1,370 research outputs found

    Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

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    A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

    The Tobacco-Related Behavioral Risks of a Nationally Representative Sample of Adolescents

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    The study\u27s purpose was to determine which factors were the strongest predictors of tobacco smoking behaviors among U.S. adolescents. The population included a nationally representative sample of 6,504 adolescents residing in the U.S. Data were collected in respondents \u27homes using trained interviewers. Weighted population estimates showed that over half (55.6%) of adolescents had ever tried smoking, nearly half of whom (48.2%) reported regular smoking. Those whose closest friends smoked were twice as likely to ever smoke (OR = 2.24, p\u3c.001), twice as likely to be a regular smoker (OK = 2.28, p \u3c.OO1), and more likely (b = 5.15p \u3c.OO1) to have smoked daily than those whose friends do not smoke. Results show the very strong influence of friendships on tobacco initiation and continuance among this national sample of adolescents. Recommendations for primary and secondary prevention are noted

    Tempo and mode of performance evolution across multiple independent origins of adhesive toe pads in lizards

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    Understanding macroevolutionary dynamics of trait evolution is an important endeavor in evolutionary biology. Ecological opportunity can liberate a trait as it diversifies through trait space, while genetic and selective constraints can limit diversification. While many studies have examined the dynamics of morphological traits, diverse morphological traits may yield the same or similar performance and as performance is often more proximately the target of selection, examining only morphology may give an incomplete understanding of evolutionary dynamics. Here, we ask whether convergent evolution of pad‐bearing lizards has followed similar evolutionary dynamics, or whether independent origins are accompanied by unique constraints and selective pressures over macroevolutionary time. We hypothesized that geckos and anoles each have unique evolutionary tempos and modes. Using performance data from 59 species, we modified Brownian motion (BM) and Ornstein–Uhlenbeck (OU) models to account for repeated origins estimated using Bayesian ancestral state reconstructions. We discovered that adhesive performance in geckos evolved in a fashion consistent with Brownian motion with a trend, whereas anoles evolved in bounded performance space consistent with more constrained evolution (an Ornstein–Uhlenbeck model). Our results suggest that convergent phenotypes can have quite distinctive evolutionary patterns, likely as a result of idiosyncratic constraints or ecological opportunities

    Re-evaluating Pleistocene-Holocene occupation of cave sites in north-west Thailand: New radiocarbon and luminescence dating

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    Established chronologies indicate a long-term 'Hoabinhian' hunter-gatherer occupation of Mainland Southeast Asia during the Terminal Pleistocene to Mid-Holocene (45 000-3000 years ago). Here, the authors re-examine the 'Hoabinhian' sequence from north-west Thailand using new radiocarbon and luminescence data from Spirit Cave, Steep Cliff Cave and Banyan Valley Cave. The results indicate that hunter-gatherers exploited this ecologically diverse region throughout the Terminal Pleistocene and the Pleistocene-Holocene transition, and into the period during which agricultural lifeways emerged in the Holocene. Hunter-gatherers did not abandon this highland region of Thailand during periods of environmental and socioeconomic change

    Fast linear algebra is stable

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    In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of nn-by-nn matrices can be done by any algorithm in O(nω+η)O(n^{\omega + \eta}) operations for any η>0\eta > 0, then it can be done stably in O(nω+η)O(n^{\omega + \eta}) operations for any η>0\eta > 0. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in O(nω+η)O(n^{\omega + \eta}) operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

    Robust high-dimensional precision matrix estimation

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    The dependency structure of multivariate data can be analyzed using the covariance matrix Σ\Sigma. In many fields the precision matrix Σ−1\Sigma^{-1} is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast

    A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities

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    We consider a manifold endowed with two different vielbeins EAΌE^{A}{}_{\mu} and LAΌL^{A}{}_{\mu} corresponding to two different metrics gΌΜg_{\mu\nu} and fΌΜf_{\mu\nu}. Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation gΌΜEAΌLBΜ=gΌΜEBΌLAΜg^{\mu\nu} E^{A}{}_{\mu} L^{B}{}_{\nu} = g^{\mu\nu} E^{B}{}_{\mu} L^{A}{}_{\nu} can be imposed (or the "Deser-van Nieuwenhuizen" gauge chosen). We clarify and correct various statements which have been made about this issue.Comment: 20 pages. Section 7, prop. 6 and 7. added. Some results made more precis

    'The show must go on': Event dramaturgy as consolidation of community

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    Event dramaturgy and cultural performance have not been examined in the literature from a strategic standpoint of fostering the social value of events. Thus, the purpose of this study was to explore the case of the Water Carnival, a celebratory event in a rural community of Southwest Texas, demonstrating the essence of this event as a symbolic social space, wherein event participants instantiate a shared and valued sense of community. A hermeneutical approach was employed, interpreting the event and its symbolisms as a text, combined with findings from ethnographic fieldwork, including participant observation, in-depth interviews and analysis of archival documents. The study examines the ways that dramaturgy in the Water Carnival helps frame the ongoing public discourse for community improvement and enhances social capital. The implications of the study for social leverage of events are discussed. It is suggested that a foundation for strategic social planning is the understanding of events as symbolic social spaces and their embeddedness in community development, which can be accomplished when events are pertinent to public discourse, address community issues, represent an inclusive range of stakeholders, and promote cooperation
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