310 research outputs found
Homotopy Relations for Topological VOA
We consider a parameter-dependent version of the homotopy associative part of
the Lian-Zuckerman homotopy algebra and provide the interpretation of
multilinear operations of this algebra in terms of integrals over certain
polytopes. We explicitly prove the pentagon relation up to homotopy and propose
a construction of higher operations.Comment: 15 pages, 1 figure, typos correcte
All Stable Characteristic Classes of Homological Vector Fields
An odd vector field on a supermanifold is called homological, if
. The operator of Lie derivative makes the algebra of smooth
tensor fields on into a differential tensor algebra. In this paper, we give
a complete classification of certain invariants of homological vector fields
called characteristic classes. These take values in the cohomology of the
operator and are represented by -invariant tensors made up of the
homological vector field and a symmetric connection on by means of tensor
operations.Comment: 17 pages, references and comments adde
Homotopy Lie algebras, lower central series and the Koszul property
Let X and Y be finite-type CW-complexes (X connected, Y simply connected),
such that the rational cohomology ring of Y is a k-rescaling of the rational
cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy
Lie algebra pi_*(Omega Y) tensor Q equals, up to k-rescaling, the graded
rational Lie algebra associated to the lower central series of pi_1(X). If Y is
a formal space, this equality is actually equivalent to the Koszulness of
H^*(X,Q). If X is formal (and only then), the equality lifts to a filtered
isomorphism between the Malcev completion of pi_1(X) and the completion of
[Omega S^{2k+1}, Omega Y]. Among spaces that admit naturally defined
homological rescalings are complements of complex hyperplane arrangements, and
complements of classical links. The Rescaling Formula holds for supersolvable
arrangements, as well as for links with connected linking graph.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol8/paper30.abs.htm
The homotopy theory of simplicial props
The category of (colored) props is an enhancement of the category of colored
operads, and thus of the category of small categories. In this paper, the
second in a series on "higher props," we show that the category of all small
colored simplicial props admits a cofibrantly generated model category
structure. With this model structure, the forgetful functor from props to
operads is a right Quillen functor.Comment: Final version, to appear in Israel J. Mat
Multi-modal dissolution testing system for pharmaceutical tablets
This project aims to develop a novel multimodal sensor system that is capable of resolving the key processes, as well as how these processes are linked to microstructure, formulation and raw material attributes
The structure of 2D semi-simple field theories
I classify all cohomological 2D field theories based on a semi-simple complex
Frobenius algebra A. They are controlled by a linear combination of
kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their
effect on the Gromov-Witten potential is described by Givental's Fock space
formulae. This leads to the reconstruction of Gromov-Witten invariants from the
quantum cup-product at a single semi-simple point and from the first Chern
class, confirming Givental's higher-genus reconstruction conjecture. The proof
uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio
-interpretation of a classification of deformations of Poisson structures in dimension three
We give an -interpretation of the classification, obtained in
[AP2], of the formal deformations of a family of exact Poisson structures in
dimension three. We indeed obtain again the explicit formulas for all the
formal deformations of these Poisson structures, together with a classification
in the generic case, by constructing a suitable quasi-isomorphism between two
-algebras, which are associated to these Poisson structures.Comment: 31 pages, Added references, minor change
Quantification and visualization of cardiovascular 4D velocity mapping accelerated with parallel imaging or k-t BLAST: head to head comparison and validation at 1.5 T and 3 T
<p>Abstract</p> <p>Background</p> <p>Three-dimensional time-resolved (4D) phase-contrast (PC) CMR can visualize and quantify cardiovascular flow but is hampered by long acquisition times. Acceleration with SENSE or k-t BLAST are two possibilities but results on validation are lacking, especially at 3 T. The aim of this study was therefore to validate quantitative in vivo cardiac 4D-acquisitions accelerated with parallel imaging and k-t BLAST at 1.5 T and 3 T with 2D-flow as the reference and to investigate if field strengths and type of acceleration have major effects on intracardiac flow visualization.</p> <p>Methods</p> <p>The local ethical committee approved the study. 13 healthy volunteers were scanned at both 1.5 T and 3 T in random order with 2D-flow of the aorta and main pulmonary artery and two 4D-flow sequences of the heart accelerated with SENSE and k-t BLAST respectively. 2D-image planes were reconstructed at the aortic and pulmonary outflow. Flow curves were calculated and peak flows and stroke volumes (SV) compared to the results from 2D-flow acquisitions. Intra-cardiac flow was visualized using particle tracing and image quality based on the flow patterns of the particles was graded using a four-point scale.</p> <p>Results</p> <p>Good accuracy of SV quantification was found using 3 T 4D-SENSE (r<sup>2 </sup>= 0.86, -0.7 ± 7.6%) and although a larger bias was found on 1.5 T (r<sup>2 </sup>= 0.71, -3.6 ± 14.8%), the difference was not significant (p = 0.46). Accuracy of 4D k-t BLAST for SV was lower (p < 0.01) on 1.5 T (r<sup>2 </sup>= 0.65, -15.6 ± 13.7%) compared to 3 T (r<sup>2 </sup>= 0.64, -4.6 ± 10.0%). Peak flow was lower with 4D-SENSE at both 3 T and 1.5 T compared to 2D-flow (p < 0.01) and even lower with 4D k-t BLAST at both scanners (p < 0.01). Intracardiac flow visualization did not differ between 1.5 T and 3 T (p = 0.09) or between 4D-SENSE or 4D k-t BLAST (p = 0.85).</p> <p>Conclusions</p> <p>The present study showed that quantitative 4D flow accelerated with SENSE has good accuracy at 3 T and compares favourably to 1.5 T. 4D flow accelerated with k-t BLAST underestimate flow velocities and thereby yield too high bias for intra-cardiac quantitative in vivo use at the present time. For intra-cardiac 4D-flow visualization, however, 1.5 T and 3 T as well as SENSE or k-t BLAST can be used with similar quality.</p
Comprehensive 4D velocity mapping of the heart and great vessels by cardiovascular magnetic resonance
<p>Abstract</p> <p>Background</p> <p>Phase contrast cardiovascular magnetic resonance (CMR) is able to measure all three directional components of the velocities of blood flow relative to the three spatial dimensions and the time course of the heart cycle. In this article, methods used for the acquisition, visualization, and quantification of such datasets are reviewed and illustrated.</p> <p>Methods</p> <p>Currently, the acquisition of 3D cine (4D) phase contrast velocity data, synchronized relative to both cardiac and respiratory movements takes about ten minutes or more, even when using parallel imaging and optimized pulse sequence design. The large resulting datasets need appropriate post processing for the visualization of multidirectional flow, for example as vector fields, pathlines or streamlines, or for retrospective volumetric quantification.</p> <p>Applications</p> <p>Multidirectional velocity acquisitions have provided 3D visualization of large scale flow features of the healthy heart and great vessels, and have shown altered patterns of flow in abnormal chambers and vessels. Clinically relevant examples include retrograde streams in atheromatous descending aortas as potential thrombo-embolic pathways in patients with cryptogenic stroke and marked variations of flow visualized in common aortic pathologies. Compared to standard clinical tools, 4D velocity mapping offers the potential for retrospective quantification of flow and other hemodynamic parameters.</p> <p>Conclusions</p> <p>Multidirectional, 3D cine velocity acquisitions are contributing to the understanding of normal and pathologically altered blood flow features. Although more rapid and user-friendly strategies for acquisition and analysis may be needed before 4D velocity acquisitions come to be adopted in routine clinical CMR, their capacity to measure multidirectional flows throughout a study volume has contributed novel insights into cardiovascular fluid dynamics in health and disease.</p
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