A Modification of von Zeipel's Method for a Choice of Canonical Variables Especially Suitable for Orbits with Small Eccentricities

1961 ◽  
Vol 66 ◽  
pp. 286 ◽  
Author(s):  
Gen-Ichiro Hori
Keyword(s):  
Canonical Variables ◽  
Von Zeipel’S Method

THYMUS VARIABILITY IN WHITE RATS EXPOSED TO FORMALDEHYDE

2019 ◽  
pp. 105-116
Author(s):  
V.N. Voloshin ◽  
I.S. Voloshina ◽  
I.Yu. Vash
Keyword(s):  
White Male ◽  
Principal Component ◽  
Middle Part ◽  
Procrustes Analysis ◽  
Male Rats ◽  
Canonical Variables ◽  
Generalized Procrustes Analysis ◽  
White Rats ◽  
Main Component ◽  
Formaldehyde Inhalation

The aim of the paper is to study thymus variability in white rats, which were exposed to formaldehyde, and to compare these data with the indicators in control animals. Materials and Methods. The trial enrolled 72 white male rats, initial body weight 40–50 g. The animals were divided into 2 groups (36 rats in each). The first group consisted of control rats. Animals of the second group were exposed to formaldehyde inhalation, 2.766 mg/m3. To characterize the variability of the organ size, centroids were determined. The superposition of landmark configurations was performed using the generalized Procrustes analysis method, MorphoJ 1.06d program. The principal component analysis and canonical analysis of the obtained data were carried out. Results. One-Way ANOVA revealed a high level of intergroup differences in Procrust distance (F=1.34; p<0.0001). The significant effect of the duration of formaldehyde exposure on centroid size was established. The Kruskal-Wallis criterion was 19.778 (p=0.0014). The analysis of the principal components indicated that each of the first 10 components stands for more than 1 % of Procrustes coordinate variance. In this case, the first 7 components compatibly explain 91.398 % of thymus variability. The proportion of the first main component to the total variance of the Procrustes coordinates is 40.236 %. PC1 (-) shows changes in the thymus shape, mostly affecting the tops of its lobes, the middle part of the right boundary and the entire left thymus boundary. The scattering ellipses of the thymus ordinates in rats exposed to formaldehyde, in the first two canonical variables are located higher than those in the control animals. Conclusion. Formaldehyde inhalation leads to thymus changes in white rat. The most significant differences with control data are determined along the second canonical variable. Keywords: thymus, form, rat, formaldehyde, geometric morphometry. Цель. Изучение изменчивости формы тимуса белых крыс, находившихся в условиях влияния формальдегида, и сравнение этих данных с показателями, полученными у контрольных животных. Материалы и методы. Работа выполнена на 72 белых крысах-самцах с начальной массой тела 40–50 г. Животные были разделены на 2 серии (по 36 крыс). Первую серию составляли контрольные крысы. Животные второй серии подвергались ингаляционному воздействию формальдегида (ФА) в концентрации 2,766 мг/м3. Для характеристики изменчивости размеров органов определяли размер их центроидов. Процедуру суперимпозиции конфигураций ландмарок выполняли методом генерализованного прокрустова анализа с использованием программы MorphoJ 1.06d. Проводили анализ главных компонент и канонический анализ полученных данных. Результаты. Однофакторный дисперсионный анализ выявил высокий уровень межгрупповых различий по показателю прокрустовых расстояний (F=1,34; р<0,0001). Установлено значительное влияние продолжительности нахождения животных в условиях воздействия ФА на размер центроида. Критерий Краскела–Уоллиса составил 19,778 (р=0,0014). Анализ главных компонент указывал на то, что каждая из первых 10 компонент объясняет более 1 % дисперсии прокрустовых координат. При этом первые 7 компонент совместно объясняют 91,398 % изменчивости формы тимуса. Вклад первой главной компоненты в общую дисперсию прокрустовых координат составляет 40,236 %. РС1 (–) показывает изменения формы тимуса, в большей степени затрагивающие верхушки его долей, среднюю часть правого контура и весь левый контур тимуса. Эллипсы рассеивания ординат тимусов, принадлежащих крысам, подвергавшимся влиянию ФА, в пространстве первых двух канонических переменных расположены выше по отношению к таковым контрольных животных. Заключение. Ингаляционное воздействие формальдегида приводит к изменению формы тимуса белых крыс. Наибольшие различия с контрольными данными определяются вдоль второй канонической переменной. Ключевые слова: тимус, форма, крыса, формальдегид, геометрическая морфометрия.

Hamiltonian Mechanics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Angular Momentum ◽  
Jacobi Equation ◽  
Modern Theory ◽  
Hamiltonian Mechanics ◽  
Lagrangian Mechanics ◽  
Canonical Transformations ◽  
Canonical Variables ◽  
Light Waves ◽  
Hamilton Jacobi Equation ◽  
Common Action

Hamilton’s genius was to understand what were the true variables of mechanics (the “p − q,” conjugate coordinates, or canonical variables), and this led to Hamilton’s Mechanics which could obtain qualitative answers to a wider ranger of problems than Lagrangian Mechanics. It is explained how Hamilton’s canonical equations arise, why the Hamiltonian is the “central conception of all modern theory” (quote of Schrödinger’s), what the “p − q” variables are, and what phase space is. It is also explained how the famous conservation theorems arise (for energy, linear momentum, and angular momentum), and the connection with symmetry. The Hamilton-Jacobi Equation is derived using infinitesimal canonical transformations (ICTs), and predicts wavefronts of “common action” spreading out in (configuration) space. An analogy can be made with geometrical optics and Huygen’s Principle for the spreading out of light waves. It is shown how Hamilton’s Mechanics can lead into quantum mechanics.

CONSISTENT CANONICAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (21) ◽  
pp. 3823-3841 ◽  
Author(s):  
FUAD M. SARADZHEV
Keyword(s):  
Canonical Quantization ◽  
Bound State ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Schwinger Model ◽  
Canonical Variables ◽  
Bound State Spectrum

For the chiral Schwinger model, the canonical quantization formulation consistent with the Gauss law constraint is developed. This requires modification of the canonical variables of the model. The formulation presented is unitary and gauge-invariant under modified gauge transformations. The bound state spectrum of the model is established.

scholarly journals Genetic diversity for physiological quality of seeds from corn (Zea mays L.) intervarietal crossbreeds

2013 ◽  
Vol 35 (4) ◽  
pp. 449-456 ◽  
Author(s):  
Daniele Nerling ◽  
Cileide Maria Medeiros Coelho ◽  
Rubens Onofre Nodari
Keyword(s):  
Genetic Diversity ◽  
Zea Mays L ◽  
Accelerated Aging ◽  
Genetic Contribution ◽  
Percentage Germination ◽  
Canonical Variables ◽  
Accelerated Aging Test ◽  
Aging Test ◽  
Physiological Quality

The physiological quality is based on the genotype and may be accompanied since the first stages of selection through the study of genetic diversity. The purpose of this study was to evaluate the parental genetic contribution in the seed physiological quality in corn intervarietal crossbreeds. The intervarietal crossbreeds were performed using landraces genotypes, open pollinated varieties and commercial hybrids. The seeds obtained from the crossbreed, their equivalents and parentals were evaluated regarding their water percentage, germination, germination speed rate, accelerated aging, field emergence and electrical conductivity. The seeds obtained in the crossbreed are viable and vivid with heterosis when compared with the parentals. The accelerated aging test was more effective for selecting the strongest genotypes. The canonical variables were useful to group the genotypes that presented similar physiological characteristics. The genotypes MPA 01 x Pixurum 05, MPA 01 x AS1565, MPA 01 x SJC5886, SJC5886 x Pixurum 05 and Fundacep 35 x SCS 154 Fortuna were the best crossbreeds regarding the production of better physiological quality seeds.

AN EVALUATION OF THE USE OF ELYTRA AND BODIES IN X-RAY ENERGY-DISPERSIVE SPECTROSCOPIC STUDIES OF THE RED TURNIP BEETLE, ENTOMOSCELIS AMERICANA (COLEOPTERA: CHRYSOMELIDAE)

1980 ◽  
Vol 112 (6) ◽  
pp. 609-614 ◽  
Author(s):  
W. J. Turnock ◽  
G. H. Gerber ◽  
D. U. Sabourin
Keyword(s):  
Discriminant Analysis ◽  
Energy Dispersive Spectroscopy ◽  
Spectroscopic Studies ◽  
Energy Dispersive ◽  
Spectroscopy Technique ◽  
X Ray ◽  
Insect Dispersal ◽  
Canonical Variables ◽  
The Mean ◽  
Individual Variables

AbstractSamples of the bodies and elytra of Entomoscelis americana Brown were analyzed separately by X-ray energy-dispersive spectroscopy. Discriminant analysis revealed that the chemoprints of the bodies of newly-emerged beetles (1 wk old) were distinct from those of post-aestivation beetles (9- to 10-wk old). However, the chemoprints of the elytra of newly-emerged and post-aestivation beetles were not as different as those of the bodies as demonstrated by the overlap in the plot of the first two canonical variables. The variances of the mean difference of individual variables between newly-emerged and post-aestivation groups generally were smaller for elytra than for bodies. This suggests that the chemoprints of the elytra of E. americana are more stable than those of the bodies and consequently the elytra should be more suitable than the bodies in insect dispersal studies utilizing the X-ray energy-dispersive spectroscopy technique.

scholarly journals Phenotypic diversity of horse breeds used in sports activities, employing multivariate analysis

2021 ◽  
Vol 19 (1) ◽  
pp. e0401
Author(s):  
Marcos P. G. Rezende ◽  
Julio C. Souza ◽  
Carlos H. M. Malhado ◽  
Paulo L. S. Carneiro ◽  
Johnny I. M. Araujo ◽  
...  
Keyword(s):  
Multivariate Analysis ◽  
Principal Components ◽  
Phenotypic Diversity ◽  
The Body ◽  
Breeding Programs ◽  
Mato Grosso ◽  
Canonical Variables ◽  
Horse Breeding ◽  
Quarter Horse ◽  
Euclidean Distances

Aim of study: Sports involving horses have notable financial importance. Breeds are evaluated to find the best-suited ones for a specific sport category. Phenotypic diversity using biometric markers was evaluated for Quarter Horse (QH), Arabic (AR), English Thoroughbred (ET), and Brazilian Equestrian (BE) horse breeds.Area of study: Mato Grosso do Sul-Brazil.Material and methods: Lengths, widths, and circumference measures of 268 horses were collected. These measures were used to estimate conformation indexes. The size-free canonical discriminant analysis was used to remove the size effect on the animal's shape. The similarity among breeds (by sex) was evaluated employing multivariate analysis (canonical analysis, MANOVA, principal components, Euclidean distances, and grouping through complete linkage), considering all linear measures and conformation indexes (included in the analysis of principal components).Main results: Four canonical variables (CANs), each one representing an equation to interpret the morpho-functionality of breeds “sustentation”, “structure”, “frame”, and “equilibrium”, were retained. The breeds presented differences when the CANs were simultaneously considered. Differences mainly were the size and the thickness of the body as well as the ability of the animal to move. ET, QH, and BE demonstrate a well-defined biometric profile. These three breeds clustered separately from AR breed.Research highlights: Canonical variables allow to verify the functional aptitudes since the responses were close to conformation indices commonly used as horse skill estimators. The implementation of these variables as selection criteria in horse breeding programs require further studies in larger populations of horses for a confirmation of the present results.

scholarly journals Bootstrapping Bloch bands

2021 ◽  
Author(s):  
Serguei Tchoumakov ◽  
Serge Florens
Keyword(s):  
Search Space ◽  
Quantum Field Theories ◽  
New Techniques ◽  
Bootstrap Methods ◽  
Quantum Operator ◽  
Canonical Variables ◽  
Distribution Probability ◽  
Anharmonic Potential ◽  
Bloch Band ◽  
Band Spectra

Abstract Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schrödinger equation with an anharmonic potential. The core of bootstrap methods builds on exact recursion relations of arbitrary moments of some quantum operator and the use of an adequate set of positivity criteria. We extend this methodology to models with continuous Bloch band spectra, by considering a single quantum particle in a periodic cosine potential. We find that the band structure can be obtained accurately provided the bootstrap uses moments involving both position and momentum variables. We also introduce several new techniques that can apply generally to other bootstrap studies. First, we devise a trick to reduce by one unit the dimensionality of the search space for the variables parametrizing the bootstrap. Second, we employ statistical techniques to reconstruct the distribution probability allowing to compute observables that are analytic functions of the canonical variables. This method is used to extract the Bloch momentum, a quantity that is not readily available from the bootstrap recursion itself.

scholarly journals Kernel functional canonical correlation analysis

2017 ◽  
Vol 5 (325) ◽  
Author(s):  
Mirosław Krzyśko ◽  
Łukasz Waszak
Keyword(s):  
Correlation Analysis ◽  
Canonical Correlation Analysis ◽  
Functional Data ◽  
Canonical Correlation ◽  
Multivariate Data ◽  
Research Interest ◽  
Canonical Correlations ◽  
Canonical Variables ◽  
Correlation Methods ◽  
The Subject

Canonical correlation methods for data representing functions or curves have received much attention in recent years. Such data, known in the literature as functional data (Ramsay and Silverman, 2005), has been the subject of much recent research interest. Examples of functional data can be found in several application domains, such as medicine, economics, meteorology and many others. Unfortunately, the multivariate data canonical correlation methods cannot be used directly for functional data, because of the problem of dimensionality and difficulty in taking into account the correlation and order of functional data. The problem of constructing canonical correlations and canonical variables for functional data was addressed by Leurgans et al. (1993), and further developments were made by Ramsay and Silverman (2005). In this paper we propose a new method of constructing canonical correlations and canonical variables for functional data.

On linear unitary transformations of two canonical variables

1989 ◽  
Vol 30 (5) ◽  
pp. 993-999 ◽  
Author(s):  
Jerzy F. Plebański ◽  
J. D. Finley
Keyword(s):  
Canonical Variables ◽  
Unitary Transformations
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