Higher Poincare Lemma and Integrability

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a proof by Voronov and yields the explicit gauge parameters connecting a flat local connective structure to the trivial one. Finally, we show how higher flatness appears as a necessary integrability condition of a linear system which featured in recently developed twistor descriptions of higher gauge theories.Comment: 1+21 pages, presentation streamlined, section on integrability for higher linear systems significantly improved, published versio

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

Three-dimensional flow characteristics in ventricular assist devices: Impact of valve design and operating conditions

ObjectiveThe use of paracorporeal ventricular assist devices has become a well-established procedure for patients with cardiogenic shock. However, implantation of ventricular assist devices is often associated with severe complications, such as thrombosis inside the ventricular assist device and subsequent embolic events. It was the purpose of this study to use flow-sensitive 4-dimensional magnetic resonance imaging for a detailed analysis of the 3-dimensional (3D) flow dynamics inside a clinical routine ventricular assist device and to study the effect of different system adjustments and a new valve design on flow patterns.MethodsA routinely used clinical paracorporeal ventricular assist device was integrated into a magnetic resonance-compatible mock loop. Flow-sensitive 3D magnetic resonance imaging was performed to measure time-resolved 3-directional flow velocities (spatial resolution ∼ 1.2 mm, temporal resolution = 42.4 ms) in the entire device under ideal conditions (full fill, full empty, ejection fraction = 88%), insufficient filling (ejection fraction = 81%), and insufficient emptying (ejection fraction = 67%) of the pump chamber. In addition, a new valve design was evaluated. Flexible control and monitoring of pressures at inlet and outlet were used to generate realistic boundary conditions.ResultsFlow pattern changes for different operating conditions were clearly identified and included reduced velocities during systolic outflow for impaired filling (78% reduction in pump flow compared with optimal operating conditions) and impaired clearing of the pump chamber for insufficient emptying (52% reduction). For all operating conditions, 3D visualization revealed vortex flow inside the ventricular assist device at typical locations of thrombus formation near the valve systems. Most noticeably, the new valve design provided similar global ventricular assist device function (pump flow 3.6 L/min), but vortex formation was eliminated.ConclusionsThe results of this study provide insight into the mechanisms underlying possible thrombus formation inside a ventricular assist device and the effect of different system adjustments. The presented methods may permit the optimization of future ventricular assist device systems with respect to optimal flow conditions

Graph complexes in deformation quantization

Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich's proof of the formality morphism is reexamined in this light and an algebraic framework for discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added, mainly concerning the tree-level approximation. Typos corrected. An abridged version will appear in Lett. Math. Phy

Molluscan mega-hemocyanin: an ancient oxygen carrier tuned by a ~550 kDa polypeptide

<p>Abstract</p> <p>Background</p> <p>The allosteric respiratory protein hemocyanin occurs in gastropods as tubular di-, tri- and multimers of a 35 × 18 nm, ring-like decamer with a collar complex at one opening. The decamer comprises five subunit dimers. The subunit, a 400 kDa polypeptide, is a concatenation of eight paralogous functional units. Their exact topology within the quaternary structure has recently been solved by 3D electron microscopy, providing a molecular model of an entire didecamer (two conjoined decamers). Here we study keyhole limpet hemocyanin (KLH2) tridecamers to unravel the exact association mode of the third decamer. Moreover, we introduce and describe a more complex type of hemocyanin tridecamer discovered in fresh/brackish-water cerithioid snails (<it>Leptoxis</it>, <it>Melanoides</it>, <it>Terebralia</it>).</p> <p>Results</p> <p>The "typical" KLH2 tridecamer is partially hollow, whereas the cerithioid tridecamer is almost completely filled with material; it was therefore termed "mega-hemocyanin". In both types, the staggering angle between adjoining decamers is 36°. The cerithioid tridecamer comprises two typical decamers based on the canonical 400 kDa subunit, flanking a central "mega-decamer" composed of ten unique ~550 kDa subunits. The additional ~150 kDa per subunit substantially enlarge the internal collar complex. Preliminary oxygen binding measurements indicate a moderate hemocyanin oxygen affinity in <it>Leptoxis </it>(p50 ~9 mmHg), and a very high affinity in <it>Melanoides </it>(~3 mmHg) and <it>Terebralia </it>(~2 mmHg). Species-specific and individual variation in the proportions of the two subunit types was also observed, leading to differences in the oligomeric states found in the hemolymph.</p> <p>Conclusions</p> <p>In cerithioid hemocyanin tridecamers ("mega-hemocyanin") the collar complex of the central decamer is substantially enlarged and modified. The preliminary O₂binding curves indicate that there are species-specific functional differences in the cerithioid mega-hemocyanins which might reflect different physiological tolerances of these gill-breathing animals. The observed differential expression of the two subunit types of mega-hemocyanin might allow individual respiratory acclimatization. We hypothesize that mega-hemocyanin is a key character supporting the adaptive radiation and invasive capacity of cerithioid snails.</p

Classes on compactifications of the moduli space of curves through solutions to the quantum master equation

In this paper we describe a construction which produces classes in a compactification of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in the open moduli space from the initial data of a cyclic A-infinity algebra. The initial data for our construction is what we call a `quantum A-infinity algebra', which arises as a type of deformation of a cyclic A-infinity algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A-infinity algebras which extend a family of cyclic A-infinity algebras, introduced by Kontsevich, which are known to produce all the Miller-Morita-Mumford classes using his construction.Comment: This version includes an updated list of reference