Large circulant graphs of fixed diameter and arbitrary degree

We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case. We present a direct product construction yielding improved bounds for small diameters and introduce a new general technique for “stitching” together circulant graphs which enables us to improve the current best known asymptotic orders for every diameter. As an application, we use our constructions in the directed case to obtain upper bounds on the minimum size of a subset A of a cyclic group of order n such that the k-fold sumset kA is equal to the whole group. We also present a revised table of largest known circulant graphs of small degree and diameter

Mutually avoiding Eulerian circuits

Two Eulerian circuits, both starting and ending at the same vertex, are avoiding if at every other point of the circuits they are at least distance 2 apart. An Eulerian graph which admits two such avoiding circuits starting from any vertex is said to be doubly Eulerian. The motivation for this definition is that the extremal Eulerian graphs, i.e. the complete graphs on an odd number of vertices and the cycles, are not doubly Eulerian. We prove results about doubly Eulerian graphs and identify those that are the `densest' and `sparsest' in terms of the number of edges.Comment: 22 pages; 9 figure

The inter-individual variability in human muscle strength and in the response to resistance training

Inter-individual differences in strength are not fully explained by muscle size, suggesting that muscle specific tension [force per unit physiological cross-sectional area (PCSA)] varies between untrained individuals. Furthermore, many reports demonstrate greater gains in muscle strength than size following resistance training, thus indicating an increase in specific tension. Moreover, there is considerable variation in the response to training that may have a genetic origin. The aims of the work described in this thesis were i) to examine the degree of variability in muscle specific tension; ii) to investigate whether specific tension changed following resistance training; iii) to quantify the variability in the response of human muscle to resistance training; iv) to identify gene variants that may be associated with the variable training responses. In a group of untrained young men and before and after 9 weeks of resistance training, the quadriceps femoris (QF) muscle specific tension was calculated from the maximum isometric voluntary contraction (MVC) torque, taking into account the contribution of voluntary activation, antagonist muscle co-activation, moment arm length, QF volume, muscle fascicle length and pennation angle. Correcting for these factors made little difference to the between subjects variance of MVC torque, thus demonstrating that muscle specific tension varies considerably between individuals. Resistance training increased QF muscle force much more than PCSA, indicating that most of the increase in force was a result of increased specific tension. This increase was not associated with a change in myosin heavy chain expression and was not accompanied by an increase in single fibre specific tension, or an increase in power per unit muscle volume measured during isokinetic cycling. The results are consistent with an increase in lateral force transmission in the muscle. Substantial variation in the training responses was observed and the final part of this thesis is concerned with linking this variation with specific gene variants

Robert Erskine Wagner to The Registrar, University of Mississippi, 19 September 1962

Erskine hopes the registrar supports Governor Barnett and mentions the sake future generations.https://egrove.olemiss.edu/west_union_um/1021/thumbnail.jp

Mind the gap! A survey comparing current strength training methods used in men’s versus women’s first team and academy soccer

Much less is known about strength and conditioning (S&C) practice in women's versus men's soccer. The aim of this study was to compare S&C practice between coaches working in men's or women's soccer, at first team or academy level, worldwide. A total of 170 participants, who were involved with S&C support at their soccer club (in Europe, USA and South America, within men's or women's first team or academy settings) completed a comprehensive online survey, designed to evaluate (i) their academic qualifications and S&C coaching experience; and their preferred methods for (ii) physical testing; (iii) strength and power development; (iv) plyometric training; (v) speed development; and (vi) periodization. Women's academies had fewer weekly in-season S&C sessions than men's academies (1.6±0.6 vs. 2.3±0.9, p=0.005). Relatively, fewer women's academy S&C coaches (6%) used Olympic weightlifting movements than men's academy S&C coaches (32%, p=0.030). Relatively, more women's academy coaches (47%) used the Nordic hamstring exercise (NHE) compared to men's academy coaches (15%, p=0.006), but relatively more women's vs. men's first team coaches (61% vs. 38%, p=0.028) and women's vs. men's academy (61% vs. 38% coaches, p=0.049) utilised rating of perceived exertion-based load prescriptions. Notable differences in S&C practice exist between coaches of men's and women's soccer squads, particularly at academy level. Fewer weekly S&C sessions in women academy players may have implications for physical development, while the greater use of subjective load prescriptions in both academy and first team women's squads may lead to sub-optimal performance gains

Physical testing and strength and conditioning practices differ between coaches working in academy and first team soccer

Scientific guidelines exist regarding strength and conditioning (S&C) best practice, for both first team and academy level soccer. However, it is not known if these research-informed guidelines are followed in such applied settings. The aim of this study was to investigate current S&C practice in first team and academy level (men's and women's) soccer, in multiple countries/continents. A total of 170 participants, who were involved with the delivery of S&C support at their soccer club, completed a comprehensive survey, describing their training methods. Data were analysed using Pearson's chi-square test of independence and independent t-tests. Statistical significance was set to p < 0.05. A greater proportion of academy compared to first team coaches assessed acceleration/sprint (92% vs. 83%, p=0.026), jump (95% vs. 83%, p=0.023) and change of direction performance (77% vs. 61%, p=0.031). The weekly training structure differed between groups, particularly within women's squads, with women's academy coaches reporting the lowest session frequency of all groups (1.59 ± 0.62 session per week, 44 ± 17 min duration). A greater proportion of academy (54%) versus first team (35%) coaches prioritised bodyweight training (p=0.031), despite a similar distribution of movement patterns trained. Overall, 44% S&C coaches reported using training intensities below strength training guidelines (≥80% 1RM). To conclude, there were many differences in S&C practice between S&C coaches working with first team and academy squads but particularly noteworthy was the greater proportion of academy coaches prioritising bodyweight training compared to first team coaches, which may limit physical development in academy players

Physical characteristics explain ball-carrying capability in sub-elite rugby union players.

The aims of the present study were two-fold: (i) to investigate the relationship between physical characteristics and the game statistics associated with ball-carrying capability amongst sub-elite rugby union players; and (ii) to predict the level of change in these physical characteristics required to improve the associated game statistic via regression analysis. Thirty-eight senior professional players (forwards, n = 22; backs, n = 16) were assessed for body mass (BM), back squat (BS) single-repetition maximum (1RM) normalised to BM (1RM/BM), 10 m sprint velocity (S10), 10 m sprint momentum (SM10), and the game statistics from 22 games within the 2019/20 RFU Championship season. The relationship between these measures and the predicted level of change in a physical measure required to improve the total number of the associated game statistic by one were assessed by Pearson's correlation coefficient and simple regression analyses. In forwards, an ~ 11.5% reduction in BM, an ~ 11.8% improvement in BS 1RM/BM, or an ~ 11.5% increase in S10 was required to improve the game statistics associated with ball-carrying capability. In backs, a ~ 19.3% increase in BM or a ~ 15.6% improvement in SM10 was required. These findings demonstrate that improvements in lower-body relative strength, acceleration performance, and position-specific alterations in body mass are required to maximise the ball-carrying capability and therefore match outcome of sub-elite rugby union players

Global differences in current strength and conditioning practice within soccer

Differences exist between top-tier soccer leagues (e.g. anthropometry and match demands), which may influence strength and conditioning (S&C) practice. Thus, the aim of this study was to investigate whether current S&C practice in men's and women's (first team and academy) squads differed between global regions. A total of 170 participants, involved in the delivery of S&C support at their soccer club (based on South America (SA), the USA, the UK, or other European countries (EUR)), completed a survey examining their S&C methods. The survey comprised six sections: (i) academic qualifications and S&C coaching experience; and their preferred methods for (ii) physical testing; (iii) strength and power development; (iv) plyometric training; (v) speed development; and (vi) periodization. Coaches in EUR conducted fewer formal S&C sessions, placed less importance on free-weight resistance training (RT), and performed less speed and plyometric training compared to coaches in other global regions (all p<0.05). While coaches working with UK squads devoted more time to physical development than those in EUR, they regarded bodyweight training as the most important RT modality in comparison to USA and SA, who prioritized free-weight RT. Finally, SA academy players are introduced to formal S&C later (14 years old) than those in the UK (12 years old, p=0.002). However, it is reasonable to suggest that the S&C practice of coaches in the USA and SA align better with scientific guidelines for strength and power development in soccer, with emphasis on free-weight RT alongside regular sprint and plyometric training, compared to coaches in the UK and EUR

Whey protein does not enhance the adaptations to elbow flexor resistance training

Purpose: It is unclear whether protein supplementation augments the gains in muscle strength and size observed after resistance training (RT) because limitations to previous studies include small cohorts, imprecise measures of muscle size and strength, and no control of prior exercise or habitual protein intake. We aimed to determine whether whey protein supplementation affected RT-induced changes in elbow flexor muscle strength and size. Methods: We pair-matched 33 previously untrained, healthy young men for their habitual protein intake and strength response to 3-wk RT without nutritional supplementation (followed by 6 wk of no training) and then randomly assigned them to protein (PRO, n = 17) or placebo (PLA, n = 16) groups. Participants subsequently performed elbow flexor RT 3 d/wk for 12 wk and consumed PRO or PLA immediately before and after each training session. We assessed elbow flexor muscle strength (unilateral 1-repetition maximum and isometric maximum voluntary force) and size (total volume and maximum anatomical cross-sectional area determined with magnetic resonance imaging) before and after the 12-wk RT. Results: PRO and PLA demonstrated similar increases in muscle volume (PRO 17.0% ± 7.1% vs PLA 14.9% ± 4.6%, P = 0.32), anatomical cross-sectional area (PRO 16.2% ± 7.1% vs PLA 15.6% ± 4.4%, P = 0.80), 1-repetition maximum (PRO 41.8% ± 21.2% vs PLA 41.4% ± 19.9%, P = 0.97), and maximum voluntary force (PRO 12.0% ± 9.9% vs PLA 14.5% ± 8.3%, P = 0.43). Conclusions: In the context of this study, protein supplementation did not augment elbow flexor muscle strength and size changes that occurred after 12 wk of RT. © 2012 by the American College of Sports Medicine