A generalized Lichnerowicz formula, the Wodzicki Residue and Gravity

We prove a generalized version of the well-known Lichnerowicz formula for the square of the most general Dirac operator $\widetilde{D}$\ on an even-dimensional spin manifold associated to a metric connection $\widetilde{\nabla}$. We use this formula to compute the subleading term $\Phi_1(x,x, \widetilde{D}^2)$\ of the heat-kernel expansion of $\widetilde{D}^2$. The trace of this term plays a key-r\hat {\petit\rm o}le in the definition of a (euclidian) gravity action in the context of non-commutative geometry. We show that this gravity action can be interpreted as defining a modified euclidian Einstein-Cartan theory.Comment: 10 pages, plain te

Familien von Differentialoperatoren über Mannigfaltigkeiten von Einbettungen und der Binz'sche Zerlegungssatz

Ausgehend von einer von Binz im Rahmen der differentialgeometrischen Beschreibung konstitutiver Gesetze der Elastizitätstheorie gemachten Beobachtung (vgl. z.B. [B2] Theorem 5.2), daß jede Bündelabblidung α(j): TM → TN über einer Einbettung j ∈ E(M, N) endlich dimensionaler Mannigfaltigkeiten in einen pseudo-exakten und pseudo-exakt freien Teil zerfällt, untersucht diese Arbeit die unterliegende unendlich-dimensionale Frechét-Geometrie. Das Resultat ist eine entsprechende Zerlegung des Frechétbündels π ∗ ε(1) ≅ ker D1 ,0 X Im D1,0, wobei D1,0 die glatte Familie von Differentialoperatoren {(j∗∇TN)∗} bezeichnet

CaMKIIalpha interacts with multi-PDZ domain protein MUPP1 in spermatozoa and prevents spontaneous acrosomal exocytosis

The success of acrosomal exocytosis, a complex process with a variety of inter-related steps, relies on the coordinated interaction of participating signaling molecules. Since the acrosome reaction resembles Ca(2+)-regulated exocytosis in neurons, we investigated whether cognate neuronal binding partners of the multi-PDZ domain protein MUPP1, which recruits molecules that control the initial tethering and/or docking between the acrosomal vesicle and the plasma membrane, are also expressed in spermatozoa, and whether they contribute to the regulation of acrosomal secretion. We observed that CaMKIIalpha colocalizes with MUPP1 in the acrosomal region of epididymal spermatozoa where the kinase selectively binds to a region encompassing PDZ domains 10-11 of MUPP1. Furthermore, we found that pre-treating mouse spermatozoa with a CaMKII inhibitor that directly blocks the catalytic region of the kinase, as well as a competitive displacement of CaMKIIalpha from PDZ domains 10-11, led to a significant increase in spontaneous acrosomal exocytosis. Since Ca(2+)-calmodulin releases CaMKIIalpha from the PDZ scaffolding protein, MUPP1 represents a central signaling platform to dynamically regulate the assembly and disassembly of binding partners pertinent to acrosomal secretion, thereby precisely adjusting an increase in Ca(2+) to synchronized fusion pore formation

Self-exciting price impact via negative resilience in stochastic order books

Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact, where trading activities of the large investor stimulate other market participants to trade in the same direction. In the paper we discuss several new qualitative effects on optimal trade execution that arise when we allow resilience to take negative values. We do this in a framework where both market depth and resilience are stochastic processes.Comment: 27 pages; title of first version: On effects of negative resilience on optimal trade execution in stochastic order book