Maximum packings of K-v-K-u with triples

We construct, for all positive integers u, and v with u less than or equal to v, a decomposition of K-v - K-u (the complete graph on v vertices with a. hole of size u) into the maximum possible number of edge disjoint triangles.

The intersection problem for K_4-e designs

A G-design of order n is a pair (P,B) where P is the vertex set of the complete graph K-n and B is an edge-disjoint decomposition of K-n into copies of the simple graph G. Following design terminology, we call these copies ''blocks''. Here K-4 - e denotes the complete graph K-4 with one edge removed. It is well-known that a K-4 - e design of order n exists if and only if n = 0 or 1 (mod 5), n greater than or equal to 6. The intersection problem here asks for which k is it possible to find two K-4 - e designs (P,B-1) and (P,B-2) of order n, with \B-1 boolean AND B-2\ = k, that is, with precisely k common blocks. Here we completely solve this intersection problem for K-4 - e designs.

Hyperplane navigation: A method to set individual scores in fMRI group datasets

Recent studies have demonstrated that spatial patterns of fMRI BOLD activity distribution over the brain may be used to classify different groups or mental states. These studies are based on the application of advanced pattern recognition approaches and multivariate statistical classifiers. Most published articles in this field are focused on improving the accuracy rates and many approaches have been proposed to accomplish this task. Nevertheless, a point inherent to most machine learning methods (and still relatively unexplored in neuroimaging) is how the discriminative information can be used to characterize groups and their differences. In this work, we introduce the Maximum Uncertainty Linear Discrimination Analysis (MLDA) and show how it can be applied to infer groups` patterns by discriminant hyperplane navigation. In addition, we show that it naturally defines a behavioral score, i.e., an index quantifying the distance between the states of a subject from predefined groups. We validate and illustrate this approach using a motor block design fMRI experiment data with 35 subjects. (C) 2008 Elsevier Inc. All rights reserved.

COMBINATION OFGENERAL AND SPECIFICWARM-UPS IMPROVES LEG-PRESS ONE REPETITION MAXIMUM COMPARED WITH SPECIFIC WARM-UP IN TRAINED INDIVIDUALS

Abad, CCC, Prado, ML, Ugrinowitsch, C, Tricoli, V, and Barroso, R. Combination of general and specific warm-ups improves leg-press one repetition maximum compared with specific warm-up in trained individuals. J Strength Cond Res 25(8): 2242-2245, 2011-Accurate assessment of muscular strength is critical for exercise prescription and functional evaluation. The warm-up protocol may affect the precision of the 1 repetition maximum (1RM) test. Testing guidelines recommend performing both general and specific warm-ups before strength tests. The general warm-up intends to raise muscle temperature, whereas the specific warm-up aims to increase neuromuscular activation. Although there is scientific evidence for performing the specific warm-up, the effects of general warm-up on strength tests are still unclear. The purpose of this study was to investigate whether the combination of a general with a specific warm-up (G + SWU) protocol would improve leg press 1RM values compared with a specific warm-up (SWU) protocol. Thirteen participants were tested for leg-press 1RM under 2 warm-up conditions. In the first condition, participants performed the SWU only, which was composed of 1 set of 8 repetitions at approximately 50% of the estimated 1RM followed by another set of 3 repetitions at 70% of the estimated 1RM. In the second condition (G + SWU), participants performed the 1RM test after a 20-minute general warm-up on a stationary bicycle at 60% of HRmax and the same specific warm-up as in the SWU. Values of 1RM in SWU and in G + SWU were compared by a paired t-test, and significance level was set at p <= 0.05. Strength values were on average 8.4% (p = 0.002) higher in the G + SWU compared with the SWU. These results suggest that the G + SWU induced temperature-dependent neuromuscular adjustments that increased muscle force production capacity. Therefore, these results support the recommendations of the testing guidelines to perform a moderate intensity general warm-up in addition to the specific warm-up before maximum strength assessments.

The application of adaptive partitioned random search in feature selection problem

Feature selection is one of important and frequently used techniques in data preprocessing. It can improve the efficiency and the effectiveness of data mining by reducing the dimensions of feature space and removing the irrelevant and redundant information. Feature selection can be viewed as a global optimization problem of finding a minimum set of M relevant features that describes the dataset as well as the original N attributes. In this paper, we apply the adaptive partitioned random search strategy into our feature selection algorithm. Under this search strategy, the partition structure and evaluation function is proposed for feature selection problem. This algorithm ensures the global optimal solution in theory and avoids complete randomness in search direction. The good property of our algorithm is shown through the theoretical analysis.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

On the Oberwolfach problem with two similar length cycles

For all in greater than or equal to 3, the Oberwolfach problem is solved for the case where the 2-factors consist of two cycles of lengths in and m + 1, and for the case where the 2-factors consist of two cycles of lengths m and m + 2.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

On the Hamilton-Waterloo problem

The Hamilton-Waterloo problem asks for a 2-factorisation of K-v in which r of the 2-factors consist of cycles of lengths a(1), a(2),..., a(1) and the remaining s 2-factors consist of cycles of lengths b(1), b(2),..., b(u) (where necessarily Sigma(i)(=1)(t) a(i) = Sigma(j)(=1)(u) b(j) = v). In thus paper we consider the Hamilton-Waterloo problem in the case a(i) = m, 1 less than or equal to i less than or equal to t and b(j) = n, 1 less than or equal to j less than or equal to u. We obtain some general constructions, and apply these to obtain results for (m, n) is an element of {(4, 6)1(4, 8), (4, 16), (8, 16), (3, 5), (3, 15), (5, 15)}.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

The GP problem: quantifying gene-to-phenotype relationships

In this paper we refer to the gene-to-phenotype modeling challenge as the GP problem. Integrating information across levels of organization within a genotype-environment system is a major challenge in computational biology. However, resolving the GP problem is a fundamental requirement if we are to understand and predict phenotypes given knowledge of the genome and model dynamic properties of biological systems. Organisms are consequences of this integration, and it is a major property of biological systems that underlies the responses we observe. We discuss the E(NK) model as a framework for investigation of the GP problem and the prediction of system properties at different levels of organization. We apply this quantitative framework to an investigation of the processes involved in genetic improvement of plants for agriculture. In our analysis, N genes determine the genetic variation for a set of traits that are responsible for plant adaptation to E environment-types within a target population of environments. The N genes can interact in epistatic NK gene-networks through the way that they influence plant growth and development processes within a dynamic crop growth model. We use a sorghum crop growth model, available within the APSIM agricultural production systems simulation model, to integrate the gene-environment interactions that occur during growth and development and to predict genotype-to-phenotype relationships for a given E(NK) model. Directional selection is then applied to the population of genotypes, based on their predicted phenotypes, to simulate the dynamic aspects of genetic improvement by a plant-breeding program. The outcomes of the simulated breeding are evaluated across cycles of selection in terms of the changes in allele frequencies for the N genes and the genotypic and phenotypic values of the populations of genotypes.

Quasiequilibrium problem in H-spaces

In the present paper, we study the quasiequilibrium problem and generalized quasiequilibrium problem of generalized quasi-variational inequality in H-spaces by a new method. Some new equilibrium existence theorems are given. Our results are different from corresponding given results or contain some recent results as their special cases. (C) 2003 Elsevier Science Ltd. All rights reserved.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.