Computation of Spatial Covariance Matrices

In an earlier article, Ghosh derived the density for the distance between two points uniformly and independently distributed in a rectangle. This article extends that work to include the case where the two points lie in two different rectangles in a lattice. This density allows one to find the expected value of certain functions of this distance between rectangles analytically or by one-dimensional numerical integration.

In the case of isotropic spatial models or spatial models with geometric anisotropy terms for agricultural experiments one can use these theoretical results to compute the covariance between the yields in different rectangular plots. As the numerical integration is one-dimensional these results are computed quickly and accurately. The types of covariance functions used come from the Matérn and power families of processes. Analytic results are derived for the de Wijs process, a member of both families and for the power models also.

Software in R is available. Examples of the code are given for fitting spatial models to the Fairfield Smith data. Other methods for the estimation of the covariance matrices are discussed and their pros and cons are outlined.     

Bayesian Multiscale Smoothing for Making Inferences About Features in Scatterplots

A rather common problem of data analysis is to find interesting features, such as local minima, maxima, and trends in a scatterplot. Variance in the data can then be a problem and inferences about features must be made at some selected level of significance. The recently introduced SiZer technique uses a family of nonparametric smooths of the data to uncover features in a whole range of scales. To aid the analysis, a color map is generated that visualizes the inferences made about the significance of the features. The purpose of this article is to present Bayesian versions of SiZer methodology. Both an analytically solvable regression model and a fully Bayesian approach that uses Gibbs sampling are presented. The prior distributions of the smooths are based on a roughness penalty. Simulation based algorithms are proposed for making simultaneous inferences about the features in the data.     

Biclustering Three-Dimensional Data Arrays With Plaid Models

Three-dimensional data arrays (collections of individual data matrices) are increasingly prevalent in modern data and pose unique challenges to pattern extraction and visualization. This article introduces a biclustering technique for exploration and pattern detection in such complex structured data. The proposed framework couples the popular plaid model together with tools from functional data analysis to guide the estimation of bicluster responses over the array. We present an efficient algorithm that first detects biclusters that exhibit strong deviations for some data matrices, and then estimates their responses over the entire data array. Altogether, the framework is useful to home in on and display underlying structure and its evolution over conditions/time. The methods are scalable to large datasets, and can accommodate a variety of dynamic patterns. The proposed techniques are illustrated on gene expression data and bilateral trade networks. Supplementary materials are available online.     

Consciousness and the structuring property of typical data

The theoretical base for consciousness, in particular, an explanation of how consciousness is defined by the brain, has long been sought by science. We propose a partial theory of consciousness as relations defined by typical data. The theory is based on the idea that a brain state on its own is almost meaningless but in the context of the typical brain states, defined by the brain's structure, a particular brain state is highly structured by relations. The proposed theory can be applied and tested both theoretically and experimentally. Precisely how typical data determines relations is fully established using discrete mathematics. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Cost efficiency measures in data envelopment analysis with data uncertainty

This paper extends the classical cost efficiency (CE) models to include data uncertainty. We believe that many research situations are best described by the intermediate case, where some uncertain input and output data are available. In such cases, the classical cost efficiency models cannot be used, because input and output data appear in the form of ranges. When the data are imprecise in the form of ranges, the cost efficiency measure calculated from the data should be uncertain as well. So, in the current paper, we develop a method for the estimation of upper and lower bounds for the cost efficiency measure in situations of uncertain input and output data. Also, we develop the theory of efficiency measurement so as to accommodate incomplete price information by deriving upper and lower bounds for the cost efficiency measure. The practical application of these bounds is illustrated by a numerical example.     

Loss and Noise Characteristics of Microwave Direct Modulated Optical Links

Loss and noise figure of optical links transmitting microwave signals —e.g. for remote antennas in wireless communications — are dealt with.Conditions are rather general and include arbitrary matching conditions, shotnoise, and laser relative intensity noise. Specific and somewhat surprisingcharacteristics are derived. Among others, it is shown, that — likepassive, purely microwave systems — noise figure is not proportional toelectrical loss and it can be even lower than loss itself. Optical powershould be as low as possible — this limit is mainly determined by therequired dynamic range of the system. Loss and noise figure were measured inan experimental setup. Results of the measurements proved the theoreticalfindings rather well. Preliminary results on the transmission of 32TCM signalsover the link are briefly presented.     

Enthalpies of Formation of the Tellurites of the Rare Earths Gd, Tb, Dy, Tm and Yb

By using a DSK of the French firm Seteram, the standard enthalpies of formation of 5 tellurites and 5 tetratellurites of the rare earths Gd, Tb, Dy, Tm and Yb were determined for the first time. Three parallel determinations for each sample were compared. The results are very similar, which is an indication of the great reliability of the method used and the correctness of the data obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

On Spectrum Congestion and Capacity of Radio Links

This paper addresses the operation of radio links under mutual interference conditions, an important problem in spectrum management and radio link design. It introduces the capacity loss and isolation index as measures of effective use of radio links and radio frequency spectrum resources.     

Dynamic data structures for fat objects and their applications

We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in or . Our planar structures are actually fitted for a more general class of objects – (β,δ)-covered objects – which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.