Automatic, computer aided geometric design of free-knot, regression splines

A new algorithm for Computer Aided Geometric Design of least squares (LS) splines with variable knots, named GeDS, is presented. It is based on interpreting functional spline regression as a parametric B-spline curve, and on using the shape preserving property of its control polygon. The GeDS algorithm includes two major stages. For the first stage, an automatic adaptive, knot location algorithm is developed. By adding knots, one at a time, it sequentially "breaks" a straight line segment into pieces in order to construct a linear LS B-spline fit, which captures the "shape" of the data. A stopping rule is applied which avoids both over and under fitting and selects the number of knots for the second stage of GeDS, in which smoother, higher order (quadratic, cubic, etc.) fits are generated. The knots appropriate for the second stage are determined, according to a new knot location method, called the averaging method. It approximately preserves the linear precision property of B-spline curves and allows the attachment of smooth higher order LS B-spline fits to a control polygon, so that the shape of the linear polygon of stage one is followed. The GeDS method produces simultaneously linear, quadratic, cubic (and possibly higher order) spline fits with one and the same number of B-spline regression functions. The GeDS algorithm is very fast, since no deterministic or stochastic knot insertion/deletion and relocation search strategies are involved, neither in the first nor the second stage. Extensive numerical examples are provided, illustrating the performance of GeDS and the quality of the resulting LS spline fits. The GeDS procedure is compared with other existing variable knot spline methods and smoothing techniques, such as SARS, HAS, MDL, AGS methods and is shown to produce models with fewer parameters but with similar goodness of fit characteristics, and visual quality

Modelling the joint distribution of competing risks survival times using copula functions

The problem of modelling the joint distribution of survival times in a competing risks model, using copula functions is considered. In order to evaluate this joint distribution and the related overall survival function, a system of non-linear differential equations is solved, which relates the crude and net survival functions of the modelled competing risks, through the copula. A similar approach to modelling dependent multiple decrements was applied by Carriere (1994) who used a Gaussian copula applied to an incomplete double decrement model which makes it difficult to calculate any actuarial functions and draw relevant conclusions. Here, we extend this methodology by studying the effect of complete and partial elimination of up to four competing risks on the overall survival function, the life expectancy and life annuity values. We further investigate how different choices of the copula function affect the resulting joint distribution of survival times and in particular the actuarial functions which are of importance in pricing life insurance and annuity products. For illustrative purposes, we have used a real data set and used extrapolation to prepare a complete multiple decrement model up to age 120. Extensive numerical results illustrate the sensitivity of the model with respect to the choice ofcopula and its parameter(s)

Two-Body Density Matrix for Closed s-d Shell Nuclei

The two-body density matrix for $^{4}He,^{16}O$ and $^{40}Ca$ within the Low-order approximation of the Jastrow correlation method is considered. Closed analytical expressions for the two-body density matrix, the center of mass and relative local densities and momentum distributions are presented. The effects of the short-range correlations on the two-body nuclear characteristics are investigated.Comment: 13 pages(LaTeX), 4 figures (ps

Advances in surface EMG signal simulation with analytical and numerical descriptions of the volume conductor

Surface electromyographic (EMG) signal modeling is important for signal interpretation, testing of processing algorithms, detection system design, and didactic purposes. Various surface EMG signal models have been proposed in the literature. In this study we focus on 1) the proposal of a method for modeling surface EMG signals by either analytical or numerical descriptions of the volume conductor for space-invariant systems, and 2) the development of advanced models of the volume conductor by numerical approaches, accurately describing not only the volume conductor geometry, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function is derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fiber orientation. In some cases (e.g., multi-pinnate muscles) accurate description of the conductivity tensor may be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibers is presented and applied to representatively investigate a bi-pinnate muscle with rectilinear and curvilinear fibers. The study thus propose an approach for surface EMG signal simulation in space invariant systems as well as new models of the volume conductor using numerical methods

Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options.

The authors develop a new Monte Carlo based method for pricing path-dependent options under the variance gamma (VG) model. The gamma bridge sampling method due to Avramidis et al. (2003) and Ribeiro and Webber (2004), is generalized to a multivariate (Dirichlet) construction, bridging ’simultaneously’ over all time partition points of the trajectory of a gamma process. The generation of the increments of the gamma process, given its value at the terminal point, is interpreted as a Dirichlet partition of the unit interval. The increments are generated in a decreasing stochastic order and, under the Kingman limit, have a known distribution. Thus, simulation of a trajectory from the gamma process requires generating only a small number of uniforms, avoiding the expensive simulation of beta variates via numerical probability integral inversion. The proposed method is then applied in simulating the trajectory of a VG process using its difference-of-gammas representation. It has been implemented both in plain Monte Carlo and QuasiMonte Carlo environments. It is tested in pricing lookback, barrier and Asian options and shown to provide consistent efficiency gains, compared to the sequential method and the difference-of-gammas bridge sampling due to Avramidis and L’Ecuyer (2006)

Improved proper motion determinations for 15 open clusters based on the UCAC4 catalog

The proper motions of 15 nearby (d < 1 kpc) open clusters were recalculated using data from the UCAC4 catalog. Only evolved or main sequence stars inside a certain radius from the center of the cluster were used. The results differ significantly from the ones presented by Dias et al. (2014). This could be explained by the different approach to taking the field star contamination into account. The present work aims to emphasize the importance of applying photometric criteria for the calculation of open cluster proper motions.Comment: 9 pages, accepted for publication in Research in Astronomy and Astrophysic

Generalized Arago-Fresnel laws: The EME-flow-line description

We study experimentally and theoretically the influence of light polarization on the interference patterns behind a diffracting grating. Different states of polarization and configurations are been considered. The experiments are analyzed in terms of electromagnetic energy (EME) flow lines, which can be eventually identified with the paths followed by photons. This gives rise to a novel trajectory interpretation of the Arago-Fresnel laws for polarized light, which we compare with interpretations based on the concept of "which-way" (or "which-slit") information.Comment: 14 pages, 6 figure

On the evaluation of finite-time ruin probabilities in a dependent risk model

This paper establishes some enlightening connections between the explicit formulas of the finite-time ruin probability obtained by Ignatovand Kaishev (2000, 2004) and Ignatov et al. (2001) for a risk model allowing dependence. The numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented. Extensive numerical comparisons and examples are provided

On finite-time ruin probabilities in a generalized dual risk model with dependence

In this paper, we study the finite-time ruin probability in a reasonably generalized dual risK model, where we assume any non-negative non-decreasing cumulative operational cost function and arbitrary capital gains arrival process. Establishing an enlightening link between this dual risk model and its corresponding insurance risk model, explicit expressions for the finite-time survival probability in the dual risk model are obtained under various general assumptions for the distribution of the capital gains. In order to make the model more realistic and general, different dependence structures among capital gains and inter-arrival times and between both are also introduced and corresponding ruin probability expressions are also given. The concept of alarm time, as introduced in Das and Kratz (2012), is applied to the dual risk model within the context of risk capital allocation. Extensive numerical illustrations are provided

Ruin and Deficit Under Claim Arrivals with the Order Statistics Property

We consider an insurance risk model with extended flexibility, under which claims arrive according to a point process with an order statistics (OS) property, their amounts may have any joint distri- bution and the premium income is accumulated following any non- decreasing, possibly discontinuous real valued function. We generalize the definition of an OS point process, assuming it is generated by an arbitrary cdf allowing jump discontinuities, which corresponds to an arbitrary (possibly discontinuous) claim arrival cumulative intensity function. The latter feature is appealing for insurance applications since it allows to consider clusters of claims arriving instantaneously. Under these general assumptions, a closed form expression for the joint distribution of the time to ruin and the deficit at ruin is derived, which remarkably involves classical Appell polynomials. Corollaries of our main result generalize previous non-ruin formulas e.g., those obtained by Ignatov and Kaishev (2000, 2004, 2006) and Lef`evre and Loisel (2009) for the case of stationary Poisson claim arrivals and by Lef`evre and Picard (2011, 2014), for OS claim arrivals