A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Quantum exchange interaction of spherically symmetric plasmoids

We study nano-sized spherically symmetric plasma structures which are radial nonlinear oscillations of electrons in plasma. The effective interaction of these plasmoids via quantum exchange forces between ions is described. We calculate the energy of this interaction for the case of a dense plasma. The conditions when the exchange interaction is attractive are examined and it is shown that separate plasmoids can form a single object. The application of our results to the theoretical description of stable atmospheric plasma structures is considered. (C) 2012 Elsevier Ltd. All rights reserved.

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

Design-based random permutation models with auxiliary information

We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

Mixed-valence state of symmetric diruthenium complexes: synthesis, characterization, and electron transfer investigation

Complexes of the type {[(pyS)Ru(NH3)(4)](2)-mu-L}(n), where pyS = 4-mercaptopyridine, L = 4,4'-dithiodipyridine (pySSpy), pyrazine (pz) and 1,4-dicyanobenzene (DCB), and n = +4 and +5 for fully reduced and mixed-valence complexes, respectively, were synthesized and characterized. Electrochemical data showed that there is electron communication between the metal centers with comproportionation constants of 33.2, 1.30 x 10(8) and 5.56 x 10(5) for L = pySSpy, pz and DCB, respectively. It was also observed that the electronic coupling between the metal centers is affected by the p-back-bonding interaction toward the pyS ligand. Raman spectroscopy showed a dependence of the intensity of the vibrational modes on the exciting radiations giving support to the assignments of the electronic transitions. The degree of electron communication between the metal centers through the bridging ligands suggests that these systems can be molecular wire materials.

Width of buccal and posterior corridors: differences between cases treated with asymmetric and symmetric extractions

OBJECTIVE: To verify if there is difference in the buccal and posterior corridor width in cases treated with extraction of one and four premolars. METHODS: Through posed smile photographs of 23 Class II patients, subdivision, treated with extraction of one premolar and 25 Class I and Class II patients, subdivision, treated with extraction of four premolars, the percentage of buccal and posterior corridor width was calculated. The two protocols of extractions were compared regarding the buccal and posterior corridor width by independent t tests. RESULTS: There was no statistically significant difference on the buccal and posterior corridor widths between patients treated with symmetric and asymmetric extraction. CONCLUSION: The buccal and posterior corridor did not differ between the evaluated protocols of extractions.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.