Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional NN-Vector Model for N=3,4,8N=3,4,8

We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various long-distance quantities like the correlation lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for $N = 3,4,8$. From these data we also extract the values of various universal nonperturbative constants, which we compare with the predictions of the $1/N$ expansion.Comment: 68456 bytes uuencoded gzip'ed (expands to 155611 bytes Postscript); 4 pages including all figures; contribution to Lattice '9

Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities

We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy-Binet formula for the determinant of a product. As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull's Capelli-type identities for symmetric and antisymmetric matrices.Comment: LaTeX2e, 43 pages. Version 2 corrects an error in the statements of Propositions 1.4 and 1.5 (see new Remarks in Section 4) and includes a Note Added at the end of Section 1 comparing our work with that of Chervov et al (arXiv:0901.0235

An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes

Grassmann Integral Representation for Spanning Hyperforests

Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff's matrix-tree theorem. Furthermore, we show that the class of integrals describing unrooted spanning (hyper)forests is induced by a theory with an underlying OSP(1|2) supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J. Phys.

New Method for the Extrapolation of Finite-Size Data to Infinite Volume

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $\sigma$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.Comment: 3 pages, 76358 bytes Postscript, contribution to Lattice '94; see also hep-lat/9409004, hep-lat/9405015 and hep-lat/941100

Drinking wine at home: Hedonic analysis of sicilian wines using quantile regression

Abstract: In recent decades, the Sicilian wine industry has experienced a booming expansion because of the growing preferences of Italian consumers for Sicilian wines, especially in extra-regional markets. These consumers have been paying closer attention to Sicilian premium wines. For this reason, the objective of this study is to inform professional investors and wine managers about the consumer preferences with respect to the most important segment categories of domestically consumed Sicilian wines. Using the quantile regression technique, we analyzed the role of wine attributes and prices as an information tool in order to value for each wine segment the implicit price of the attributes affecting wine consumers\u2019 choices. The results indicate that Protected Designation of Origin (PDO) and Geographical Indication (PGI) certification is the main determinant in the wine price mechanisms and certified wines achieve premium prices that are progressively higher as the price level of the wine increases. Furthermore the effect of the brand on price formation seems to have a significant impact for low-end wines, whereas it has no specific impact on the price mechanism for high-end wines. Keywords: Consumer Scan Dataset, Geographic Origin, Hedonic Price, Robust Regression, Wine Consumptio

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure