Bridge number and integral Dehn surgery

In a 3-manifold M, let K be a knot and R be an annulus which meets K transversely. We define the notion of the pair (R,K) being caught by a surface Q in the exterior of the link given by K and the boundary curves of R. For a caught pair (R,K), we consider the knot K^n gotten by twisting K n times along R and give a lower bound on the bridge number of K^n with respect to Heegaard splittings of M -- as a function of n, the genus of the splitting, and the catching surface Q. As a result, the bridge number of K^n tends to infinity with n. In application, we look at a family of knots K^n found by Teragaito that live in a small Seifert fiber space M and where each K^n admits a Dehn surgery giving the 3-sphere. We show that the bridge number of K^n with respect to any genus 2 Heegaard splitting of M tends to infinity with n. This contrasts with other work of the authors as well as with the conjectured picture for knots in lens spaces that admit Dehn surgeries giving the 3-sphere

Bridge number, Heegaard genus and non-integral Dehn surgery

We show there exists a linear function w: N->N with the following property. Let K be a hyperbolic knot in a hyperbolic 3-manifold M admitting a non-longitudinal S^3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g-1.Comment: 76 page, 48 figures; referee comments incorporated and typos fixed; accepted at TAM

Homology Based Motif Generation

Generating motifs from known active sites and matching those motifs to an uncharacterized protein is a classic way of determining protein function. Until now, the generation of motifs has been based purely on enzymatic function. This approach does not account for situations where highly different active sites can arrive at the same function by processes like convergent evolution. As such, a secondary metric on which to base the generation of motifs is necessary. This metric exists in the form of UniProt designation for homologous proteins on a global scale or PFam for designation of homologous proteins at the active site level. Here, we describe a tool to generate highly selective motifs using the aforementioned metrics. We were able to collapse a large number of proteins into their representative motifs with little loss in sensitivity, creating an “average” representation of each motif. These motifs will aid the characterizing proteins of known structure but unknown function

Brill-Noether theory of squarefree modules supported on a graph

We investigate the analogy between squarefree Cohen-Macaulay modules supported on a graph and line bundles on a curve. We prove a Riemann-Roch theorem, we study the Jacobian and gonality of a graph, and we prove Clifford's theorem.Comment: Major revision, new author added, paper restructured, results correcte

Stability of trusses by graphic statics.

This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell-Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the 'product forces' that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses

Industrial altruism

This research project aims to assess the changing nature of society by studying one of its most rapidly growing industries, altruism. Altruistic practices are rapidly growing but are becoming morally polluted. The findings of this research will hopefully inspire reflection and action to improve the ways we do good

Do not revise Ockham's razor without necessity

Ockham’s razor asks that we not multiply entities beyond necessity. The razor is a powerful methodological tool, enabling us to articulate reasons for preferring one theory to another. There are those, however, who would modify the razor. Schaffer (2010: 313—our italics), for one, tells us that, ‘I think the proper rendering of Ockham’s razor should be ‘Do not multiply fundamental entities without necessity’. Our aim, here, is to challenge such re-workings of Ockham’s razor

Semiclassical Quantization of Effective String Theory and Regge Trajectories

We begin with an effective string theory for long distance QCD, and evaluate the semiclassical expansion of this theory about a classical rotating string solution, taking into account the the dynamics of the boundary of the string. We show that, after renormalization, the zero point energy of the string fluctuations remains finite when the masses of the quarks on the ends of the string approach zero. The theory is then conformally invariant in any spacetime dimension D. For D=26 the energy spectrum of the rotating string formally coincides with that of the open string in classical Bosonic string theory. However, its physical origin is different. It is a semiclassical spectrum of an effective string theory valid only for large values of the angular momentum. For D=4, the first semiclassical correction adds the constant 1/12 to the classical Regge formula.Comment: 65 pages, revtex, 3 figures, added 2 reference

Are there cross-cultural differences in emotional processing and social problem-solving?

Emotional processing and social problem-solving are important for mental well-being. For example, impaired emotional processing is linked with depression and psychosomatic problems. However, little is known about cross-cultural differences in emotional processing and social problem-solving and whether these constructs are linked. This study examines whether emotional processing and social problem-solving differs between Western (British) and Eastern European (Polish) cultures. Participants (N = 172) completed questionnaires assessing both constructs. Emotional processing did not differ according to culture, but Polish participants reported more effective social problem-solving abilities than British participants. Poorer emotional processing was also found to relate to poorer social problem-solving. Possible societal reasons for the findings and the implications of the findings for culture and clinical practice are discussed