Partitioning orthogonal polygons into at most 8-vertex pieces, with application to an art gallery theorem

We prove that every simply connected orthogonal polygon of $n$ vertices can be partitioned into $\left\lfloor\frac{3 n +4}{16}\right\rfloor$ (simply connected) orthogonal polygons of at most 8 vertices. It yields a new and shorter proof of the theorem of A. Aggarwal that $\left\lfloor\frac{3 n +4}{16}\right\rfloor$ mobile guards are sufficient to control the interior of an $n$-vertex orthogonal polygon. Moreover, we strengthen this result by requiring combinatorial guards (visibility is only required at the endpoints of patrols) and prohibiting intersecting patrols. This yields positive answers to two questions of O'Rourke. Our result is also a further example of the "metatheorem" that (orthogonal) art gallery theorems are based on partition theorems.Comment: 20 pages, 12 figure

Block of T cell development in P53-deficient mice accelerates development of lymphomas with characteristic RAG-dependent cytogenetic alterations

SummaryMice deficient in the DNA damage sensor P53 display normal T cell development but eventually succumb to thymic lymphomas. Here, we show that inactivation of the TCR β gene enhancer (Eβ) results in a block of T cell development at stages where recombination-activating genes (RAG) are expressed. Introduction of the Eβ mutation into p53−/− mice dramatically accelerates the onset of lethal thymic lymphomas that harbor RAG-dependent aberrant rearrangements, chromosome 14 and 12 translocations, and amplification of the chromosomal region 9A1–A5.3. Phenotypic and genetic analyses suggest that lymphomas emerge through a normal thymocyte development pathway. These findings provide genetic evidence that block of lymphocyte development at stages with RAG endonuclease activity can provoke lymphomagenesis on a background with deficient DNA damage responses

The Relationships Between Energy Balance, Timing and Quantity of Protein Consumption, and Body Composition in Collegiate Football Players

Background Timing and quantity of protein (PRO) consumption are important considerations for muscle protein synthesis (MPS), fat-free mass (FFM) accretion, and body fat % (BF%) reduction. The effect of PRO ingestion on changes in FFM is mediated by many variables. Past studies have focused on specific composition of carbohydrate (CHO) and PRO consumption (CHO vs. PRO + CHO), and have also investigated PRO intake timing at pre-exercise, post-exercise, or both. Other studies have investigated FFM maintenance and growth with increased PRO consumption during catabolic or anabolic phases of energy balance (EB). These mechanisms have been studied in various populations, including healthy untrained individuals, overweight and obese people, and endurance athletes. However, studies have not explored relationships between the amount and timing of PRO ingested, and the state of EB, as it relates to FFM%. Method/Design A retrospective analysis design was used to assess relationships between PRO ingestion, timing, and EB on FFM in collegiate football players. Subjects were members of an intercollegiate Division 1 football team, had completed a one-day food and activity record, and had body composition assessed as part of a regular team screening procedure. Data acquisition was supervised by a PhD/Registered Dietitian. Food and activity records were analyzed using NutriTiming®, which predicts RMR via the Harris-Benedict equation, uses a MET-based relative intensity activity scale, and accesses the USDA Nutrient Database for Standard Reference, Release 26 to predict hourly EB and PRO consumption. EB was assessed as ±400 kcal EB (EBR), \u3c 0 kcal EB (NEGEB), and \u3e 0 kcal EB (POSEB). Total useable PRO (TUP) was defined as the sum of PRO consumed in units up to 30g max/meal, a value also assessed relative to EB at the time of ingestion. The goal was to assess the amount and timing of PRO intake with EB as these factors relate to FFM. Results Pearson\u27s correlations found that BF% was negatively associated with TUP while in EBR (r=-.253; p=0.049), and FFM% was positively associated TUP in EBR (r=0.279; p=0.030) and in POSEB (r=0.282; p=0.028). NEGEB was positively associated with BF% (r=0.325; p=0.011), and negatively associated with FFM% (r=-0.322; p=0.011). Conclusions Results elucidate that players who ingest PRO in a relatively good energy-balanced state had higher FFM% and a lower BF%. Further, those players consuming TUP while in POSEB had an even stronger positive association with FFM% and a stronger inverse association with BF%. These data reject the null hypothesis that football players who consume PRO in POSEB have less FFM% than those who consume PRO in NEGEB