1,441 research outputs found
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
- …