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"Rounding"
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Sir Cumference and the roundabout battle : a math adventure
\"When Steward Edmund Rounds and Sir Cumference notice that there are strangers camped nearby, Rounds II decides to investigate despite being involved with the task of learning how to make accurate counts of the castle's stores of food, supplies, and weaponry. When he reports back that an enemy is lying in wait, everyone moves quickly to defend the castle. But wait! Will Rounds II be able to figure out how many bows and arrows they have to create an appropriate battle plan? Using rounding techniques to figure out the totals more quickly, Rounds II is just in time to help stave off a potentially disastrous attack.\"--Amazon.com.
Book
Pandemic insights: what COVID-19 has revealed about traditional rounding structure
Due to social distancing policies and concerns over patient and provider safety, early in the COVID-19 pandemic many healthcare institutions temporarily converted to various, non-traditional rounding models. The abrupt and unprecedented change in workflow has enabled re-assessment of the reasons for the traditional rounding structures in medical education and comparison to newer strategies for rounding which have developed out of necessity during the pandemic. In this Perspectives article, we examine the positive and negative aspects of rounding models borne out of the pandemic and suggest aspects which may be carried forward, as well as future directions for research.
Journal Article
Rounding
When a quick guess is needed to count something, rounding can make math faster and fun! Read about two friends who are helping at a school fair earn that measuring, adding, and subtracting is easier if the numbers are rounded to whole numbers first. The children figure out ways to use rounding to estimate the amount of money raised at the fair, too!
Book
UAVs rounding up inspired by communication multi-agent depth deterministic policy gradient
UAVs rounding up is a game between UAV swarm and targets. The main challenge lies in achieving efficient collaboration between UAVs and the setting of rounding-up points. This paper extends our work in three aspects, including establishing an information interaction strategy model, dynamic rounding-up points, and detailed reward function settings. Inspired by the intelligence of the biological swarm, this paper constructs a communication multi-agent depth deterministic policy gradient (COM-MADDPG) framework, based on the communication topology during the rounding-up process, which proposes an information interaction strategy as action policy in reinforcement learning. When carrying out rounding up, it is no longer limited to a fixed threshold, and a dynamic rounding-up points is proposed to judge the success of the mission, each UAV has own area of rounding-up and cooperate to complete the swarm mission. In view of the situation where the target is at the corner or edge, the reward function of reinforcement learning is redefined, which effectively avoids the problem of rounding-up failure under special circumstances. Furthermore, the simulation results verify the COM-MADDPG framework perform better than DDPG and MADDPG in rounding-up tasks, and can be help for improving the success rate, which confirms the effectiveness of decision-making in those special situations. Those all have shown promise due to their robustness.
Journal Article
Guess it!
\"Carefully leveled text and vibrant photographs introduce early fluent readers to estimation using numerous real-world examples. Includes activity, glossary, and index.\"-- Provided by publisher.
Book
An O(log n/log log n)-Approximation Algorithm for the Asymmetric Traveling Salesman Problem
We present a randomized
O
(log
n
/log log
n
)-approximation algorithm for the asymmetric traveling salesman problem (ATSP). This provides the first asymptotic improvement over the long-standing Θ(log
n
)-approximation bound stemming from the work of Frieze et al. (1982) [Frieze AM, Galbiati G, Maffioki F (1982) On the worst-case performance of some algorithms for the asymmetric traveling salesman problem.
Networks
12(1):23–39].
The key ingredient of our approach is a new connection between the approximability of the ATSP and the notion of so-called thin trees. To exploit this connection, we employ maximum entropy rounding—a novel method of randomized rounding of LP relaxations of optimization problems. We believe that this method might be of independent interest.
Journal Article
Reporting only relative effect measures was potentially misleading: some good practices for improving the soundness of epidemiological results
•There is a growing tendency to report an excessive number of decimal digits; this can be misleading.•We combined statistical reasoning about the precision of relative risks with the meaning of the decimal part of the same measures from biological perspectives.•A general rule depending on the background absolute rate is proposed.•Relative and absolute risk measures should be reported. The use of more than two decimal digits is justified only when the background rate is high (ie, 1/10 py).
In the medical and epidemiological literature there is a growing tendency to report an excessive number of decimal digits (often three, sometimes four), especially when measures of relative occurrence are small; this can be misleading.
We combined mathematical and statistical reasoning about the precision of relative risks with the meaning of the decimal part of the same measures from biological and public health perspectives.
We identified a general rule for minimizing the mathematical error due to rounding of relative risks, depending on the background absolute rate, which justifies the use of one or more decimal digits for estimates close to 1.
We suggest that both relative and absolute risk measures (expressed as a rates) should be reported, and two decimal digits should be used for relative risk close to 1 only if the background rate is at least 1/1,000 py. The use of more than two decimal digits is justified only when the background rate is high (ie, 1/10 py).
Journal Article
Cutting edge—flatting and roughness measurement—to monitor blunting and chipping of the drill cutting edge when drilling CFRP
Tool wear is a major challenge when drilling CFRP. Cutting edge rounding quantifies the blunting of the cutting edge by considering the events happening in the flank–cutting edge–rake zone together by fitting a circle to this zone. The two interface zones, however, undergo wear in different ways. While the flank–cutting edge interface becomes rounded, the rake–cutting edge interface flattens out with drilling. Two new parameters, flank rounding (FR) and cutting edge flatting (CEF), are introduced to measure the damage to the flank and cutting edge, respectively. The nature of CEF and FR variation along the cutting edge shows that both are related. The chipping of the cutting edges is studied using a parameter called cutting edge roughness by monitoring the cutting edge topography. The progression of FR and cutting edge roughness along the length of the cutting edge shows that chipping may be related to the nature of FR progression. CEF could be easily measured using a simple measuring microscope and can be used to monitor drill wear.
Journal Article
Regulation of cell cycle progression by cell-cell and cell-matrix forces
It has long been proposed that the cell cycle is regulated by physical forces at the cell-cell and cell-extracellular matrix (ECM) interfaces
. However, the evolution of these forces during the cycle has never been measured in a tissue, and whether this evolution affects cell cycle progression is unknown. Here, we quantified cell-cell tension and cell-ECM traction throughout the complete cycle of a large cell population in a growing epithelium. These measurements unveil temporal mechanical patterns that span the entire cell cycle and regulate its duration, the G1-S transition and mitotic rounding. Cells subjected to higher intercellular tension exhibit a higher probability to transition from G1 to S, as well as shorter G1 and S-G2-M phases. Moreover, we show that tension and mechanical energy are better predictors of the duration of G1 than measured geometric properties. Tension increases during the cell cycle but decreases 3 hours before mitosis. Using optogenetic control of contractility, we show that this tension drop favours mitotic rounding. Our results establish that cell cycle progression is regulated cooperatively by forces between the dividing cell and its neighbours.
Journal Article
Rounding theory and method for the pitch curves of the variable center distance non-circular gear pair based on working conditions
Based on the working conditions of the variable center distance non-circular gear pair, this research provides the rounding theories and methods for the theoretical pitch curves of the gear pair, including establish the working conditions model of the variable center distance non-circular gear pair; group and classify the instantaneous working conditions and the instantaneous meshing arcs; design rounding algorithms for instantaneous meshing arc group category 1, 2, and 3; and propose the dynamic allocation strategy for distribute the total rounding amount on each pair of instantaneous meshing arcs. Finally, with the help of a variable center distance non-circular gear pair example, this research successfully proved the correctness and effectiveness of the above rounding theory and method, achieve the goal of rounding the theoretical pitch curves of the variable center distance non-circular gear pair.
Journal Article