On contact tops and integrable tops

In this paper, we introduce a geometric structure called top, which is a trivialized bundle of plane pencils over a Riemannian 3-manifold, defined as the set of kernels of a circle of 1-forms (e.g. of contact and integrable forms) with particular properties with respect to the metric. We classify the manifolds which admit tops and we describe the associated metrics.Comment: 20 page

An optimized TOPS+ comparison method for enhanced TOPS models

This article has been made available through the Brunel Open Access Publishing Fund.Background Although methods based on highly abstract descriptions of protein structures, such as VAST and TOPS, can perform very fast protein structure comparison, the results can lack a high degree of biological significance. Previously we have discussed the basic mechanisms of our novel method for structure comparison based on our TOPS+ model (Topological descriptions of Protein Structures Enhanced with Ligand Information). In this paper we show how these results can be significantly improved using parameter optimization, and we call the resulting optimised TOPS+ method as advanced TOPS+ comparison method i.e. advTOPS+. Results We have developed a TOPS+ string model as an improvement to the TOPS [1-3] graph model by considering loops as secondary structure elements (SSEs) in addition to helices and strands, representing ligands as first class objects, and describing interactions between SSEs, and SSEs and ligands, by incoming and outgoing arcs, annotating SSEs with the interaction direction and type. Benchmarking results of an all-against-all pairwise comparison using a large dataset of 2,620 non-redundant structures from the PDB40 dataset [4] demonstrate the biological significance, in terms of SCOP classification at the superfamily level, of our TOPS+ comparison method. Conclusions Our advanced TOPS+ comparison shows better performance on the PDB40 dataset [4] compared to our basic TOPS+ method, giving 90 percent accuracy for SCOP alpha+beta; a 6 percent increase in accuracy compared to the TOPS and basic TOPS+ methods. It also outperforms the TOPS, basic TOPS+ and SSAP comparison methods on the Chew-Kedem dataset [5], achieving 98 percent accuracy. Software Availability: The TOPS+ comparison server is available at http://balabio.dcs.gla.ac.uk/mallika/WebTOPS/.This article is available through the Brunel Open Access Publishing Fun

Buckets of Tops

Reconstructing hadronically decaying top quarks is a key challenge at the LHC, affecting a long list of Higgs analyses and new physics searches. We propose a new method of collecting jets in buckets, corresponding to top quarks and initial state radiation. This method is particularly well suited for moderate transverse momenta of the top quark, closing the gap between top taggers and traditional top reconstruction. Applying it to searches for supersymmetric top squarks we illustrate the power of buckets.Comment: 14 pages, 7 figures, 5 table

Tagging single Tops

Top taggers which identify and reconstruct boosted top quarks have been established as novel tools for a multitude of LHC analyses. We show how single top production in association with a light-flavor or bottom jet can be observed in the boosted phase space regime. The full top reconstruction as part of the tagging algorithm allows us to define a distinctive kinematic angle which clearly separates different single top production processes.Comment: 13 pages, 9 figure

A novel method for comparing topological models of protein structures enhanced with ligand information

This article is available open access through the publisher’s website through the link below. Copyright @ 2008 The Authors.We introduce TOPS+ strings, a highly abstract string-based model of protein topology that permits efficient computation of structure comparison, and can optionally represent ligand information. In this model, we consider loops as secondary structure elements (SSEs) as well as helices and strands; in addition we represent ligands as first class objects. Interactions between SSEs and between SSEs and ligands are described by incoming/outgoing arcs and ligand arcs, respectively; and SSEs are annotated with arc interaction direction and type. We are able to abstract away from the ligands themselves, to give a model characterized by a regular grammar rather than the context sensitive grammar of the original TOPS model. Our TOPS+ strings model is sufficiently descriptive to obtain biologically meaningful results and has the advantage of permitting fast string-based structure matching and comparison as well as avoiding issues of Non-deterministic Polynomial time (NP)-completeness associated with graph problems. Our structure comparison method is computationally more efficient in identifying distantly related proteins than BLAST, CLUSTALW, SSAP and TOPS because of the compact and abstract string-based representation of protein structure which records both topological and biochemical information including the functionally important loop regions of the protein structures. The accuracy of our comparison method is comparable with that of TOPS. Also, we have demonstrated that our TOPS+ strings method out-performs the TOPS method for the ligand-dependent protein structures and provides biologically meaningful results. Availability: The TOPS+ strings comparison server is available from http://balabio.dcs.gla.ac.uk/mallika/WebTOPS/topsplus.html.University of Glasgo

Can gravitation accelerate neutrinos?

The Lagrangian equations of motion for massive spinning test particles (tops) moving on a gravitational background using General Relativity are presented. The paths followed by tops are nongeodesic. An exact solution for the motion of tops on a Schwarzschild background which allows for superluminal propagation of tops is studied. It is shown that the solution becomes relevant for particles with small masses, such as neutrinos. This general result is used to calculate the necessary condition to produce superluminal motion in part of the trajectory of a small mass particle in a weak gravitational field. The condition for superluminal motion establishes a relation between the mass, energy and total angular momentum of the particle.Comment: 7 pages, accepted in Class. Quantum Gra

Tops and Writhing DNA

The torsional elasticity of semiflexible polymers like DNA is of biological significance. A mathematical treatment of this problem was begun by Fuller using the relation between link, twist and writhe, but progress has been hindered by the non-local nature of the writhe. This stands in the way of an analytic statistical mechanical treatment, which takes into account thermal fluctuations, in computing the partition function. In this paper we use the well known analogy with the dynamics of tops to show that when subjected to stretch and twist, the polymer configurations which dominate the partition function admit a local writhe formulation in the spirit of Fuller and thus provide an underlying justification for the use of Fuller's "local writhe expression" which leads to considerable mathematical simplification in solving theoretical models of DNA and elucidating their predictions. Our result facilitates comparison of the theoretical models with single molecule micromanipulation experiments and computer simulations.Comment: 17 pages two figure

On Domains That Admit Well-behaved Strategy-proof Social Choice Functions

In this paper, we investigate domains which admit "well-behaved", strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982). We provide sharper versions of the results above when tops-onlyness is replaced by tops-selectivity and the richness condition is weakened.Voting-rules, Strategy-proofness, Restricted Domains, Tops-Only domains.