A variant of the Mukai pairing via deformation quantization

We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler, Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped that our method is useful for generalization to settings involving certain singular varieties.Comment: 8 pages. Comments and suggestions welcom

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

Courant-Dorfman algebras and their cohomology

We introduce a new type of algebra, the Courant-Dorfman algebra. These are to Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson algebras to Poisson manifolds. We work with arbitrary rings and modules, without any regularity, finiteness or non-degeneracy assumptions. To each Courant-Dorfman algebra (\R,\E) we associate a differential graded algebra \C(\E,\R) in a functorial way by means of explicit formulas. We describe two canonical filtrations on \C(\E,\R), and derive an analogue of the Cartan relations for derivations of \C(\E,\R); we classify central extensions of \E in terms of H^2(\E,\R) and study the canonical cocycle \Theta\in\C^3(\E,\R) whose class $[\Theta]$ obstructs re-scalings of the Courant-Dorfman structure. In the nondegenerate case, we also explicitly describe the Poisson bracket on \C(\E,\R); for Courant-Dorfman algebras associated to Courant algebroids over finite-dimensional smooth manifolds, we prove that the Poisson dg algebra \C(\E,\R) is isomorphic to the one constructed in \cite{Roy4-GrSymp} using graded manifolds.Comment: Corrected formulas for the brackets in Examples 2.27, 2.28 and 2.29. The corrections do not affect the exposition in any wa

A randomised phase I study of etrolizumab (rhuMAb β7) in moderate to severe ulcerative colitis.

ObjectiveEtrolizumab (rhuMAb β7, anti-β7, PRO145223) is a humanised monoclonal antibody targeting the β7 subunit of the heterodimeric integrins α4β7 and αEβ7, which are implicated in leucocyte migration and retention in ulcerative colitis (UC). This randomised phase I study evaluated the safety and pharmacology of etrolizumab in patients with moderate to severe UC.DesignIn the single ascending dose (SAD) stage, etrolizumab (0.3, 1.0, 3.0, 10 mg/kg intravenous, 3.0 mg/kg subcutaneous (SC) or placebo) was administered 4:1 (n=25) in each cohort. In the multiple dose (MD) stage, new patients received monthly etrolizumab (0.5 mg/kg SC (n=4), 1.5 mg/kg SC (n=5), 3.0 mg/kg SC (n=4), 4.0 mg/kg intravenous (n=5)) or placebo (n=5). The pharmacokinetics was studied and Mayo Clinic Score evaluated at baseline, day 29 (SAD), and days 43 and 71 (MD).ResultsIn the SAD stage, there were no dose limiting toxicities, infusion or injection site reactions. Two impaired wound healing serious adverse events occurred in two patients receiving etrolizumab. In the MD stage, there were no dose limiting toxicities, and no infusion or injection site reactions. Headache was the most common adverse event, occurring more often in etrolizumab patients. Antietrolizumab antibodies were detected in two subjects. The duration of β7 receptor full occupancy was dose related. A clinical response was observed in 12/18 patients, and clinical remission in 3/18 patients treated with etrolizumab in the MD stage, compared with 4/5 and 1/5 placebo patients, respectively.ConclusionEtrolizumab is well tolerated in moderate to severe UC. Further investigation is warranted

Causal blankets : Theory and algorithmic framework

Funding Information: F.R. was supported by the Ad Astra Chandaria foundation. P.M. was funded by the Wellcome Trust (grant no. 210920/Z/18/Z). M.B. was supported by a grant from Tem-pleton World Charity Foundation, Inc. (TWCF). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of TWCF. Publisher Copyright: © 2020, Springer Nature Switzerland AG. This is a post-peer-review, pre-copyedit version of Rosas, F. E., Mediano, P. A. M., Biehl, M., Chandaria, S., & Polani, D. (2020). Causal blankets: Theory and algorithmic framework. In T. Verbelen, P. Lanillos, C. L. Buckley, & C. De Boom (Eds.), Active Inference - First International Workshop, IWAI 2020, Co-located with ECML/PKDD 2020, Proceedings (pp. 187-198). (Communications in Computer and Information Science; Vol. 1326). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-64919-7_19We introduce a novel framework to identify perception-action loops (PALOs) directly from data based on the principles of computational mechanics. Our approach is based on the notion of causal blanket, which captures sensory and active variables as dynamical sufficient statistics—i.e. as the “differences that make a difference.” Furthermore, our theory provides a broadly applicable procedure to construct PALOs that requires neither a steady-state nor Markovian dynamics. Using our theory, we show that every bipartite stochastic process has a causal blanket, but the extent to which this leads to an effective PALO formulation varies depending on the integrated information of the bipartition

Predictors of duloxetine response in patients with oxaliplatinâ induced painful chemotherapyâ induced peripheral neuropathy (CIPN): a secondary analysis of randomised controlled trial â CALGB/alliance 170601

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136306/1/ecc12421_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136306/2/ecc12421.pd

EXAFS Structural Determination of the Pt2(P2O5H2)44– Anion in Solution

We present the first structural determination of the Pt2(P2O5H2)44– anion in solution by analyzing the extended X-ray absorption fine structure (EXAFS) spectrum of the Pt LIII edge. The data could be fit with a simple model involving single and multiple scattering paths to near and far P-atoms, bridging O-atoms, and the other Pt-atom in the binuclear complex. A Pt–Pt distance of 2.876(28) Å and a Pt–P bond length of 2.32(4) Å are obtained. These values are in line with distances found in previous X-ray diffraction studies. The assignment of the EXAFS spectrum of the Pt2(P2O5H2)44– anion in its ground state is required for future time-resolved X-ray absorption measurements with the goal of determining the structure and dynamics of the complex in the 1,3A2u excited states

Topological A-Type Models with Flux

We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. Generically these are topological membrane models, and we show that the fluxes are related to deformations of the Courant bracket which generalize the twist by a closed 3-from $H$, in the sense that satisfying the AKSZ master equation implies the integrability conditions for an almost generalized complex structure with respect to the deformed Courant bracket. In addition, the master equation imposes conditions on the fluxes that generalize $dH=0$. The membrane model can be defined on a large class of $U(m)$- and $U(m) \times U(m)$-structure manifolds, including geometries inspired by $(1,1)$ supersymmetric $\sigma$-models with additional supersymmetries due to almost complex (but not necessarily complex) structures in the target space. Furthermore, we show that the model can be defined on three particular half-flat manifolds related to the Iwasawa manifold. When only $H$-flux is turned on it is possible to obtain a topological string model, which we do for the case of a Calabi-Yau with a closed 3-form turned on. The simplest deformation from the A-model is due to the $(2,0)+ (0,2)$ component of a non-trivial $b$-field. The model is generically no longer evaluated on holomorphic maps and defines new topological invariants. Deformations due to $H$-flux can be more radical, completely preventing auxiliary fields from being integrated out.Comment: 30 pages. v2: Improved Version. References added. v3: Minor changes, published in JHE

Asymmetric function theory

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.Comment: 36 pages, 8 figures, 1 table. Written for the proceedings of the Schubert calculus conference in Guangzhou, Nov. 201