Brane-world creation and black holes

An inflating brane world can be created from ``nothing'' together with its anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap m=(3/2)H, where H is the Hubble rate. We consider the analogue of the Nariai solution and argue that it describes the pair production of ``black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing or the production of AdS black holes in the vicinity of a pre-existing inflating brane world. The Lorentzian evolution of the brane world after creation is briefly discussed. An additional ``integration constant'' in the Friedmann equation-accompanying a term which dilutes like radiation-describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. In general, this could be a 5-dimensional black hole or a ``parallel'' brane world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the AdS/CFT correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Exact gravitational shockwaves and Planckian scattering on branes

We obtain a solution describing a gravitational shock wave propagating along a Randall-Sundrum brane. The interest of such a solution is twofold: on the one hand, it is the first exact solution for a localized source on a Randall-Sundrum three-brane. On the other hand, one can use it to study forward scattering at Planckian energies, including the effects of the continuum of Kaluza-Klein modes. We map out the different regimes for the scattering obtained by varying the center-of-mass energy and the impact parameter. We also discuss exact shock waves in ADD scenarios with compact extra dimensions.

Optimization of laser interferometers for the detection of gravitational waves from coalescing binaries

Coalescing compact binary systems are important sources of gravitational waves. Here we investigate the detectability of this gravitational radiation by the recently proposed laser interferometers. The spectral density of noise for various practicable configurations of the detector is also reviewed. This includes laser interferometers with delay lines and Fabry-Prot cavities in the arms, both in standard and dual recycling arrangements. The sensitivity of the detector in all those configurations is presented graphically and the signal-to-noise ratio is calculated numerically. For all configurations we find values of the detector's parameters which maximize the detectability of coalescing binaries, the discussion comprising Newtonian- as well as post-Newtonian-order effects. Contour plots of the signal-to-noise ratio are also presented in certain parameter domains which illustrate the interferometer's response to coalescing binary signals.

MORPHOLOGICAL AND MICROMORPHOLOGICAL CHANGES IN THE STRUCTURE OF A RHODIC HAPLUDOX AS A RESULT OF AGRICULTURAL MANAGEMENT

In evaluation of soil quality for agricultural use, soil structure is one of the most important properties, which is influenced not only by climate, biological activity, and management practices but also by mechanical and physico-chemical forces acting in the soil. The purpose of this study was to evaluate the influence of conventional agricultural management on the structure and microstructure of a Latossolo Vermelho distroférrico típico (Rhodic Hapludox) in an experimental area planted to maize. Soil morphology was described using the crop profile method by identifying the distinct structural volumes called Morphologically Homogeneous Units (MHUs). For comparison, we also described a profile in an adjacent area without agricultural use and under natural regrowth referred to as Memory. We took undisturbed samples from the main MHUs so as to form thin sections and blocks of soil for micromorphological and micromorphometrical analyses. Results from the application of the crop profile method showed the occurrence of the following structural types: loose (L), fragmented (F) and continuous (C) in both profiles analyzed. In the Memory soil profile, the fragmented structures were classified as Fptμ∆+tf and Fmt∆μ, whose micromorphology shows an enaulic-porphyric (porous) relative distribution with a great deal of biological activity as indicated by the presence of vughs and channels. Lower down, from 0.20 to 0.35 m, there was a continuous soil volume (sub-type C∆μ), with a subangular block microstructure and an enaulic-porphyric relative distribution, though in this case more compact and with aggregate coalescence and less biological activity. The micromorphometrical study of the soil of the Memory Plot showed the predominance of complex pores in NAM (15.03 %), Fmt∆μ (11.72 %), and Fptμ∆+tf (7.73 %), and rounded pores in C∆μ (8.21 %). In the soil under conventional agricultural management, we observed fragmented structures similar to the Memory Plot from 0.02 to 0.20 m, followed by a volume with a compact continuous structure (C∆μ), without visible porosity and with few roots. In the MHUs under conventional management, reduction in the packing pores (40 %) was observed, mainly in the continuous units (C). The microstructure had well-defined blocks, with the occurrence of planar pores and less evidence of biological activity. In conclusion, the morphological and micromorphological analyses of the soil profiles studied offered complementary information regarding soil structural quality, especially concerning the changes in pore types as result of mechanical stress undergone by the soil.

New horizons for black holes and branes

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes

Detection and Characterization of Preferential Flow Paths in the Downstream Area of a Hazardous Landfill

We have used surface-based electrical resistivity tomography to detect and characterize preferential hydraulic pathways in the immediate downstream area of an abandoned, hazardous landfill. The landfill occupies the void left by a former gravel pit and its base is close to the groundwater table and lacking an engineered barrier. As such, this site is remarkably typical of many small- to medium-sized waste deposits throughout the densely populated and heavily industrialized foreland on both sides of the Alpine arc. Outflows of pollutants lastingly contaminated local drinking water supplies and necessitated a partial remediation in the form of a synthetic cover barrier, which is meant to prevent meteoric water from percolating through the waste before reaching the groundwater table. Any future additional isolation of the landfill in the form of lateral barriers thus requires adequate knowledge of potential preferential hydraulic pathways for outflowing contaminants. Our results, inferred from a suite of tomographically inverted surfaced-based electrical resistivity profiles oriented roughly perpendicular to the local hydraulic gradient, indicate that potential contaminant outflows would predominantly occur along an unexploited lateral extension of the original gravel deposit. This finds its expression as a distinct and laterally continuous high-resistivity anomaly in the resistivity tomograms. This interpretation is ground-truthed through a litholog from a nearby well. Since the probed glacio-fluvial deposits are largely devoid of mineralogical clay, the geometry of hydraulic and electrical pathways across the pore space of a given lithological unit can be assumed to be identical, which allows for an order-of-magnitude estimation of the overall permeability structure. These estimates indicate that the permeability of the imaged extension of the gravel body is at least two to three orders-of-magnitude higher than that of its finer-grained embedding matrix. This corroborates the preeminent role of the high-resistivity anomaly as a potential preferential flow path.

Discriminant ECOC: a heuristic method for application dependent design of error correcting output codes

We present a heuristic method for learning error correcting output codes matrices based on a hierarchical partition of the class space that maximizes a discriminative criterion. To achieve this goal, the optimal codeword separation is sacrificed in favor of a maximum class discrimination in the partitions. The creation of the hierarchical partition set is performed using a binary tree. As a result, a compact matrix with high discrimination power is obtained. Our method is validated using the UCI database and applied to a real problem, the classification of traffic sign images.

Subclass problem-dependent design for error-correcting output codes

A common way to model multiclass classification problems is by means of Error-Correcting Output Codes (ECOCs). Given a multiclass problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each subgroup of classes from each binary problem. However, we cannot guarantee that a linear classifier model convex regions. Furthermore, nonlinear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multiclass classification problems using subclass information in the ECOC framework. Complex problems are solved by splitting the original set of classes into subclasses and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceal the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size.

On the existence of doubling measures with certain regularity properties

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the pseudo-metric. Then we construct a doubling measure for which the measure of a dilated ball is closely related to these dimensions.

Extrapolation theory for the real interpolation method

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

Carleson Measures and Logvinenko-Sereda sets on compact manifolds

Given a compact Riemannian manifold $M$ of dimension $m \geq 2$, we study the space of functions of $L^2(M)$generated by eigenfunctions ofeigenvalues less than $L \geq 1$ associated to the Laplace-Beltrami operator on $M$. On these spaces we give a characterization of the Carleson measures and the Logvinenko-Sereda sets.

Evidence for two different bonding mechanisms of Al on Si(111)

By means of the ab initio cluster-model approach, we present theoretical evidence for two different mechanisms of bonding of atomic Al to Si(111). On the atop site (T1) the interaction of atomic Al to Si(111) is characteristic of an ionic bond whereas interaction above the threefold eclipsed site (T4) leads to the formation of a typical covalent bond. Moreover, both sites have a similar interaction energy if electronic correlation effects are included. While the conclusions regarding the nature of the chemisorption bond in the two sites do not depend either on the cluster-model size, the kind of embedding hydrogen atoms used, or the quality of the wave function (Hartree-Fock or configuration interaction), the chemisorption energy depends strongly on the wave function used. In fact, inclusion of correlation energy is necessary to properly describe the interaction energies.