Standard Formula for the Uniform Shape Component in Landmark Data

1996 ◽  
pp. 153-168 ◽  
Author(s):  
Fred L. Bookstein
Keyword(s):  
Standard Formula ◽  
Landmark Data ◽  
Shape Component

scholarly journals A New Method for Landmark-Based Studies of the Dynamic Stability of Growth, with Implications for Evolutionary Analyses

2021 ◽  
Author(s):  
Fred L. Bookstein
Keyword(s):  
Growth Regulation ◽  
Pattern Analysis ◽  
Developmental Time ◽  
Dynamical Stability ◽  
New Method ◽  
Data Sets ◽  
Data Set ◽  
Landmark Data ◽  
Study Designs ◽  
Changes Over Time

AbstractA matrix manipulation new to the quantitative study of develomental stability reveals unexpected morphometric patterns in a classic data set of landmark-based calvarial growth. There are implications for evolutionary studies. Among organismal biology’s fundamental postulates is the assumption that most aspects of any higher animal’s growth trajectories are dynamically stable, resilient against the types of small but functionally pertinent transient perturbations that may have originated in genotype, morphogenesis, or ecophenotypy. We need an operationalization of this axiom for landmark data sets arising from longitudinal data designs. The present paper introduces a multivariate approach toward that goal: a method for identification and interpretation of patterns of dynamical stability in longitudinally collected landmark data. The new method is based in an application of eigenanalysis unfamiliar to most organismal biologists: analysis of a covariance matrix of Boas coordinates (Procrustes coordinates without the size standardization) against their changes over time. These eigenanalyses may yield complex eigenvalues and eigenvectors (terms involving $$i=\sqrt{-1}$$ i = - 1 ); the paper carefully explains how these are to be scattered, gridded, and interpreted by their real and imaginary canonical vectors. For the Vilmann neurocranial octagons, the classic morphometric data set used as the running example here, there result new empirical findings that offer a pattern analysis of the ways perturbations of growth are attenuated or otherwise modified over the course of developmental time. The main finding, dominance of a generalized version of dynamical stability (negative autoregressions, as announced by the negative real parts of their eigenvalues, often combined with shearing and rotation in a helpful canonical plane), is surprising in its strength and consistency. A closing discussion explores some implications of this novel pattern analysis of growth regulation. It differs in many respects from the usual way covariance matrices are wielded in geometric morphometrics, differences relevant to a variety of study designs for comparisons of development across species.

Methods for Studying Morphological Integration and Modularity

2010 ◽  
Vol 16 ◽  
pp. 213-243 ◽  
Author(s):  
Anjali Goswami ◽  
P. David Polly
Keyword(s):  
Distance Matrix ◽  
Japanese Macaques ◽  
Morphological Integration ◽  
Matrix Analysis ◽  
Euclidean Distance Matrix ◽  
Phenotypic Data ◽  
Graphical Modelling ◽  
Landmark Data ◽  
Competing Models ◽  
Matrix Correlation

Morphological integration and modularity are closely related concepts about how different traits of an organism are correlated. Integration is the overall pattern of intercorrelation; modularity is the partitioning of integration into evolutionarily or developmentally independent blocks of traits. Modularity and integration are usually studied using quantitative phenotypic data, which can be obtained either from extant or fossil organisms. Many methods are now available to study integration and modularity, all of which involve the analysis of patterns found in trait correlation or covariance matrices. We review matrix correlation, random skewers, fluctuating asymmetry, cluster analysis, Euclidean distance matrix analysis (EDMA), graphical modelling, two-block partial least squares, RV coefficients, and theoretical matrix modelling and discuss their similarities and differences. We also review different coefficients that are used to measure correlations. We apply all the methods to cranial landmark data from and ontogenetic series of Japanese macaques,Macaca fuscatato illustrate the methods and their individual strengths and weaknesses. We conclude that the exploratory approaches (cluster analyses of various sorts) were less informative and less consistent with one another than were the results of model testing or comparative approaches. Nevertheless, we found that competing models of modularity and integration are often similar enough that they are not statistically distinguishable; we expect, therefore, that several models will often be significantly correlated with observed data.

Analysis and Modeling of Defects in Unsupported Overhanging Features in Micro-Stereolithography

2016 ◽  
Author(s):  
Vito Basile ◽  
Francesco Modica ◽  
Irene Fassi
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Numerical Approach ◽  
Fe Analysis ◽  
Test Cases ◽  
Layer By Layer ◽  
Failure Condition ◽  
Micro Scale ◽  
Part Geometry ◽  
Shape Component

In the present paper, a numerical approach to model the layer-by-layer construction of cured material during the Additive Manufacturing (AM) process is proposed. The method is developed by a recursive mechanical finite element (FE) analysis and takes into account forces and pressures acting on the cured material during the process, in order to simulate the behavior and investigate the failure condition sources, which lead to defects in the final part geometry. The study is focused on the evaluation of the process capability Stereolithography (SLA), to build parts with challenging features in meso-micro scale without supports. Two test cases, a cantilever part and a bridge shape component, have been considered in order to evaluate the potentiality of the approach. Numerical models have been tuned by experimental test. The simulations are validated considering two test cases and briefly compared to the printed samples. Results show the potential of the approach adopted but also the difficulties on simulation settings.

Complex Chi-Squares: Matrix Notation and Calculation

1972 ◽  
Vol 30 (3) ◽  
pp. 743-746 ◽  
Author(s):  
Edward F. Gocka
Keyword(s):  
Computational Algorithms ◽  
Behavioral Sciences ◽  
Matrix Notation ◽  
Standard Formula ◽  
The Matrix ◽  
Matrix Formula

A matrix formula available for the calculation of complex chi-squares allows several computational variations, each of which requires fewer steps than the standard formula. However, neither the matrix formula nor the associated computational algorithms have been given adequate exposure in statistical texts for the behavioral sciences. This paper reintroduces the formula, expands the notation, and shows how several computational variations can be derived.

scholarly journals Safety and Tolerance Evaluation of Milk Fat Globule Membrane-Enriched Infant Formulas: A Randomized Controlled Multicenter Non-Inferiority Trial in Healthy Term Infants

2014 ◽  
Vol 8 ◽  
pp. CMPed.S16962 ◽  
Author(s):  
Claude Billeaud ◽  
Giuseppe Puccio ◽  
Elie Saliba ◽  
Bernard Guillois ◽  
Carole Vaysse ◽  
...  
Keyword(s):  
Weight Gain ◽  
Milk Fat ◽  
Bovine Milk ◽  
Control Group ◽  
Infant Formulas ◽  
Term Infants ◽  
Milk Fat Globule Membrane ◽  
Standard Formula ◽  
Milk Fat Globule ◽  
Fat Globule

Objective This multicenter non-inferiority study evaluated the safety of infant formulas enriched with bovine milk fat globule membrane (MFGM) fractions. Methods Healthy, full-term infants ( n = 119) age ≤14 days were randomized to standard infant formula (control), standard formula enriched with a lipid-rich MFGM fraction (MFGM-L), or standard formula enriched with a protein-rich MFGM fraction (MFGM-P). Primary outcome was mean weight gain per day from enrollment to age 4 months (non-inferiority margin: –3.0 g/day). Secondary (length, head circumference, tolerability, morbidity, adverse events) and exploratory (phospholipids, metabolic markers, immune markers) outcomes were also evaluated. Results Weight gain was non-inferior in the MFGM-L and MFGM-P groups compared with the control group. Among secondary and exploratory outcomes, few between-group differences were observed. Formula tolerance rates were high (>94%) in all groups. Adverse event and morbidity rates were similar across groups except for a higher rate of eczema in the MFGM-P group (13.9% vs control [3.5%], MFGM-L [1.4%]). Conclusion Both MFGM-enriched formulas met the primary safety endpoint of non-inferiority in weight gain and were generally well tolerated, although a higher rate of eczema was observed in the MFGM-P group.

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