The local motivic DT/PT correspondence

We show that the Quot scheme $Q_L^n = \textrm{Quot}_{\mathbb A^3}(\mathscr I_L,n)$ parameterising length $n$ quotients of the ideal sheaf of a line in $\mathbb{A}^3$ is a global critical locus, and calculate the resulting motivic partition function (varying $n$), in the ring of relative motives over the configuration space of points in $\mathbb{A}^3$. As in the work of Behrend-Bryan-Szendr\H{o}i this enables us to define a virtual motive for the Quot scheme of $n$ points of the ideal sheaf $\mathscr I_C\subset \mathscr O_Y$, where $C\subset Y$ is a smooth curve embedded in a smooth 3-fold $Y$, and we compute the associated motivic partition function. The result fits into a motivic wall-crossing type formula, refining the relation between Behrend's virtual Euler characteristic of $\textrm{Quot}_Y(\mathscr I_C,n)$ and of the symmetric product $\textrm{Sym}^nC$. Our "relative" analysis leads to results and conjectures regarding the pushforward of the sheaf of vanishing cycles along the Hilbert-Chow map $Q_L^n \rightarrow \textrm{Sym}^n(\mathbb{A}^3)$, and connections with cohomological Hall algebra representations

Shockley model description of surface states in topological insulators

We show that the surface states in topological insulators can be understood based on a well-known Shockley model, a one-dimensional tight-binding model with two atoms per elementary cell, connected via alternating tunneling amplitudes. We generalize the one-dimensional model to the three-dimensional case corresponding to the sequence of layers connected via the amplitudes, which depend on the in-plane momentum p = (p_x,p_y). The Hamiltonian of the model is described a (2 x 2) Hamiltonian with the off-diagonal element t(k,p) depending also on the out-of-plane momentum k. We show that the complex function t(k,p) defines the properties of the surface states. The surface states exist for the in-plane momenta p, where the winding number of the function t(k,p) is non-zero as k is changed from 0 to 2pi. The sign of the winding number defines the sublattice on which the surface states are localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional momentum space. The projection of the vortex line on the two-dimensional momentum p space encircles the domain where the surface states exist. We illustrate how our approach works for a well-known TI model on a diamond lattice. We find that different configurations of the vortex lines are responsible for the "weak" and "strong" topological insulator phases. The phase transition occurs when the vortex lines reconnect from spiral to circular form. We discuss the Shockley model description of Bi_2Se_3 and the applicability of the continuous approximation for the description of the topological edge states. We conclude that the tight-binding model gives a better description of the surface states.Comment: 18 pages, 17 figures; version 3: Sections I-IV revised, Section VII added, Refs. [33]-[35] added; Corresponds to the published versio

The Canine POMC Gene, Obesity in Labrador Retrievers and Susceptibility to Diabetes Mellitus.

BACKGROUND: Diabetes mellitus (DM) in dogs is a common endocrinopathy with a complex genetic architecture. Disease susceptibility in several breeds is associated with polymorphisms in immune response genes, but in the Labrador retriever breed, no genetic associations with DM have been identified. A deletion in the pro-opiomelanocortin (POMC) gene in Labrador retrievers is associated with increased appetite and risk of obesity. HYPOTHESIS/OBJECTIVES: To characterize the POMC deletion in Labrador retrievers, to develop a simple genetic test for this mutation, and to test the hypothesis that the POMC gene deletion is associated with an increased risk of DM in this breed. ANIMALS: Sixty-one non-diabetic Labrador retrievers aged >6 years and 57 Labrador retrievers with DM. METHODS: Case-control genotyping study to compare the frequency of the POMC deletion in dogs with and without DM. After polymerase chain reaction (PCR) and sequencing to characterize the mutation, a PCR-based test was developed and validated using 2 different restriction fragment length polymorphism assays. RESULTS: A 14-base-pair deletion was confirmed and localized to exon 3 of the canine POMC gene. A PCR-based test for the deletion was successfully developed. There was no association between the presence of the POMC deletion mutation and DM in this population of Labrador retriever dogs (P = .31). CONCLUSIONS AND CLINICAL IMPORTANCE: This study adds to the existing scientific literature indicating that there is little evidence for a direct link between obesity and DM in dogs

Genome sequence of an alphaherpesvirus from a beluga whale (Delphinapterus leucas)

Beluga whale alphaherpesvirus 1 was isolated from a blowhole swab taken from a juvenile beluga whale. The genome is 144,144 bp in size and contains 86 putative genes. The virus groups phylogenetically with members of the genus Varicellovirus in subfamily Alphaherpesvirinae and is the first alphaherpesvirus sequenced from a marine mammal

A study of the gravitational wave form from pulsars II

We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, taking into account the rotation and orbital motion of the Earth. We also briefly discuss the Zak-Gelfand Integral Transform. The Zak-Gelfand Integral Transform that arises in our analytic approach has also been useful for Schrodinger operators in periodic potentials in condensed matter physics (Bloch wave functions).Comment: 6 pages, Sparkler talk given at the Amaldi Conference on Gravitational waves, July 10th, 2001. Submitted to Classical and Quantum Gravit

Probability Models for Degree Distributions of Protein Interaction Networks

The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally, the functional form for the degree distribution has been determined in an ad-hoc fashion, with clear power-law like behaviour often only extending over a limited range of connectivities. Here we apply formal model selection techniques to decide which probability distribution best describes the degree distributions of protein interaction networks. Contrary to previous studies this well defined approach suggests that the degree distribution of many molecular networks is often better described by distributions other than the popular power-law distribution. This, in turn, suggests that simple, if elegant, models may not necessarily help in the quantitative understanding of complex biological processes.

Story in health and social care

This paper offers a brief consideration of how narrative, in the form of people‟s own stories, potentially figures in health and social care provision as part of the impulse towards patient-centred care. The rise of the epistemological legitimacy of patients‟ stories is sketched here. The paper draws upon relevant literature and original writing to consider the ways in which stories can mislead as well as illuminate the process of making individual treatment care plans

Plasticity, elasticity, and adhesion energy of plant cell walls: nanometrology of lignin loss using atomic force microscopy

International audienceThe complex organic polymer, lignin, abundant in plants, prevents the efficient extraction of sugars from the cell walls that is required for large scale biofuel production. Because lignin removal is crucial in overcoming this challenge, the question of how the nanoscale properties of the plant cell ultrastructure correlate with delignification processes is important. Here, we report how distinct molecular domains can be identified and how physical quantities of adhesion energy, elasticity, and plasticity undergo changes, and whether such quantitative observations can be used to characterize delignification. By chemically processing biomass, and employing nanometrology, the various stages of lignin removal are shown to be distinguished through the observed morphochemical and nanomechanical variations. Such spatially resolved correlations between chemistry and nanomechanics during deconstruction not only provide a better understanding of the cell wall architecture but also is vital for devising optimum chemical treatments

Momentum relaxation from the fluid/gravity correspondence

We provide a hydrodynamical description of a holographic theory with broken translation invariance. We use the fluid/gravity correspondence to systematically obtain both the constitutive relations for the currents and the Ward identity for momentum relaxation in a derivative expansion. Beyond leading order in the strength of momentum relaxation, our results differ from a model previously proposed by Hartnoll et al. As an application of these techniques we consider charge and heat transport in the boundary theory. We derive the low frequency thermoelectric transport coefficients of the holographic theory from the linearised hydrodynamics.Comment: 19 pages + appendix, v2: references added, typos corrected, v3: version published in JHE