Determinant Bundles, Quillen Metrics, and Mumford Isomorphisms Over the Universal Commensurability Teichm\"uller Space

There exists on each Teichm\"uller space $T_g$ (comprising compact Riemann surfaces of genus $g$), a natural sequence of determinant (of cohomology) line bundles, $DET_n$, related to each other via certain ``Mumford isomorphisms''. There is a remarkable connection, (Belavin-Knizhnik), between the Mumford isomorphisms and the existence of the Polyakov string measure on the Teichm\"uller space. This suggests the question of finding a genus-independent formulation of these bundles and their isomorphisms. In this paper we combine a Grothendieck-Riemann-Roch lemma with a new concept of $C^{*} \otimes Q$ bundles to construct such an universal version. Our universal objects exist over the universal space, $T_\infty$, which is the direct limit of the $T_g$ as the genus varies over the tower of all unbranched coverings of any base surface. The bundles and the connecting isomorphisms are equivariant with respect to the natural action of the universal commensurability modular group.Comment: ACTA MATHEMATICA (to appear); finalised version with a note of clarification regarding the connection of the commensurability modular group with the virtual automorphism group of the fundamental group of a closed Riemann surface; 25 pages. LATE

Thurston boundary of Teichm\"uller spaces and the commensurability modular group

If $p : Y \to X$ is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to $p$, from the Teichm\"uller space ${\cal T}(X)$, for $X$, to ${\cal T}(Y)$ actually extends to an embedding between the Thurston compactification of the two Teichm\"uller spaces. Using this result, an inductive limit of Thurston compactified Teichm\"uller spaces has been constructed, where the index for the inductive limit runs over all possible finite unramified coverings of a fixed compact oriented surface of genus at least two. This inductive limit contains the inductive limit of Teichm\"uller spaces, constructed in \cite{BNS}, as a subset. The universal commensurability modular group, which was constructed in \cite{BNS}, has a natural action on the inductive limit of Teichm\"uller spaces. It is proved here that this action of the universal commensurability modular group extends continuously to the inductive limit of Thurston compactified Teichm\"uller spaces.Comment: AMSLaTex file. To appear in Conformal Geometry and Dynamic

Physical Characteristics, Movement Pattern and Heart Rate Response of Indian Cricketers During Batting in Twenty20 (T20) Matches

International Journal of Exercise Science 16(6): 1413-1425, 2023. The study aims to provide a morphological profile of Indian cricketers and find physiological demands and positional differences of the batsmen in T20 matches according to their batting order. Eighty-three male cricketers (age: 17.93 ± 2.23 years) participated in this study and categorized into upper-order (n = 36), middle-order (n = 35) and lower-order (n = 12) batsmen. Height, weight, body fat%, and somatotype were measured. Movement analysis and heart rate (HR) responses were recorded during batting in T20 matches using PolarV800 smart-watch and H7 HR sensor. Descriptive statistics, one-way ANOVA followed by post-hoc analysis examined group differences. Results indicated that upper-order batsmen were balanced mesomorph, middle-order batsmen were mesomorphic-endomorph, and lower-order batsmen were mesomorphic-ectomorph. Cricket-specific movement patterns showed that standing made-up the majority of time spent (54.1 - 60.9%), while maximum distance was covered by walking (68.5 - 73.3%) during batting. Lower-order batsmen spent significantly lesser time (p \u3c 0.01; d = 1.02) in the crease and covered lesser total distance (p \u3c 0.05; d = 0.85) compared to upper and middle-order batsmen, respectively. Upper-order batsmen maintained a significantly lower average HR throughout batting compared to middle (p \u3c 0.01; d = 1.07) and lower-order (p \u3c 0.01; d = 2.04) batsmen. Moreover, upper-order batsmen spent significantly more time in the low-intensity target HR (THR) zone (∼9.9%) compared to the middle (∼3.2%; p \u3c 0.01; d = 0.72) and lower-order (∼2.3%; p \u3c 0.05; d = 0.69). Additionally, upper-order batsmen spent significantly less time (20.8%; p \u3c 0.01) in the high-intensity THR compared to the middle (55.3%) and lower-order (52.2%) batsmen. Therefore, the findings highlight distinct movement and physiological demands associated with batting at different orders during T20 matches, which conditioning coaches and cricketers can utilize to optimize training programs and enhance individual performance

Interactions of Mineral Surfaces and Adsorbates: A Computational Modeling Approach.

Calcite and apatite are the two major minerals on the Earth’s surface that interact with organic molecules to create biominerals. We have studied the interaction of small, 3-amino acid peptides and long, 12-amino acid peptides with the energetically stable calcite (104) surface (and steps thereon). These organic adsorbate molecules were chosen to test the hypothesis that building blocks of complex biomolecules can modify the morphology of biominerals. Our studies indicate that the arrangement of polar functional groups in peptides and their direct interaction with mineral surface ions is more important than steric hindrance of different side-chains of amino acids to control the growth of biominerals. Langmuir films have been used in previous experimental studies to mimic matrix-controlled biomineralization. In our simulations on the growth of calcite nuclei under Langmuir films consisting of amide-containing phospholipids, the polar calcite (100) surface resulted in the most negative interfacial energy. These molecular-dynamics simulations give insight in the mechanism of matrix-controlled calcite nuclei formation in aqueous environments. Hydroxyapatite and carbonated apatite are the major inorganic minerals found in vertebrates, and their interactions with cell-adhesion peptides govern mineral growth and bone-regeneration processes. Molecular modeling studies on the interaction with RGD and YIGSR peptides with the hydroxyapatite (001) surface and surface steps show that final orientation of the peptides parallel to the [010] step direction is most favorable. A quantum-mechanical approach was chosen to study electron transfer between redox couples through a mineral surface to investigate the long-range interaction of As (OH)3 through a galena (100) surface with different oxidants. As(III) is a toxic element that can be immobilized by adsorption/oxidation on a mineral surface to limit its concentration in groundwater. In all cases studied, the galena surface was found to be an effective medium to shuttle electrons from As(III) over some distance to the respective oxidants (O, O2, and Fe(III)). Molecular modeling studies applied in this thesis to adsorbate-mineral surface interactions can elucidate reaction mechanisms that are usually out-of reach in bench-top experiments, while providing insight in predicting and mimicking natural biomineralization and redox phenomena.Ph.D.GeologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58378/1/biswass_1.pd

Demographic Insights Into College-Going Students in India: A Morphological Analysis

Introduction: In the context of India's diverse culture and changing education system, it is crucial to understand the morphological characteristics of college students, especially with the government actively supporting sports through initiatives like the "Khelo India" program to aid young athletes.  The purpose of the study was to investigate the morphological characteristics of college-level athletes and non-athletes in India. Methods: 287 college students have been randomly selected to acquire a comprehensive set of demographic and anthropometric data. Results: The study revealed significant differences in body mass index (p=0.004), endomorphy (p=0.001), ectomorphy (p=0.02), and body fat percentage (p=0.001). However, no significant difference in mesomorphy (p=0.09) was identified, and only minimal differences in fat-free mass (p=0.57) were observed. College-level athletes exhibit an ectomorphic-mesomorphic physique (2.9-3.9-3.0), characterized by a distinct blend of muscularity and leanness. Non-athletes are mesomorphic-endomorphs (5.0-4.3-2.4), exhibiting higher body fat content and muscularity. Athletes had a significantly lower body fat percentage, highlighting the positive influence of sports training and regular physical exercise on reducing adiposity. The analysis of percentile rankings provides comprehensive insights into the distribution of anthropometric metrics among athletes and non-athletes, assisting in customizing training regimens, identifying areas for potential improvement, and enhancing a comprehensive assessment of individuals' physical characteristics. Conclusion: The study sheds light on the crucial role of morphological traits in discerning differences between college-level athletes and non-athletes within the broader context of the "Fit India Movement." The study will help design an effective training module to improve the overall health of college students.Introducción: En el contexto de la cultura diversa de la India y el cambiante sistema educativo, es crucial comprender las características morfológicas de los estudiantes universitarios, especialmente ahora que el gobierno apoya activamente los deportes a través de iniciativas como el programa "Khelo India" para ayudar a los atletas jóvenes. El propósito del estudio fue investigar las características morfológicas de los atletas y no atletas de nivel universitario en la India. Métodos: Se seleccionaron aleatoriamente 287 estudiantes universitarios para adquirir un conjunto completo de datos demográficos y antropométricos. Resultados: El estudio reveló diferencias significativas en el índice de masa corporal (p=0,004), endomorfia (p=0,001), ectomorfia (p=0,02) y porcentaje de grasa corporal (p=0,001). Sin embargo, no se identificaron diferencias significativas en la mesomorfia (p=0,09) y sólo se observaron diferencias mínimas en la masa magra (p=0,57). Los atletas de nivel universitario exhiben un físico ectomórfico-mesomórfico (2,9-3,9-3,0), caracterizado por una combinación distintiva de musculatura y delgadez. Los no deportistas son endomorfos mesomórficos (5,0-4,3-2,4) y exhiben mayor contenido de grasa corporal y musculatura. Los deportistas presentaban un porcentaje de grasa corporal significativamente menor, destacando la influencia positiva del entrenamiento deportivo y el ejercicio físico regular en la reducción de la adiposidad. El análisis de las clasificaciones percentiles proporciona información integral sobre la distribución de métricas antropométricas entre atletas y no atletas, lo que ayuda a personalizar los regímenes de entrenamiento, identificar áreas de posible mejora y mejorar una evaluación integral de las características físicas de los individuos. Conclusión: El estudio arroja luz sobre el papel crucial de los rasgos morfológicos a la hora de discernir las diferencias entre los atletas de nivel universitario y los no atletas dentro del contexto más amplio del "Movimiento Fit India". El estudio ayudará a diseñar un módulo de formación eficaz para mejorar la salud general de los estudiantes universitarios

ЧСС у стані спокою та серцево-судинна витривалість провінційних гравців у крикет і бігунів на середню дистанцію: спостереження

Resting heart rate is a reliable biomarker for measuring fitness in terms of cardiovascular health as well as analyzing an athlete’s recovery. The study purpose was to explore the resting heart rate and cardiovascular endurance of the cricketers and middle-distance runners of West Bengal. Materials and methods. Forty male sub-elite athletes with a mean age of 19.8±2.4 years, height of 1.66±0.05 m, and body mass of 55.5±7.0 kg were randomly selected and categorized as cricketers (20) and middle-distance runners (20). Five-minute RR intervals were recorded during a resting state in the supine position using a Polar V800 smart watch along with a Polar H10 chest strap and a Polar H7 heart rate sensor. Cardiovascular endurance (predicted VO2max) was measured using the Yo-Yo intermittent recovery test Level 1. Results. Mean resting heart rate, SDNN, rMSSD, pNN50, and predicted VO2max of cricketers and middle-distance runners have been found to be 57.2±5.9 bpm, 53.5±26.6 ms, 68.4±36.8 ms, 40.9±23.2%, and 48.4±1.7 ml/kg/min and 61.7±7.3 bpm, 47.0±18.8 ms, 59.2±27.3 ms 32.4±20.9%, and 49.0±2.2 ml/kg/min, respectively. No significant difference was observed in time domain parameters and predicted VO2max, but a significant difference (p=0.033) was observed in resting heart rate of two groups. A significant negative (r= -0.62, p=<0.001) association has been observed between resting heart rate and predicted VO2max. Conclusions. The low resting heart rate of the cricketers may possibly have come from higher training load borne by the young players. Based on the players’ predicted VO2max, it looks like having good cardiovascular fitness is just as important in modern cricket as it is in middle-distance running. Показник частоти серцевих скорочень у стані спокою є надійним біомаркером для вимірювання фізичної підготовленості в частині здоров’я серцево-судинної системи, а також для аналізу відновлення спортсмена. Метою дослідження було вивчення ЧСС у стані спокою та серцево-судинної витривалості гравців у крикет і бігунів на середню дистанцію зі штату Західна Бенгалія (Індія). Матеріали та методи. Учасниками дослідження стали 40 висококласних спортсменів регіонального рівня чоловічої статі середнім віком 19,8±2,4 року, зростом 1,66±0,05 м та з індексом маси тіла 55,5±7,0 кг, які були відібрані випадковим чином і поділені на категорії гравців у крикет (20) та бігунів на середню дистанцію (20). Реєстрували п’ятихвилинні кардіоінтервали (RR-інтервали) у стані спокою в положенні лежачи на спині з використанням смарт-годинника «Polar V800» разом із нагрудним ременем-пульсометром «Polar H10» і датчиком ЧСС «Polar H7». Вимірювання показників серцево-судинної витривалості (прогнозоване значення максимального споживання кисню – МСК) здійснювали за допомогою інтервального тесту на відновлення Йо-Йо, Рівень 1. Результати. Було встановлено, що середні показники ЧСС у стані спокою, статистичного відхилення нормальних RR-інтервалів (SDNN), стандартного відхилення RR-інтервалів (rMSSD), відсотку послідовних RR-інтервалів із відмінністю понад 50 мс (pNN50) та прогнозованого МСК гравців у крикет і бігунів на середню дистанцію дорівнюють 57,2±5,9 уд./хв, 53,5±26,6 мс, 68,4±36,8 мс, 40,9±23,2%, 48,4±1,7 мл/кг/хв та 61,7±7,3 уд./хв, 47,0±18,8 мс, 59,2±27,3 мс, 32,4±20,9%, 49,0±2,2 мл/кг/хв відповідно. Жодної статистично значущої різниці параметрів у часовій області та прогнозованого МСК не спостерігалося, але спостерігалася статистично значуща різниця (p=0,033) показників ЧСС у стані спокою двох груп. Спостерігався статистично значущий негативний (r= -0,62, p=<0,001) зв’язок між ЧСС у стані спокою та прогнозованим МСК. Висновки. Низький показник ЧСС у стані спокою гравців у крикет, можливо, є результатом вищого тренувального навантаження, яке несуть молоді гравці. З огляду на прогнозований показник МСК гравців, здається, що наявність гарного функціонального стану серцево-судинної системи є не меншою мірою важливою в сучасному крикеті, ніж у бігу на середню дистанцію.&nbsp