Graphical Interpretation Research Articles

Evaluation of Lower Extremities Power, Movement, Position and Effectiveness in Volleyball

Background: This paper presents research on the comparison and evaluation of lower limb power, movement, position on the court, and effectiveness in the players of men’s volleyball. The study involved professional players in the first division of a men’s volleyball team. The main aim of this paper was to show the correlation between lower limb power, movement, position on the pitch, and volleyball efficiency. Methods: The authors presented basic somatic characteristics of anthropology metrics, advanced research results obtained with the Optojump measuring system, players’ results statistics obtained with the Data Volley software (v.4.2024.01), and by applying scientific statistical methods and graphics interpretation. Results: The analyses with the Kruskal-Wallis test showed statistically significant differences in all the variables studied. Flight time (TF, H = 122.967; p < 0.001.) was the shortest for the players in the libero position, then the setter, attacker, middle and longest flight time was shown by the receiving players. The height of the jumps (JH, H = 123.018; p < 0.001) was the highest for receiving and mid players, and then attackers and setters, and the lowest jumps were recorded by libero players. The highest power of lower limbs (P, H = 20.392; p < 0.001) was characteristic for receivers, setters, mid-players and, curiously, libero achieved a better result than attackers. Conclusions: The analysis shows that the power of the lower extremities in volleyball players is associated with the function they perform on the court.

THE STUDY OF THE SPATIO-TEMPORAL ORIENTATION ABILITY OF STUDENTS PRACTICING SPORTS DANCE AT THE UNIVERSITY OF BUCHAREST

Background. Sports dance is characterized by a complex coordination, its most important components being, in our opinion: the segmental, general and multisegmental coordination; the capacity of kinesthetic differentiation; the static and dynamic coordination, the ability of spatio-temporal orientation; the ability to perceive and reproduce musical rhythm and tempo. Sports dance lessons are held in the University of Bucharest with students who opt for this discipline without having a prior selection. In sports dance, all the motor capacities are involved in different weights, but we proposed for this study to analyze from the perspective of the coordinative capacities, the spatio-temporal orientation. Objectives. The subjects in this study are students in the 1st and 2nd years, belonging to different faculties of the university and they were divided into the control and the experimental groups. Both groups worked to test a salsa choreography during the lessons. In the experimental group, the choreography was practiced facing points 1,3,5,7, and in the control group, the choreography was practiced facing point 1. The test was realized with reference to point 5. Methods. The working methods used are observation, testing method, statistical-mathematical and graphical interpretation method. Results. The results were significantly better in the experimental group compared to the control group. The subjects in the experimental group were able to orient themselves better in space and time in a percentage of 85% and in the control group the percentage was about 30% Conclusion. We believe that the orientation in space and time can be improved by simple means, prepared by the teacher in the sports discipline, the methodological work being implemented according to the groups.

Optimizing System Efficiency and Reliability: Integrating Semi-Markov Processes and Regenerative Point Techniques for Maintenance Strategies in Plate Manufacturing

This paper offers a modeling methodology to evaluate similar systems’ performance and optimize system effectiveness with customized maintenance plans. This strategy, which combines regeneration point techniques with semi-Markov processes, is used to assess a plate manufacturing company’s system. Key insights are obtained using a thorough cost-benefit analysis that includes numerical analysis, graphical interpretations, and system efficacy indicators. The study clarifies the dynamics of the system’s reliability under different repair rates by showing an inverse relationship between Mean Time to System Failures (MTSF) and failure rate. Additionally, the analysis clarifies how profit is affected by failure rate, highlighting the necessity of efficient maintenance plans from an economic standpoint. This research highlights the growing significance of availability and dependability in technology-driven sectors and emphasizes the need for dependable systems. This paper makes a substantial contribution to the knowledge already available in the field of reliability engineering by providing a thorough framework that combines regeneration point approaches and semi-Markov processes. The metrics that are obtained offer a comprehensive understanding of the behavior of the system, which in turn helps industry practitioners make well-informed decisions.

Precision detection and identification method for apparent damage in timber components of historic buildings based on portable LiDAR equipment

For the purpose of preservation and restoration of historic timber buildings, it is critical that damage to timber components must be detected and identified accurately since proper detection and identification lay the foundation for scientific utilization and preservation of cultural heritage. Portable smart devices with integrated LiDAR sensor technology have significantly advanced, enabling them to be major pedestals for damage detection. An iPhone Pro based technique is therefore suggested for the precise detection and diagnosis of apparent damage to the timber components. The study consists of three major procedures. First, an apparent data collection of the timber components was conducted. A high-resolution triangular mesh model was utilized for precision detection and identification. Point cloud and texture data were the main constituents of this data collection. Second, a technique for image processing and apparent damage analysis was proposed for crack detection in historic timber buildings. This approach can be used to identify, recognize,and assess damage to timber components such as cracks, rotting, and knots. Finally, actual measurements of the timber components in Datong, Shanxi Province, at the Great Temple Corner, proved the effectiveness of the iPhone 12 Pro as a substitute approach to the conventional inspection equipment. The findings indicate that the iPhone 12 Pro, which has a built-in LiDAR sensor, performs exceptionally well in terms of effectiveness, accuracy, and graphical interpretation when identifying apparent damage to historic timber components. Moreover, it has the potential to substitute traditional measurement, 3D scanning, and other detection and identification techniques. Even though damage detection and identification of historical timber buildings has reached a mature stage in terms of portable, refined, and digital transformation, such technique can serve as a compatible addition as a safe, affordable, and paradigm shifting technical solution for detection and identification of historic building components.

Octonion quadratic-phase Fourier transform: inequalities, uncertainty principles, and examples

In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt’s and sharp Hausdorff–Young’s inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark’s, and Heisenberg’s uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases.

Heatwave Intensifications in Armenia: Evidence From Temporal and Spatial Analysis of Observational Data Over the Last Decades

ABSTRACTIncreasing temperatures cause the weather to become more severe. Studying how heatwaves (HWs) impact individual heat exposure and susceptibility is vital for building climate change mitigation and adaptation measures. So, this study explores the impact of HWs on individual heat exposure and susceptibility. The assessment was based on the highly complex topographic region contribution to HWs in the Republic of Armenia (RA) using data from 16 meteorological stations for the extended warm season (May–September). We developed a regional HW catchment program to estimate the HW indices' responses to climatic change and to present them in terms of topography changes. The Mann–Kendall (MK) test was used to determine the statistical significance of the trends for 10 distinct HW indicators using linear and exponential trends along with graphical interpretations. This study reveals a large‐scale, significant increasing trend in annual maximum temperatures (Tmax) and observed HWs over the period 1955–2019. The rising temperature is accompanied by an increase in HW indices, particularly at low altitudes up to 1250 m above sea level (ASL), where the main population centres and national crop production are concentrated. According to our classification, the above‐mentioned areas have faced extreme and severe increases in HW intensity, covering more than 60% of the country's territory. Moreover, not only the intensity and frequency have been identified but the HW period extension as well. This extreme increase has been found in the low‐lying highly populated and intensively cultivated areas, such as in the Ararat valley. These results have implications for future climate assessments, adaptation strategies, agriculture and public health in Armenia. The development of targeted mitigation measures and adaptation strategies informed by these findings is essential for addressing the escalating challenges posed by HWs in the region.

Study of first-order quantum corrections of thermodynamics to a Dyonic black hole solution surrounded by a perfect fluid

In this work, we review the metric for a dyonic global monopole with a perfect fluid. To calculate the standard temperature of a Dyonic black hole surrounded by a perfect fluid, we analyze the graphical interpretation of the Hawking temperature concerning the horizon under the effects of the black hole's surrounding field and electric-magnetic charges. For this purpose, we follow the semi-classical method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Lagrangian equation in the presence of quantum gravity as seen in the generalized uncertainty principle (GUP). We calculate the improved temperature of a Dyonic black hole using a bosonic tunneling strategy based on the Hamilton-Jacobi technique. We observe that the physical state of the Dyonic black hole is surrounded by a perfect fluid under the effects of the black hole solution and the gravity parameter. Further, we examine the improved entropy to study the influences of quantum gravity and black hole geometry on entropy. We explore the graphical behavior of entropy based on the black hole's horizon structure and analyze the influence of perfect fluid parameters, electric charge, magnetic charge, and quantum gravity on entropy. Finally, we investigate the unstable and stable conditions of a black hole via graphical results.

A new solution approach to proportion delayed and heat like fractional partial differential equations

The importance of fractional partial differential equations (FPDEs) may be observed in many fields of science and engineering. On the same hand their solutions and the approaches for the same are also very important to notice due to the effectiveness of the methods and accuracy of the results. This work discusses the diverse estimated analytic description of fractional partial differential equations (with proportion delay and heat like equation), applying the Iterative Laplace Transform Method. The specified method represents a significant advancement in the tool case of applied mathematicians and scientists. Its ability to efficiently and accurately solve complex differential equations, especially FPDEs. Here in this work, the solution of four test problems of FPDEs related to proportion delay and heat like equations is obtained for testing the validity and asset of the Iterative Laplace Transform Method. Further their numerical and graphical interpretations are also mentioned.

Covalent Labeling Automated Data Analysis Platform for High Throughput in R (coADAPTr): A Proteome-Wide Data Analysis Platform for Covalent Labeling Experiments.

Covalent labeling methods coupled to mass spectrometry have emerged in recent years for studying the higher order structure of proteins. Quantifying the extent of modification of proteins in multiple states (i.e., ligand free vs ligand-bound) can provide information on protein interaction sites and regions of conformational change. Though there are several software platforms that are used to quantify the extent of modification, the process can still be time-consuming, particularly for proteome-wide studies. Here, we present an open-source software for quantitation called Covalent labeling Automated Data Analysis Platform for high Throughput in R (coADAPTr). coADAPTr tackles the need for more efficient data analysis in covalent labeling mass spectrometry for techniques such as hydroxyl radical protein footprinting (HRPF). Traditional methods like Excel's Power Pivot (PP) are cumbersome and time-intensive, posing challenges for large-scale analyses. coADAPTr simplifies analysis by mimicking the functions used in the previous quantitation platform using PowerPivot in Microsoft Excel but with fewer steps, offering proteome-wide insights with enhanced graphical interpretations. Several features have been added to improve the fidelity and throughput compared to those of PowerPivot. These include filters to remove any duplicate data and the use of the arithmetic mean rather than the geometric mean for quantitation of the extent of modification. Validation studies confirm coADAPTr's accuracy and efficiency while processing data up to 200 times faster than conventional methods. Its open-source design and user-friendly interface make it accessible for researchers exploring intricate biological phenomena via HRPF and other covalent labeling MS methods. coADAPTr marks a significant leap in structural proteomics, providing a versatile and efficient platform for data interpretation. Its potential to transform the field lies in its seamless handling of proteome-wide data analyses, empowering researchers with a robust tool for deciphering complex structural biology data.

Combining categorical boosting and Shapley additive explanations for building an interpretable ensemble classifier for identifying mineralization-related geochemical anomalies

The vast majority of shallow and deep learning techniques used to identify mineralization-related geochemical anomalies are black-box algorithms that lack the ability to elucidate the individual contributions of each element towards the model predictions. In addition, most of the anomaly identification models established by both shallow and deep learning algorithms lack robustness. Establishing interpretable and robust machine learning models is a challenge in applying machine learning techniques to geochemical anomaly identification. To this end, the categorical boosting (CatBoost) algorithm was employed to build a robust ensemble classifier to identify mineralization-related anomalies from the 1:50,000 geochemical reconnaissance data (stream sediment survey) in the Yeniugou area of Xinjiang (China). The receiver operating characteristic curve (ROC) and precision-recall (P-R) curve of the ensemble model were plotted, and the area under the ROC curve (AUC) as well as the area under the P-R curve (AUPRC) of the ensemble model were calculated to measure the performance of the ensemble model. The ROC curve of the ensemble model approximates that of the perfect classification model. The P-R curve of the ensemble model is close to the upper right corner of the P-R space. The AUC and AUPRC values of the ensemble model reaches 0.9981 and 0.7816, respectively. The identified polymetallic mineralization-related geochemical anomalies account for 3% of the whole exploration area, correctly identifying all known polymetallic deposits. To enhance the interpretability of the CatBoost model, the Shapley additive explanations (SHAP) tool was adopted to graphically interpret the predictions of the ensemble model. The graphic interpretation shows that the importance order of the 14 elements is Ni-Au-Ag-Sn-As-Cr-Zn-Cu-Pb-Sb-W-Bi-Mo-Co. Cu and Ni are most likely metallogenic elements of the study area. Cu interacts with Ni, Ag, As, Sn, Cr, Zn, Pb, Sb, W, Bi, and Co; and Ni interacts with Au, Sn, As, Zn, Cu, W, Bi, and Co. Two polymetallic prospective areas were delineated in the study area. One is Cu-Ni-polymetallic mineralization prospective area, and the other is Ni-polymetallic mineralization prospective area. It can be concluded that the combination of CatBoost and SHAP is an effective way to construct an interpretable ensemble model with high-performance and robustness in identifying mineralization-related geochemical anomalies.

Cattaneo-Christov fluxes for nonlinear mixed convective entropy generated Reiner-Rivlin material flow

Thermal and solutal transportation processes involve in tremendous useful applications related to heat exchanger, scientific, micro-electronic device technologies and industry sectors like nuclear reactors cooling, marine engineering, nanotechnology, thin-film technology, biomedical applications and thermal conduction in soft tissue. In view of such useful applications the Cattaneo-Christov analysis for nonlinear mixed convective Reiner-Rivlin material flow in presence of constant applied magnetic field is considered. Heat source, magnetohydrodynamics and radiation are incorporated in energy equation. Cattaneo-Christov flux is employed to discuss the thermal and mass transport characteristics. Entropy calculation in radiating flow is discussed. The proposed non-linear systems are transformed into dimensionless ordinary systems through appropriate transformation. Non-linear ordinary expressions are computed for convergent series solutions through Optimal homotopy analysis technique (OHAM). Graphical interpretations for quantities under interest against pertinent variables are explored. Large magnetic parameter has opposite impact for entropy and fluid flow. An increase of temperature through thermal relaxation time parameter is noticed. Velocity has same trend for both mixed convection and Reiner-Rivlin fluid variables. Reduction in concentration is seen for solutal relaxation time parameter. Temperature enhancement is witnessed in presence of heat generation. Entropy rate enhancement for radiation is observed. Decrease in concentration is noticed for reaction. Entropy rate increases against diffusion variable is enhanced.

Peristaltic Flow of Jeffrey Fluid in an Inclined Porous Tube with Multi-Thrombosis

The fact that multiple thrombosis opposes blood flow and flow is rare in blood vessels is refined to a normal condition with catheter application. The inner surface of the circular blood arteries may not be smooth in the majority of diseased instances. Additionally, the small blood vessel peristalsis mechanism is formed. In this paper, we discuss a mathematical model for the flow of biological fluid (blood) in a circular tube with multi-thrombosis considered under peristaltic wave propagation. The blood flow in this tube is restricted due to the many thromboses present, and the flow is redesigned with the aid of a catheter. We model this non-Newtonian blood flow issue for Jeffrey fluid. In most pathological cases, the inner surface of the circular blood vessels may not be smooth. Further, the mechanism of the peristalsis is established for small blood vessels. Because of this biological phenomenon, the peristaltic movement of Jeffrey fluid in a porous annulus with slip is examined. Equations that govern energy and momentum are solved exactly, and graphical interpretation is made using mathematical software. Streamline graphs show the many thromboses that increase in height. The wall shear stress graphs show a sinusoidally advancing wave with peaks and dips of different amplitudes. This tube's unique crest and trough amplitude are caused by the presence of multiple thromboses. We obtained the impact of the pressure gradient on the permeability parameter (β). The pressure gradient falls as the permeability parameter rises.

The origin of interparticle aggregation: Probing the long-range hydrophobic forces between particles induced by nanobubbles in aqueous solutions

The processes of particle–particle collision, adhesion, and detachment are omnipresent in the solid particle separation and purification processes. Nanobubbles, serving as a critical medium for interactions between particles, play a pivotal role in numerous fields of separation and purification such as mineral flotation, hydrometallurgy, chemical engineering, materials, and more. The elucidation of the principles governing nanobubbles’ involvement in interparticle interactions holds significant implications for enhancing and controlling separation and purification processes. The impact of nanobubbles on interparticle interactions between calcite particles was investigated in this study by measuring the forces between particles with and without nanobubbles and analysing them using DLVO and EDLVO theories. The experimental results demonstrate the occurrence of long-range attractive forces and significant adhesion between particles in the presence of nanobubbles under natural pH and ultrapure water conditions, phenomena that cannot be explained by classical DLVO theory. The generation of long-range hydrophobic attraction at the particle interface due to nanobubbles was confirmed through further EDLVO calculations and modifications, enhancing the stability of particle flocculation. Additionally, for the first time, the entire process from contact to detachment between the “particle-nanobubble” system in atomic force microscopy (AFM) simulations was described by combining experimental force curves with stepwise graphical interpretation. This approach provides valuable guidance for the analysis of bubble and soft matter interactions under AFM. The results of this study indicate that nanobubbles can indirectly alter the hydrophilicity and hydrophobicity of particles, increasing the probability of particle adhesion and reducing the probability of desorption, thereby enhancing the stability of particle flocculation.

Leveraging Collaborative Partnerships to Enhance NWS and Emergency Management Communications through Exercising

Abstract Tabletop exercises examining weather-related hazards are not uncommon but are often built around somewhat generic scenarios that only touch on the meteorological communication environment at a very shallow level. A recent exercise in central Oklahoma sought to change that. A local emergency manager, personnel from a National Weather Service (NWS) forecast office, and a severe weather researcher with a background in exercise design and facilitation worked together to create and deliver a realistic severe weather simulation. Exercise participants were exposed to detailed forecast information via NWSChat—a dedicated communication tool used to connect NWS forecasters, emergency managers, and media members for real-time information sharing. NWS forecasters were able to both actively play in the exercise due to the use of NWSChat and observe how local decision-makers interpreted and utilized the impact-based decision support service (IDSS) graphics and short-term forecast updates. The collaborative approach of developing a detailed scenario with numerous real-world IDSS graphics, along with the use of NWSChat for real-time delivery, resulted in overwhelmingly positive feedback from the participants. The local emergency management office identified numerous areas for improvement in communicating real-time forecast information across their jurisdiction, along with gaps in current plans and resources. Meanwhile, the NWS forecast office had the opportunity to experiment with using the new NWSChat platform in a high-impact severe weather environment before a real-world event took place. Forecasters also gained insight into current IDSS graphic interpretation, noting areas for improved messaging to end users, such as adding storm motion to existing severe weather graphics.

Development of computational thinking of students – future teachers by means of solving problems on the processing of structured data

The problem and the purpose. Computational thinking is one of the categories that currently assesses the quality of specialist training, including that of a future teacher. The mentor of a digital school needs computational thinking skills for the successful implementation of work functions and for determining the trajectory of his personal development. The purpose of the study is to identify the possibilities of structured data processing tools for the development of computational thinking of future teachers. Research methods. Structured data is information organized in the form of tables and files of other formats. The research was conducted on the basis of Vyatka State University (Russian Federation). The experiment involved 330 students studying in the field of training: 44.03.05 Pedagogical studies (with two specialties). The use of structured data processing tools was purposefully carried out in the classes of the design discipline from the block “Digital technologies in education”. A set of techniques was used to determine the level of computational thinking such as “Geometric figures”, “Quantitative relations”, “Complex analogies”. For statistical processing of data, Pearson's χ2 (chi-square) criterion is used. Results. Interaction in the experimental group was implemented in stages: the study of basic tools; development of skills of graphical interpretation; the use of functions that allow analyzing and protecting the contents of structured data. The features of the proposed information interaction are: students with different educational paths are involved; the technology of reasoned discourse is applied at every stage. Statistically significant differences were revealed in the qualitative changes that occurred in the pedagogical system (χ2 = 7.024; p < 0.05). Conclusion. The tasks on the processing of structured data that maximize the development of computational thinking are formulated: conditional formatting; establishing links between the source data and the result; automatic recalculation of the result; filtering, sorting, etc. The difficulties that complicate the use of the proposed innovations are defined: how to state a task and to adapt it to the specifics of the field of training; how to organize a reasoned discourse.

Investigating the Temperature-Dependent Kinetics in Humidity-Resilient Tin–Titanium-Based Metal Oxide Gas Sensors

Humidity is a well-known interference factor in metal oxide (MOX) gas sensors, significantly impacting their performance in various applications such as environmental monitoring and medical diagnostics. This study investigates the effects of adsorbed water on MOX conductivity using two different materials: pure tin oxide (SnO2) and a tin–titanium–niobium oxide mixture (SnTiNb)xO2 (STN). The results reveal that (SnTiNb)xO2 sensors exhibit reduced sensitivity to humidity compared to pure tin oxide, rendering them more suitable for applications where humidity presence is critical. We aimed to shed light on a still controversial debate over the mechanisms involved in the water surface interactions for the aforementioned materials also by exploring theoretical studies in the literature. Experimental analysis involves varying temperatures (100 to 800 °C) to understand the kinetics of surface reactions. Additionally, a brief high-temperature heating method is demonstrated to effectively remove adsorbed humidity from sensor surfaces. The study employs Arrhenius-like plots for graphical interpretation, providing insights into various water adsorption/desorption phenomena. Overall, this research contributes to a deeper understanding of the role of humidity in MOX gas sensor mechanisms and offers practical insights for sensor design and optimization.

Exploring the role of disciplinary knowledge in students’ covariational reasoning during graphical interpretation

BackgroundThis study investigates undergraduate STEM students’ interpretation of quantities and quantitative relationships on graphical representations in biology (population growth) and chemistry (titration) contexts. Interviews (n = 15) were conducted to explore the interplay between students’ covariational reasoning skills and their use of disciplinary knowledge to form mental images during graphical interpretation.ResultsOur findings suggest that disciplinary knowledge plays an important role in students’ ability to interpret scientific graphs. Interviews revealed that using disciplinary knowledge to form mental images of represented quantities may enhance students’ covariational reasoning abilities, while lacking it may hinder more sophisticated covariational reasoning. Detailed descriptions of four students representing contrasting cases are analyzed, showing how mental imagery supports richer graphic sense-making.ConclusionsIn the cases examined here, students who have a deep understanding of the disciplinary concepts behind the graphs are better able to make accurate interpretations and predictions. These findings have implications for science education, as they suggest instructors should focus on helping students to develop a deep understanding of disciplinary knowledge in order to improve their ability to interpret scientific graphs.

Determination of the Duration of Installation Using a Digital Model of the Technological Cycle of a Tower Crane

Satement of the problem. The initial information for the development of working organizational and technological documentation is the quantitative values established by the project (for example, the duration and load capacity of a tower crane). Recommendations on the choice of the leading machine of the technological process of installation of precast concrete structures (adj. B STO NOSTROY 2.7.211-2016) do not provide for an assessment of the change in the duration of the technological cycle depending on the height of the installation horizon. Such an omission inevitably leads to an increase in the duration of construction and installation work. In this paper, it is assumed that the construction of a digital model of the technological cycle of a tower crane for the installation of each reinforced concrete structure will provide a higher reliability of calculating the duration of work, and with the help of such a model, it is possible to determine the requirements for the lifting/lowering speed of a tower crane. Results. The requirements for the initial data that are necessary to build a digital model of the technological cycle of a tower crane during the installation of precast concrete are formed. An analytical dependence and its graphical interpretation are obtained to determine the duration of the technological cycle depen-ding on the height of the installation horizon. The comparison of the duration value set by the calendar schedule and obtained as a result of summing the durations of each technological cycle of the tower crane is carried out. Conclusions. In the recommendations for choosing a tower crane for the installation of reinforced concrete structures, it is necessary to add characteristics that describe the high-speed mode of movement of the building structure. The influence of the speed modes of the tower crane on the duration set by the project should be assessed using a digital moth of the technological cycle of the tower crane. The assessment of compliance with the speed modes of the tower crane should be carried out based on a comparison of the estimated duration of the work set by the project and the sum of the durations of each technological cycle of the tower crane obtained as a result of the use of a digital model.

Diagnostics for categorical response models based on quantile residuals and distance measures

Polytomous categorical data are frequent in studies, that can be obtained with an individual or grouped structure. In both structures, the generalized logit model is commonly used to relate the covariates on the response variable. After fitting a model, one of the challenges is the definition of an appropriate residual and choosing diagnostic techniques. Since the polytomous variable is multivariate, raw, Pearson, or deviance residuals are vectors and their asymptotic distribution is generally unknown, which leads to difficulties in graphical visualization and interpretation. Therefore, the definition of appropriate residuals and the choice of the correct analysis in diagnostic tools is important, especially for nominal data, where a restriction of methods is observed. This paper proposes the use of randomized quantile residuals associated with individual and grouped nominal data, as well as Euclidean and Mahalanobis distance measures, as an alternative to reduce the dimension of the residuals. We developed simulation studies with both data structures associated. The half-normal plots with simulation envelopes were used to assess model performance. These studies demonstrated a good performance of the quantile residuals, and the distance measurements allowed a better interpretation of the graphical techniques. We illustrate the proposed procedures with two applications to real data.

Features of the Development of the Circular Economy in Livestock Production of the Agricultural Sector in the Context of Climate Change

The goal is to analyze the current state of development of agro-industrial production in the context of circular and climate economy of Kazakhstan with emphasis on identifying the elements of its key aspects in livestock farming and determining the influence of climatic factors on this economic system. Methods – statistical analysis and graphical interpretation of data, comparative assessment of linear and circular economic models. Materials from scientific publications, regulations, as well as interviews with experts were used. Results - recommendations for transition to sustainable circular economy structure in agricultural sector of Kazakhstan have been developed, aimed at increasing the efficiency of resource potential, reducing negative impact on environment and creating new opportunities for business and innovation in the country's agro-industrial complex. Measures have been proposed to improve the infrastructure for processing and disposal of agricultural waste and use of modern technologies in the industry. Conclusions - implementation of the principles of circular economy helps to increase energy efficiency and reduce negative impact on biosphere and ecosystems, creating conditions for expanding the scope of innovative entrepreneurship - “green” business: new jobs, appropriate infrastructure, “green” logistics, etc. Principles of circular economy: circular supply (limited resources are replaced by completely renewable sources); extending the life cycle of products through modernization and reconstruction; recycling (restoration and recycling of product residues). Resourceefficient modification is an opportunity for innovation at all stages of new value formation, which gives not only good final results, but also leads to them with lower material, energy and environmental costs.