Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper. we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests. (C) 2010 Elsevier B.V. All rights reserved.

Efficient bulk-loading on dynamic metric access methods

This paper presents a new technique and two algorithms to bulk-load data into multi-way dynamic metric access methods, based on the covering radius of representative elements employed to organize data in hierarchical data structures. The proposed algorithms are sample-based, and they always build a valid and height-balanced tree. We compare the proposed algorithm with existing ones, showing the behavior to bulk-load data into the Slim-tree metric access method. After having identified the worst case of our first algorithm, we describe adequate counteractions in an elegant way creating the second algorithm. Experiments performed to evaluate their performance show that our bulk-loading methods build trees faster than the sequential insertion method regarding construction time, and that it also significantly improves search performance. (C) 2009 Elsevier B.V. All rights reserved.

Benders, metric and cutset inequalities for multicommodity capacitated network design

Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities. We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

On the semi-Riemannian bumpy metric theorem

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold M, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the C(k)-topology, k=2, ..., infinity, in the set of metrics of a given index on M. A higher-order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

The Wijsman hyperspace of a metric hereditarily Baire space is Baire

In this paper, we show that the Wijsman hyperspace of a metric hereditarily Baire space is Baire. This solves a recent question posed by Zsilinszky. (C) 2009 Elsevier B.V. All rights reserved.

Analytical solutions of accreting black holes immersed in a Lambda CDM model

The evolution of the mass of a black hole embedded in a universe filled with dark energy and cold dark matter is calculated in a closed form within a test fluid model in a Schwarzschild metric, taking into account the cosmological evolution of both fluids. The result describes exactly how accretion asymptotically switches from the matter-dominated to the Lambda-dominated regime. For early epochs, the black hole mass increases due to dark matter accretion, and on later epochs the increase in mass stops as dark energy accretion takes over. Thus, the unphysical behaviour of previous analyses is improved in this simple exact model. (C) 2010 Elsevier B.V. All rights reserved.

EXACT AND QUASI-EXACT MODELS OF STRANGE STARS

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

Quantized fields and gravitational particle creation in f (R) expanding universes

The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic universes is discussed in the context of f (R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the universe. (C) 2010 Elsevier B.V. All rights reserved.

Craniometric Similarities Within and Between Human Populations in Comparison with Neutral Genetic Data

The statement that pairs of individuals from different populations are often more genetically similar than pairs from the same population is a widespread idea inside and outside the scientific community. Witherspoon et al. [""Genetic similarities within and between human populations,"" Genetics 176:351-359 (2007)] proposed an index called the dissimilarity fraction (omega) to access in a quantitative way the validity of this statement for genetic systems. Witherspoon demonstrated that, as the number of loci increases, omega decreases to a point where, when enough sampling is available, the statement is false. In this study, we applied the dissimilarity fraction to Howells`s craniometric database to establish whether or not similar results are obtained for cranial morphological traits. Although in genetic studies thousands of loci are available, Howells`s database provides no more than 55 metric traits, making the contribution of each variable important. To cope with this limitation, we developed a routine that takes this effect into consideration when calculating. omega Contrary to what was observed for the genetic data, our results show that cranial morphology asymptotically approaches a mean omega of 0.3 and therefore supports the initial statement-that is, that individuals from the same geographic region do not form clear and discrete clusters-further questioning the idea of the existence of discrete biological clusters in the human species. Finally, by assuming that cranial morphology is under an additive polygenetic model, we can say that the population history signal of human craniometric traits presents the same resolution as a neutral genetic system dependent on no more than 20 loci.

Seamlessly integrating similarity queries in SQL

Modern database applications are increasingly employing database management systems (DBMS) to store multimedia and other complex data. To adequately support the queries required to retrieve these kinds of data, the DBMS need to answer similarity queries. However, the standard structured query language (SQL) does not provide effective support for such queries. This paper proposes an extension to SQL that seamlessly integrates syntactical constructions to express similarity predicates to the existing SQL syntax and describes the implementation of a similarity retrieval engine that allows posing similarity queries using the language extension in a relational DBM. The engine allows the evaluation of every aspect of the proposed extension, including the data definition language and data manipulation language statements, and employs metric access methods to accelerate the queries. Copyright (c) 2008 John Wiley & Sons, Ltd.

Generating Segmented Quality Meshes from Images

Techniques devoted to generating triangular meshes from intensity images either take as input a segmented image or generate a mesh without distinguishing individual structures contained in the image. These facts may cause difficulties in using such techniques in some applications, such as numerical simulations. In this work we reformulate a previously developed technique for mesh generation from intensity images called Imesh. This reformulation makes Imesh more versatile due to an unified framework that allows an easy change of refinement metric, rendering it effective for constructing meshes for applications with varied requirements, such as numerical simulation and image modeling. Furthermore, a deeper study about the point insertion problem and the development of geometrical criterion for segmentation is also reported in this paper. Meshes with theoretical guarantee of quality can also be obtained for each individual image structure as a post-processing step, a characteristic not usually found in other methods. The tests demonstrate the flexibility and the effectiveness of the approach.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.