Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

Cosmic rays as probes of large extra dimensions and TeV gravity

If there are large extra dimensions and the fundamental Planck scale is at the TeV scale, then the question arises of whether ultrahigh energy cosmic rays might probe them. We study the neutrino-nucleon cross section in these models. The elastic forward scattering is analyzed in some detail, hoping to clarify earlier discussions. We also estimate the black hole production rate. We study energy loss from graviton mediated interactions and conclude that they cannot explain the cosmic ray events above the GZK energy limit. However, these interactions could start horizontal air showers with characteristic profile and at a rate higher than in the standard model.

Particle creation due to cosmological contraction of extra dimensions

Particle production in a cosmological spacetime with extra dimensions is discussed. A five-dimensional cosmological model with a three-dimensional space expanding isotropically like in a radiative Friedmann-Robertson-Walker model and an internal space contracting to a constant small size is considered. The parameters of the model are adjusted so that time variations in internal space are compatible with present limits on time variations of the fundamental constants. By requiring that the energy density of the particles produced be less than the critical density at the radiation era we set restrictions on two more parameters: namely, the initial time of application of the semiclassical approach and the relative sizes between the internal space and the horizon of the ordinary Universe at this time. Whereas the production of massless particles allows a large range of variation to these parameters, the production of massive particles sets severe constraints on them, since, if they are overproduced, their energy density might very soon dominate the Universe and make cosmological dimensional reduction by extradimensional contraction unlikely.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Affirmative Action through Extra Prizes

Some affirmative action policies establish that a set of disadvantaged competitors has access to an extra prize. Examples are gender quotas or a prize for national competitors in an international competition. We analyse the effects of creating an extra prize by reducing the prize in the main competition. Contestants differ in ability and agents with relatively low ability belong to a disadvantaged minority. All contestants compete for the main prize, but only disadvantaged agents can win the extra prize. We show that an extra prize is a powerful tool to ensure participation of disadvantaged agents. Moreover, for intermediate levels of the disadvantage of the minority, introducing an extra prize increases total equilibrium effort compared to a standard contest. Thus, even a contest designer not interested in affirmative action might establish an extra prize in order to enhance competition. Keywords: Asymmetric contest, equality of opportunity, affirmative action, discrimination, prize structure, exclusion principle. JEL: C72, D72, I38, J78

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Comments on "On the relationship between fractal dimension and the performance of multi-resonant dipole antennas using Koch curves"

Comentaris referits a l'article següent: K. J. Vinoy, J. K. Abraham, and V. K. Varadan, “On the relationshipbetween fractal dimension and the performance of multi-resonant dipoleantennas using Koch curves,” IEEE Transactions on Antennas and Propagation, 2003, vol. 51, p. 2296–2303.

Projecte d'implantació d'una almàssera per a una capacitat de 200t d'oli d'oliva verge extra de producció integrada al municipi del Catllar (Tarragona)

L’objecte del projecte és la implantació d’una almàssera per a l’obtenció de 200 t d’oli d’oliva verge extra produït mitjançant producció integrada, ja que aquest mètode és més respectuós amb el medi ambient. En la redacció del projecte, s’han projectat totes les instal·lacions i serveis per al correcte funcionament de l’almàssera, així com tots els documents necessaris per a la seva execució. Finalment, hi ha un estudi econòmic per valorar la viabilitat d’una indústria agroalimentària d’aquestes característiques.

Effects of extra mass on the pelagic behavior of a seabird

Satellite transmitters and geographic-positioning-system devices often add substantial mass to birds to which they are attached. Studies on the effects of such instruments have focused on indirect measures, whereas the direct influence of extra mass on pelagic behavior is poorly known. We used 2.5-g geolocators to investigate the effect of extra mass on the pelagic behavior of Cory's Shearwaters (Calonectris diomedea) by comparing the traits of a single foraging trip among a group carrying 30-g weights, a group carrying 60-g weights, and a control group. The weights were attached to the birds' backs using typical techniques for attaching satellite transmitters to seabirds. The extra mass increased the duration of the birds' trips and decreased their foraging efficiency and mass gained at sea. These indirect effects may be related to foraging traits: weighted birds showed a greater search effort than control birds, traveled greater distances, covered a greater foraging area, and increased the maximum foraging range. Furthermore, the time spent on the sea surface at night was greater for weighted than for control groups, which showed that the extra mass also affected activity patterns. Our results underline the need to quantify the effects of monitoring equipment commonly used to study the pelagic behavior of seabirds. We suggest that geolocators can be used to obtain control data on foraging-trip movements and activity patterns.

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attractors are observed. Even in the quasiperiodic regime, attractors with a certain degree of strangeness may exist. From the observed multifractal dimensions, the deterministic nature of the chaotic oscillations is clearly identified.