Periods and global invariants of automorphic representations

We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic L-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two such periods. We compute this invariant in some cases.Comment: Switched to the language of co-invariants. Change of titl

Subconvexity bounds for triple L-functions and representation theory

We describe a new method to estimate the trilinear period on automorphic representations of PGL(2,R). Such a period gives rise to a special value of the triple L-function. We prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value of the triple L-function. Our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of PGL(2,R).Comment: Revised version. To appear in Annals of Math

The influence of bovine serum albumin on β-lactoglobulin denaturation, aggregation and gelation

peer-reviewedThe effect of bovine serum albumin (BSA) on the heat-induced denaturation, aggregation and subsequent acid-induced gelation of β-lactoglobulin (β-lg) was investigated in this work. Changes in the denaturation kinetics of β-lg during heating at 78 °C were determined by monitoring the disappearance of the native protein by reverse-phase chromatography. Replacing β-lg with increasing amounts of BSA, while keeping the total protein concentration constant at 5% (w/w), significantly increased the denaturation rate of β-lg from 2.57±0.30×10−3(g L−1)(1−n)s−1 to 5.07±0.72×10−3(g L−1)(1−n)s−1 (β-lg: BSA ratio of 3:1 w/w). The reaction order for β-lg was 1.40±0.09. Partial replacement of β-lg with BSA (β-lg: BSA ratio of 3:1 w/w) significantly increased the reaction order to 1.67±0.13. Heat-induced aggregates between β-lg and BSA were studied by dynamic light scattering, two-dimensional electrophoresis and size exclusion chromatography. The partial replacement of β-lg with BSA significantly changed the gelling properties of the acid-induced gels. A rapid rate of acidification resulted in a significant decrease, while a slow acidification rate resulted in a significant increase in gel strength. Size exclusion chromatography demonstrated that intermolecular disulphide bond formation occurred during both heat-induced denaturation/aggregation and subsequent acid-induced gelation. Results clearly indicate that BSA contributed to the formation of these disulphide bonds.This work was funded under the Food Institutional Research Measure (FIRM) of the National Development Plan 2000-2006. J. Kehoe is funded by the Teagasc Walsh Fellowship schem

SALIVARY BIOMARKER ASSESSMENT OF ELITE COLLEGIATE BASKETBALL PLAYERS ACROSS AN NCAA SEASON

The ratio between testosterone and cortisol (TC) has been used to monitor training stress and performance in athletes. PURPOSE: To monitor free testosterone (T), cortisol (C), and the ratio of testosterone to cortisol (TC) in elite NCAA Division I basketball athletes, weekly, throughout an entire season. METHODS: Twenty-two athletes (12 male, 10 female) gave a salivary sample before an afternoon practice in the middle of each week for 30 consecutive weeks, beginning in the pre-season and ending one week after the end of post-season competition. Salivary samples were assayed for T and C. Additionally, a composite value composed of Z-scores (COMP) for weekly practice minutes, game minutes, resistance training repetitions, academic stress, and travel stress was used in an attempt to quantify weekly cumulative stress so that an increase in COMP suggested an increase in cumulative stress. One-way RM ANOVA with LSD pairwise comparisons were used to determine which weekly values were different (α=.05) from the season average. RESULTS: For T, 10 weeks were different from baseline (5.1 nmol/L) for men while 4 weeks were different from baseline (2.2 nmol/L) for women. For C, 11 weeks were different from baseline (9.0 nmol/L) for men while 4 weeks were different from baseline (6.5 nmol/L) for women. For TC, weeks 7 (p=.007), 17 (p=.007), and 25 (p=.005) were different from baseline (TC=0.69) for men while weeks 6 (p=.004), 16 (p=.024), 24 (p=.003), and 27 (p=.008) were significantly different from baseline (TC=0.42) for women. CONCLUSIONS: The large increase in TC at Wk7 (men) suggested that these athletes were recovered from stressful pre-season training and physiologically prepared for the first week of regular season competition. The decrease in TC at Wk17 (men), despite the current win-streak, suggests that the lengthy season was having a physical effect on the student-athletes. Despite a brief 3-game losing streak during Wks20-21, TC was not significantly impacted (men). Finally, following a decrease in TC before post-season competition and a trend towards a decrease in Wk28 (p=.073; 1.5SD below baseline), the athletes were able to return to hormonal baseline one week after the end of the season (men). For women, during Wk6, one week prior to the first exhibition game, TC was below baseline and corresponded with an increase in COMP. However, TC returned to baseline by Wk7, which was the first week of exhibition play. During Wk16, which was collected the week after holiday break, TC was below baseline despite a decrease in COMP. During Week 24, TC was below baseline and corresponded with an increase in COMP. During Wk27, which was collected immediately before the team's first match of the NCAA tournament, TC was below baseline and corresponded with a decrease in COMP. However, the athletes returned to baseline during the tournament and remained at baseline up to and beyond their 4th round elimination. While these athletes experienced significant decreases in TC throughout the season, the overall hormonal profile appeared to remain stable compared to baseline despite constant variation in cumulative student-athlete stress and also suggested that the athletes were able to return to hormonal baseline by the end of the season. PRACTICAL APPLICATIONS: The methods of this study can be used for monitoring fatigue management by assessing how one's athletes adapt to stressful pre-season training and whether or not they recover in time for regular season play, in addition to how the athletes handle the stressors of the competitive season, and is useful for female athletes