Evaluating basketball player’s rotation line-ups performance via statistical markov chain modelling

Coaches in basketball often need to know how specific rotation line-ups perform in either offense or defense and choose the most efficient formation, according to their specific needs. In this research, a sample of 1131 ball possession phases of Greek Basket League was utilized, in order to estimate the offensive and defensive performance of each formation. Offensive and defensive ratings for each formation were calculated as a function of points scored or received, respectively, over possessions, where possessions were estimated using a multiple regression model. Furthermore, a Markov chain model was implemented to estimate the probabilities of the associated formation’s performance in the long run. The model could allow us to distinguish between overperforming and underperforming formations and revealed the probabilities over the evolution of the game, for each formation to be in a specific rating category. The results indicated that the most dominant formation, in terms of offense, is Point Guard-Point Guard-Small Forward-Power Forward-Center, while defensively schema Point Guard-Shooting Guard-Small Forward-Center-Center had the highest rating. Such results provide information, which could operate as a supplementary tool for the coach’s decisions, related to which rotation line-up patterns are mostly suitable during a basketball game.

The excitation temperature of the CH 3335-MHz line

ABSTRACT Molecular hydrogen is the main constituent of dense molecular clouds, but is expected to also be a dominant constituent in many environments where CO can no longer be seen, the so-called ‘CO-dark molecular gas’. Based on comparisons of ultraviolet spectroscopy of H2 and optical line observations (4300 Å), CH is a prime candidate to trace H2. Since the optical line (and the UV lines at 3143, 3890, and 3878 Å) require bright background sources (and the CH N = 2←1 ground state rotation line at 149 µm requires space-based, or stratospheric, observations), the hyperfine structure transition at 3335 MHz is a potentially important tool for probing the CO-dark molecular gas. However, the excitation of this transition is complicated, and has often been found to be inverted, making column density determinations uncertain. To clarify the potential use of the 3.3-GHz line as a proxy for H2, we have observed the CH 3335-MHz line with the Arecibo 305-m radio telescope along 16 lines of sight towards stars with existing measurements of the 4300-Å line. By comparing the CH column densities from optical and UV absorption lines to the CH radio emission line, we can derive the excitation temperature (Tex) of the 3335-MHz transition. We obtain a wide range of excitation temperatures for nine lines of sight, including some with |Tex| < 5 K. The common assumption that Tex for the 3335-MHz line is always much larger than the background temperature (Tbg) is not always warranted and can lead to significant errors in the value of N(CH).

Consistency Between Posterior Condylar Axis (+3˚ external rotation) Line and Clinical Transepicondylar Axis Line in Primary Total Knee Arthroplasty

Objectives: Purpose of this study is to as certain consistency between posterior condylar axis (PCA) + 3˚ external rotation line and clinical transepicondylar axis (cTEA) line in primary total knee arthroplasty cases. Materials-Methods: During surgery, following distal femoral cut PCA +3 degree external rotation line and cTEA line drawn on the distal femoral cutting surface by ruler and pencil. The both lines on distal femur were recorded by digital camera and relationship between lines was ascertained in reference to PCA +3 degree external rotation [parallel (P), Internal rotation (IR) and External Rotation (ER)]. Results: 9 knees of 9 patients [1 men, 8 women; average age 67 (59-80 age)] were constituted the study group. Evaluation results of the photographs revealed that clinical TEA line in comparison PCA +3 degrees external rotation line was ER in 9 knees (100%) whose mean angles 2.7˚ (1-6) and detected external roation with mean angle 4.7˚ (2-7) in 9 knees. Conclusion:: For determination of FC rotation in surgery setting, different results between cTEA and PCA + 3 degrees techniques possibly may due to disadvantages of techniques and anatomic variation of distal femur. Thus, using both techniques for check each other’s results seems unsafe. In custom made prosthesis, which can be done in the future it will be measured by CT. Keywords: Total knee arthroplasty, femoral component, rotational alignment, femoral transepicondylar axis, posterior condylar axis