Methodology for the latent indicators formation

The food industry is the most important link in the food realm of the country, determining the possibility of its autonomous existence in critical situations. This type of industry plays a leading role in solving the issue of providing the population with food products in a sufficient range and quantity. The food industry is in demand all over the world, since the need for food is the basic need of every person. The uniqueness of the Russian food industry is determined by its close connection to regional peculiarities and, as a result, the uneven distribution of food industry enterprises across the country. The study is devoted to the analysis of interrelationships of the food industry indicators with the indicators of the socio-economic sphere and the formation of latent indicators of the economy according to the indicators of de- velopment of the food industry on the example of the Volga Federal District. The paper presents a multidimensional study of the closeness of relationship between the indicators of the food industry and the indicators of the socio- economic sphere using canonical analysis. The indicators of the food industry have the greatest connection with the indicators of public health, since the significant coefficient of canonical correlation in 2019 was more than 0.6. In this group of indicators, the analysis of canonical correlation revealed that such indicators as the production of livestock and poultry for slaughter, as well as the gross harvest of vegetables, have the most significant influence. The coefficients for the indicators of total fertility and mortality rates are dramatically high in the studied groups. This indicates that the de- terioration in the quality and quantity of products will lead to a decrease in the birth rate and an increase in the mortality rate. In this paper, based on canonical variables, the visualization of multidimensional data is carried out and a method for classifying regions in according to their resources and potential is proposed. The results of clustering focusing on the plant resources and trade potential show which territorial authorities situated close can exchange technological experi- ence and provide support to each other. The paper also ranks the entities of the Volga Federal District, according the degree of impact of the food sector indicators with the use of latent indicators.

Bootstrapping Bloch bands

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.

Carroll contractions of Lorentz-invariant theories

We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same “contraction” procedure of taking the ultrarelativistic limit c → 0 where c is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories (p-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of p-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.

Synthesis of a time-optimal control system for an extremal object

The paper presents the derivation of the synthesis method for the algorithm of the time-optimal controller for a third order dynamic system. A model with an extreme second-order transient response with delay was adopted as an object of research. The constant speed actuator is represented by an integrator. The synthesis is based on using the Pontryagin’s maximum principle and describing the dynamics of a system in the state space using canonical variables. The verification of the correctness of the result obtained by the theorem of Feldbaum A.A. on the number of switchings of the direction of movement of the regulating body during the control interval has been executed. To calculate the canonical state variables, it is proposed to use the position of the regulator, the controlled value and the derivative calculated from its values, measured on real objects.

Correlations and canonical variables applied to the distinction of soybean cultivars in a tropical environment

The objective of this study was to evaluate the performance of soybean cultivars through their correlations and canonical variables in a tropical environment. The study was conducted in the municipality of Mineiros, GO, Brazil. The soil was classified as Quartzarenic Neosol (Entisol). The experimental design used was in randomized blocks consisting of 10 soybean cultivars (Bônus, Desafio, Flecha, Foco, ICS7019, M5917, M7110, Power, ST721 and ST797) in four replications. Before planting, pre-planting desiccation was performed. The fertilizer used was 450 kg ha-1 of fertilizer 05-25-15 applied in the furrow and in a single dose next to the seeding. During the conduct of the experiment, pest control was carried out respecting good practices and integrated management. At the end of the cycle of each cultivar, 10 plants were collected at random and then the agronomic attributes were taken. The data obtained were submitted to the assumptions of the statistical model, verifying the normality and homogeneity of the residual variances, as well as the additivity of the model. Univariate and multivariate models were used. The analyzes were performed on the Rbio and R interface, in addition to the Software Genes. According to the summary of analysis of variance, it was observed that all cultivars differed for all characteristics. It was concluded that the soybean cultivars Flecha and M5917 presented the highest yields among the others in a tropical environment; the cultivars differed, showing a strong correlation between the number of grains per plant and yield, with the other variables analyzed; the univariate and multivariate tools were efficient and complementary in data analysis.

A multivariate approach to study the maintenance of soil fertility and soil health in relation to yield and nutrition of rice (Oryza sativa)

Understanding the relationship between soil properties and grain yield and yield related traits is an important objective in crop production programme. The purpose of this study was to evaluate maintenance of soil health in terms of soil chemical properties in relation to rice yield using multivariate analytical methods. Canonical correlation analysis is one of the most popular multivariate analysis techniques to estimate dependent relationship between soil properties with grain yield and yield attributing characters .In this study, five canonical correlation coefficients ( CCCs) were estimated and the first three of them were significant( R1: 1, R2: 0.99 and R3: 0.84, p<0.001).The findings obtained from the CCA indicate that available N, available Cu and Zn in soil and N content in grain had the largest contribution for the explanatory capacity of canonical variables estimated from grain yield, straw yield, number of panicles/m2 and filled grains / panicle.

Comparison between two multivariate analyses for the evaluation of genetic divergence for carcass and meat quality traits in alternative lines of chicken

The univariate analysis is becoming harder to use due the increasing number of characteristics of economic importance in agricultural industry. The multivariate approach provides an answer to this issue, allowing to analyze several traits when comparing different methodologies, genetics and products. This study aimed to use and compare the canonical variable analysis (CVA) and principal component analysis (PCA) to evaluate 7 genotypes of alternative lines of chicken (Caboclo, Carijó, Colorpak, Gigante Negro, Pesadão Vermelho, Naked Neck and Tricolor). The study evaluated 840 male chicks reared at 91 days from these genotypes, in a completely randomized design with 4 replicates per genotype. Different traits (23) were measured, and only 7 remained relevant after the multivariate approach: Carcass yield, Breast Yield, Back Yield, Cooking Loss, lightness, yellowness and water holding capacity. Both analyses remained with two variables explaining the variating. The Pearson correlation was used to measure the traits responsible for the most variance between genotypes. On the principal component cooking loss, carcass and breast yields, and the color parameters lightness and yellowness were the most relevant, while on canonical variables it was carcass yield, breast yield, lightness, yellowness and back yield. Both analysis resulted in similar conclusion, allowing to classify the genotypes in three major groups: 1 (Pesadão vermelho, Carijó, Colorpak, Nacked Neck), 2 (Gigante Negro and Caboclo) and 3 (Tricolor). PCA and CVA facilitate the interpretation of data with several traits of importance, showing the main traits responsible for genetic divergence.

Quantum Behavior of a Nonextensive Oscillatory Dissipative System in the Coherent State

We investigate the nonextensivity of a generalized dissipative oscillatory system in the Glauber coherent state. We introduce a parameter q as a measure of the nonextensivity of the system. Considering the characteristic of nonextensivity, the system is described by a deformed Caldirola–Kanai oscillator, which is represented in terms of q. We manage the system by describing the associated Hamiltonian in terms of the harmonic oscillator ladder operators. The time evolutions of the canonical variables, the Hamiltonian expectation value, the quantum energy, and the symmetry-breaking in the evolution of the system, are analyzed in detail regarding their dependence on q, damping factor, and the external driving force. The amplitude of the oscillator is slightly quenched as q becomes large, whereas the amplitude of the canonical momentum is enhanced in response to the growth in q. As q increases, the dissipation of the quantum energy becomes a little faster as a manifestation of the nonextensivity of the system. Our results are compared to the classical results, as well as to those in the previous research performed on the basis of the SU(1,1) coherent states. The coherent states, including the Glauber coherent states, can be convenient resources for carrying information, which is crucial in quantum information processing.

Components of resistance to Olivea neotectonae in Tectona grandis Linn F. as a criterion for selecting promising genotypes

The aim of this paper was to identify the best components involving resistance to the O. neotectonae fungus, allowing for adequate selection of promising teak genotypes to explore in improvement programs or for disease management. Thirty different clonal teak genotypes were evaluated in a greenhouse from PROTECA Biotecnologia Florestal. The experimental design was a randomized block design with three replications and three plants per plot. The following characteristics were evaluated: average latent period, number of pustules per cm2, area below the number of pustules progress curve (ABNPPC), frequency of infection, and number of urediniospores per pustule. The data for the resistance characteristics were submitted to ANOVA and multivariate analysis applying grouping techniques and canonical variables. High genetic variability was observed among the 30 T. grandis genotypes regarding resistance to the O. neotectonae fungus. Both for the Unweighted Pair Group Method with Arithmetic Mean (UPGMA), the canonical variables method and Best Linear Unbiased Prediction (BLUP) the genotypes that showed the greatest resistance to the fungus were genotypes 03 and 10

Hydropedological behavior of a chromic vertisol under different plant covers

Vertisols present edaphic limiting factors primarily of a physical nature. The study of their hydropedology, supported by multivariate techniques, is of vital importance. The work was developed with the objective of determining, through multivariate analysis, the hydropedological behavior of a Chromic Vertisol under different plant covers. In areas under natural grass, sugarcane, and secondary forest, belonging to the Holguín Sugarcane Provincial Research Station, three random points were chosen in each. Soil penetration resistance, soil bulk density, gravimetric moisture, and volumetric moisture at depths of 0-10, 10-20 and 20-30cm were determined. A Principal Component Analysis and Canonical Correlations were performed using Statistica 7 and Statgraphics Plus XV.II. The first two components made the greatest contribution to the variance, with 83.09%. The greatest contributions (1st component) were given by moisture at all depths and by soil compaction at a depth of 20-30 cm. The 2nd component was influenced by soil compaction in the 0-10 and 10-20cm layers. There was a contrast between the variables that characterize the solid phase with which they describe the liquid phase of the soil. There was a correlation between soil moisture and compaction. The first two pairs of canonical variables showed a strong linear correlation and regularly dispersed along the central values of the model, with a remarkable grouping by depths.