding transitions of the two models within the hexagon approximation of the Cluster Variation Method. Depending on the type of randomness, the system shows different behaviors. We finally discuss a Hopfield-like model as an extension of the physical randomness problem to account for the case where several different configurations are stored in the prior pre-folding process.Comment: 12 pages, Tex (harvmac.tex), 4 figures. J.Phys.A (in press

A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations

We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the dependence of the coefficients is nonlinear and nonlocal in time with respect to the unknowns. We extend the numerical scheme proposed and studied recently by the authors for a single FPK equation of this type. We analyse the convergence of the scheme and we study its applicability in two examples. The first one concerns a population model involving two interacting species and the second one concerns two populations Mean Field Games

From Operator Algebras to Superconformal Field Theory

We make a review on the recent progress in the operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory and noncommutative geometry

Comparison of accuracy of single crowns generated from digital and conventional impressions: An in vivo controlled trial

Aim With the advances of digital technology, intraoral digital impression (DI) technique has become a major trend in prosthodontics with respect to traditional impression (TI) techniques; despite that, very few data are available concerning its accuracy. Thus, the purpose of this study was to compare the effectiveness of DI versus TI considering both marginal and internal gap (MG, IG, respectively) in cobalt-chromium (Co-Cr) single crowns manufactured by mean of computer-aided design and computer-aided manufacturing (CAD/CAM) technology. Material and methods Thirty posterior teeth were considered for this study. For each abutment tooth, sixty and thirty copings were produced with the aid of TI and DI, respectively. Thirty of the sixty copings of the TI-group were then randomly selected to be veneered and cemented onto existing abutments. The space existing between the internal surface of the coping and the abutment tooth was evaluated onto an in vitro replica; the MG and IG were measured by Scanning Electron Microscope. The data were analysed by the Wilcoxon test (1-tailed). Results The mean MG was 75.04 μm (SD = 13.12) and 55.01 μm (SD = 7.01) for the TI group and DI group, respectively. As regards the mean IGs, the values recorded were of 78.36 μm (SD = 19.66) for the TI-group and 59.20 μm (SD=3.33) for the DI-group. A statistically significant difference was found between the two groups (p-value = 0.001). Conclusions Copings manufactured from DI showed better MGs and IGs with respect to copings produced from TI. However, both approaches produced clinically acceptable results

Worldsheet Covariant Path Integral Quantization of Strings

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on non-covariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit non-covariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired. After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value $D= 26$ of the critical dimension.Comment: 64 pages, minor edits in expositio