Off-center coherent-state representation and an application to semiclassics

By using the overcompleteness of coherent states we find an alternative form of the unit operator for which the ket and the bra appearing under the integration sign do not refer to the same phase-space point. This defines a new quantum representation in terms of Bargmann functions, whose basic features are presented. A continuous family of secondary reproducing kernels for the Bargmann functions is obtained, showing that this quantity is not necessarily unique for representations based on overcomplete sets. We illustrate the applicability of the presented results by deriving a semiclassical expression for the Feynman propagator that generalizes the well-known van Vleck formula and seems to point a way to cope with long-standing problems in semiclassical propagation of localized states

Memory and self-induced shocks in an evolutionary population competing for limited resources

We present a detailed discussion of the role played by memory, and the nature of self-induced shocks, in an evolutionary population competing for limited resources. Our study builds on a previously introduced multi-agent system [Phys. Rev. Lett 82, 3360 (1999)] which has attracted significant attention in the literature. This system exhibits self-segregation of the population based on the `gene' value p (where 0<=p<=1), transitions to `frozen' populations as a function of the global resource level, and self-induced large changes which spontaneously arise as the dynamical system evolves. We find that the large, macroscopic self-induced shocks which arise, are controlled by microscopic changes within extreme subgroups of the population (i.e. subgroups with `gene' values p~0 and p~1).Comment: 27 pages, 31 figure

Nonparametric option pricing with no-arbitrage constraints

We propose a completely kernel based method of estimating the call price function or the state price density of options. The new estimator of the call price function fulfills the constraints like monotonicity and convexity given in Breeden and Litzenberger (1978) without necessarily estimating the state price density for an underlying asset price from its option prices. It can be shown that the estimator is pointwise consistent and asymptotically normal. In a simulation study we compare the new estimator to the unconstrained kernel estimator and to the estimator given in Aït-Sahalia and Duarte (2003). --call pricing function b,constrained nonparametric estimation,monotone rearrangements,state price density

A comparative study of monotone nonparametric kernel estimates

In this paper we present a detailed numerical comparison of three monotone nonparametric kernel regression estimates, which isotonize a nonparametric curve estimator. The first estimate is the classical smoothed isotone estimate of Brunk (1958). The second method has recently been proposed by Hall and Huang (2001) and modifies the weights of a commonly used kernel estimate such that the resulting estimate is monotone. The third estimate was recently proposed by Dette, Neumeyer and Pilz (2003) and combines density and regression estimation techniques to obtain a monotone curve estimate of the inverse of the isotone regression function. The three concepts are briefly reviewed and their finite sample properties are studied by means of a simulation study. Although all estimates are first order asymptotically equivalent (provided that the unknown regression function is isotone) some differences for moderate samples are observed. --isotonic regression,order restricted inference,Nadaraya-Watson estimator,local linear regression,monte carlo simulation

Study of meshing of beveled gears with normally decreasing arc teeth

The meshing of beveled gears was studied by the direct and inverse approaches. Gear wheels with teeth of equal height are studied, and wheels with normally-decreasing arc teeth. Different coordinate systems are utilized to plot the determination of the rotation of the originating gear wheel and the meshing line of the gear wheel which is cut. Matrices are used to determine the equations of the originating surfaces and the unit vectors of the normals to these originating surfaces

Improvement of conditions for meshing spiral bevel gears

The effect of axial pinion displacement on gear meshing conditions during cutting and correction of the rolling chain gear ratio are analyzed. The so-called inverse problem-solving method is used

Perfect Quantum Routing in Regular Spin Networks

Regular families of coupled quantum networks are described such the unknown state of a qubit can be perfectly routed from any node to any other node in a time linear in the distance. Unlike previous constructions, the transfer can be achieved perfectly on a network that is local on any specified number of spatial dimensions. The ability to route the state, and the regularity of the networks, vastly improve the utility of this scheme in comparison to perfect state transfer schemes. The structures can also be used for entanglement generation.Comment: 4 pages, 3 figure

Evolutionary quantum game

We present the first study of a dynamical quantum game. Each agent has a `memory' of her performance over the previous m timesteps, and her strategy can evolve in time. The game exhibits distinct regimes of optimality. For small m the classical game performs better, while for intermediate m the relative performance depends on whether the source of qubits is `corrupt'. For large m, the quantum players dramatically outperform the classical players by `freezing' the game into high-performing attractors in which evolution ceases.Comment: 4 pages in two-column format. 4 figure

A simple nonparametric estimator of a monotone regression function

In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. The main idea of the new approach is to construct a density estimate from the estimated values ˆm(i/N) (i = 1, . . . ,N) of the regression function to use these “data” for the calculation of an estimate of the inverse of the regression function. The final estimate is then obtained by a numerical inversion. Compared to the conventially used techniques for monotone estimation the new method is computationally more efficient, because it does not require constrained optimization techniques for the calculation of the estimate. We prove asymptotic normality of the new estimate and compare the asymptotic properties with the unconstrained estimate. In particular it is shown that for kernel estimates or local polynomials the monotone estimate is first order asymptotically equivalent to the unconstrained estimate. We also illustrate the performance of the new procedure by means of a simulation study. --isotonic regression,order restricted inference,Nadaraya-Watson estimator,local linear regression