3,967 research outputs found
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 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
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
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 , 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
. The membrane model can be defined on a large class of - and -structure manifolds, including geometries inspired by
supersymmetric -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 -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
component of a non-trivial -field. The model is generically no longer
evaluated on holomorphic maps and defines new topological invariants.
Deformations due to -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
Measuring Granger Causality between Cortical Regions from Voxelwise fMRI BOLD Signals with LASSO
Functional brain network studies using the Blood Oxygen-Level Dependent (BOLD) signal from functional Magnetic Resonance Imaging (fMRI) are becoming increasingly prevalent in research on the neural basis of human cognition. An important problem in functional brain network analysis is to understand directed functional interactions between brain regions during cognitive performance. This problem has important implications for understanding top-down influences from frontal and parietal control regions to visual occipital cortex in visuospatial attention, the goal motivating the present study. A common approach to measuring directed functional interactions between two brain regions is to first create nodal signals by averaging the BOLD signals of all the voxels in each region, and to then measure directed functional interactions between the nodal signals. Another approach, that avoids averaging, is to measure directed functional interactions between all pairwise combinations of voxels in the two regions. Here we employ an alternative approach that avoids the drawbacks of both averaging and pairwise voxel measures. In this approach, we first use the Least Absolute Shrinkage Selection Operator (LASSO) to pre-select voxels for analysis, then compute a Multivariate Vector AutoRegressive (MVAR) model from the time series of the selected voxels, and finally compute summary Granger Causality (GC) statistics from the model to represent directed interregional interactions. We demonstrate the effectiveness of this approach on both simulated and empirical fMRI data. We also show that averaging regional BOLD activity to create a nodal signal may lead to biased GC estimation of directed interregional interactions. The approach presented here makes it feasible to compute GC between brain regions without the need for averaging. Our results suggest that in the analysis of functional brain networks, careful consideration must be given to the way that network nodes and edges are defined because those definitions may have important implications for the validity of the analysis
A Low Dimensional Description of Globally Coupled Heterogeneous Neural Networks of Excitatory and Inhibitory Neurons
Neural networks consisting of globally coupled excitatory and inhibitory nonidentical neurons may exhibit a complex dynamic behavior including synchronization, multiclustered solutions in phase space, and oscillator death. We investigate the conditions under which these behaviors occur in a multidimensional parametric space defined by the connectivity strengths and dispersion of the neuronal membrane excitability. Using mode decomposition techniques, we further derive analytically a low dimensional description of the neural population dynamics and show that the various dynamic behaviors of the entire network can be well reproduced by this reduced system. Examples of networks of FitzHugh-Nagumo and Hindmarsh-Rose neurons are discussed in detail
Glycoprotein Ib activation by thrombin stimulates the energy metabolism in human platelets
<div><p>Thrombin-induced platelet activation requires substantial amounts of ATP. However, the specific contribution of each ATP-generating pathway <i>i</i>.<i>e</i>., oxidative phosphorylation (OxPhos) versus glycolysis and the biochemical mechanisms involved in the thrombin-induced activation of energy metabolism remain unclear. Here we report an integral analysis on the role of both energy pathways in human platelets activated by several agonists, and the signal transducing mechanisms associated with such activation. We found that thrombin, Trap-6, arachidonic acid, collagen, A23187, epinephrine and ADP significantly increased glycolytic flux (3–38 times <i>vs</i>. non-activated platelets) whereas ristocetin was ineffective. OxPhos (33 times) and mitochondrial transmembrane potential (88%) were increased only by thrombin. OxPhos was the main source of ATP in thrombin-activated platelets, whereas in platelets activated by any of the other agonists, glycolysis was the principal ATP supplier. In order to establish the biochemical mechanisms involved in the thrombin-induced OxPhos activation in platelets, several signaling pathways associated with mitochondrial activation were analyzed. Wortmannin and LY294002 (PI3K/Akt pathway inhibitors), ristocetin and heparin (GPIb inhibitors) as well as resveratrol, ATP (calcium-release inhibitors) and PP1 (Tyr-phosphorylation inhibitor) prevented the thrombin-induced platelet activation. These results suggest that thrombin activates OxPhos and glycolysis through GPIb-dependent signaling involving PI3K and Akt activation, calcium mobilization and protein phosphorylation.</p></div
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