Parallel bucket sorting on graphics processing units based on convex optimization

We found an interesting relation between convex optimization and sorting problem. We present a parallel algorithm to compute multiple order statistics of the data by minimizing a number of related convex functions. The computed order statistics serve as splitters that group the data into buckets suitable for parallel bitonic sorting. This led us to a parallel bucket sort algorithm, which we implemented for many-core architecture of graphics processing units (GPUs). The proposed sorting method is competitive to the state-of-the-art GPU sorting algorithms and is superior to most of them for long sorting keys.

Review of applications of the Cutting Angle methods

The theory of abstract convexity provides us with the necessary tools for building accurate one-sided approximations of functions. Cutting angle methods have recently emerged as a tool for global optimization of families of abstract convex functions. Their applicability have been subsequently extended to other problems, such as scattered data interpolation. This paper reviews three different applications of cutting angle methods, namely global optimization, generation of nonuniform random variates and multivatiate interpolation.

Solving DC programs using the cutting angle method

In this paper, we propose a new algorithm for global minimization of functions represented as a difference of two convex functions. The proposed method is a derivative free method and it is designed by adapting the extended cutting angle method. We present preliminary results of numerical experiments using test problems with difference of convex objective functions and box-constraints. We also compare the proposed algorithm with a classical one that uses prismatical subdivisions. © 2014 Springer Science+Business Media New York.

A penalty-based aggregation operator for non-convex intervals

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.

Molecular basis of copper transport: cellular and physiological functions of Menkes and Wilson disease proteins (ATP7A and ATPB)

Eukaryotic cells prevent copper-induced, free radical damage to cell components by employing copper-binding proteins and transporters that minimize the likelihood of free copper ions existing in the cell. In the cell, copper is actively transported from the cytoplasm during the biosynthesis of secreted coppercontaining proteins and, as a protective measure, when there is an excess of copper. In humans, this is accomplished by two related copper-transporting ATPases (ATP7A and ATP7B), which are the affected genes in two distinct human genetic disorders of copper transport, Menkes disease (copper deficiency) and Wilson disease (copper toxicosis). The study of these ATPases has revealed their molecular mechanisms of copper transport and their roles in physiological copper homeostasis. Both ATP7A and ATP7B are expressed in specific brain regions and neurological abnormalities are important clinical features in Menkes and Wilson disease.

Comparison of Two Methods for Caluculating the Partition Functions of Various Spatial Statistical Models

Likelihood computation in spatial statistics requires accurate and efficient calculation of the normalizing constant (i.e. partition function) of the Gibbs distribution of the model. Two available methods to calculate the normalizing constant by Markov chain Monte Carlo methods are compared by simulation experiments for an Ising model, a Gaussian Markov field model and a pairwise interaction point field model.

Interpolation of Lipschitz functions

This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.

Density based fuzzy c-means clustering of non-convex patterns

We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-convex shape. We present a modification of the fuzzy c-means algorithm, which uses the data induced metric, defined with the help of Delaunay triangulation. We detail computation of the distances in such a metric using graph algorithms. To find optimal positions of cluster prototypes we employ the discrete gradient method of non-smooth optimization. The new clustering method is capable to identify non-convex overlapped d-dimensional clusters.

Fuzzy clustering of non-convex patterns using global optimization

This paper discusses various extensions of the classical within-group sum of squared errors functional, routinely used as the clustering criterion. Fuzzy c-means algorithm is extended to the case when clusters have irregular shapes, by representing the clusters with more than one prototype. The resulting minimization problem is non-convex and non-smooth. A recently developed cutting angle method of global optimization is applied to this difficult problem

A comparison of search functions and other navigational tools provided on government websites

This paper reports the outcomes of a study that evaluated the effectiveness of search functions compared to other navigational tools available on government websites. The study used an observation exercise triangulated with a post observation interview. Results suggest that while there wasn't any significant difference in effectiveness between search functions and other navigational tools, the skill with which the search function is implemented and participants' familiarity with the website, are fundamental determinants of users' opinions. Implications of the findings for research and practice are discussed.

Convex hulls as an hypothesis language bias

Classification learning is dominated by systems which induce large numbers of small axis-orthogonal decision surfaces which biases such systems towards particular hypothesis types. However, there is reason to believe that many domains have underlying concepts which do not involve axis orthogonal surfaces. Further, the multiplicity of small decision regions mitigates against any holistic appreciation of the theories produced by these systems, notwithstanding the fact that many of the small regions are individually comprehensible. We propose the use of less strongly biased hypothesis languages which might be expected to model' concepts using a number of structures close to the number of actual structures in the domain. An instantiation of such a language, a convex hull based classifier, CHI, has been implemented to investigate modeling concepts as a small number of large geometric structures in n-dimensional space. A comparison of the number of regions induced is made against other well-known systems on a representative selection of largely or wholly continuous valued machine learning tasks. The convex hull system is shown to produce a number of induced regions about an order of magnitude less than well-known systems and very close to the number of actual concepts. This representation, as convex hulls, allows the possibility of extraction of higher level mathematical descriptions of the induced concepts, using the techniques of computational geometry.

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the computer enumeration of bent functions by Meng et al.

Determination of yield and erosion damage functions using subjectively elicited data: application to small holder tea in Sri Lanka

Tea has been Sri Lanka's major export earner for several decades. However, soil erosion on tea-producing land has had considerable on-site and off-site effects. This study quantifies soil erosion impacts for smallholder tea farms in Sri Lanka by estimating a yield damage function and an erosion damage function using a subjective elicitation technique. The Mitscherlich-Spillman type of function was found to yield acceptable results. The study indicates that high rates of soil erosion require earlier adoption of soil conservation measures than do low rates of erosion. Sensitivity analysis shows the optimum year to change to a conservation practice is very sensitive to the discount rate but less sensitive to the cost of production and price of tea.