Fuzzy functional dependency (FFD) is a kind of semantic knowledge and can be discovered from a large volume of business data. Sectional FFD and Attribute FFD are discussed so as to reflect semantics of the business world and express useful information that is natural for people to comprehend. The experimental results on an insurance data set show that the proposed method can extract knowledge e...

Spherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analys...

In this paper we will discuss the version of the Fourier analysis and pseudodifferential operators on the torus. Using the toroidal Fourier transform we will show several simplifications of the standard theory. We will also discuss the corresponding toroidal version of Fourier integral operators. To distinguish them from those defined using the Euclidean Fourier transform, we will call them Fou...

A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measu...

In the two space dimensions of screens in optical systems, rotations, gyrations, and fractional Fourier transformations form the Fourier subgroup of the symplectic group of linear canonical transformations: U(2)F⊂Sp(4,R). Here, we study the action of this Fourier group on pixelated images within generic rectangular Nx×Ny screens; its elements here compose properly and act unitarily, i.e., witho...

This work introduces novel duality relations that allow one to identify classical ground states of soft many-particle interactions using the ground states of the dual (Fourier-transformed) potentials. For potentials with the same functional form under Fourier transform, one can analytically relate the low-and high-density ground state energies and confi gurations. Bounded interactions are parti...

This paper provides an overview of recent econometric advances on testing of functional form with semiparametric methods and their application to the estimation of the environmental Kuznets curve (EKC). The EKC in environmental economics is estimated using panel data models and provides a fertile ground for the adoption of recent panel data developments. The paper provides a discussion of recen...

Estimation of flexible functional forms for large consumer or producer demand systems is often precluded due to computational difficulties or due to a lack of degrees of freedom. We propose the concept of a semiflexible form, which is a special case of a flexible form but which requires fewer free parameters. Our proposed method of estimation allows the researcher to choose the degree of flexib...

In most event history models, the effect of a covariate on the hazard is assumed to have a log-linear functional form. For continuous covariates, this assumption is often violated as the effect is highly nonlinear. Assuming a log-linear functional form when the nonlinear form applies causes specification errors leading to erroneous statistical conclusions. Scholars can, instead of ignoring the ...

Parsimonious regression models using locational data often yield non-normal, heteroskedastic, and spatially dependent residuals. This manuscript develops a model which simultaneously performs spatial and functional form transformations to mitigate these problems. We apply the model to 11,006 observations on housing prices in Baton Rouge. For these data, the model reduces the interquartile range...