Distributed computation of fixed points of infinity-nonexpansive maps

The distributed implementation of an algorithm for computing fixed points of an infinity-nonexpansive map is shown to converge to the set of fixed points under very general conditions.

Holistic Schema Mappings for XML-on-RDBMS

When hosting XML information on relational backends, a mapping has to be established between the schemas of the information source and the target storage repositories. A rich body of recent literature exists for mapping isolated components of XML Schema to their relational counterparts, especially with regard to table configurations. In this paper, we present the Elixir system for designing industrial-strength mappings for real-world applications. Specifically, it produces an information-preserving holistic mapping that transforms the complete XML world-view (XML schema with constraints, XML documents XQuery queries including triggers and views) into a full-scale relational mapping (table definitions, integrity constraints, indices, triggers and views) that is tuned to the application workload. A key design feature of Elixir is that it performs all its mapping-related optimizations in the XML source space, rather than in the relational target space. Further, unlike the XML mapping tools of commercial database systems, which rely heavily on user inputs, Elixir takes a principled cost-based approach to automatically find an efficient relational mapping. A prototype of Elixir is operational and we quantitatively demonstrate its functionality and efficacy on a variety of real-life XML schemas.

Holomorphic Mappings between Domains in C-2

An extension theorem for holomorphic mappings between two domains in C-2 is proved under purely local hypotheses.

Some regularity theorems for CR mappings

The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved.

Proper holomorphic mappings between hyperbolic product manifolds

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

Proper holomorphic mappings of balanced domains in C-n

We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in . Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in , is an automorphism. The main novelty of our proof is the use of a recent result of Opshtein on the behaviour of the iterates of holomorphic self-maps of a certain class of domains. We use Opshtein's theorem, together with the tools made available by finiteness of type, to deduce that the aforementioned map is unbranched. The monodromy theorem then delivers the result.

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.

Effect of Short Duration of Load increment on the Compressibility of Soils

This study concerns the effect of duration of load increment (up to 24 h) on the consolidation properties of expansive black cotton soil (liquid limit = 81%) and nonexpansive kaolinite (liquid limit = 49%). It indicates that the amount and rate of compression are not noticeably affected by the duration of loading for a standard sample of 25 mm in height and 76.2 mm in diameter with double drainage. Hence, the compression index and coefficient of consolidation can be obtained with reasonable accuracy even if the duration of each load increment is as short as 4 h. The secondary compression coefficient (C-alpha epsilon) for kaolinite can be obtained for any pressure range with 1/2 h of loading, which, however, requires 4 h for black cotton soil. This is because primary consolidation is completed early in the case of kaolinite. The paper proves that the conventional consolidation test can be carried out with much shorter duration of loading (less than 4 h) than the standard specification of 24 h or more even for remolded fine-grained soils.

PocketAlign A Novel Algorithm for Aligning Binding Sites in Protein Structures

A fundamental task in bioinformatics involves a transfer of knowledge from one protein molecule onto another by way of recognizing similarities. Such similarities are obtained at different levels, that of sequence, whole fold, or important substructures. Comparison of binding sites is important to understand functional similarities among the proteins and also to understand drug cross-reactivities. Current methods in literature have their own merits and demerits, warranting exploration of newer concepts and algorithms, especially for large-scale comparisons and for obtaining accurate residue-wise mappings. Here, we report the development of a new algorithm, PocketAlign, for obtaining structural superpositions of binding sites. The software is available as a web-service at http://proline.physicslisc.emetin/pocketalign/. The algorithm encodes shape descriptors in the form of geometric perspectives, supplemented by chemical group classification. The shape descriptor considers several perspectives with each residue as the focus and captures relative distribution of residues around it in a given site. Residue-wise pairings are computed by comparing the set of perspectives of the first site with that of the second, followed by a greedy approach that incrementally combines residue pairings into a mapping. The mappings in different frames are then evaluated by different metrics encoding the extent of alignment of individual geometric perspectives. Different initial seed alignments are computed, each subsequently extended by detecting consequential atomic alignments in a three-dimensional grid, and the best 500 stored in a database. Alignments are then ranked, and the top scoring alignments reported, which are then streamed into Pymol for visualization and analyses. The method is validated for accuracy and sensitivity and benchmarked against existing methods. An advantage of PocketAlign, as compared to some of the existing tools available for binding site comparison in literature, is that it explores different schemes for identifying an alignment thus has a better potential to capture similarities in ligand recognition abilities. PocketAlign, by finding a detailed alignment of a pair of sites, provides insights as to why two sites are similar and which set of residues and atoms contribute to the similarity.

On isometries of the Kobayashi and Caratheodory metrics

This article considers C-1-smooth isometries of the Kobayashi and Caratheodory metrics on domains in C-n and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that B-n cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C-0-isometries f : D-1 -> D-2 to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C-0-isometry between a strongly pseudoconvex domain in C-2 and certain classes of weakly pseudoconvex finite type domains in C-2.

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard ``contour-improved'' expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the tau lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, alpha(s)(M-tau(2)) = 0.3189(-0.0151)(+0.0173), which translates to alpha(s)(M-Z(2)) = 0.1184(-0.0018)(+0.0021). DOI: 10.1103/PhysRevD.87.014008

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Condition R and proper holomorphic maps between equidimensional product domains

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as a product of proper mappings between the factor domains. (C) 2013 Elsevier Inc. All rights reserved.

Optimal Timer-Based Best Node Selection for Wireless Systems with Unknown Number of Nodes

The distributed, low-feedback, timer scheme is used in several wireless systems to select the best node from the available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Delta s of the transmission by the best node. We derive the optimal metric-to-timer mappings for the practical scenario where the number of nodes is unknown. We consider two cases in which the probability distribution of the number of nodes is either known a priori or is unknown. In the first case, the optimal mapping maximizes the success probability averaged over the probability distribution. In the second case, a robust mapping maximizes the worst case average success probability over all possible probability distributions on the number of nodes. Results reveal that the proposed mappings deliver significant gains compared to the mappings considered in the literature.

FeatureMatch: A General ANNF Estimation Technique and its Applications

In this paper, we propose FeatureMatch, a generalised approximate nearest-neighbour field (ANNF) computation framework, between a source and target image. The proposed algorithm can estimate ANNF maps between any image pairs, not necessarily related. This generalisation is achieved through appropriate spatial-range transforms. To compute ANNF maps, global colour adaptation is applied as a range transform on the source image. Image patches from the pair of images are approximated using low-dimensional features, which are used along with KD-tree to estimate the ANNF map. This ANNF map is further improved based on image coherency and spatial transforms. The proposed generalisation, enables us to handle a wider range of vision applications, which have not been tackled using the ANNF framework. We illustrate two such applications namely: 1) optic disk detection and 2) super resolution. The first application deals with medical imaging, where we locate optic disks in retinal images using a healthy optic disk image as common target image. The second application deals with super resolution of synthetic images using a common source image as dictionary. We make use of ANNF mappings in both these applications and show experimentally that our proposed approaches are faster and accurate, compared with the state-of-the-art techniques.