The hypertoric intersection cohomology ring

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category. The computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice stratified space to sheaves on a poset.Comment: Significant revisions in Section 5, with several corrected proof

Equivariant log concavity and representation stability

We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In the case of the Coxeter arrangement for the Lie algebra $\mathfrak{sl}_n$, we exploit the theory of representation stability to give computer assisted proofs of these conjectures in low degree

A semi-small decomposition of the Chow ring of a matroid

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring, recovering the main result of [AHK18]. We also show that a similar semi-small orthogonal decomposition holds for the augmented Chow ring of M

Poisson-de Rham homology of hypertoric varieties and nilpotent cones

We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson-de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson-de Rham-Poincare polynomial, and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham. We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.Comment: 25 page

Topological Order in Projected Wave Functions and Effective Theories of Quantum Antiferromagnets

We study the topological order in RVB state derived from Gutzwiller projection of BCS-like mean field state. We propose to construct the topological excitation on the projected RVB state through Gutzwiller projection of mean field state with inserted $Z_{2}$ flux tube. We prove that all projected RVB states derived from bipartite effective theories, no matter the gauge structure in the mean field ansatz, are positive definite in the sense of the Marshall sign rule, which provides a universal origin for the absence of topological order in such RVB state.Comment: 5 pages, 1 figure

A New Scintillator Tile/Fiber Preshower Detector for the CDF Central Calorimeter

A detector designed to measure early particle showers has been installed in front of the central CDF calorimeter at the Tevatron. This new preshower detector is based on scintillator tiles coupled to wavelength-shifting fibers read out by multi-anode photomultipliers and has a total of 3,072 readout channels. The replacement of the old gas detector was required due to an expected increase in instantaneous luminosity of the Tevatron collider in the next few years. Calorimeter coverage, jet energy resolution, and electron and photon identification are among the expected improvements. The final detector design, together with the R&D studies that led to the choice of scintillator and fiber, mechanical assembly, and quality control are presented. The detector was installed in the fall 2004 Tevatron shutdown and started collecting colliding beam data by the end of the same year. First measurements indicate a light yield of 12 photoelectrons/MIP, a more than two-fold increase over the design goals.Comment: 5 pages, 10 figures (changes are minor; this is the final version published in IEEE-Trans.Nucl.Sci.

The influence of personality on trajectories of distress, health and functioning in mild-to-moderately depressed adults with type 2 diabetes

Identification of mental health risk is important for optimising diabetes care in type 2 diabetes mellitus (T2DM). Personality is linked to diabetes health and may assist detection of individuals with T2DM most at risk of chronic mental health difficulties. This study examined the moderator effect of personality factors on changes in psychological distress and functioning in adults with T2DM and mild-to-moderate depressive symptoms across a 12-month period. Data were obtained from participants in a randomised controlled trial of adults with T2DM.  Participants completed measures of depression (Patient Health Questionnaire-9), anxiety (General Anxiety Disorder-7), general functioning (Work and Social Adjustment Scale), diabetes distress (Diabetes Distress Scale), and diabetes self-management (Self-Management Profile for Type 2 Diabetes) at baseline, 3-, 6- and 12-months. Glycaemic control (HbA1c) was measured at baseline, 6- and 12-months. Two hundred trial completers agreed to complete a personality inventory (Big Five Inventory). Low neuroticism was linked with reduced depression, anxiety, functional impairment and diabetes distress over the year. High extraversion was associated with decreased anxiety and functional impairment. High conscientiousness was linked to increased healthy eating. No personality trait moderated HbA1c levels. Personality screening may help identify mental health risk and guide medical carer approach in T2DM patients

Development of FTK architecture: a fast hardware track trigger for the ATLAS detector

The Fast Tracker (FTK) is a proposed upgrade to the ATLAS trigger system that will operate at full Level-1 output rates and provide high quality tracks reconstructed over the entire detector by the start of processing in Level-2. FTK solves the combinatorial challenge inherent to tracking by exploiting the massive parallelism of Associative Memories (AM) that can compare inner detector hits to millions of pre-calculated patterns simultaneously. The tracking problem within matched patterns is further simplified by using pre-computed linearized fitting constants and leveraging fast DSP's in modern commercial FPGA's. Overall, FTK is able to compute the helix parameters for all tracks in an event and apply quality cuts in approximately one millisecond. By employing a pipelined architecture, FTK is able to continuously operate at Level-1 rates without deadtime. The system design is defined and studied using ATLAS full simulation. Reconstruction quality is evaluated for single muon events with zero pileup, as well as WH events at the LHC design luminosity. FTK results are compared with the tracking capability of an offline algorithm.Comment: To be published in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C09072