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Happens before-based dynamic analysis is the go-to technique for detecting data races in large scale software projects due to the absence of false positive reports. However, such analyses are expensive since they employ expensive vector clock updates at each event, rendering them usable only for in-house testing. In this paper, we present a sampling-based, randomized race detector that processes onlyconstantly manyevents of the input trace even in the worst case. This is the firstsub-lineartime (i.e., running ino(n) time wherenis the length of the trace) dynamic race detection algorithm; previous sampling based approaches like run in linear time (i.e.,O(n)). Our algorithm is a property tester for -race detection — it is sound in that it never reports any false positive, and on traces that are far, with respect to hamming distance, from any race-free trace, the algorithm detects an -race with high probability. Our experimental evaluation of the algorithm and its comparison with state-of-the-art deterministic and sampling based race detectors shows that the algorithm does indeed have significantly low running time, and detects races quite often.
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Optimally controlling nutrition and propulsion force in a long distance running race
IntroductionRunners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout the race and the propulsion force of the runner. As nutrition is an integral part of successfully running long distance races, it needs to be included in models of running strategies. MethodsWe formulate a system of ordinary differential equations to represent the velocity, fat energy, glycogen energy, and nutrition for a runner competing in a long-distance race. The energy compartments represent the energy sources available in the runner's body. We allocate the energy source from which the runner draws, based on how fast the runner is moving. The food consumed during the race is a source term for the nutrition differential equation. With our model, we are investigating strategies to manage the nutrition and propulsion force in order to minimize the running time in a fixed distance race. This requires the solution of a nontrivial singular control problem. ResultsAs the goal of an optimal control model is to determine the optimal strategy, comparing our results against real data presents a challenge; however, in comparing our results to the world record for the marathon, our results differed by 0.4%, 31 seconds. Per each additional gel consumed, the runner is able to run 0.5 to 0.7 kilometers further in the same amount of time, resulting in a 7.75% increase in taking five 100 calorie gels vs no nutrition. DiscussionOur results confirm the belief that the most effective way to run a race is to run approximately the same pace the entire race without letting one's energies hit zero, by consuming in-race nutrition. While this model does not take all factors into account, we consider it a building block for future models, considering our novel energy representation, and in-race nutrition.
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- Award ID(s):
- 2031213
- PAR ID:
- 10481504
- Publisher / Repository:
- frontiersin.org
- Date Published:
- Journal Name:
- Frontiers in Nutrition
- Volume:
- 10
- ISSN:
- 2296-861X
- Subject(s) / Keyword(s):
- optimization differential equation models running nutrition metabolism bioenergetics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fnut.2023.1096194
