On the roots of matrices.

Reprinted from the American journal of mathematics, v.14.

Muestras de los nuevos punzones y matrices para la letra de imprenta executados por orden de S.M. y de su caudal destinado a la dotacion de su Real Biblioteca.

Palau,

Multivariate analyses of variance and covariance for simulation studies involving normal time series

Photocopy.

Theory of matrices.

Mode of access: Internet.

Eddy covariance and environmental data of boreal bogs plant species

In boreal bogs plant species are low in number, but they differ greatly in their growth forms and photosynthetic properties. We assessed how ecosystem carbon (C) sink dynamics were affected by seasonal variations in photosynthetic rate and leaf area of different species. Photosynthetic properties (light-response parameters), leaf area development and areal cover (abundance) of the species were used to quantify species-specific net and gross photosynthesis rates (PN and PG, respectively), which were summed to express ecosystem-level PN and PG. The ecosystem-level PG was compared with a gross primary production (GPP) estimate derived from eddy covariance measurements (EC). Species areal cover rather than differences in photosynthetic properties determined the species with the highest PG of both vascular plants and Sphagna. Species-specific contributions to the ecosystem PG varied over the growing season, which in turn determined the seasonal variation in ecosystem PG. The upscaled growing-season PG estimate, 230 g C/m**2, agreed well with the GPP estimated by the EC, 243 g C/m**2. Sphagna were superior to vascular plants in ecosystem-level PG throughout the growing season but had a lower PN. PN results indicated that areal cover of the species together with their differences in photosynthetic parameters shape the ecosystem-level C balance. Species with low areal cover but high photosynthetic efficiency appear to be potentially important for the ecosystem C sink. Results imply that functional diversity may increase the stability of C sink of boreal bogs.

Thermal characterization of polyester-melamine coating matrices prepared under nonisothermal conditions

Thermal analysis methods (differential scanning calorimetry, thermogravimetric analysis, and dynamic mechanical thermal analysis) were used to characterize the nature of polyester-melamine coating matrices prepared under nonisothermal, high-temperature, rapid-cure conditions. The results were interpreted in terms of the formation of two interpenetrating networks with different glass-transition temperatures (a cocondensed polyester-melamine network and a self-condensed melamine-melamine network), a phenomenon not generally seen in chemically similar, isothermally cured matrices. The self-condensed network manifested at high melamine levels, but the relative concentrations of the two networks were critically dependent on the cure conditions. The optimal cure (defined in terms of the attainment of a peak metal temperature) was achieved at different oven temperatures and different oven dwell times, and so the actual energy absorbed varied over a wide range. Careful control of the energy absorption, by the selection of appropriate cure conditions, controlled the relative concentrations of the two networks and, therefore, the flexibility and hardness of the resultant coatings. (C) 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Cbem 41: 1603-1621, 2003.

The genetic covariance among clinal environments after adaptation to an environmental gradient in Drosophila serrata

We examined the genetic basis of clinal adaptation by determining the evolutionary response of life-history traits to laboratory natural selection along a gradient of thermal stress in Drosophila serrata. A gradient of heat stress was created by exposing larvae to a heat stress of 36degrees for 4 hr for 0, 1, 2, 3, 4, or 5 days of larval development, with the remainder of development taking place at 25degrees. Replicated lines were exposed to each level of this stress every second generation for 30 generations. At the end of selection, we conducted a complete reciprocal transfer experiment where all populations were raised in all environments, to estimate the realized additive genetic covariance matrix among clinal environments in three life-history traits. Visualization of the genetic covariance functions of the life-history traits revealed that the genetic correlation between environments generally declined as environments became more different and even became negative between the most different environments in some cases. One exception to this general pattern was a life-history trait representing the classic trade-off between development time and body size, which responded to selection in a similar genetic fashion across all environments. Adaptation to clinal environments may involve a number of distinct genetic effects along the length of the cline, the complexity of which may not be fully revealed by focusing primarily on populations at the ends of the cline.

Orientation of the genetic variance-covariance matrix and the fitness surface for multiple male sexually selected traits

Stabilizing selection has been predicted to change genetic variances and covariances so that the orientation of the genetic variance-covariance matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic variance, more than 99% of the genetic variance was orientated 74.9degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear ( convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection.

Genetic and environmental sources of covariance between reading tests used in neuropsychological assessment and IQ subtests

In this study, we examined genetic and environmental influences on covariation among two reading tests used in neuropsychological assessment (Cambridge Contextual Reading Test [CCRT], [Beardsall, L., and Huppert, F. A. ( 1994). J. Clin. Exp. Neuropsychol. 16: 232 - 242], Schonell Graded Word Reading Test [SGWRT], [ Schonell, F. J., and Schonell, P. E. ( 1960). Diagnostic and attainment testing. Edinburgh: Oliver and Boyd.]) and among a selection of IQ subtests from the Multidimensional Aptitude Battery (MAB), [Jackson, D. N. (1984). Multidimensional aptitude battery, Ontario: Research Psychologists Press.] and the Wechsler Adult Intelligence Scale-Revised (WAIS-R) [Wechsler, D. (1981). Manual for the Wechsler Adult Intelligence Scale-Revised (WAIS-R). San Antonio: The Psychological Corporation]. Participants were 225 monozygotic and 275 dizygotic twin pairs aged from 15 years to 18 years ( mean, 16 years). For Verbal IQ subtests, phenotypic correlations with the reading tests ranged from 0.44 to 0.65. For Performance IQ subtests, phenotypic correlations with the reading tests ranged from 0.23 to 0.34. Results of Structural Equation Modeling (SEM) supported a model with one genetic General factor and three genetic group factors ( Verbal, Performance, Reading). Reading performance was influenced by the genetic General factor ( accounting for 13% and 20% of the variance for the CCRT and SGWRT, respectively), the genetic Verbal factor ( explaining 17% and 19% of variance for the CCRT and SGWRT), and the genetic Reading factor ( explaining 21% of the variance for both the CCRT and SGWRT). A common environment factor accounted for 25% and 14% of the CCRT and SGWRT variance, respectively. Genetic influences accounted for more than half of the phenotypic covariance between the reading tests and each of the IQ subtests. The heritabilities of the CCRT and SGWRT were 0.54 and 0.65, respectively. Observable covariance between reading assessments used by neuropsychologists to estimate IQ and IQ subtests appears to be largely due to genetic effects.

Wurst: a protein threading server with a structural scoring function, sequence profiles and optimized substitution matrices

Wurst is a protein threading program with an emphasis on high quality sequence to structure alignments (http://www.zbh.uni-hamburg.de/wurst). Submitted sequences are aligned to each of about 3000 templates with a conventional dynamic programming algorithm, but using a score function with sophisticated structure and sequence terms. The structure terms are a log-odds probability of sequence to structure fragment compatibility, obtained from a Bayesian classification procedure. A simplex optimization was used to optimize the sequence-based terms for the goal of alignment and model quality and to balance the sequence and structural contributions against each other. Both sequence and structural terms operate with sequence profiles.

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

A study of the effects of postcure treatments on polyester-melamine coating matrices

The effect of postcure high energy (gamma), ultraviolet (UV) and thermal treatment on the properties of polyester-melamine clearcoats of a range of compositions has been investigated. Two initial cure conditions were used, of which one was '' optimally '' cured and the other undercured. It was found that postcure treatments, particularly gamma and UV, led to coatings of similar mechanical and thermal properties irrespective of initial cure, although the change in properties on postcure treatment was greater for the under-cured samples. The results were interpreted in terms of the effect of the treatments on the structure of the crosslinked matrices. The study suggests the possibility of the development of a dual-cure process for polyester-melamines, whereby cure optimization and property improvement can be achieved. This could also be used to '' correct '' for small variations in thermal cure levels brought about by adventitious online fluctuations in cure oven conditions.

Hydrodynamic evaluation of kangaroo aortic valve matrices for tissue valve engineering

We evaluated the hydrodynamic performance of kangaroo aortic valve matrices (KMs) (19, 21, and 23 mm), as potential scaffolds in tissue valve engineering using a pulsatile left heart model at low and high cardiac outputs (COs) and heart rates (HRs) of 60 and 90 beats/min. Data were measured in two samples of each type, pooled in two CO levels (2.1 +/- 0.7 and 4.2 +/- 0.6 L/min; mean +/- standard errors on the mean), and analyzed using analysis of variance with CO level, HR, and valve type as fixed factors and compared to similar porcine matrices (PMs). Transvalvular pressure gradient (Delta P) was a function of HR (P < 0.001) and CO (P < 0.001) but not of valve type (P = 0.39). Delta P was consistently lower in KMs but not significantly different from PMs. The effective orifice area and performance index of kangaroo matrices was statistically larger for all sizes at both COs and HRs.