An Efficient Nominal Unification Algorithm

Nominal Unification is an extension of first-order unification where terms can contain binders and unification is performed modulo α equivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearly-reduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for first-order unification. Second, we prove that solvability of these reduced problems may be checked in quadràtic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently

Escacs, un sistema intel·ligent

Des dels inicis dels ordinadors com a màquines programables, l’home ha intentat dotar-los de certa intel•ligència per tal de pensar o raonar el més semblant possible als humans. Un d’aquests intents ha sigut fer que la màquina sigui capaç de pensar de tal manera que estudiï jugades i guanyi partides d’escacs. En l’actualitat amb els actuals sistemes multi tasca, orientat a objectes i accés a memòria i gràcies al potent hardware del que disposem, comptem amb una gran varietat de programes que es dediquen a jugar a escacs. Però no hi ha només programes petits, hi ha fins i tot màquines senceres dedicades a calcular i estudiar jugades per tal de guanyar als millors jugadors del món. L’objectiu del meu treball és dur a terme un estudi i implementació d’un d’aquests programes, per això es divideix en dues parts. La part teòrica o de l’estudi, consta d’un estudi dels sistemes d’intel•ligència artificial que es dediquen a jugar a escacs, estudi i cerca d’una funció d’avaluació vàlida i estudi dels algorismes de cerca. La part pràctica del treball es basa en la implementació d’un sistema intel•ligent capaç de jugar a escacs amb certa lògica. Aquesta implementació es porta a terme amb l’ajuda de les llibreries SDL, utilitzant l’algorisme minimax amb poda alfa-beta i codi c++. Com a conclusió del projecte m’agradaria remarcar que l’estudi realitzat m’ha deixat veure que crear un joc d’escacs no era tan fàcil com jo pensava però m’ha aportat la satisfacció d’aplicar tot el que he après durant la carrera i de descobrir moltes altres coses noves.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

A search for microquasar candidates at low galactic latitudes

Recent studies of relativistic jet sources in the Galaxy, also known as microquasars, have been very useful in trying to understand the accretion/ejection processes that take place near compact objects. However, the number of sources involved in such studies is still small. In an attempt to increase the number of known microquasars we have carried out a search for new Radio Emitting X-ray Binaries (REXBs). These sources are the ones to be observed later with VLBI techniques to unveil their possible microquasar nature. To this end, we have performed a cross-identification between the X-ray ROSAT all sky survey Bright Source Catalog (RBSC) and the radio NRAO VLA Sky Survey (NVSS) catalogs under very restrictive selection criteria for sources with |b|<5 degrees. We have also conducted a deep observational radio and optical study for six of the selected candidates. At the end of this process two of the candidates appear to be promising, and deserve additional observations aimed to confirm their proposed microquasar nature.

Search for very high energy gamma-ray emission from pulsar-pulsar wind nebula systems with the MAGIC telescope

The MAGIC collaboration has searched for high-energy gamma-ray emission of some of the most promising pulsar candidates above an energy threshold of 50 GeV, an energy not reachable up to now by other ground-based instruments. Neither pulsed nor steady gamma-ray emission has been observed at energies of 100 GeV from the classical radio pulsars PSR J0205+6449 and PSR J2229+6114 (and their nebulae 3C58 and Boomerang, respectively) and the millisecond pulsar PSR J0218+4232. Here, we present the flux upper limits for these sources and discuss their implications in the context of current model predictions.

Numerical algorithm for Ginzburg-Landau equations with multiplicative noise: Application to domain growth

We consider stochastic partial differential equations with multiplicative noise. We derive an algorithm for the computer simulation of these equations. The algorithm is applied to study domain growth of a model with a conserved order parameter. The numerical results corroborate previous analytical predictions obtained by linear analysis.

Spin-2 gravitational trace anomaly

The part proportional to the Euler-Poincar characteristic of the contribution of spin-2 fields to the gravitational trace anomaly is computed. It is seen to be of the same sign as all the lower-spin contributions, making anomaly cancellation impossible. Subtleties related to Weyl invariance, gauge independence, ghosts, and counting of degrees of freedom are pointed out.

Search for nonstandard Higgs boson in diphoton events at p anti-p collisions

We estimate the attainable limits on the coupling of a nonstandard Higgs boson to two photons taking into account the data collected by the Fermilab collaborations on diphoton events. We based our analysis on a general set of dimension-6 effective operators that give rise to anomalous couplings in the bosonic sector of the standard model. If the coefficients of all blind operators have the same magnitude, indirect bounds on the anomalous triple vector-boson couplings can also be inferred, provided there is no large cancellation in the Higgs-gamma-gamma coupling.

Gravitational wave pulse and soliton wave collision

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einsteins equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.

Spin-3/2 gravitational trace anomaly

It is argued that previous computations of the spin-(3/2 anomaly have spurious contributions, as there is Weyl-invariance breaking already at the classical level. The genuine, gauge-invariant, spin-(3/2 gravitational trace anomaly is computed here.

Majorization arrow in quantum-algorithm design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.

Leaving the cave in search of life (A Platonic reading of R. Sirera's La caverna (The Cave)

The aim of this article is to show how a contemporary playwright thinks once more of the Platonic image of the cave in order to reflect on the necessary existential journey of men and women as in the case of a Bildungsroman. Sooner or later men and women must abandon the protection that any sort of cavern such as home, the family garden or family itself can offer. In spite of writing from a by no means idealistic or metaphysical point of view, thanks to R. Sirera and to the very applicability of Platonic images, Plato becomes once again a classical reference which is both useful and even unavoidable if one bears in mind the Platonic origin of all the literary caverns.

Numerical algorithm for spectroscopic ellipsometry of thick transparent films

We present a numerical method for spectroscopic ellipsometry of thick transparent films. When an analytical expression for the dispersion of the refractive index (which contains several unknown coefficients) is assumed, the procedure is based on fitting the coefficients at a fixed thickness. Then the thickness is varied within a range (according to its approximate value). The final result given by our method is as follows: The sample thickness is considered to be the one that gives the best fitting. The refractive index is defined by the coefficients obtained for this thickness.

Gravitational wave pulse and soliton wave collision

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einsteins equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.