Derived categories of cubic fourfolds

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page

On the existence of a compact generator on the derived category of a noetherian formal scheme

In this paper, we prove that for a noetherian formal scheme X, its derived category of sheaves of modules with quasi-coherent torsion homologies D_qct(X) is generated by a single compact object. In an appendix we prove that the category of compact objects in D_qct(X) is skeletally small.Comment: 13 page

Evidence for cervical muscle morphometric changes on magnetic resonance images after whiplash: A systematic review and meta-analysis

INTRODUCTION Morphometric changes to cervical musculature in whiplash associated disorder have been reported in several studies with varying results. However, the evidence is not clear because only a limited number of cohorts have been studied and one cohort has been reported in multiple publications. The aim of this study was to assess the evidence for cervical muscle morphometric changes on magnetic resonance (MR) images after whiplash using a systematic review with meta-analysis. MATERIALS AND METHODS PubMed, MEDLINE and Cochrane Library were searched without language restriction using combinations of the MeSH terms "muscles", "whiplash injuries", and "magnetic resonance imaging". Studies of acute and chronic whiplash were included if they compared whiplash and control cervical spine muscle morphometry measurements from MR images. The search identified 380 studies. After screening, eight studies describing five cohorts (one acute, three chronic, one both acute and chronic) met the inclusion criteria. Participant characteristics and outcome measures were extracted using a standard extraction format. Quality of eligible studies was assessed using the Newcastle-Ottawa Scale. Muscle cross-sectional area (CSA) and fat infiltrate (MFI) for acute and chronic whiplash cohorts were compared using mean difference and 95% confidence intervals. Meta-analysis models were created when data from more than two eligible cohorts was available, using inverse-variance random-effects models (RevMan5 version 5.3.5). RESULTS Quality assessment was uniformly good but only two studies blinded the assessor. Analysis of the acute cohorts revealed no consensus with respect to CSA. MFI was not measured in the acute cohorts. Analysis of the chronic cohorts revealed CSA is probably increased in some muscles after whiplash but there is insufficient evidence to confirm whether MFI is also increased. Because the available data were limited, meta-analyses of only multifidus were performed. In chronic whiplash multifidus CSA was significantly increased at C5 (Z = 3.51, p < 0.01) and C6 (Z = 2.66, p < 0.01); and MFI was significantly increased at C7 only (Z = 2.52, p < 0.01) but the heterogeneity was unacceptably high (I2 = 83%). CONCLUSIONS The strength of the evidence for cervical muscle morphometric changes on MR images after whiplash is inconsistent for CSA and MFI. Future study designs should be standardised with quantification of three-dimensional muscle morphometry

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Majority Dynamics and Aggregation of Information in Social Networks

Consider n individuals who, by popular vote, choose among q >= 2 alternatives, one of which is "better" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the n individuals would result in the correct outcome, with probability approaching one exponentially quickly as n tends to infinity. Our interest in this paper is in a variant of the process above where, after forming their initial opinions, the voters update their decisions based on some interaction with their neighbors in a social network. Our main example is "majority dynamics", in which each voter adopts the most popular opinion among its friends. The interaction repeats for some number of rounds and is then followed by a population-wide plurality vote. The question we tackle is that of "efficient aggregation of information": in which cases is the better alternative chosen with probability approaching one as n tends to infinity? Conversely, for which sequences of growing graphs does aggregation fail, so that the wrong alternative gets chosen with probability bounded away from zero? We construct a family of examples in which interaction prevents efficient aggregation of information, and give a condition on the social network which ensures that aggregation occurs. For the case of majority dynamics we also investigate the question of unanimity in the limit. In particular, if the voters' social network is an expander graph, we show that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.Comment: 22 page

Development and validation of a VISA tendinopathy questionnaire for greater trochanteric pain syndrome, the VISA-G

BACKGROUND Greater trochanteric pain syndrome (GTPS) is common, resulting in significant pain and disability. There is no condition specific outcome score to evaluate the degree of severity of disability associated with GTPS in patients with this condition. OBJECTIVE To develop a reliable and valid outcome measurement capable of evaluating the severity of disability associated with GTPS. METHODS A phenomenological framework using in-depth semi structured interviews of patients and medical experts, and focus groups of physiotherapists was used in the item generation. Item and format clarification was undertaken via piloting. Multivariate analysis provided the basis for item reduction. The resultant VISA-G was tested for reliability with the inter class co-efficient (ICC), internal consistency (Cronbach's Alpha), and construct validity (correlation co-efficient) on 52 naïve participants with GTPS and 31 asymptomatic participants. RESULTS The resultant outcome measurement tool is consistent in style with existing tendinopathy outcome measurement tools, namely the suite of VISA scores. The VISA-G was found to be have a test-retest reliability of ICC2,1 (95% CI) of 0.827 (0.638-0.923). Internal consistency was high with a Cronbach's Alpha of 0.809. Construct validity was demonstrated: the VISA-G measures different constructs than tools previously used in assessing GTPS, the Harris Hip Score and the Oswestry Disability Index (Spearman Rho:0.020 and 0.0205 respectively). The VISA-G did not demonstrate any floor or ceiling effect in symptomatic participants. CONCLUSION The VISA-G is a reliable and valid score for measuring the severity of disability associated GTPS.The study was funded through the Australian National University, Monash University and LaTrobe University. Prof Cook was supported by the Australian Centre for Research into Sports Injury and its Prevention, which is one of the International Research Centres for Prevention of Injury and Protection of Athlete Health supported by the International Olympic Committee (IOC). Prof Cook is a NHMRC practitioner fellow (ID 1058493)

Chern character, loop spaces and derived algebraic geometry.

International audienceIn this note we present a work in progress whose main purpose is to establish a categorified version of sheaf theory. We present a notion of derived categorical sheaves, which is a categorified version of the notion of complexes of sheaves of modules on schemes, as well as its quasi-coherent and perfect versions. We also explain how ideas from derived algebraic geometry and higher category theory can be used in order to construct a Chern character for these categorical sheaves, which is a categorified version of the Chern character for perfect complexes with values in cyclic homology. Our construction uses in an essential way the derived loop space of a scheme X, which is a derived scheme whose theory of functions is closely related to cyclic homology of X. This work can be seen as an attempt to define algebraic analogs of elliptic objects and characteristic classes for them. The present text is an overview of a work in progress and details will appear elsewhere

Nano-sized SQUID-on-tip for scanning probe microscopy

We present a SQUID of novel design, which is fabricated on the tip of a pulled quartz tube in a simple 3-step evaporation process without need for any additional processing, patterning, or lithography. The resulting devices have SQUID loops with typical diameters in the range 75–300 nm. They operate in magnetic fields up to 0.6 T and have flux sensitivity of 1.8 μΦ0/Hz1/2 and magnetic field sensitivity of 10−7 T/Hz1/2, which corresponds to a spin sensitivity of 65 μB/Hz1/2 for aluminum SQUIDs. The shape of the tip and the small area of the SQUID loop, together with its high sensitivity, make our device an excellent tool for scanning SQUID microscopy: With the SQUID-on-tip glued to a tine of a quartz tuning fork, we have succeeded in obtaining magnetic images of a patterned niobium film and of vortices in a superconducting film in a magnetic field.Physic

On Albanese torsors and the elementary obstruction

We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X. Arithmetic applications are given