Breaking the limits: The Taylor series method

Barrio, Roberto; Rodríguez, Marcos; Abad, Alberto; Blesa, Fernando

doi:10.1016/j.amc.2011.02.080

Cited by 65 publications

(52 citation statements)

References 34 publications

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“…Due to the complex nature of the survey data, variance was estimated using the Taylor series method. 23 Differences between categorical variables were tested using the Rao-Scott chi-square test which is a design-adjusted version of the Pearson chi-square appropriate to sample data. 24 Logistic regression models, weighted to account for deviations from a pure equal probability sample design, sampling and non-sampling error, sample design and nonresponse, were used to assess the following: (a) independent associations of smoking behaviors and intentions with e-cigarette use among all smokers; (b) independent associations of reasons for use of e-cigarettes with intentions to quit smoking cigarettes among e-cigarette users; and (c) independent associations of reasons for use of e-cigarettes with impact of use of e-cigarettes on current cigarette smoking among e-cigarette users.…”

Section: Discussionmentioning

confidence: 99%

Use of E-Cigarettes Among Current Smokers: Associations Among Reasons for Use, Quit Intentions, and Current Tobacco Use

Rutten

Blake

Agunwamba

et al. 2015

NICTOB

173

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Introduction: Research has documented growing availability and use of e-cigarettes in the United States over the last decade. Methods: We conducted a national panel survey of current adult cigarette smokers to assess attitudes, beliefs, and behaviors relating to e-cigarette use in the United States (N = 2,254). Results: Among current cigarette smokers, 20.4% reported current use of e-cigarettes on some days and 3.7% reported daily use. Reported reasons for e-cigarette use included: quit smoking (58.4%), reduce smoking (57.9%), and reduce health risks (51.9%). No significant differences in sociodemographic characteristics between e-cigarette users and nonusers were observed. Prior quit attempts were reported more frequently among e-cigarette users (82.8%) than nonusers (74.0%). Intention to quit was reported more frequently among e-cigarette users (64.7%) than nonusers (46.8%). Smokers intending to quit were more likely to be e-cigarette users than those not intending to quit (odds ratio [OR] = 1.90, CI =1.36-2.65). Those who used e-cigarettes to try to quit smoking (OR = 2.25, CI = 1.25-4.05), reduce stress (OR = 3.66, CI = 1.11-12.09), or because they cost less (OR = 3.42, CI = 1.64-7.13) were more likely to report decreases in cigarette smoking than those who did not indicate these reasons. Smokers who reported using e-cigarettes to quit smoking (OR = 16.25, or reduce stress (OR = 4.30, CI = 1.32-14.09) were significantly more likely to report an intention to quit than those who did not indicate those reasons for using e-cigarettes. Conclusions: Nearly a quarter of smokers in our study reported e-cigarettes use, primarily motivated by intentions to quit or reduce smoking. These findings identify a clinical and public health opportunity to re-engage smokers in cessation efforts.

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Section: Discussionmentioning

confidence: 99%

Use of E-Cigarettes Among Current Smokers: Associations Among Reasons for Use, Quit Intentions, and Current Tobacco Use

Rutten

Blake

Agunwamba

et al. 2015

NICTOB

173

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“…While adaptive algorithms have been widely studied, high-order algorithms are not mainstream because they are expensive in practice. Variable order methods have been used in [11], [16], [21], [5], [1] and some polynomial time algorithms have been obtained over compact domains or over arbitrary domains but with stronger hypothesis.…”

Section: Related Workmentioning

confidence: 99%

Computational complexity of solving polynomial differential equations over unbounded domains

Pouly

Graça²

2016

Theoretical Computer Science

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In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) y = p(y) over unbounded time domains, where p is a vector of polynomials. Contrarily to the bounded (compact) time case, this problem has not been well-studied, apparently due to the "intuition" that it can always be reduced to the bounded case by using rescaling techniques. However, as we show in this paper, rescaling techniques do not seem to provide meaningful insights on the complexity of this problem, since the use of such techniques introduces a dependence on parameters which are hard to compute.We present algorithms which numerically solve these ODEs over unbounded time domains. These algorithms have guaranteed accuracy, i.e. given some arbitrarily large time t and error bound ε as input, they will output a valueỹ which satisfies y(t) −ỹ ≤ ε. We analyze the complexity of these algorithms and show that they computeỹ in time polynomial in several quantities including the time t, the accuracy of the output ε and the length of the curve y from 0 to t, assuming it exists until time t. We consider both algebraic complexity and bit complexity.

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“…In many problems, high-precision arithmetic is required to obtain accurate results, and so for such problems the Taylor scheme is the only reliable method among the standard methods. The right graph in Figure 2 shows the error for an unstable orbit using 500-digit arithmetic using the TIDES code [52]. TIDES code with 300 digits, compared with just one time period using IEEE 64-bit floating-point arithmetic.…”

Section: Dynamical Systemsmentioning

confidence: 99%

High-Precision Arithmetic in Mathematical Physics

Bailey

Borwein

2015

Mathematics

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For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

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Breaking the limits: The Taylor series method

Cited by 65 publications

References 34 publications

Use of E-Cigarettes Among Current Smokers: Associations Among Reasons for Use, Quit Intentions, and Current Tobacco Use

Use of E-Cigarettes Among Current Smokers: Associations Among Reasons for Use, Quit Intentions, and Current Tobacco Use

Computational complexity of solving polynomial differential equations over unbounded domains

High-Precision Arithmetic in Mathematical Physics

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