Bond markets where prices are driven by a general marked point process

We investigate the term structure for the case when interest rates are allowed to be driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure, as well as completeness of the bond market. We also give sufficient conditions for the existence of an affine term structure. Developing the appropriate forward measures we give formulas for interest rate derivatives.Term structure of interest rates; arbitrage; bond markets; interest rates; martingales; jump processes; completeness; affine term structure

Quantum error correction may delay, but also cause, entanglement sudden death

Dissipation may cause two initially entangled qubits to evolve into a separable state in a finite time. This behavior is called entanglement sudden death (ESD). We study to what extent quantum error correction can combat ESD. We find that in some cases quantum error correction can delay entanglement sudden death but in other cases quantum error correction may cause ESD for states that otherwise do not suffer from it. Our analysis also shows that fidelity may not be the best measure to compare the efficiency of different error correction codes since the fidelity is not directly coupled to a state's remaining entanglement.Comment: 3 figure

CDO term structure modelling with Levy processes and the relation to market models

This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipovi\'c, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite dimensional L\'evy process. The contribution of this work is twofold: we provide conditions for absence of arbitrage in this generalized framework. Furthermore, we study the relation to market models by embedding them in the forward rate framework in spirit of Brace, Gatarek and Musiela (1997).Comment: 16 page

Entanglement invariant for the double Jaynes-Cummings model

We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings hamiltonians, via the entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as "entanglement sudden death". We find a natural entanglement invariant under evolution demonstrating that entanglement sudden death is caused by ignoring (tracing over) some of the system's degrees of freedom that become entangled through the interaction.Comment: Sec. V has largely been rewritten. An error pertaining to the entanglement invariant has been corrected and a correct invariant valid for a much larger set of states have been found, Eq. (25

Interest Rates and Information Geometry

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discount function with respect to the maturity date gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that the general arbitrage-free yield curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. We also derive the dynamics for the central moments associated with the distribution determined by the yield curve.Comment: 20 pages, 3 figure

α2-macroglobulin and α1-inhibitor-3 mRNA expression in the rat liver after slow interleukin-1 stimulation

In this study we have investigated total fiver RNA and the expression of mRNA in the rat fiver in vivo after a slow stimulation of interleukin-1. A total dose of 4 μg interleukin-1β was administered via a subcutaneously implanted osmotic minipump over a period of 7 days. Plasma concentrations of α2-macroglobulin manifested a rapid increase, reaching a peak on day 2, while α1-inhibitor-3 manifested a marked initial decrease to 50% of the baseline level, followed by a tendency to increase again. For measurement of total RNA and specific mRNAs from the fiver, rats were sacrificed at different times during the experimental period. Total RNA peaked at 6 h, the level being approximately 60% higher than baseline value. Specific mRNA from the liver for α2-macroglobulin and α1-inhibitor-3 were quantified using laser densitometry on slot blots. The amounts measured during the experimental period agreed with the pattern of corresponding plasma protein levels. From barely detectable amounts at baseline, α2-macroglobulin mRNA peaked on day 1, and then declined. Levels of α1-inhibitor-3 mRNA manifested an initial increase at 3 h, but then declined and remained low until day 5 when there was a tendency towards an increase. It was concluded that the levels of plasma concentrations of α2-macroglobulin and α1-inhibitor-3 are mainly regulated at the protein synthesis level, and that long-term interleukin-1β release could not override the initial acute phase protein counteracting mechanism triggered

Tunable effective g-factor in InAs nanowire quantum dots

We report tunneling spectroscopy measurements of the Zeeman spin splitting in InAs few-electron quantum dots. The dots are formed between two InP barriers in InAs nanowires with a wurtzite crystal structure grown by chemical beam epitaxy. The values of the electron g-factors of the first few electrons entering the dot are found to strongly depend on dot size and range from close to the InAs bulk value in large dots |g^*|=13 down to |g^*|=2.3 for the smallest dots. These findings are discussed in view of a simple model.Comment: 4 pages, 3 figure

The colored Jones function is q-holonomic

A function of several variables is called holonomic if, roughly speaking, it is determined from finitely many of its values via finitely many linear recursion relations with polynomial coefficients. Zeilberger was the first to notice that the abstract notion of holonomicity can be applied to verify, in a systematic and computerized way, combinatorial identities among special functions. Using a general state sum definition of the colored Jones function of a link in 3-space, we prove from first principles that the colored Jones function is a multisum of a q-proper-hypergeometric function, and thus it is q-holonomic. We demonstrate our results by computer calculations.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper29.abs.htm

Two-photon imaging and quantum holography

It has been claimed that ``the use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever strength of the correlations between the two photons'' [A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001)]. While we believe that the cited statement is true, we show that the method proposed in that paper, with ``bucket detection'' of one of the photons, will give identical results for entangled states as for appropriately prepared classically correlated states.Comment: 4 pages, 2 figures, REVTe