Monte Carlo Euler approximations of HJM term structure financial models

We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on \Ito stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates

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

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

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

Homalg: A meta-package for homological algebra

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.Comment: clarified some points, added references and more interesting example

Entanglement measure for general pure multipartite quantum states

We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits states.Comment: 5 page

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state was used to perform such measurements. Each of the photons carries (partial) information of the initial state thus leaving a room for measurements of two complementary observables on every member in an ensemble.Comment: 4 pages, 4 figures, REVTeX, submitted to PR

On the efficiency of quantum lithography

Quantum lithography promises, in principle, unlimited feature resolution, independent of wavelength. However, in the literature at least two different theoretical descriptions of quantum lithography exist. They differ in to which extent they predict that the photons retain spatial correlation from generation to the absorption, and while both predict the same feature size, they differ vastly in predicting how efficiently a quantum lithographic pattern can be exposed. Until recently, essentially all experiments reported have been performed in such a way that it is difficult to distinguish between the two theoretical explanations. However, last year an experiment was performed which gives different outcomes for the two theories. We comment on the experiment and show that the model that fits the data unfortunately indicates that the trade-off between resolution and efficiency in quantum lithography is very unfavourable.Comment: 19 pages, extended version including a thorough mathematical derivatio

Fly-The-Bee: A Game Imitating Concept Learning in Bees

AbstractThis article presents a web-based game functionally imitating a part of the cognitive behavior of a living organism. This game is a prototype implementation of an artificial online cognitive architecture based on the usage of distributed data representations and Vector Symbolic Architectures. The game demonstrates the feasibility of creating a lightweight cognitive architecture, which is capable of performing rather complex cognitive tasks. The cognitive functionality is implemented in about 100 lines of code and requires few tens of kilobytes of memory for its operation, which make the concept suitable for implementing in low-end devices such as minirobots and wireless sensors

Hamiltonian Formalism in Quantum Mechanics

Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum mechanics are not, or at least not what they appear to be; their properties are formulated in a series of Conjectures