Canonical Variables Research Articles

Statistical matching using kernel canonical correlation analysis and super-organizing map

The potential to study and improve different aspects of our lives is ever growing thanks to the abundance of data available in today’s modern society. Scientists and researchers often need to analyze data from different sources; the observations, which only share a subset of the variables, cannot always be paired to detect common individuals. This is the case, for example, when the information required to study a certain phenomenon is coming from different sample surveys. Statistical matching is a common practice to combine these data sets. In this paper, we investigate and extend to statistical matching two methods based on Kernel Canonical Correlation Analysis (KCCA) and Super-Organizing Map (Super-OM). These methods are designed to deal with various variable types, sample weights and incompatibilities among categorical variables. In the first case, we use KCCA, a non-linear extension of CCA, to create canonical variables that we can compare in the two data sets. In the second case, Super-OM uses organizing maps to create subgroups of individuals who share the same characteristics. We use the 2017 Belgian Statistics on Income and Living Conditions (SILC) and we compare the performance of the proposed statistical matching methods by means of a cross-validation technique, as if the data were available from two separate sources. The results indicate that our proposed methods are superior to existing methods because they preserve the distribution of generated variables while also providing good predictions. Existing methods typically only achieve one or the other. These new techniques open the door to improving statistical matching in other applications such as medicine, economics, …

Origin of the Andronovans: A Statistical Approach

The origin of the Andronovo population is explored using a statistical rather than typological approach. Four questions are raised. Which Eastern European populations of the Middle Bronze and the transition to the Late Bronze Age had taken part in Andronovo origins? What was the contribution of the southern groups? What was the role of the autochthonous Siberian substratum? What was the population background of the dichotomy between two major Andronovo cultural traditions, Fedorovka and Alakul? To address these questions, measurements of 12 male Andronovo cranial samples (nine relating to Fedorovka and three to Alakul) and 85 male cranial samples from Eastern Europe, Siberia, Kazakhstan, Southwestern Central Asia, Southern Caucasus, and the Near East were subjected to canonical variate analysis, and minimum spanning trees were constructed. The results suggest that the most likely ancestors of Andronovans were Late Catacomb tribes of Northern Caucasus, people of Poltavka, Sintashta, and those associated with the Abashevo-Sintashta horizon. While no direct parallels with Southern Caucasian, Southwestern Central Asian or Near Eastern populations were found among Andronovo groups, some of them could have inherited the southern component from either the Abashevo or the Catacomb people. In the former case, one should postulate a gradient: Fatyanovo → Balanovo → Abashevo → Sintashta → Petrovka → Andronovo; in the latter case, the variation within Andronovo is directly derivable from that among the Catacomb populations. Andronovo groups displaying an autochthonous Siberian tendency demonstrate various degrees of “mutual assimilation” between immigrants and pre-Mongoloid natives. Differences between the Fedorovka and Alakul samples are significant but very small. A special role of Petrovka in the origin of Alakul is not supported by the analysis.

Diversidade genética em progênies de meios-irmãos de couve: Uma abordagem multivariada

ABSTRACT Kale is one of the most widely cultivated leafy vegetables in Brazil, but its breeding genetic is still limited. Therefore, it is crucial to develop research that explores the genetic diversity of the available germplasms, aiming to establish promising crosses in the studied populations. The present study aimed to evaluate the genetic divergence between half-sibling progenies of kale, obtained through recurrent selection, using multivariate methods to select the most promising progenies for forming a recombinant population. The plants obtained from the seeds of 25 pre-selected half-sibling progenies and three commercial cultivars were evaluated as treatment groups. These seeds were produced in 2018 by subjecting the clones of the progenies to recombination, followed by the selection of appropriate seeds from plants with superior agronomic performance. In the present study, plants in each plot were evaluated for twelve quantitative and fifteen qualitative traits. Genetic divergence was studied based on canonical variables to obtain quantitative data. The UPGMA method was applied to the quantitative, qualitative, and combined data, and Mahalanobis genetic distance was adopted. The first three canonical variables explained 73.75% of the total cumulative variation compared to the commercial cultivars and 55.29% when considering the half-sibling progenies exclusively. The half-sibling progenies P1, P2, P3, P4, P5, P9, P11, P15, P16, P18, P20, P22, P23, P24, and P25 were the most divergent and should, therefore, be prioritized when composing the recombinant population for the third cycle of recurrent selection because, in addition to genetic variation, these progenies also present characteristics of interest to the kale genetic breeding program. The commercial cultivars exhibited the most divergent genotypes and should, therefore, be included in the next recombination cycle.

Determination of Sexual Dimorphism and Morphological Variation of Pool Barb, Puntius sophore (Cypriniformes, Cyprinidae), Using Landmark Based Geometric Morphometric Analysis

Geometric morphometrics is an efficient way to quantify biological shape variation and its covariation with other biotic or abiotic factors. The geometric information of an object is measured in a non-linear shape space after removing size, orientation, and position-related effects. This study was aimed to determine sexual dimorphism and morphological variation in body shape using landmark-based morphometrics by means of relative warp analysis. The indigenous freshwater fish Puntius sophore (Cyprinidae) was selected as the model organism for the study. Adult male and female individuals were collected during July-August 2019 (breeding season) and March–April 2019 (non-breeding season) from the ponds of Bolpur, West Bengal, India. Prior to analysis, the images were digitised using the appropriate fourteen landmarks and relative wrap analysis was performed using appropriate software. The results were then analysed, and the maximum relative displacements of adjacent landmarks were interpreted using canonical variate analysis (CVA) and principal component analysis (PCA). Significant body shape differences were found to be present in the non-breeding season and breeding season (male and female) populations of the species. Thus, geometric morphometrics can be used to understand the sexual dimorphism in natural populations of small fish species.

Quantitative Analysis of Fish Morphology Through Landmark and Outline-based Geometric Morphometrics with Free Software.

Morphology underpins key biological and evolutionary processes that remain elusive. This is in part due to the limitations in robustly and quantitatively analyzing shapes within and between groups in an unbiased and high-throughput manner. Geometric morphometrics (GM) has emerged as a widely employed technique for studying shape variation in biology and evolution. This study presents a comprehensive workflow for conducting geometric morphometric analysis of fish morphology. The step-by-step manual provides detailed instructions for using popular free software, such as the TPS series, MorphoJ, ImageJ, and R, to carry out generalized Procrustes analysis (GPA), principal component analysis (PCA), discriminant function analysis (DFA), canonical variate analysis (CVA), mean shape analysis, and thin plate spline analysis (TPS). The Momocs package in R is specifically utilized for in-depth analysis of fish outlines. In addition, selected functions from the dplyr package are used to assist in the analysis. The full process of fish outline analysis is covered, including extracting outline coordinates, converting and scaling data, defining landmarks, creating data objects, analyzing outline differences, and visualizing results. In conclusion, the current protocol compiles a detailed method for evaluating fish shape variation based on landmarks and outlines. As the field of GM continues to evolve and related software develops rapidly, the limitations associated with morphological analysis of fish are expected to decrease. Interoperable data formats and analytical methods may facilitate the sharing of morphological data and help resolve related scientific problems. The convenience of this protocol allows for fast and effective morphological analysis. Furthermore, this detailed protocol could be adapted to assess image-based differences across a broader range of species or to analyze morphological data of the same species from different origins. Key features • This protocol provides a comprehensive set of commonly used GM-analyzing methods and visualizing skills plus supporting information to help assess the appropriate analysis method • By incorporating both landmarks and outlines, this protocol facilitates a thorough analysis of two-dimensional shape variation in fish, covering a wide range of morphological features • The simplified workflow and detailed procedures make it accessible for non-experienced users to successfully complete the analysis while also providing valuable insights for experienced users Graphical overview Workflow for conducting geometric morphometrics analysis on fish. The steps include image acquisition as data sources, digitization of fish morphology using landmark-based methods, analysis of shape variation characteristics, and visualization of the results in relation to biological interpretation. Largemouth bass (Micropterus salmoides) is used as an example in the schematic representation.

Nonlinear squeezing of stochastic motion

Linearized stochastic nanomechanical systems operating at nonzero temperatures and constant frequency and damping are restricted in their capacity to reduce noise in nonlinear combinations of the canonical variables. Nonlinear dynamics are then required in order to overcome these limits. Here we demonstrate how to make these limits explicit in the form of a threshold for nonlinear squeezing of the motional variables. Noise suppression below the threshold cannot be explained by linearized dynamics and is helpful in low-noise nonlinear devices at an ambient temperature. We predict that a state of the art levitating particle, exposed to cubic or quartic trapping potentials for a short interval will display nonlinear squeezing of stochastic motion that cannot be replicated by linear motion.

The Cerebellum and Cognitive Function: Anatomical Evidence from a Transdiagnostic Sample

Multiple lines of evidence across human functional, lesion, and animal data point to a cerebellar role, in particular of crus I, crus II, and lobule VIIB, in cognitive function. However, a mapping of distinct facets of cognitive function to cerebellar structure is missing. We analyzed structural neuroimaging data from the Healthy Brain Network (HBN). Cerebellar parcellation was performed with a validated automated segmentation pipeline (CERES) and stringent visual quality check (n = 662 subjects retained from initial n = 1452). Canonical correlation analyses (CCA) examined regional gray matter volumetric (GMV) differences in association to cognitive function (quantified with NIH Toolbox Cognition domain, NIH-TB), accounting for psychopathology severity, age, sex, scan location, and intracranial volume. Multivariate CCA uncovered a significant correlation between two components entailing a latent cognitive canonical (NIH-TB subscales) and a brain canonical variate (cerebellar GMV and intracranial volume, ICV), surviving bootstrapping and permutation procedures. The components correspond to partly shared cerebellar-cognitive function relationship with a first map encompassing cognitive flexibility (r = 0.89), speed of processing (r = 0.65), and working memory (r = 0.52) associated with regional GMV in crus II (r = 0.57) and lobule X (r = 0.59) and a second map including the crus I (r = 0.49) and lobule VI (r = 0.49) associated with working memory (r = 0.51). We show evidence for a structural subspecialization of the cerebellum topography for cognitive function in a transdiagnostic sample.

Two-channel optimal energy-efficient control of distributed parameter systems

A formulation and method for solving the problem of the energy-efficient two-channel programmed control of an object with distributed parameters with a given-precision uniform approximation of the resulting spatial distribution of the controlled quantity to the required state is proposed. Two internal controls on the power of heat sources in the electromagnetic field of the inductor are considered as control actions. Proposed solution approach involves a special-form preliminary parametrization procedure for control actions on finite-dimensional subsets of the terminal values of conjugate variables in the boundary-value problem of Pontryagin’s maximum principle, in combination with the subsequent reduction to a semi-infinite optimization problem, which is solved with respect to the requisite parameter vector using the alternance method based on additional information about fundamental laws of the subject area. An example of optimal energy-efficient control of transient heat conduction, which is of independent interest, is given.

Investigation of the relationships between selenium fractions and soil properties by canonical correlation

The availability and distribution of an element are determined by soil conditions and the geochemical fractions. In this study, canonical correlation (CCA) was used to examine the associations between the soil parameters (X set) of the Amik plain and the fractions of selenium (Se) (Y set). A statistically significant correlation (P < 0.01) of 0.391 ± 0.06 was observed between the first canonical variable pair (FCVP). The clay, sand, and silt variables exhibited the greatest standardized canonical coefficients, with values of 74.55, 75.83, and 94.77, respectively. Additionally, the B3 percent had a standardized canonical coefficient of 1.029. The analysis of the FCVP showed that the original variables of the X set and/or its canonical variable (U1) had the strongest linear connection (0.770) with organic matter (OM) and the B3 percentage in the Y set (0.603). The OM (0.3012) exhibited the most substantial linear structural correlations between the canonical variables of the Y set and the original variables of the X set. However, the canonical redundancy analysis revealed that in the FCVP, the variance of the X set was described by its canonical variables to the extent of 20.97%, whereas the Y set was explained by 21.96%. Hence, it can be inferred that the use of canonical correlation is effective in elucidating the relationship between soil parameters and various components of plant nutrition.

Directions and dynamics of population processes in Siberia and the Far East during the Neolithic-Bronze and Early Iron Ages: cranial metric evidence

The purpose of the study is estimation of direction and dynamics of population processes from Neolithic to historical times on the vast territories of Northern Eurasia including Siberia, Russian Far East and Japanese archipelago. To achieve this cranial metric data on 62 ancient and 40 historical samples were analyzed by means of canonical variate analysis using mean intra-group correlation matrix. The obtained results reveal that in Neolithic three basal group of population can be detected in Siberia and Far East mainland. Basically the interaction of these groups explains morphological population landscape in post-Neolithic times. The first group, represented by the Baraba Neolithic series, is obviously the descendants of the Upper Paleolithic tribes of Western and Central Siberia. The second group is related to Boisman-2 sample from Primorye. The cranial characteristics of this series can be detected in Neolithic from Primorye to Baikal region. The third group is represented by a cranial series from the Diring-Yuryakh burial ground of the Ymyakhtakh culture located in Yakutia (Sаkha). Although this sample is not closely related to other ancient series used in the analyses it contributed to historical ethnic groups adjacent to Tuva and Mongolia. In Western Siberia massive gene flow related to Afanasievo in Eneolithic and especially Andronovo people in Bronze Age is detected. At the end of the Early Iron Age, the western migration vector changed to the eastern one. The results of canonical variate analysis reveal high level of morphological similarity between Baraba Neolithic sample, Jomon, and Epi-jomon. This result needs to be verified by other independent sources including morphologic and genetic studies.

Selection of popcorn genotypes resistant to Spodoptera frugiperda and identification of resistance-related key traits


 The Spodoptera frugiperda, is one of the most deleterious pests of popcorn and the identification of resistant genotypes is determinant in breeding programs. The objective of this study was to select popcorn genotypes resistant to S. frugiperda and the key traits related to the identification of resistance. The popcorn varieties UEM J1, Composto Márcia, Arachida, Composto Gaúcho, and Zapalote Chico (resistant check) were evaluated in a completely randomized design with 100 replications. The experimental unit consisted of one Petri dish, containing plant material and a caterpillar The following traits were evaluated: larval stage duration (LSt), food intake weight(IW), final larva weight (FW), mean larva weight (MW), feces (F), assimilated (A) and metabolized food weight (M), relative consumption rate (RCR), relative metabolic rate (RMR), relative growth rate (RGR), conversion efficiency of ingested food (CEI), apparent digestibility (AD), conversion efficiency of digested food (CED), and leaf area consumed (LAC). The diagnosis of multicollinearity, analysis of canonical variables, genetic divergence, hierarchical clustering, factor analysis and canonical correspondence analysis were carried out to perform multivariate analysis. After the multicollinearity test, the traits FW, IW, RCR, AD, and LAC were maintained for further analysis. The traits IW, FW and AD were determinant in the resistance by antixenosis expressed by the varieties Zapalote Chico and Arachida, for the varieties Composto Gaúcho and Composto Márcia the determining characteristics were RCR and LAC and for the variety UEM J1 the variable LAC showed greater importance. Variety Arachida was considered resistant to S. frugiperda by antixenosis and can be used in the future as a source of favorable alleles to breed resistant popcorn hybrids. The traits relative consumption rate, apparent digestibility and leaf area consumed were considered key traits in the identification of resistance against S. frugiperda in popcorn genotypes.

Geometric morphometry enables species hypotheses testing and the assignment of historical type specimens in the genus Callirhinus Blanchard (Coleoptera: Scarabaeidae: Anomalini)

Abstract Assignation of old type specimens is important for nomenclatural stability, but when it comes to ancient specimens, the use of certain techniques is sometimes not appropriate, due to the condition or age of the specimen. In this study, the supposedly polymorphic and monotypic genus Callirhinus Blanchard was analysed with geometric morphometric techniques and photographs of the pronotum, with the purpose of identifying the locality of the old type specimen (19th century) and to test a priori defined hypothetical species by cumulation of evidence within an integrative taxonomic protocol using geometric morphometry, complemented by morphology and geographical discontinuity. Five morphotypes were defined a priori, and principal component, canonical variates analysis, and distances tests for the assignment of the type specimen based on canonical scores and Procrustes distances between means of groups were carried out. Statistical significance was found in four axes validating the species hypotheses, discovering that the type specimen belongs to the morphotype from Jalisco state. Additionally, a taxonomic treatment, the description of four new species, C. choperi Ramírez-Ponce & Zaragoza sp. nov., C. nanduRamírez-Ponce & Zaragoza sp. nov., C. huiinisRamírez-Ponce & Zaragoza sp. nov., and C. veemeRamírez-Ponce & Zaragoza sp. nov. , keys for the species determination, new distributional records, and a map are provided. The present work demonstrates that Geometric Morphometry is an adequate analytical tool that supports taxonomic identification at low cost and without damaging historical specimens.

Development of an Optimal Control Algorithm for the Course Movement of an Unmanned Vehicle

The article presents an algorithm for controlling a ground unmanned vehicle. The main task is to obtain a solution to control problems that allows you to transfer an unmanned vehicle from the initial position to a given final position at a certain time. Currently, autonomous vehicles are being actively introduced in all areas. Including in Russia, you can find unmanned trucks on the federal highway. Given the development of microprocessor technology and the significant economic benefits of using unmanned vehicles, this task is relevant. A lot of research in the field of control of unmanned vehicles concerns the issue of their use in urban environments and on rough terrain. In this paper, we present a solution to the problem of optimal control of an unmanned vehicle using the maximum principle. The problem of optimal control is solved in a deterministic setting with an integro-terminal criterion. The solution of the two-point boundary value problem arising from the maximum principle was carried out using Newton’s method. The ranges of initial values of conjugate variables are obtained, which ensure the convergence of calculations. For the chosen mathematical model of the course movement of the car, solutions to the problem were obtained. The results of numerical simulation are presented, showing the possibility of using the proposed algorithm to control an unmanned vehicle under various initial and final conditions. The developed algorithm has been successfully applied in the presence of a penalty zone. The algorithm can be used when applying the concept of " flexible trajectories" in the tasks of controlling moving objects.

DIGITALISATION AS A FACTOR OF SOCIOECONOMIC DEVELOPMENT AND ECONOMIC SECURITY OF THE STATE

The modern Ukrainian economy is in a dire situation. It cannot function normally when active hostilities are taking place in the country. Therefore, the problem of determining the factors of the socioeconomic development of the state and its economic security now comes to the fore. Among them, the digitalisation of the country plays an important role. Considering the relevance of the recovery of the Ukrainian economy, which suffered a decline due to the war, it is considered appropriate to carry out a comprehensive analysis of the digitisation state of the country by modern methods. The paper is devoted to the problem of interdependence estimation of the digitisation and socioeconomic development indices of the country. The article aims to improve the complex of mathematical models for assessment and analysis of the digitisation state of the country, which will be supplemented with a model of interdependence indicators of digitisation and socioeconomic development of the state. Implementing the model will allow for determining digitalisation development directions, estimating the socioeconomic development level of the state, as well as ensuring its economic security. In the process of research, the following tasks were set to be solved: to select and form a base of indicators necessary for modelling; to develop a model; to investigate the canonical correlation between socioeconomic and digital development indicators by the canonical analysis methods; to investigate the dispersion of canonical variables observations and to find out the most significant areas of digitalisation improvement. As a result of the study, the highest correlation was evaluated between the network readiness index and the socioeconomic progress index (coefficient 0.98). The socioeconomic progress index is also related to the e-government development index (0.92) and the information and communication technology development index (0.90). Thus, the analysis performed in the paper of the correlation between the sets of digitalisation and the socioeconomic development indexes allows us to conclude the presence of a high level of their significant influence and the importance of forming a system of measures to ensure the proper level of the digital development of the country in these directions. Keywords: modelling, methods, canonical analysis, digitalisation, socioeconomic development, economic security of the state.

Classical relativistic electron-field dynamics: Hamiltonian approach to radiation reaction

Motivated by the renewed interest due to the presently available extreme light sources, the dynamics of a single classical relativistic (spinless) extended electron interacting with a classical electromagnetic field (an incoming radiation and the field radiated by the electron) is revisited. The field is treated in Lorentz gauge, with the Lorentz condition. By assumption, there is a crucial finite cut-off k max on the magnitude of any wavevector contributing to the field (preventing a point electron) and, for a simple formulation, the initial conditions for particle and fields are given in the infinitely remote past. In an infinite three-dimensional vacuum and in an inertial system, Hamilton’s dynamical equations for the particle and the complex field amplitudes acting as canonical variables (a's) yield an exact Lorentz force equation for the former, that includes the incoming radiation and an exact radiation reaction force F RR due to the field radiated by the electron. Uniform motion is obtained as a test of consistency. Based upon numerical computations, some approximations on F RR are given. A covariant formulation is also presented.

Guiding centre motion for particles in a ponderomotive magnetostatic end plug

The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is expressed in terms of canonical action-angle variables, and then an approximate integrable Hamiltonian is introduced, using another set of actions and angles, which describe the centre of oscillation for the particle. The perturbation introduces an effective ponderomotive potential, which to leading order is positive. At the second order, the pseudopotential consists of a sum of terms of the Miller form, and can have either sign. Additionally, at second order, the ponderomotive interaction introduces a modification to the particle effective mass, when considering the motion along the column axis. It is found that particles can be axially confined by the ponderomotive potentials, but acquire radial excursions which scale as the confining potential. The radial excursions of the particle along its trajectory are investigated, and a condition for the minimal rotation frequency for which the particle remains radially confined is derived. Last, we comment on the changes to the aforementioned solution to the pseudopotentials and particle trajectory in the case of resonant motion, that is, a motion which has the same periodicity as the perturbation.

Novel Data-Driven Deep Learning Assisted CVA for Ironmaking System Prediction and Control

Effective control of blast furnace ironmaking system (IS) is crucial to maintain the metallurgical industry in smooth operation. Also, the quality of molten iron (MIQ) can be assessed using indices of phosphorus P, sulfur S, and silicon Si contents, which provide insight into the current state of the molten iron and internal operations of the blast furnace. In this paper, we propose a novel deep learning assisted canonical variate analysis (DLaCVA) method for modeling and predicting MIQ and optimizing IS control. Due to the highly complex physical and chemical reactions within IS, we build a nonlinear state-space model and estimate its state, utilizing DLaCVA. Moreover, we theoretically analyze of how deep learning can aid in state-space modeling, such as deriving the corresponding optimization objective and learning gradient, laying the basis for exploring deep learning in system identification further. Ultimately, we devise a predictive control strategy based on a quadratic performance index to attain optimal MIQ control performance. Experiments utilizing genuine IS data display that DLaCVA outperforms other methods concerning modeling accuracy and control effectiveness.

Alterations to the bovine bacterial ocular surface microbiome in the context of infectious bovine keratoconjunctivitis

BackgroundInfectious bovine keratoconjunctivitis (IBK) is a common cause of morbidity in cattle, resulting in significant economic losses. This study aimed to characterize the bovine bacterial ocular surface microbiome (OSM) through conjunctival swab samples from Normal eyes and eyes with naturally acquired, active IBK across populations of cattle using a three-part approach, including bacterial culture, relative abundance (RA, 16 S rRNA gene sequencing), and semi-quantitative random forest modeling (real-time polymerase chain reaction (RT-PCR)).ResultsConjunctival swab samples were obtained from eyes individually classified as Normal (n = 376) or IBK (n = 228) based on clinical signs. Cattle unaffected by IBK and the unaffected eye in cattle with contralateral IBK were used to obtain Normal eye samples. Moraxella bovis was cultured from similar proportions of IBK (7/228, 3.07%) and Normal eyes (1/159, 0.63%) (p = 0.1481). Moraxella bovoculi was cultured more frequently (p < 0.0001) in IBK (59/228, 25.88%) than Normal (7/159, 4.40%) eyes. RA (via 16 S rRNA gene sequencing) of Actinobacteriota was significantly higher in Normal eyes (p = 0.0045). Corynebacterium variabile and Corynebacterium stationis (Actinobacteriota) were detected at significantly higher RA (p = 0.0008, p = 0.0025 respectively) in Normal eyes. Rothia nasimurium (Actinobacteriota) was detected at significantly higher RA in IBK eyes (p < 0.0001). Alpha-diversity index was not significantly different between IBK and Normal eyes (p > 0.05). Alpha-diversity indices for geographic location (p < 0.001), age (p < 0.0001), sex (p < 0.05) and breed (p < 0.01) and beta-diversity indices for geographic location (p < 0.001), disease status (p < 0.01), age (p < 0.001), sex (p < 0.001) and breed (p < 0.001) were significantly different between groups. Modeling of RT-PCR values reliably categorized the microbiome of IBK and Normal eyes; primers for Moraxella bovoculi, Moraxella bovis, and Staphylococcus spp. were consistently the most significant canonical variables in these models.ConclusionsThe results provide further evidence that multiple elements of the bovine bacterial OSM are altered in the context of IBK, indicating the involvement of a variety of bacteria in addition to Moraxella bovis, including Moraxella bovoculi and R. nasimurium, among others. Actinobacteriota RA is altered in IBK, providing possible opportunities for novel therapeutic interventions. While RT-PCR modeling provided limited further support for the involvement of Moraxella bovis in IBK, this was not overtly reflected in culture or RA results. Results also highlight the influence of geographic location and breed type (dairy or beef) on the bovine bacterial OSM. RT-PCR modeling reliably categorized samples as IBK or Normal.

Forecasting in Stock Markets Using the Formalism of Statistical Mechanics

The possibility and expediency of forecasting in the stock markets are analyzed analytically using the methods and approaches of statistical mechanics. The apparatus of statistical mechanics is used to analyze and forecast one of the most important indicators of the market – the distribution of its logarithmic profitability. The Lotka-Volterra model used in ecology to describe systems of the "predator-prey" type was used as the initial model. It approximates market dynamics adequately. In the article, its Hamiltonian property is used, which makes it possible to apply the apparatus of statistical mechanics. The apparatus of statistical mechanics (using the principle of maximum entropy) makes it possible to implement a probabilistic approach that is adapted to the conditions of stock market uncertainty. The canonical variables of the Hamiltonian are presented as logarithms of stock and bond prices, the joint probability distribution function of stock and bond prices is obtained as a Gibbs distribution. The Boltzmann factor, included in the Gibbs distribution, allows us to estimate the probability of the occurrence of certain stock and bond prices and obtain an analytical expression for calculating the logarithmic return, which gives more accurate results than the widely used normal (Gaussian) distribution. According to its characteristics, the resulting distribution resembles the Laplace distribution. The main characteristics of the resulting distribution are calculated – the mean value, variance, asymmetry, and kurtosis. Mathematical results are presented graphically. An explanation is given of the cause-and-effect mechanism that causes a change in the profitability of the market. For this, the idea of Theodore Modis about the competition between stocks and bonds for the attention and money of investors is developed (by analogy with the turnover of biomass in models of the "predator-prey" type in biology). The results of the study are of interest to investors, theorists, and practitioners of the stock market. They allow us to make thoughtful and balanced investment decisions due to a more realistic idea of the expected return and a more adequate assessment of investment risk.

Macro- and Micronutrient Contents and Their Relationship with Growth in Six Eucalyptus Species

Knowing nutrient allocation dynamics in the tissues and the characteristics related to growth in different forest species is crucial to fertilization management and selecting better species for specific environments, ensuring greater fertilization efficiency and consequent sustainability in the forestry sector through the rational use of fertilizers. The objectives of this study were (i) to evaluate the content of macro- and micronutrients in different tissues of eucalyptus species and (ii) to relate them with their growth. The treatments were composed of six eucalyptus species (Eucalyptus camaldulensis Dehnh., Corymbia citriodora Hook., E. saligna Sm., E. grandis W. Hill ex Maiden, E. urograndis, and E. urophylla S. T. Blake). Macro- (nitrogen, phosphorus, potassium, calcium, magnesium, and sulfur) and micronutrient (boron, copper, iron, manganese, and zinc) contents were determined in the leaves, bark, and sapwood. To study the functional patterns in macro- and micronutrient contents, Canonical Variable Analysis (CVA) was performed. The first two canonical variables in nutrient content of leaves, bark, and sapwood and the growth variables of eucalyptus species accumulated values greater than 80% of variance. The species E. grandis and E. urograndis showed the highest means for volume and total height but showed no differences regarding the concentration of major elements in the tissues, except the iron content in the bark, which was higher compared to other species. CVA proved to be an excellent tool for understanding, identifying, and classifying the strategies of Eucalyptus sp. regarding the content of nutrients in the shoot biomass tissues and may support genetic improvement programs aiming at identifying potential species. Future research involving the use of remotely piloted aircraft and remote sensors could be a strategy to monitor nutrient contents in different parts of trees throughout the cycle of different eucalyptus species.