Generalized Linear Models for Geometrical Current predictors. An application to predict garment fit

The aim of this paper is to model an ordinal response variable in terms of vector-valued functional data included on a vector-valued RKHS. In particular, we focus on the vector-valued RKHS obtained when a geometrical object (body) is characterized by a current and on the ordinal regression model. A common way to solve this problem in functional data analysis is to express the data in the orthonormal basis given by decomposition of the covariance operator. But our data present very important differences with respect to the usual functional data setting. On the one hand, they are vector-valued functions, and on the other, they are functions in an RKHS with a previously defined norm. We propose to use three different bases: the orthonormal basis given by the kernel that defines the RKHS, a basis obtained from decomposition of the integral operator defined using the covariance function, and a third basis that combines the previous two. The three approaches are compared and applied to an interesting problem: building a model to predict the fit of children’s garment sizes, based on a 3D database of the Spanish child population. Our proposal has been compared with alternative methods that explore the performance of other classifiers (Suppport Vector Machine and k-NN), and with the result of applying the classification method proposed in this work, from different characterizations of the objects (landmarks and multivariate anthropometric measurements instead of currents), obtaining in all these cases worst results

Polynomials, Riemann surfaces, and reconstructing missing-energy events

We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.Comment: 28 pages, 6 figures; version accepted for publication, with discussion of Higgs to tau tau deca

Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD

The combination of a non-overlapping Schwarz preconditioner and the Hybrid Monte Carlo (HMC) algorithm is shown to yield an efficient simulation algorithm for two-flavour lattice QCD with Wilson quarks. Extensive tests are performed, on lattices of size up to 32x24x24x24, with lattice spacings a~0.08 fm and at bare current-quark masses as low as 21 MeV.Comment: Plain TeX file, 32 pages, 9 figures include

Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications

We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric Gauss-Manin connection for B type branes we study the integrability and flatness conditions. The B model geometry defines an interesting ring structure of operators. For the mirror A model this indicates the existence of an open-string extension of the so-called A model connection, whereas the discovered ring structure should be part of the open-string A model quantum cohomology. We obtain predictions for genuine Ooguri-Vafa invariants for Lagrangian branes on the quintic in P4 that pass some non-trivial consistency checks. We discuss the lift of the brane compactifications to F-theory on Calabi-Yau 4-folds and the effective couplings in the effective supergravity action as determined by the N = 1 special geometry of the open-closed deformation space.Comment: 49 pages, 1 table; v2: Appendix and references added, minor corrections; v3: discussion in sect. 2 extended, version published in Nucl.Phys.

The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time

(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of {\it (Bergmann) observable. This clarification leads to the proposal of a {\it main conjecture} asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict connection with the Hamiltonian treatment of the initial value problem in metric gravity for the class of Christoudoulou -Klainermann space-times, in which the temporal evolution is ruled by the {\it weak} ADM energy. It is crucial the re-interpretation of {\it active} diffeomorphisms as {\it passive and metric-dependent} dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (nearly unknown) connection to gauge transformations on-shell; this is expounded in the first paper (gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsic pseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinate systems for the 4-dimensional {\it mathematical} manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent {\it Dirac observables}), and to realize the {\it physical individuation} of the points of space-time as {\it point-events} as a gauge-fixing problem, also associating a non-commutative structure to each 4-coordinate system.Comment: 41 pages, Revtex

SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry

We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on $S^3$. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains at the leading order an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. This can be understood as arising from the relation between Chern-Simons theory on the boundary of a region, and a theory defined by an $F^2$ action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL(2,C) Chern-Simons theory in 3-dimensions with knotted graph defects.Comment: 54+11 pages, 9 figure

Active Ranking using Pairwise Comparisons

This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Specifically, we assume that the objects can be embedded into a $d$-dimensional Euclidean space and that the rankings reflect their relative distances from a common reference point in $R^d$. We show that under this assumption the number of possible rankings grows like $n^{2d}$ and demonstrate an algorithm that can identify a randomly selected ranking using just slightly more than $d log n$ adaptively selected pairwise comparisons, on average. If instead the comparisons are chosen at random, then almost all pairwise comparisons must be made in order to identify any ranking. In addition, we propose a robust, error-tolerant algorithm that only requires that the pairwise comparisons are probably correct. Experimental studies with synthetic and real datasets support the conclusions of our theoretical analysis.Comment: 17 pages, an extended version of our NIPS 2011 paper. The new version revises the argument of the robust section and slightly modifies the result there to give it more impac