Search Results (57)

The Lambert W is a Bernstein function and hence the cumulant function of a positive infinitely divisible law, the Lambert law $L(\Lambda )$. The Lambert law is self-decomposable with a unit rate compound Poisson background driving Lévy process (BDLP) with a certain jump law $L\left(J\right)$. Thus, it satisfies the random perpetuity relation $\Lambda \stackrel{L}{=}U(\Lambda +J)$, where U has the standard uniform law, as well as the relation $\Lambda \stackrel{L}{=}U\mathcal{S}J$, where $\mathcal{S}$ is the stationary-excess operator. If the law of J is unspecified, then these two in-law relations together characterise the law of $\Lambda$. Generalisations are pursued in which the Poisson jump rate a is arbitrary. If $a\ne 1$, the above two conditions determine a family of positive infinitely divisible laws for which the Laplace–Stieltjes transforms satisfy an algebraic trinomial equation investigated by Lambert and Euler. These laws occur as limiting distributions of shot noise processes and continuous-time branching processes. A sequence of n-times self-decomposable positive laws derived from a given subordinator is called a BDLP ladder. The BDLP ladder that includes the Lambert law has cumulant functions which are polynomial forms of the Lambert function. Under moment conditions, general BDLP ladder laws are asymptotically normal or stable. Full article

Cell Painting enables high-dimensional phenotypic profiling of cellular states, but retrieval-based interpretation depends on whether the chosen feature space preserves task-relevant biological relationships. With pretrained Cell Painting feature extractors increasingly available, feature spaces should be qualified before downstream biological retrieval. Here, we developed a task-aware workflow for evaluating Cell Painting feature spaces on a curated U2OS JUMP-MOA reference plate. Three pretrained models, CellPaintSSL, OpenPhenom, and uniDINO, were applied in a zero-shot setting to the same image set, and the resulting profiles were analyzed using a copairs-based mean average precision (mAP) retrieval framework. We assessed compound-induced activity relative to dimethyl sulfoxide (DMSO) controls, same-compound profile resolution among active perturbations, and mechanism-of-action (MOA) annotation recovery at the compound-profile level. All three feature spaces showed strong prerequisite performance, with a large proportion of compounds passing both activity and distinctiveness criteria. However, MOA annotation recovery was partial and model-dependent. Although the overall number of recovered MOA annotations was similar across feature spaces, the specific MOA annotations recovered by each model differed. These results show that prerequisite profile quality does not guarantee recovery of the biological relationship being tested, such as shared MOA annotation, and support task-aware qualification of feature spaces before downstream interpretation. Full article

Background: Acute fatigue is frequently experienced during handball training and match play and may impair throwing performance; however, findings across studies are inconsistent. This systematic review and meta-analysis examined the acute effects of fatigue on throwing velocity and accuracy in handball. Methods: PubMed, MEDLINE Complete, CINAHL, and Scopus were searched from inception to 24 January 2026, supplemented by Google Scholar and citation tracking. Eligible studies included handball players exposed to an acute fatigue protocol with throwing-performance outcomes. Random-effects meta-analyses were conducted using standardized mean differences (Hedges’ g), oriented so that negative values indicated worse performance under fatigue. Results: Τen studies met the inclusion criteria for qualitative synthesis. For quantitative synthesis, 10 comparisons contributed to the throwing-velocity meta-analysis and 6 comparisons contributed to the throwing-accuracy meta-analysis. Fatigue showed a small-to-moderate tendency to reduce throwing velocity (g = −0.31, 95% CI −0.65 to 0.03; I² = 77.8%). For throwing accuracy, the pooled estimate suggested a possible decline under fatigue (g = −0.82, 95% CI −1.95 to 0.31), but heterogeneity was very high (I² = 95.8%) and findings were sensitive to influential effects. Conclusions: Acute fatigue showed a small-to-moderate tendency to reduce throwing velocity in handball players, with more consistent impairments observed during jump-shot tasks and after localized upper-limb fatigue protocols. In contrast, no robust conclusion can be drawn for throwing accuracy/precision because heterogeneity was extremely high and studies used substantially different outcome definitions, including hit counts, success percentages, points-based scores, and spatial error. Therefore, accuracy findings should be interpreted with considerable caution. Full article

This case report documents the multi-season development of a 38-year-old elite F12 shot putter with macular degeneration (<10% functional vision) who improved from 13.00 m to a personal best of 14.41 m between 2021 and 2023. Athletes classified as F11–F13 compete with significant visual impairment that limits spatial feedback during rotational tasks, yet longitudinal evidence describing integrated training frameworks remains scarce. A 12-month macrocycle integrated phase-dependent velocity-based resistance training using mean concentric velocity targets (0.70–1.00 m·s⁻¹) monitored via linear position transducers with a 10% velocity loss threshold, combined with structured auditory and tactile cueing, including metronome pacing and environmental anchors. High-volume warm-ups and prehabilitation addressed a prior L4–L5 disk herniation. The athlete achieved 14.41 m at the 2023 U.S. Para Athletics Trials, with TrackMan^®-verified release velocity of 11.3 m·s⁻¹. Bench throw velocity improved by 35.4% (0.65 to 0.88 m·s⁻¹) and squat jump velocity improved by 22.9% (1.18 to 1.45 m·s⁻¹), while post-session RPE remained manageable, indicating improved neuromuscular readiness and training tolerance. No lumbar symptom recurrence occurred. This case illustrates that integrating velocity autoregulation, multisensory stabilization, and injury-informed preparation can support meaningful performance gains in visually impaired throwers and offers an applied framework for coaches working with F11–F13 athletes. Full article

Background: This study investigates how both jump-related (jump height and flight time) and ball-related parameters (release height, release angle, and velocity) influence shooting accuracy in basketball under different contextual constraints. Methods: Eighteen senior players competing in the national championship (11 females and 7 males; 22.0 ± 3.7 years) performed 90 shots each across three positions (left 45°, middle 90°, right 45°) and three shooting conditions (baseline, simulated gym audience noise, and simulated opposition). Jump variables were derived from force platforms, while ball kinematics were extracted using a high-speed Qualisys camera system. Results: A three-way ANOVA revealed no systematic effects of position or opposition, and only a small effect of noise on flight time (p = 0.019), which was not confirmed by the Linear Mixed Model. Comparisons between successful and missed shots indicated significantly higher flight time, jump height, and release height, and a tendency for higher release velocity in successful attempts, with no differences in release angle. Spearman correlation showed weak associations between biomechanical variables and shooting accuracy (R² = 0.005–0.012). Conclusions: These findings suggest that while adaptive biomechanical changes occur under contextual constraints, their isolated impact on shot success is limited. Successful performance appears to rely more strongly on release-related parameters, emphasizing the need for a holistic approach to training that integrates technical, perceptual, and psychological dimensions. Full article

Whole-body electromyostimulation (WB-EMS) is a time-efficient, joint-friendly, and highly customizable training technology that particularly attracts sportspeople and athletes looking to enhance performance, accelerate regeneration, and prevent injuries with WB-EMS. Based on a systematic review of the literature, the present evidence map aimed to provide an overview of outcomes addressed by WB-EMS in exercising cohorts of different levels. In summary, the search identified 34 research projects with 39 studies and 43 publications that addressed 79 outcome categories (e.g., isometric strength) with more than 300 single outcomes (e.g., isometric strength of leg extensors). Thirty-one studies focused on performance-related outcomes, four studies addressed regeneration-related outcomes, and eight studies reported outcomes related to anthropometry. A further 14 studies reported health- and safety-related outcomes. Twenty-five of the 31 studies that reported performance parameters addressed strength, ten power, 18 jumping, ten sprinting, six agility, six endurance, five anaerobic power, and one each flexibility or balance, and five studies reported sport-specific performance outcomes (e.g., shot velocity). Apart from outcomes concerning injury prevention or sport-specific complaints, there are in particular evidence gaps relating to the acute effects of WB-EMS on regeneration, particularly with respect to muscle recovery. Semiprofessionals/professionals were rarely addressed, and if so, primarily cohorts from team sports were evaluated, while no study focused on elite strength, endurance, or precision sports athletes. Full article

Existing research points to sex-specific biological and physiological differences, but the effects of sex and age on water polo-specific motor skills have not yet been sufficiently investigated. The current study investigated sex- and age-related disparities in in-water vertical jump, change of direction ability, sprint performance, aerobic fitness and shot velocity, hypothesising that these variables are related to the players’ specific motor performance. Sixty-six players (47 males, 19 females) were split into an adult and a young group (each with n = 33). Two-way (sex and age as factors) analysis of variance and Tukey’s post hoc test were employed to evaluate the influence of sex and age on specific water polo skill performance. The male players’ in-water vertical jump (135.4 ± 8.1 vs. 121.5 ± 6.1 cm), shot velocity with previous displacement (68.3 ± 6.4 vs. 51.0 ± 2.5 km·h⁻¹) and without displacement (68.5 ± 5.7 vs. 52.2 ± 2.9 km·h⁻¹), 10 m sprint (5.6 ± 0.9 vs. 6.6 ± 0.4 s), aerobic fitness (311.7 ± 92.1 vs. 235.7 ± 70.3 m) and change of direction (3.3 ± 0.4 vs. 3.9 ± 0.4 s) scores were superior to those of female players. No significant age-related differences were observed in shot velocity with previous displacement (F (1,53) = 2.124, p = 0.151, η²p = 0.039) or 10 m sprint performances (F(1,62) = 0.935, p = 0.337, η²p = 0.015). Male players outperformed females in most water polo-specific motor skills, while age-related differences were limited. Full article

Objective: This study aims to investigate the effect of shot selection on the muscle coordination characteristics during basketball shooting. Methods: A three-dimensional motion capture system, force platform, and wireless surface electromyography (sEMG) were used to simultaneously collect shooting data from 14 elite basketball players. An inverse mapping model of sEMG signals and spinal α-motor neuron pool activity was developed based on the Debra muscle segment distribution theory. Non-negative matrix factorization (NMF) and K-means clustering were used to extract muscle coordination features. Results: (1) Significant differences in spinal segment activation timing and amplitude were observed between stationary and jump shots at different distances. In close-range stationary shots, the C5-S3 segments showed higher activation during the TP phase and lower activation during the RP phase. For mid-range shots, the C6-S3 segments exhibited greater activation during the TP phase. In long-range shots, the C7-S3 segments showed higher activation during the TP phase, whereas the L3-S3 segments showed lower activation during the RP phase (p < 0.01). (2) The spatiotemporal structure of muscle coordination modules differed significantly between stationary and jump shots. In terms of spatiotemporal structure, the second and third coordination groups showed stronger activation during the RP phase (p < 0.01). Significant differences in muscle activation levels were also observed between the coordination modules within each group in the spatial structure. Conclusion: Shot selection plays a significant role in shaping neuromuscular control strategies during basketball shooting. Targeted training should focus on addressing the athlete’s specific shooting weaknesses. For stationary shots, the emphasis should be on enhancing lower limb stability, while for jump shots, attention should be directed toward improving core stability and upper limb coordination. Full article

The scissor jump (SKJ) is vital in badminton, particularly for backcourt shots, but fatigue increases lower limb load and injury risk. This study investigates how quadriceps fatigue affects biomechanical characteristics and load during SKJ landing, aiming to understand its impact on injury risk. This study involved 27 amateur male badminton players from Ningbo University. Quadriceps fatigue was induced via knee exercises and footwork drills. Biomechanical data before (prior fatigue—PRF) and after fatigue (post fatigue—POF) were recorded using a force platform and motion capture system. Muscle activation was measured with EMG and analyzed through musculoskeletal modeling, with paired t-tests and SPM 1D (Statistical Parametric Mapping 1D) for statistical analysis. Under the POF condition, knee flexion angle increased, and power decreased (p < 0.001, p < 0.001, respectively); ankle plantarflexion angle increased, and power decreased (p < 0.001, p < 0.001, respectively). As fatigue progressed, joint reaction forces initially decreased but later increased. Joint energy dissipation decreased, with differences more pronounced in the coronal than sagittal plane. Achilles tendon force and anterior–posterior tibial shear force decreased, while coronal plane center-of-mass displacement increased. Findings show quadriceps fatigue harms limb stability, upping knee and ankle loads, disrupting the movement pattern, and risking coronal plane injuries. It is recommended that athletes enhance quadriceps endurance, improve neuromuscular control, and refine landing techniques to maintain stability and prevent injuries when fatigued. Full article

The purpose of this study was to assess the validity and reliability of an inertial measurement unit (IMU) system against an optical motion capture system in detecting motion in the dynamically complex and constraint-governed task of the basketball layup shot. Ten basketball players performed 10 trials with and 10 without a defender. Key kinematic variables (jump height, take-off angle, joint angles, and centre of mass (COM) displacement) were derived, and agreement (intraclass correlation coefficient (ICC) and Bland–Altman plots) and disagreement (root mean square difference (RMSD) and statistical parametric mapping (SPM)) calculations were carried out for each trial. The IMU system provided agreeable results for jump height and take-off angle, while joint angles and COM displacement agreement were plane-specific. A between-condition analysis demonstrated the IMU system reliably detected joint angle differences between defended and undefended conditions comparable to the optical system for nine out of twelve joint angles, with shoulder flexion-extension and external-internal and elbow external-internal joint angles showing inconclusive results. Ultimately, the IMU system was generally able to detect similar magnitudes of difference between conditions to those detected by the optical motion-based system. Therefore, conclusions can be drawn for between-condition comparisons if data are derived from either system. Full article

Background/Aims: Table tennis performance is influenced by various factors such as technique, tactics, and fitness. Additionally, many shots are executed at high speeds, developing significant levels of explosive strength in the lower extremities. This study aimed to assess the jump capacity and the elasticity index of the lower limbs among young table tennis players based on sex. Additionally, this study assessed leg asymmetries between the dominant and non-dominant limbs during jump tests. Methods: A total of 40 players (20 boys and 20 girls), aged 16–18 years, participated in the study. Vertical countermovement jump, squat jump, and horizontal jump tests were conducted to evaluate both vertical and horizontal jumping capacities, as well as leg asymmetries between the dominant and non-dominant limbs. Results: Differences were observed in both vertical and horizontal jumps, with male players achieving better results in all jumping capacities. However, female players obtained better values in elastic index. Additionally, significant differences were found between dominant and non-dominant legs in both male and female players. Conclusions: Considering that explosive strength is one of the most essential physical capacities in this sport, this information could prove valuable for talent identification, the design of training programs, and the optimization of physical performance monitoring systems in table tennis. Full article

A common approach to simulating a Lévy process is to truncate its shot-noise representation. We focus on subordinators and introduce the remainder process, which represents the jumps that are removed by the truncation. We characterize when these processes are self-similar and show that, in the self-similar case, they can be indexed by a parameter $\alpha \in (-\infty ,1)$. When $\alpha \in (0,1)$, they correspond to $\alpha$-stable distributions, and when $\alpha =0$, they correspond to certain generalizations of the Dickman distribution. Thus, the Dickman distribution plays the role of a 0-stable distribution in this context. Full article

(1) Background: The pull-up jump shot is a commonly used scoring technique in basketball. This study aimed to investigate the biomechanical effects of knee brace stiffness on knee joint mechanics during the pull-up jump shot in female basketball players and to evaluate the potential risk of non-contact anterior cruciate ligament (ACL) injuries associated with different stiffness levels. (2) Methods: Sixty-six female basketball players performed pull-up jump shot drills while kinematic and kinetic data were collected using a Vicon motion capture system and a Kistler ground reaction force (GRF) plate. (3) Results: A one-way analysis of variance (ANOVA) revealed that both low-stiffness and high-stiffness knee braces significantly reduced knee flexion angles (p = 0.001) but increased indirect contact forces in the sagittal plane (p < 0.01). Notable differences were observed between low-stiffness and high-stiffness braces, as well as between braced and unbraced conditions. However, no significant differences were detected between the effects of low-stiffness and high-stiffness braces. (4) Conclusions: Athletes should select knee braces based on the intensity of competition and training, and those with ACL concerns should opt for high-stiffness knee braces for enhanced joint stability. Full article

Background: This study aimed to analyze the effect of caffeine ingestion on basketball performance in semi-professional female players. Methods: A double-blind, placebo-controlled, randomized experimental design was conducted, in two different periods separated by a week. Twelve female basketball players ingested 3 mg of caffeine/kg of body mass or a placebo. After 60 min, participants completed two repetitions of the specified sequence: Abalakov jump, countermovement jump (CMJ), 5-0-5 (505) test, and 20 m sprint. Later, external loads and game statistics were recorded during a 30-min simulated basketball game. Results: Significant improvements were observed in CMJ height and 505 test with caffeine ingestion compared to the placebo. Significant moderate differences were evident between conditions in external load variables, specifically, an increased number of high-intensity changes of direction during simulated games with caffeine ingestion. Two-point shot efficiency significantly improved after pre-caffeine ingestion compared with placebo. Conclusions: Three mg of caffeine per kg of body mass may serve as an effective ergogenic aid to increase physical performance and some variables of performance index in highly trained basketball players. Full article

Recent studies have shown that lower-limb plyometric training can effectively enhance muscle strength and explosiveness, which are particularly important for improving jumping ability. The purpose of this study was to evaluate the effects of plyometric training on vertical, lateral, and horizontal jumping abilities, and their subsequent impact on basketball shooting performance and sports injury prevention. A quasi-experimental design was used, recruiting 30 male college-level basketball players from Taiwan, who were randomly assigned to an experimental group (n = 15) and a control group (n = 15). Both groups participated in 2 h of basketball training daily, while the experimental group additionally engaged in plyometric training twice a week. The results revealed significant improvements in the experimental group in several key areas, including rate of force development (RFD), ground reaction force (GRF), jump height, jump distance, and both horizontal and vertical forces, across vertical, lateral, and horizontal jumps. Specifically, vertical jumps required the highest ground reaction force, followed by lateral jumps, with horizontal (step-back) jumps requiring the least. The optimal angles for the resultant force during take-off were found to be between 66.1° and 66.8° for lateral jumps, and between 56.2° and 57.2° for step-back jumps, while vertical jumps did not show significant variation in take-off angle. In terms of basketball performance, the experimental group demonstrated significantly better post-test results in all three types of jump shots, with the highest accuracy observed in the vertical jump shot, followed by the lateral jump shot, and the lowest in the step-back jump shot. Furthermore, the experimental group experienced a substantial reduction in sports injury rates, with the injury rate decreasing to 6%. These findings indicate that plyometric training not only enhances jumping performance, but also contributes to injury prevention by strengthening lower-limb muscles. This study provides a theoretical basis for coaches to develop comprehensive training programs that improve athletic performance and reduce injury risk. Full article