Set Systems Containing Many Maximal Chains

The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of $(n+1)$-element chains in the power set $\mathcal{P}(\{1,2,\dots,n\})$? We will show that for each fixed $\alpha>0$ there is a family of $\alpha 2^n$ sets containing $(\alpha+o(1))n!$ such chains, and that this is asymptotically best possible. For smaller set systems we are unable to answer the question. We conjecture that a `tower of cubes' construction is extremal. We finish by mentioning briefly a connection to an extremal problem on posets and a variant of our question for the grid graph.Comment: 5 page

Multi-mode photonic crystal fibers for VCSEL based data transmission

Quasi error-free 10 Gbit/s data transmission is demonstrated over a novel type of 50 micron core diameter photonic crystal fiber with as much as 100 m length. Combined with 850$ nm VCSEL sources, this fiber is an attractive alternative to graded-index multi-mode fibers for datacom applications. A comparison to numerical simulations suggests that the high bit-rate may be partly explained by inter-modal diffusion.Comment: Accepted for Optics Expres

Recreational Rights and Titles to Bed on Western Lakes and Streams

What rights do riparians, their licensees, and the public have to use the small lakes and streams of the West when the beds are privately owned? This is the question which this Article attempts to answer. However, to do this, an analysis had to be made of which lake and stream beds were privately owned. Thus, the Article covers both the questions of title to beds and rights of surface use. This Article represents the first time that an effort has been made to systematically and comprehensively survey the lake and stream surface use cases of the Western part of the Nation, or of any large section of the Nation, and to critically compare and evaluate these cases

Recreational Rights and Titles to Beds on Western Lakes and Streams

What rights do riparians, their licensees, and the public have to use the small lakes and streams of the West when the beds are privately owned? This is the question which this Article attempts to answer. However, to do this, an analysis had to be made of which lake and stream beds were privately owned. Thus, the Article covers both the questions of title to beds and rights of surface use. This Article represents the first time that an effort has been made to systematically and comprehensively survey the lake and stream surface use cases of the Western part of the Nation, or of any large section of the Nation, and to critically compare and evaluate these cases

Degradation of Polymeric Biomaterials

Environmental and processing factors affecting the biostability of medical devices made from traditionally stable polymers, such as isotactic polypropylene (PP) and ultrahigh molecular weight polyethylene (UHMW-PE) , were analyzed and their undesirable degradation was related to performance of typical medical devices. Among the critical phenomena determining the biological performance of UHMW-PE and PP devices are oxidation during melt-processing and the propensity of the polymer chains to radiolyse and radio-oxidize. Polyesters and their biomedical devices , which can be designed to degrade predictably, are addressed with some focus on the less obvious determinants of performance

Process of making a bone healing device

The present invention is directed to polymeric bone fixation devices and processes for making the devices. In making the bone fixation devices, a polymeric material having a crystalline portion is deformed by a compressive force along a particular direction which causes molecular chains contained within the polymer to orient. The resulting polymer has increased mechanical properties including increased tensile strength and modulus. The polymeric material used to make the bone fixation device can be a bioabsorbable polymer which, once implanted, is broken down and absorbed by the patient\u27s body, eliminating the need for removal

Degradation of Polymeric Biomaterials

Environmental and processing factors affecting the biostability of medical devices made from traditionally stable polymers, such as isotactic polypropylene (PP) and ultrahigh molecular weight polyethylene (UHMW-PE) , were analyzed and their undesirable degradation was related to performance of typical medical devices. Among the critical phenomena determining the biological performance of UHMW-PE and PP devices are oxidation during melt-processing and the propensity of the polymer chains to radiolyse and radio-oxidize. Polyesters and their biomedical devices , which can be designed to degrade predictably, are addressed with some focus on the less obvious determinants of performance

The between-week reliability of neuromuscular, endocrine, and mood markers in soccer players and the repeatability of the movement demands during small-sided games

BACKGROUND: Establishing the reliability and repeatability of both the movement demands and the consequential responses of athletes applied settings is important. Therefore, the primary aim of this study was to assess the between-week reliability of potential fatigue monitoring methods in soccer players. Secondary aims were to establish the repeatability of the movement demands and the changes in monitoring variables from the same small-sided game (SSG) protocol programmed on consecutive weeks. METHODS: Twelve semi-professional soccer players (age, 21±2 years; mass, 80.1±6.8kg; height, 1.81±0.06m) performed the same SSG protocol (4vs4+goalkeepers; 6x7-min, 2-min inter-set recovery) separated by 7 days. Movement demands were monitored using global positioning systems (GPS), with countermovement jump (CMJ), saliva (testosterone and cortisol), and brief assessment of mood (BAM+) collected immediately pre and post SSG training. RESULTS: Results suggest that CMJ variables and hormonal markers have good between-week reliability when measuring athletes at rest (CV, 2.1–7.7%; ICC, 0.82–0.98), however BAM+ did not (CV, 23.5%; ICC, 0.47). GPS variables presented low to high repeatability during SSG training, with reliability statistics varying between metrics (CV, 4.4–62.4%; ICC, 0.30–0.81). In detecting responses from pre- to post-SSG training, CMJ and hormonal markers showed moderate to very-high reliability (ICC, 0.68–0.99), whilst BAM + did not (ICC, 0.12). CONCLUSIONS: The findings from this study suggest CMJ and hormonal markers provide good between-week reliability, yet caution should be applied when using short subjective questionnaires. Additionally, some movement demands may not be repeatable when programming the same SSG session on separate occasions

The effect of training order on neuromuscular, endocrine and mood response to small-sided games and resistance training sessions over a 24-h period

Objectives: This study examined the acute effect of small-sided-game (SSG) and resistance training sequence on neuromuscular, endocrine and mood response over a 24-hour (h) period. Design: Repeated measures Methods: Fourteen semi-professional soccer players performed SSG-training (4vs4 + goalkeepers; 6x7-min, 2-min inter-set recovery) followed by resistance training 2h later (back-squat, Romanian deadlift, barbell-hip-thrust; 4x4 repetitions, 4-min inter-set recovery; 85% 1 rep-max) (SSG+RES), and on a separate week reversed the session order (RES+SSG). Physical demands of SSG’s were monitored using global positioning systems (GPS) and ratings of perceived exertion (RPE). Countermovement-jump (CMJ; peak power output; jump height) and brief assessment of mood were collected before (pre), during (0h) and after (+24h) both protocols. Salivary testosterone and cortisol concentrations were obtained at the same time-points but with the inclusion of a measure immediately prior to the second training session (+2h). Results: GPS outputs and RPE were similar between SSG-training during both protocols. Between-protocol comparisons revealed no significant differences at +24h in CMJ performance, mood, and endocrine markers. Testosterone was higher at 0h during RES+SSG in comparison to SSG+RES (moderate-effect; +21.4±26.7 pg·ml-1; p= 0.010), yet was similar between protocols by +2h. Conclusions: The order of SSG and resistance training does not appear to influence the physical demands of SSG’s with sufficient recovery between two sessions performed on the same day. Session order did not influence neuromuscular, endocrine or mood responses at +24h, however a favourable testosterone response from the resistance first session may enhance neuromuscular performance in the second session of the day