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We present algorithms for finding the diameter, centroid(s), and median(s) for tree structured networks subject to transient faults. In our solutions, the system reaches its final correct configuration in a finite time after the faults cease. The fault-tolerance is achieved using Dijkstra's paradigm of self-stabilization. A self-stabilizing algorithm, regardless of the initial system configuration, converges, in finite time, to a set of legitimate configurations.

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though, leading us to consider the implications of using realistic probes in defining an effective spacetime geometry. As an example, we consider de Sitter spacetime and employ the centroid of various composite probes to obtain its effective sectional curvature, which is found to depend on the probe's internal energy, spatial extension, and spin. Possible refinements of our approach are pointed out and remarks are made on the relevance of our results to the quest for a quantum theory of gravity.

Differential Evolution (DE) is a population-based Evolutionary Algorithm (EA) for solving optimization problems over continuous spaces. Many optimization problems are constrained and have a bounded search space from which some vectors leave when the mutation operator of DE is applied. Therefore, it is necessary the use of a boundary constraint-handling method (BCHM) in order to repair the invalid mutant vectors. This paper presents a generalized and improved version of the Centroid BCHM in order to keep the search within the valid ranges of decision variables in constrained numerical optimization problems (CNOPs), which has been tested on a robust and comprehensive set of experiments that include a variant of DE specialized in dealing with CNOPs. This new version, named Centroid$K+1$, relocates the mutant vector in the centroid formed by K random vectors and one vector taken from the population that is within or near the feasible region. The results show that this new version has a major impact on the algorithm’s performance, and it is able to promote better final results through the improvement of both, the approach to the feasible region and the ability to generate better solutions.

Sharing data to a third party for the mutual benefit of the data owners plays a vital need in all computer applications. Ensuring the privacy of sensitive data is an important issue in data sharing and hence there is a need for privacy preserving data mining algorithms. Traditional privacy preserving algorithms are prone to attacks, have high information loss and sometimes fail to achieve the privacy constraints. In this paper, a (G,S) clustering algorithm is proposed to achieve clusters each with S diverse sensitive values for the sensitive attribute. The number of distinct sensitive values in each cluster would be exactly equal to the number of sensitive values in the given data set. The clusters’ formed are anonymized by replacing the actual values with the centroid(G) of the cluster. The algorithm achieves the maximum possible diverse sensitive values in each cluster making it resilient to similarity attack. The method guarantees high degree of privacy with very minimal loss of information. The privacy degree of the clusters formed is at least equal to the number of distinct values in the sensitive attribute. The worst case linking probability would be as low as 0.5. The significance of this algorithm is its resilience to similarity attack. The performance of the algorithm is proved to be better than the existing algorithms in terms of KL Divergence, Discernibility metric and few other metrics.

The existence of nondegenerate invariant bilinear forms is one of the most important tools in the study of Kac–Moody Lie algebras and extended affine Lie algebras. In practice, these forms are created, or shown to exist, either by assumption or in an ad hoc basis. The purpose of this work is to describe the nature of the space of invariant bilinear forms of certain algebras given by faithfully flat descent (which includes the affine Kac–Moody Lie algebras, as well as Azumaya algebras and multiloop algebras) within a functorial framework. This will allow us to conclude the existence, uniqueness and nature of invariant bilinear forms for many important classes of algebras.

An analytical model for double-gate (DG) MOSFETs considering quantum mechanical effects is proposed in this paper. Schrödinger and Poisson's equations are solved simultaneously using a variational approach. Solving the Poisson and Schrödinger equations simultaneously reveals quantum effects (QME) that influence the performance of DG MOSFETs. This model is developed to provide an analytical expression for inversion charge distribution function for all regions of device operation. This expression is used to calculate the other important parameters like inversion layer centroid, inversion charge, gate capacitance, drain current and transconductance. We systematically evaluate and analyze the parameters of DG MOSFETs considering QME. The analytical solutions are simple, accurate and provide good physical insight into the quantization caused by quantum confinement under various gate biases. The analytical results of this model are verified by comparing the data obtained with one-dimensional self-consistent numerical solutions of Poisson and Schrödinger equations known as SCHRED.

The chains of ideals of differentiably simple (non-associative) color algebras and those of their centroids are studied. It is proved that for any finite-dimensional differentiably simple (non-associative) color algebra A and any set D of its color derivations, A is D-simple if and only if its centroid 𝙲(A) is D*-simple, where 𝙲(A) is a unitary ∊-commutative associative color algebra, and D* is the set of the color derivations determined by D.

This is a survey of methods of proving or disproving the rapid decay property in groups. We present a centroid property of group actions on metric spaces. That property is a generalized (and corrected) version of the "(**)-relative hyperbolicity" from [9] and implies the rapid decay (RD) property. We show that several properties which are known to imply RD also imply the centroid property. Thus uniform lattices in many semi-simple Lie groups, graph products of groups, Artin groups of large type and the mapping class groups have the (relative) centroid property. We also present a simple "non-amenability-like" property that follows from RD, and give an easy example of a group without RD and without any amenable subgroup with superpolynomial growth.

Consider a Hom–Lie superalgebra, denoted by ${𝒯}$. In this paper, we inquire the Lie triple derivation $hTDer({𝒯})$ and generalized Lie triple derivation $hGTDer({𝒯})$ of Hom–Lie superalgebra. Later, we address the triple centroid, triple quasi-centroid and central triple derivations of Hom–Lie superalgebra. Moreover, we attempt to show the relationship of triple centroid, triple quasi-centroid and central triple derivation with $hTDer({𝒯})$ and $hGTDer({𝒯})$. We give complete classification of triple derivations of Hom–Lie superalgebra, where we show that for the simple Hom–Lie superalgebras $hTDer({𝒯})=hDer({𝒯})$.

In this paper, the tilt correction of computerized tomography (CT) and magnetic resonance (MR) medical images is the main point of interest. The centroid of the medical subimage is calculated, and the rotation angle α is obtained by separately using two methods: singular value decomposition (SVD) and principal component analysis (PCA), respectively. In addition, the whole medical image is rotated around the centroid by -α to correct the tilt. Based on this, according to the uniformity of the medical subimage the rotation angle α is further adjusted, which achieves better correction effect and performance. The experimental results show that the correction effect of SVD is the same as that of PCA, the proposed methods are fairly reliable and accurate for the determination of tilt angles, and are practical and effective tilt correction techniques. In addition, the correction methods are regarded as the preprocesses of image registration, and hence are used to get the registering parameters by incorporating the pattern search method. The experimental results reveal that they can significantly reduce the computational load, accurately get transformation parameters, and overcome the problem of easily getting into the local optimum.

Nodes localization problem now has became the core of the problems in agricultural wireless sensor network. In this paper, according to the characteristics of agricultural application, an improved algorithm is proposed based on DV-Hop algorithm and some existed improved algorithms. The algorithm joins a new anchor nodes selection strategy in the localization stage and locates nodes by the idea of weighted centroid. The simulation results show that the new algorithm improves the localization accuracy and has lower energy cost and better stability.