Levene tests of homogeneity of variance for general block and treatment designs

This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plot.

A subset-oriented algorithm for minimizing the number of steps required for synthesis of cyclic-peptide libraries

Libraries of cyclic peptides are being synthesized using combinatorial chemistry for high throughput screening in the drug discovery process. This paper describes the min_syn_steps.cpp program (available at http://www.imb.uq.edu.au/groups/smythe/tran), which after inputting a list of cyclic peptides to be synthesized, removes cyclic redundant sequences and calculates synthetic strategies which minimize the synthetic steps as well as the reagent requirements. The synthetic steps and reagent requirements could be minimized by finding common subsets within the sequences for block synthesis. Since a brute-force approach to search for optimum synthetic strategies is impractically large, a subset-orientated approach is utilized here to limit the size of the search. (C) 2002 Elsevier Science Ltd. All rights reserved.

The effects of level of dietary protein on the milk production and rumen physiology of dairy cows fed a diet based on a tropical grass hay

zFour rumen-fistulated, multiparous Holstein-Friesian cows in early lactation were offered mixed diets based on rhodes grass hay (Chloris gayana) cv. Callide containing 13, 14, 15 or 16% crude protein (CP) on a dry matter basis, in a 4 x 4 latin square design. The estimated undegradable protein concentration in these diets was similar with rumen degradable protein concentration varying. Cows fed a diet containing 13% CP had lower (P = 0.07) milk yields than cows in other treatments (20.4 vs 21.9, 22.0 and 22.2 L/d for 13, 14, 15 and 16% CP, respectively). A positive linear relationship was found (P = 0.06) between organic matter intake and dietary CP%. There were negative linear relationships between dietary CP% and digestibilities of dry matter (P = 0.09), organic matter (P = 0.06) and neutral detergent fibre (P = 0.02). Feeding a diet containing 13% CP resulted in significantly lower (P = 0.001) molar proportions (%) of rumen valerate in comparison with other treatments. The molar proportions of isovalerate differed (P = 0.001) between treatments (0.66, 0.78, 0.89 and 1.04%) for 13, 14, 15 and 16% CP, respectively). Dietary protein level had no effect on rates of passage, in situ digestion of rhodes grass hay or ratios of allantoin: creatinine in urine. These data showed that increasing the dietary CP concentration of lactating cows fed diets based on rhodes grass hay increased intakes and not significantly improved at dietary CP concentrations above 14% DM.

EMG activity normalization for trunk muscles in subjects with and without back pain

Purpose: The aims of the present study were to examine electromyographic (EMG) activity of six bilateral trunk muscles during maximal contraction in three cardinal planes, and to determine the direction of contraction that gives maximal activation for each muscle. both for healthy subjects and back-pain patients. Methods: Twenty-eight healthy subjects and 15 back-pain patients performed maximum voluntary contractions in three cardinal planes, Surface EMG signals were recorded from rectus abdominis, external oblique, internal oblique, latissimus dorsi, iliocostalis lumborum, and multifidus bilaterally. Root mean square values of the EMG data were calculated to quantify I the amplitude of EMG signals. Results: For both healthy subjects and back-pain patients. one single direction of contraction was found to give the maximum EMG signals for most muscles. Rectus abdominis demonstrated maximal activity in trunk flexion, external oblique in lateral flexion. internal oblique in axial rotation, and multifidus in extension. For the latissimus dorsi and iliocostalis lumborum. maximal activity was demonstrated in more than one cardinal plane. Conclusion: This study has implications for future research involving normalization of muscle activity to maximal levels required in many trunk EMG studies. As the latissimus dorsi and iliocostalis lumborum demonstrate individual differences in the plane that gives maximal activity, these muscles may require testing in more than one plane.

On the volume of 4-cycle trades

A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two collections of 4-cycles have no 4-cycles in common. The foundation of the trade is v = \V(G)\. This paper determines for which values oft and a there exists a 4-cycle trade of volume t and foundation v.

An electromyographic analysis of the deep cervical flexor muscles in performance of craniocervical flexion

Background and Purpose. This study evaluated an electromyographic technique for the measurement of muscle activity of the deep cervical flexor (DCF) muscles. Electromyographic signals were detected from the DCF, sternocleidomastoid (SCM), and anterior scalene (AS) muscles during performance of the craniocervical flexion (CCF) test, which involves performing 5 stages of increasing craniocervical flexion range of motion-the anatomical action of the DCF muscles. Subjects. Ten volunteers without known pathology or impairment participated in this study. Methods. Root-mean-square (RMS) values were calculated for the DCF, SCM, and AS muscles during performance of the CCF test. Myoelectric signals were recorded from the DCF muscles using bipolar electrodes placed over the posterior oropharyngeal wall. Reliability estimates of normalized RMS values were obtained by evaluating intraclass correlation coefficients and the normalized standard error of the mean (SEM). Results. A linear relationship was evident between the amplitude of DCF muscle activity and the incremental stages of the CCF test (F=239.04, df=36, P<.0001). Normalized SEMs in the range 6.7% to 10.3% were obtained for the normalized RMS values for the DCF muscles, providing evidence of reliability for these variables. Discussion and Conclusion. This approach for obtaining a direct measure of the DCF muscles, which differs from those previously used, may be useful for the examination of these muscles in future electromyographic applications.

The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.

More on exact bicoverings of 12 points

The minimum number of incomplete blocks required to cover, exactly lambda times, all t-element subsets from a set V of cardinality v (v > t) is denoted by y(lambda, t; v). The value of g(2, 2; v) is known for v = 3, 4,..., 11. It was previously known that 14 less than or equal to g(2, 2; 12) less than or equal to 16. We prove that g(2, 2; 12) greater than or equal to 15.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).