We describe a method for computing a continuous time estimate of dynamic changes in tracer density using list mode PET data. The tracer density in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be represented using a cubic B-spline basis. An estimate of these rate functions is obtained by maximizing the likelihood of the arrival times of each detected photon p...

We devise a framework encompassing the classical theory of characteristics and the theory valid in the convex case recently obtained by R.T. Rockafellar and P. Wolenski. It relies on a notion of transform introduced by I. Ekeland. It involves a class of functions called Ekeland functions which is large enough to encompass convex functions, concave functions and linear-quadratic functions, as we...

Abstract: This study proposes new C rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets. Sufficient conditions for the positivity and data constrained modeling of the rational interpolant are derived on one parameter while the remaining two parameters can further be utilized to change and modify t...

The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Fortran and some exam...

Dispersion parameters for the number of piglets born alive were estimated using a repeatability and random regression model. Six sow breeds/lines were included in the analysis: Swedish Landrace, Large White and both crossbred lines between them, German Landrace and their cross with Large White. Fixed part of the model included sow genotype, mating season as month-year interaction, parity and we...

In this paper the approximation of the optimal compressor function using the first-degree spline functions and quadratic spline functions is done. Coefficients on which we form approximative spline functions are determined by solving equation systems that are formed from treshold conditions. For Gaussian source at the input of the quantizer, using the obtained approximate spline functions a com...

Empirical Mode Decomposition (EMD) has been widely used to analyze non-stationary and nonlinear signal by decomposing data into a series of intrinsic mode functions (IMFs) and a trend function through sifting processes. For lack of a firm mathematical foundation, the implementation of EMD is still empirical and ad hoc. In this paper, we prove mathematically that EMD, as practiced now, only give...

We construct a generalized Cr-Fractal Interpolation Function (Cr-FIF) f by prescribing any combination of r values of the derivatives f (k), k = 1, 2, . . . , r, at boundary points of the interval I = [x0, xN ]. Our approach to construction settles several questions of Barnsley and Harrington [J. Approx Theory, 57 (1989), pp. 14–34] when construction is not restricted to prescribing the values ...