In [7], Greene introduced the notion of general hypergeometric series over finite fields or Gaussian hypergeometric series, which are analogous to classical hypergeometric series. The motivation for his work was to develop the area of character sums and their evaluations through parallels with the theory of hypergeometric functions. The basis for this parallel was the analogy between Gauss sums...

The main purpose of this paper consists of demonstrating advantages of using implicit filtering schemes (noncausal IIR filters, in the signal processing language) for some basic image processing and geometric modeling applications. In particular, applications of implicit filtering for curve subdivision, image filtering, estimating image derivatives, and deblurring Gaussian blur are considered.

We present a framework for modeling right-hand gestures in bowed-string instrument playing, applied to violin. Nearly non-intrusive sensing techniques allow for accurate acquisition of relevant timbre-related bowing gesture parameter cues. We model the temporal contour of bow transversal velocity, bow pressing force, and bow-bridge distance as sequences of short segments, in particular Bézier c...

In spite of the interest in and appeal of convolution-based approaches for nonstationary spatial modeling, off-the-shelf software for model fitting does not as of yet exist. Convolution-based models are highly flexible yet notoriously difficult to fit, even with relatively small data sets. The general lack of pre-packaged options for model fitting makes it difficult to compare new methodology i...

We consider two Gaussian measures. In the "initial" measure the state variable is Gaussian, with zero drift, and time-varying volatility. In the "target measure" the state variable follows an Ornstein-Uhlenbeck process, with a free set of parameters, namely the time-varying speed of mean-reversion. We look for the speed of mean reversion that minimizes the variance of the Radon-Nikodym derivati...

We calculate the two-, threeand (for the first time) four-point correlation functions of the COBE -DMR 4-year sky maps, and search for evidence of non-Gaussianity by comparing the data to Monte Carlo-simulations of the functions. The analysis is performed for the 53 and 90 GHz channels, and five linear combinations thereof. For each map, we simulate an ensemble of 10 000 Gaussian realisations b...

introduction: nowadays,  considerable developments  in  the field  of  radiotherapy have  been  achieved.  they  include  the  advances  made  in  the  equipments  and  treatment  planning  techniques  which  require  highly complex calculations. such achievements have made it possible to treat cancer patients not only  with  higher  radiation  dose  but  also  with  higher  precision  and  con...

We propose a formalism for estimating the skewness and angular power spectrum of a general Cosmic Microwave Background data set. We use the Edgeworth Expansion to define a non-Gaussian likelihood function that takes into account the anisotropic nature of the noise and the incompleteness of the sky coverage. The formalism is then applied to estimate the skewness of the publicly available 4 year ...

FamilySearch captures millions of digital images annually using digital cameras at sites throughout the world. The top image quality problem encountered during this image capture process is blurriness due to an out of focus camera and/or motion during capture. Several automatic measurements of digital image blur exist, but have been found to not be very accurate at correctly classifying blurry ...

In numerous contexts, one has to forecast a full curve from some explanatory variables. For that purpose, one aims at deriving simultaneous confidence bands. In this article theoretical and numerical results on the maximum of Gaussian sequences are used to construct those simultaneous confidence bands.