Inter-team variability in game play under critical game scenarios: a study in high-level men’s volleyball using social network analysis (Variabilidad entre equipos en el juego bajo escenarios críticos de juego: un estudio en voleibol masculino de alto ni

Critical scenarios are highly relevant to match analysis because they contribute to a better understanding of performance and provide essential information about team evolution. The goal of this study was to investigate inter-team variability in high-level men's volleyball during critical game scenarios (i.e., non-ideal setting conditions). Ten matches of the Men’s 2019 Volleyball Nations League Finals (Russia, USA, Poland, Brazil, Iran, France) were analyzed (n = 649 plays). Six independent Eigenvector Centrality networks were created (632 nodes; 3507 edges) using Social Network Analysis. When playing under critical scenarios the top two ranked teams differed in side-out attack. Specifically, the USA presented quick attacks, mainly in zone 4, using both the strong attack and exploration of the block. Conversely, Russia presented a game with high attack tempos and strong attacks. The USA and Russia also differed from Poland and Brazil in their approach to the game, the latter two teams using a varied attack (between strong, exploited, and directed attacks). After one error in attack, most teams presented a game style characterized by strong attacks, although Russia played using exploration of the block. The study shows teams competing at the same competitive level have differences in game patterns. The variability in approaches to the attack in critical scenarios (e.g., under non-ideal setting conditions and/or after consecutive attack errors) revealed that teams find different solutions for similar problems. Findings imply that match analysis should focus on exploring inter-team differences in gameplay while being cautious when interpreting aggregate data. Resumen. Los escenarios críticos son muy relevantes para el análisis de partidos porque contribuyen a una mejor comprensión del rendimiento y proporcionan información esencial sobre la evolución del equipo. El objetivo de este estudio fue investigar la variabilidad entre equipos en el voleibol masculino de alto nivel durante escenarios críticos de juego (principalmente en condiciones de colocación no ideales). Se analizaron diez partidos de las Finales de la Liga de Naciones de Voleibol Masculino 2019 (Rusia, Estados Unidos, Polonia, Brasil, Irán, Francia) (n=649 jugadas). Se crearon seis redes de centralidad de autovector independientes (632 nodos; 3507 bordes) utilizando el análisis de redes sociales. Cuando se jugaba en escenarios críticos, los dos mejores equipos clasificados diferían en ataque lateral. Específicamente, los Estados Unidos presentaron ataques rápidos, principalmente en la zona 4, utilizando tanto el fuerte ataque como la exploración del bloqueo. Por el contrario, Rusia presentó un juego con altos ritmos de ataque y ataques fuertes. Los Estados Unidos y Rusia también se diferenciaron de Polonia y Brasil en su enfoque del juego, los dos últimos equipos utilizando un ataque variado (entre ataques fuertes, explotados y dirigidos). Después de un error en ataque, la mayoría de los equipos presentaron un estilo de juego caracterizado por ataques fuertes, aunque Rusia jugó utilizando la exploración del bloque. El estudio muestra que los equipos que compiten al mismo nivel competitivo tienen diferencias en los patrones de juego. La variabilidad en los enfoques del ataque en escenarios críticos (en condiciones de colocación no ideales y/o después de errores de ataque consecutivos) reveló que los equipos encuentran diferentes soluciones para problemas similares. Los hallazgos implican que el análisis de partidos debe centrarse en explorar las diferencias entre equipos en el juego y, al mismo tiempo, ser cauteloso al interpretar los datos agregados.

The Application of PCA and SVM in Rolling Bearing Fault Diagnosis

The key to the fault diagnosis is feature extracting and fault pattern classifying. Principal components analysis (PCA) and support vector machine (SVM) method are introduced to recognize the fault pattern of the rolling bearing in this paper. Multidimensional correlated variable is converted into low dimensional independent eigenvector by means of PCA. The pattern recognition and the nonlinear regression are achieved by the method of SVM. In the light of the feature of vibrating signals, eigenvector is obtained using PCA, fault diagnosis of rolling bearing is recognized correspondingly using SVM fault classifier. Theory and experiment show that the recognition of fault diagnosis of rolling bearing based on PCA and SVM theory is available in the fault pattern recognition and provides a new approach to intelligent fault diagnosis.

Degenerate and Near Degenerate Materials

The Stroh formalism presented in Sections 5.3 and 5.5 assumes that the 6×6 fundamental elasticity matrix N is simple, i.e., the three pairs of eigenvalues pα are distinct. The eigenvectors ξα (α=l,2,3) are independent of each other, and the general solution (5.3-10) consists of three independent solutions. The formalism remains valid when N is semisimple. In this case there is a repeated eigenvalue, say p2=p1 ,but there exist two independent eigenvectors ξ2 and ξ1 associated with the repeated eigenvalue. The general solution (5.3-10) continues to consist of three independent solutions. Moreover one can always choose ξ2 and ξ1 such that the orthogonality relations (5.5-11) and the subsequent relations (5.5-13)-(5.5- 17) hold. When N is nonsemisimple with p2=p1, there exists only one independent eigenvector associated with the repeated eigenvalue. The general solution (5.3-10) now contains only two independent solutions. The orthogonality relations (5.5-11) do not hold for α,β=l,2 and 4,5, and the relations (5.5-13)-(5.5-17) are not valid. Anisotropic elastic materials with a nonsemisimple N are called degenerate materials. They are degenerate in the mathematical sense, not necessarily in the physical sense. Isotropic materials are a special group of degenerate materials that happen to be degenerate also in the physical sense. There are degenerate anisotropic materials that have no material symmetry planes (Ting, 1994). It should be mentioned that the breakdown of the formalism for degenerate materials is not limited to the Stroh formalism. Other formalisms have the same problem. We have seen in Chapters 8 through 12 that in many applications the arbitrary constant q that appears in the general solution (5.3-10) can be determined analytically using the relations (5.5-13)-(5.5- 17). These solutions are consequently not valid for degenerate materials. Alternate to the algebraic representation of S, H, L in (5.5-17), it is shown in Section 7.6 that one can use an integral representation to determine S, H, L without computing the eigenvalues pα and the eigenvectors ξα. If the final solution is expressed in terms of S, H, and L the solution is valid for degenerate materials.

Stiff systems of ordinary differential equations. Part 1. Completely stiff, homogeneous systems

For the completely stiff real homogeneous systemwhere e is a small positive parameter, a method is given for the construction of a basis for the solution space.If A has n linearly independent eigenvector functions, then there exists a choice of these, {si}, with corresponding eigenvalue functions {λi}, such that there is a local basis for solution, that takes the formwhere vi is a vector that tends to zero with e. In general, a basis of this form exists only on an interval in which the distinct eigenvalues have their real parts ordered. A construction is provided for continuing any solution across the boundaries of any such interval. These results are proved for a finite or infinite interval for which there are only a finite number of points at which the ordering of the real parts of eigenvalues changes.