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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
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
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
On the convergence of the gradient descent method with stochastic fixed-point rounding errors under the Polyak–Łojasiewicz inequality
In the training of neural networks with low-precision computation and fixed-point arithmetic, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers. This study provides insights into the choice of appropriate stochastic rounding strategies to mitigate the adverse impact of roundoff errors on the convergence of the gradient descent method, for problems satisfying the Polyak–Łojasiewicz inequality. Within this context, we show that a biased stochastic rounding strategy may be even beneficial in so far as it eliminates the vanishing gradient problem and forces the expected roundoff error in a descent direction. Furthermore, we obtain a bound on the convergence rate that is stricter than the one achieved by unbiased stochastic rounding. The theoretical analysis is validated by comparing the performances of various rounding strategies when optimizing several examples using low-precision fixed-point arithmetic.
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
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
When is p-hacking detectable?
Some forms of p-hacking cannot be detected by examining the t-curve (or p-curve). Standard tests may also fail to find even detectable forms of selective reporting. We propose a novel test that is consistent against every detectable form of p-hacking and remains interpretable even when the t-scores are not exactly normal. The test statistic is the distance between the smoothed empirical t-curve and the set of all distributions that would be possible in the absence of any selective reporting. This novel projection test can only be evaded in large meta-samples by selective reporting that also evades all other valid tests of restrictions on the t-curve. A second benefit of the projection test is that under the null hypothesis of no p-hacking we can check whether the projection residual could have been produced by other distortions not related to selective reporting, e.g. rounding and de-rounding. Applying the test to the Brodeur et al. (2020) meta-data, we find that the t-curves for RCTs, IVs, and DIDs are more distorted than could arise by chance. We confirm that these distortions cannot be explained by (de)rounding of t-scores or by the limited degrees of freedom of the underlying studies.
Paper
Stochastic Rounding for Image Interpolation and Scan Conversion
The stochastic rounding (SR) function is proposed to evaluate and demonstrate the effects of stochastically rounding row and column subscripts in image interpolation and scan conversion. The proposed SR function is based on a pseudorandom number, enabling the pseudorandom rounding up or down any non-integer row and column subscripts. Also, the SR function exceptionally enables rounding up any possible cases of subscript inputs that are inferior to a pseudorandom number. The algorithm of interest is the nearest-neighbor interpolation (NNI) which is traditionally based on the deterministic rounding (DR) function. Experimental simulation results are provided to demonstrate the performance of NNI-SR and NNI-DR algorithms before and after applying smoothing and sharpening filters of interest. Additional results are also provided to demonstrate the performance of NNI-SR and NNI-DR interpolated scan conversion algorithms in cardiac ultrasound videos.
Journal Article
NETosis proceeds by cytoskeleton and endomembrane disassembly and PAD4-mediated chromatin decondensation and nuclear envelope rupture
Neutrophil extracellular traps (NETs) are web-like DNA structures decorated with histones and cytotoxic proteins that are released by activated neutrophils to trap and neutralize pathogens during the innate immune response, but also form in and exacerbate sterile inflammation. Peptidylarginine deiminase 4 (PAD4) citrullinates histones and is required for NET formation (NETosis) in mouse neutrophils. While the in vivo impact of NETs is accumulating, the cellular events driving NETosis and the role of PAD4 in these events are unclear. We performed high-resolution time-lapse microscopy of mouse and human neutrophils and differentiated HL-60 neutrophil-like cells (dHL-60) labeled with fluorescent markers of organelles and stimulated with bacterial toxins or Candida albicans to induce NETosis. Upon stimulation, cells exhibited rapid disassembly of the actin cytoskeleton, followed by shedding of plasma membrane microvesicles, disassembly and remodeling of the microtubule and vimentin cytoskeletons, ER vesiculation, chromatin decondensation and nuclear rounding, progressive plasma membrane and nuclear envelope (NE) permeabilization, nuclear lamin meshwork and then NE rupture to release DNA into the cytoplasm, and finally plasma membrane rupture and discharge of extracellular DNA. Inhibition of actin disassembly blocked NET release. Mouse and dHL-60 cells bearing genetic alteration of PAD4 showed that chromatin decondensation, lamin meshwork and NE rupture and extracellular DNA release required the enzymatic and nuclear localization activities of PAD4. Thus, NETosis proceeds by a stepwise sequence of cellular events culminating in the PAD4-mediated expulsion of DNA.
Journal Article
NEGATIVE ASSOCIATION, ORDERING AND CONVERGENCE OF RESAMPLING METHODS
We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost sure weak convergence of measures output from Kitagawa’s [J. Comput. Graph. Statist. 5 (1996) 1–25] stratified resampling method. Carpenter, Ckiffird and Fearnhead’s [IEE Proc. Radar Sonar Navig. 146 (1999) 2–7] systematic resampling method is similar in structure but can fail to converge depending on the order of the input samples. We introduce a new resampling algorithm based on a stochastic rounding technique of [In 42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001) (2001) 588–597 IEEE Computer Soc.], which shares some attractive properties of systematic resampling, but which exhibits negative association and, therefore, converges irrespective of the order of the input samples. We confirm a conjecture made by [J. Comput. Graph. Statist. 5 (1996) 1–25] that ordering input samples by their states in ℝ yields a faster rate of convergence; we establish that when particles are ordered using the Hilbert curve in ℝ
d
, the variance of the resampling error is 𝓞(N
−(1+1/d)) under mild conditions, where N is the number of particles. We use these results to establish asymptotic properties of particle algorithms based on resampling schemes that differ from multinomial resampling.
Journal Article