Szego coordinates, quadrature domains, and double quadrature domains

We define Szego coordinates on a finitely connected smoothly bounded planar domain which effect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature domain with respect to boundary arc length. When these Szego coordinates coincide with Bergman coordinates, the result is a double quadrature domain with respect to both area and arc length. We enumerate a host of interesting and useful properties that such double quadrature domains possess, and we show that such domains are in fact dense in the realm of bounded finitely connected domains with smooth boundaries.Comment: 19 page

The Effects Of Caffeine Supplementation When Manipulating The Time Of Ingestion Prior To Simulated Rugby Union Activity

Introduction: Caffeine is a commonly used supplement, incorporated among athletes for enhancing sports specific performance via physiological and cognitive responses. Rugby is practiced worldwide, played by men and women, requiring varying physical and skill components. Although the effects of caffeine on sports performance have been heavily researched and scrutinized, a suitable time frame for caffeine ingestion prior to activity to elicit an ergogenic effect remains unclear. Methods: Athletes from a women and men\u27s university club rugby squad were recruited for this study (n=22). Athletes were measured for height, weight, body composition, and resting blood pressure. Body composition was measured utilizing air displacement (Cosmed, USA). Athletes each completed five trials (one familiarization) followed by four trials (two trials caffeine (3mg*kg-1 BM) or placebo 30 minutes prior to activity and two trials caffeine or placebo 60 minutes before activity). Trials involved an eight-station circuit that was completed for ten consecutive rounds. Measurements for speed, pushup repetitions, passing accuracy, and medicine ball throws were recorded. Data was normalized for placebo trials at 30 minutes pre exercise with comparisons between trial mean values measuring percent change for statistical significance. Results: Data was analyzed using ANOVA with alpha set at 0.05. Placebo trials at 30 minutes were normalized and comparisons were made between caffeine ingestion 30 and 60 minutes pre exercise. Passing accuracy attempts (1.2289 ± 0.34) and rugby specific sprint performances (.9300 ± 0.04) were enhanced with caffeine ingestion 60 minutes pre exercise. Rugby specific sprint performances (.9559 ± 0.06) were enhanced with caffeine ingestion 30 minutes pre exercise. Conclusion: Modest amounts of caffeine, ingested 30 and 60 minutes pre simulated rugby activity, will elicit an ergogenic effect on skill-based performances. Typically, double the dosage of caffeine (6mg*kg-1) is ingested for such studies. 3mg*kg-1 was administered for this study, with most of the results trending but not definitive. More research should be conducted with alterations in timing and dosage to narrow the time for ingestion and determine suitable dosage

Guarding a Non-Maneuverable Translating Line with an Attached Defender

In this paper we consider a target-guarding differential game where the defender must protect a linearly translating line-segment by intercepting an attacker who tries to reach it. In contrast to common target-guarding problems, we assume that the defender is attached to the target and moves along with it. This assumption affects the defenders' maximum speed in inertial frame, which depends on the target's direction of motion. Zero-sum differential game of degree for both the attacker-win and defender-win scenarios are studied, where the payoff is defined to be the distance between the two agents at the time of game termination. We derive the equilibrium strategies and the Value function by leveraging the solution for the infinite-length target scenario. The zero-level set of this Value function provides the barrier surface that divides the state space into defender-win and attacker-win regions. We present simulation results to demonstrate the theoretical results.Comment: 8 pages, 8 figures. arXiv admin note: text overlap with arXiv:2207.0409

Policy Stitching: Learning Transferable Robot Policies

Training robots with reinforcement learning (RL) typically involves heavy interactions with the environment, and the acquired skills are often sensitive to changes in task environments and robot kinematics. Transfer RL aims to leverage previous knowledge to accelerate learning of new tasks or new body configurations. However, existing methods struggle to generalize to novel robot-task combinations and scale to realistic tasks due to complex architecture design or strong regularization that limits the capacity of the learned policy. We propose Policy Stitching, a novel framework that facilitates robot transfer learning for novel combinations of robots and tasks. Our key idea is to apply modular policy design and align the latent representations between the modular interfaces. Our method allows direct stitching of the robot and task modules trained separately to form a new policy for fast adaptation. Our simulated and real-world experiments on various 3D manipulation tasks demonstrate the superior zero-shot and few-shot transfer learning performances of our method. Our project website is at: http://generalroboticslab.com/PolicyStitching/ .Comment: CoRL 202

Output Feedback Adaptive Optimal Control of Affine Nonlinear systems with a Linear Measurement Model

Real-world control applications in complex and uncertain environments require adaptability to handle model uncertainties and robustness against disturbances. This paper presents an online, output-feedback, critic-only, model-based reinforcement learning architecture that simultaneously learns and implements an optimal controller while maintaining stability during the learning phase. Using multiplier matrices, a convenient way to search for observer gains is designed along with a controller that learns from simulated experience to ensure stability and convergence of trajectories of the closed-loop system to a neighborhood of the origin. Local uniform ultimate boundedness of the trajectories is established using a Lyapunov-based analysis and demonstrated through simulation results, under mild excitation conditions.Comment: 16 pages, 5 figures, submitted to 2023 IEEE Conference on Control Technology and Application

The alcohol-preferring (P) and high-alcohol-drinking (HAD) rats – Animal Models of Alcoholism

The objective of this article is to review the literature on the utility of using the selectively bred alcohol-preferring (P) and high-alcohol-drinking (HAD) lines of rats in studies examining high alcohol drinking in adults and adolescents, craving-like behavior, and the co-abuse of alcohol with other drugs. The P line of rats meets all of the originally proposed criteria for a suitable animal model of alcoholism. In addition, the P rat exhibits high alcohol-seeking behavior, demonstrates an alcohol deprivation effect (ADE) under relapse drinking conditions, consumes amounts of ethanol during adolescence equivalent to those consumed in adulthood, and co-abuses ethanol and nicotine. The P line also exhibits excessive binge-like alcohol drinking, attaining blood alcohol concentrations (BACs) of 200 mg% on a daily basis. The HAD replicate lines of rats have not been as extensively studied as the P rats. The HAD1,2 rats satisfy several of the criteria for an animal model of alcoholism, e.g., these rats will voluntarily consume ethanol in a free-choice situation to produce BACs between 50–200 mg%. The HAD1,2 rats also exhibit an ADE under repeated relapse conditions, and will demonstrate similar levels of ethanol intake during adolescence as seen in adults. Overall, the P and HAD1,2 rats have characteristics attributed to an early onset alcoholic, and can be used to study various aspects of alcohol use disorders

Daily patterns of ethanol drinking in adolescent and adult, male and female, high alcohol drinking (HAD) replicate lines of rats

The rationale for our study was to determine the pattern of ethanol drinking by the high alcohol-drinking (HAD) replicate lines of rats during adolescence and adulthood in both male and female rats. Rats were given 30 days of 24 h free-choice access to ethanol (15%, v/v) and water, with ad lib access to food, starting at the beginning of adolescence (PND 30) or adulthood (PND 90). Water and alcohol drinking patterns were monitored 22 h/day with a “lickometer” set-up. The results indicated that adolescent HAD-1 and HAD-2 males consumed the greatest levels of ethanol and had the most well defined ethanol licking binges among the age and sex groups with increasing levels of ethanol consumption throughout adolescence. In addition, following the first week of adolescence, male and female HAD-1 and HAD-2 rats differed in both ethanol consumption levels and ethanol licking behavior. Adult HAD-1 male and female rats did not differ from one another and their ethanol intake or licking behaviors did not change significantly over weeks. Adult HAD-2 male rats maintained a relatively constant level of ethanol consumption across weeks, whereas adult HAD-2 female rats increased ethanol consumption levels over weeks, peaking during the third week when they consumed more than their adult male counterparts. The results indicate that the HAD rat lines could be used as an effective animal model to examine the development of ethanol consumption and binge drinking in adolescent male and female rats providing information on the long-range consequences of adolescent alcohol drinking