The factors that underpin heterogeneity in muscle hypertrophy following resistance exercise training (RET) remain largely unknown. We examined circulating hormones, intramuscular hormones, and intramuscular hormone-related variables in resistance-trained men before and after 12 weeks of RET. Backward elimination and principal component regression evaluated the statistical significance of proposed circulating anabolic hormones (e.g., testosterone, free testosterone, dehydroepiandrosterone, dihydrotestosterone, insulin-like growth factor-1, free insulin-like growth factor-1, luteinizing hormone, and growth hormone) and RET-induced changes in muscle mass (n = 49). Immunoblots and immunoassays were used to evaluate intramuscular free testosterone levels, dihydrotestosterone levels, 5α-reductase expression, and androgen receptor content in the highest- (HIR; n = 10) and lowest- (LOR; n = 10) responders to the 12 weeks of RET. No hormone measured before exercise, after exercise, pre-intervention, or post-intervention was consistently significant or consistently selected in the final model for the change in: type 1 cross sectional area (CSA), type 2 CSA, or fat- and bone-free mass (LBM). Principal component analysis did not result in large dimension reduction and principal component regression was no more effective than unadjusted regression analyses. No hormone measured in the blood or muscle was different between HIR and LOR. The steroidogenic enzyme 5α-reductase increased following RET in the HIR (P < 0.01) but not the LOR (P = 0.32). Androgen receptor content was unchanged with RET but was higher at all times in HIR. Unlike intramuscular free testosterone, dihydrotestosterone, or 5α-reductase, there was a linear relationship between androgen receptor content and change in LBM (P < 0.01), type 1 CSA (P < 0.05), and type 2 CSA (P < 0.01) both pre- and post-intervention. These results indicate that intramuscular androgen receptor content, but neither circulating nor intramuscular hormones (or the enzymes regulating their intramuscular production), influence skeletal muscle hypertrophy following RET in previously trained young men.

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Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none for clustering with mixtures of skewed matrix variate distributions. Four finite mixtures of skewed matrix variate distributions are considered. Parameter estimation is carried out using an expectation-conditional maximization algorithm, and both simulated and real data are used for illustration.

Three-way data can be conveniently modelled by using matrix variate distributions.Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix variate distributions that incorporate skewness, as well as other flexible properties such as concentration, are discussed. Equivalences to multivariate analogues are presented, and moment generating functions are derived. Maximum likelihood parameter estimation is discussed, and simulated data is used for illustration.

Abstract. We produce new non-Kähler, non-Einstein, complete expanding gradient Ricci solitons with conical asymptotics and underlying manifold of the form R 2 × M2 × · · · × Mr, where r ≥ 2 and Mi are arbitrary closed Einstein spaces with positive scalar curvature. We also find numerical evidence for complete expanding solitons on the vector bundles whose sphere bundles are the twistor or Sp(1) bundles over quaternionic projective space.Mathematics Subject Classification (2000): 53C25, 53C44 IntroductionIn [BDGW] we constructed complete steady gradient Ricci soliton structures (including Ricci-flat metrics) on manifolds of the form R 2 × M 2 × . . . × M r where M i , 2 ≤ i ≤ r, are arbitrary closed Einstein manifolds with positive scalar curvature. We also produced numerical solutions of the steady gradient Ricci soliton equation on certain non-trivial R 3 and R 4 bundles over quaternionic projective spaces. In the current paper we will present the analogous results for the case of expanding solitons on the same underlying manifolds.Recall that a gradient Ricci soliton is a manifold M together with a smooth Riemannian metric g and a smooth function u, called the soliton potential, which give a solution to the equation:for some constant ǫ. The soliton is then called expanding, steady, or shrinking according to whether ǫ is greater, equal, or less than zero. A gradient Ricci soliton is called complete if the metric g is complete. The completeness of the vector field ∇u follows from that of the metric (cf [Zh]). If the metric of a gradient Ricci soliton is Einstein, then either Hess u = 0 (i.e., ∇u is parallel) or we are in the case of the Gaussian soliton (cf [PW] or [PRS]).At present most examples of non-Kählerian expanding solitons arise from left-invariant metrics on nilpotent and solvable Lie groups (resp. nilsolitons, solvsolitons), as a result of work by J. Lauret [La1], [La3], M. Jablonski [Ja], and many others (cf the survey [La2]). These expanders are however not of gradient type, i.e., they satisfy the more general equationwhere X is a vector field on M and L denotes Lie differentiation.A large class of complete, non-Einstein, non-Kählerian expanders of gradient type (with dimension ≥ 3) consists of an r-parameter family of solutions to (0.1) on R k+1 × M 2 × . . . × M r where k > 1 and M i are positive Einstein manifolds. The special case r = 1 (i.e., no M i ) is due to Bryant [Bry] and the solitons have positive sectional curvature. The r = 2 case is due to Gastel and Kronz [GK], who adapted Böhm's construction of complete Einstein metrics with negative scalar curvature to the soliton case. The case of arbitrary r was treated in [DW3] via a generalization