Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces

We obtain an improvement of the bilinear estimates of Burq, G\'erard and Tzvetkov in the spirit of the refined Kakeya-Nikodym estimates of Blair and the second author. We do this by using microlocal techniques and a bilinear version of H\"ormander's oscillatory integral theorem.Comment: 19 pages, 1 figure. Affiliation correcte

National Football League Skilled and Unskilled Positions Vary in Opportunity and Yield in Return to Play After an Anterior Cruciate Ligament Injury.

BACKGROUND: Anterior cruciate ligament (ACL) injuries pose a significant risk to the careers of players in the National Football League (NFL). The relationships between draft round and position on return to play (RTP) among NFL players are not well understood, and the ability to return to preinjury performance levels remains unknown for most positions. PURPOSE: To test for differences in RTP rates and changes in performance after an ACL injury by position and draft round. We hypothesized that skilled positions would return at a lower rate compared to unskilled positions. We further hypothesized that early draft-round status would relate to a greater rate of RTP and that skilled positions and a lower draft round would correlate with decreased performance for players who return to sport. STUDY DESIGN: Case-control study; Level of evidence, 3. METHODS: Utilizing a previously established database of publicly available information regarding ACL tears among NFL players, athletes with ACL tears occurring between the 2010 and 2013 seasons were identified. Generalized linear models and Kaplan-Meier time-to-event models were used to test the study hypotheses. RESULTS: The overall RTP rate was 61.7%, with skilled players and unskilled players returning at rates of 64.1% and 60.4%, respectively (P = .74). Early draft-round players and unskilled late draft-round players had greater rates of RTP compared to skilled late draft-round players and both unskilled and skilled undrafted free agents (UDFAs). Skilled early draft-round players constituted the only cohort that played significantly fewer games after an injury. Unskilled UDFAs constituted the only cohort to show a significant increase in the number of games started and ratio of games started to games played, starting more games in which they played, after an injury. CONCLUSION: Early draft-round and unskilled players were more likely to return compared to their later draft-round and skilled peers. Skilled early draft-round players, who displayed relatively high rates of RTP, constituted the only cohort to show a decline in performance. Unskilled UDFAs, who exhibited relatively low rates of RTP, constituted the only cohort to show an increase in performance. The significant effect of draft round and position type on RTP may be caused by a combination of differences in talent levels and in opportunities given to returning to play

Site selective reading of epigenetic markers by a dual-mode synthetic receptor array.

Variably functionalized self-folding deep cavitands form an arrayed, fluorescent indicator displacement assay system for the detection of post-translationally modified (PTM) histone peptides. The hosts bind trimethyllysine (KMe3) groups, and use secondary upper rim interactions to provide more sensitive discrimination between targets with identical KMe3 binding handles. The sensor array uses multiple different recognition modes to distinguish between miniscule differences in target, such as identical lysine modifications at different sites of histone peptides. In addition, the sensor is affected by global changes in structure, so it is capable of discriminating between identical PTMs, at identical positions on amino acid fragments that vary only in peptide backbone length, and can be applied to detect non-methylation modifications such as acetylation and phosphorylations located multiple residues away from the targeted binding site. The synergistic application of multiple variables allows dual-mode deep cavitands to approach levels of recognition selectivity usually only seen with antibodies

Fiber reinforced polymer culvert bridges—a feasibility study from structural and lcc points of view

Soil–steel composite bridges (SSCB) have become increasingly popular for short-span bridges as an alternative to concrete slab bridges mainly due to their low initial cost, rapid manufac-ture, simplified construction, and geometrical adaptability. SSCBs have a variety of applications and can be used over waterways or roadways. While conventional bridges tend to lose their load-carrying capacity due to degradation, SSCBs gain strength because of backfill soil consolidation. However, the load carrying capacity and integrity of such structures highly depends on the condition and load-carrying capacity of the steel arch element. A major drawback of SSCBs, especially those located on waterways or with poor drainage, is corrosion and subsequent loss of cross-sectional capacity. Unfortunately, the inspection of such bridges is not straightforward and any damage/collapse will be very costly to repair/replace. Fiber reinforced polymer (FRP) composites offer an attractive alternative to replace the steel in these types of bridges. FRP composites have significantly improved durability characteristics compared to steel, which will reduce maintenance costs and improve life-cycle costs (LLCs). This paper presents a new concept to use glass FRP as a construction material to construct soil–FRP composite bridges (SFCB). Various aspects of design and manufacturing are presented along with results and conclusions from a case study involving alternative bridge designs in steel and FRP composites