Variograms and covariance functions are key tools in geostatistics. However, various properties, characterizations, and decomposition theorems have been established for covariance functions only. We present analogous results for variograms and explore the connections to covariance functions. Our ndings include criteria for covariance functions on intervals, and we apply them to exponential mode...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical N P-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a ...

We have theoretically proved the Liu-Wei’s closedform formula for computing the coefficients of onedimensional (1-D) variable fractional-delay (VFD) finiteimpulse-response (FIR) digital filter derived from N -th order interpolating polynomial. In this paper, we extend the 1-D VFD filter design to the two-dimensional (2-D) case and show that the image interpolation using VFD filtering can achiev...

Stability and performance of a system can be inferred from the evolution of statistical characteristic (i.e. mean, variance...) of system states. The polynomial chaos of Wiener provides a computationally effective framework for uncertainty quantification of stochastic dynamics in terms of statistical characteristic. In this work, polynomial chaos is used for uncertainty quantification of fracti...

Unit disk graphs are the intersection graphs of equal sized circles in the plane. In this paper, we consider the maximum independent set problems on unit disk graphs. When the given unit disk graph is de ned on a slab whose width is k, we propose an algorithm for nding a maximum independent set in O(n 4 d 2k= p 3 e ) time where n denotes the number of vertices. We also propose a (1 1=r)-approxi...

BACKGROUND There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). METHODS We related parental social class to height from birth to ...

In this paper we introduce a polynomial filter structure for filterand-sum beamforming applied to microphone array application. The structure is a multi-dimensional extension of well-known Farrow structure, which has mainly been used for fractional delay filtering and interpolation of 1-D signals. The proposed method enables an easy, smooth, and efficient control of beamforming filter character...

Canonical duality theory is a potentially powerful methodology, which can be used to solve a wide class of discrete and continuous global optimization problems. This paper presents a brief review and recent developments of this theory with applications to some well-know problems including polynomial minimization, mixed integer and fractional programming, nonconvex minimization with nonconvex qu...

Data analysts are often faced with many covariates and a suitable model for explanation requires the selection of a subset of variables with a relevant influence on the outcome. For continuous variables it is important to determine a suitable function which fits the data well. We will introduce the basic concept and philosophy of the multivariable fractional polynomial (MFP) approach, which tac...

We study the surface defect in $\mathcal{N}=2^*$ $U(N)$ gauge theory four dimensions and its relation to quantum Hall states two dimensions. first prove that partition function becomes Jack polynomial of variables describing brane positions by imposing Higgsing condition taking bulk decoupling limit. Further tuning adjoint mass parameter, we may obtain various fractional states, including Laugh...