On uniform convergence of Fourier series

We consider the space $U(\mathbb T)$ of all continuous functions on the circle $\mathbb T$ with uniformly convergent Fourier series. We show that if $\varphi: \mathbb T\rightarrow\mathbb T$ is a continuous piecewise linear but not linear map, then $\|e^{in\varphi}\|_{U(\mathbb T)}\simeq\log n$

Séries de Taylor et séries trigonométriques universelles au sens de Menchoff

RésuméLe résultat principal de cet article est qu'il existe une série trigonométrique universelle au sens de Menchoff qui est la restriction au cercle unité d'une série de Taylor dont les coefficients tendent vers zéro.Il nous a paru bon, avant de présenter ce résultat et ses variantes, de récapituler des éléments connus de la théorie des séries trigonométrique universelles et de celle des séries de Taylor universelles.AbstractHere is the principal result: there exists a trigonometric series of the Taylor type, with coefficients tending to zero, and universal in the sense of Mens̆ov. The article recapitulates known results on universal trigonometric series and universal Taylor series before presenting the main result and its developments

Knowledge Cartography for Controversies: The Iraq Debate

In analysing controversies and debates—which would include reviewing a literature in order to plan research, or assessing intelligence to formulate policy—there is no one worldview which can be mapped, for instance as a single, coherent concept map. The cartographic challenge is to show which facts are agreed and contested, and the different kinds of narrative links that use facts as evidence to define the nature of the problem, what to do about it, and why. We will use the debate around the invasion of Iraq to demonstrate the methodology of using a knowledge mapping tool to extract key ideas from source materials, in order to classify and connect them within and across a set of perspectives of interest to the analyst. We reflect on the value that this approach adds, and how it relates to other argument mapping approaches

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Approximated maximum likelihood estimation in multifractal random walks

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the R computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.Comment: 8 pages, 3 figures, 2 table

Functional neuroimaging and withdrawal of life-sustaining treatment from vegetative patients

Recent studies using functional magnetic resonance imaging of patients in a vegetative state have raised the possibility that such patients retain some degree of consciousness. In this paper, the ethical implications of such findings are outlined, in particular in relation to decisions about withdrawing life-sustaining treatment. It is sometimes assumed that if there is evidence of consciousness, treatment should not be withdrawn. But, paradoxically, the discovery of consciousness in very severely brain-damaged patients may provide more reason to let them die. Although functional neuroimaging is likely to play an increasing role in the assessment of patients in a vegetative state, caution is needed in the interpretation of neuroimaging findings

Observational evidence of the formation of cyanopolyynes in CRL618 through the polimerization of HCN

The abundance ratio of consecutive members of the cyanopolyynes family has been explored in CRL618 using data acquired in a complete line survey covering the frequency range 81-356 GHz. The Jup range explored for the different molecules is the following: 1 to 4 for HCN and HNC, 9 to 39 for HC3N, 31 to 133 for HC5N, and 72 to 85 for HC7N (not detected beyond Jup=85). The lowest vibrationally excited state of HC7N (nu_15 at 62 cm^-1) has been tentatively detected. Data analysis has been performed by extending our previous geometrical and radiative transfer model of the slowly expanding envelope (SEE) surrounding the compact central continuum source of CRL 618, that was established from the study of rotational lines in several vibrationally excited states of HC_3N. The new lines analyzed here require to model the high velocity wind (HVW) component and the colder circumstellar gas, remnant of the AGB phase of CRL618. The derived HC3N/HC5N and HC5N/HC7N abundance ratios from this set of uniformly calibrated lines are between 3 and 6 in the different regions, similar to standard values in the CSM and ISM, and consistent with previous estimates obtained from ISO observations and chemical models. However, the abundance ratios of HC3N, HC5N and HC7N with respect to HCN are at least two orders of magnitude larger than those typical for AGB C-rich stars, such as IRC+10216. This fact indicates that, in the short transition toward the Planetary Nebula phase, HCN is quickly reprocessed into longer cyanopolyyne chains. A similar behavior was previously found in this object for the polyacetylenic chains (C(2n)H2).Comment: 8 figures, accepted in ApJ main journa

Stakeholder and citizen roles in public deliberation

This paper explores theoretical and practical distinctions between individual citizens (`citizens) and organized groups ('stakeholder representatives' or `stakeholders for short) in public participation processes convened by government as part of policy development. Distinctions between `citizen and `stakeholder involvement are commonplace in government discourse and practice; public involvement practitioners also sometimes rely on this distinction in designing processes and recruiting for them. Recognizing the complexity of the distinction, we examine both normative and practical reasons why practitioners may lean towardor away fromrecruiting citizens, stakeholders, or both to take part in deliberations, and how citizen and stakeholder roles can be separated or combined within a process. The article draws on a 2012 Canadian-Australian workshop of deliberation researchers and practitioners to identify key challenges and understandings associated with the categories of stakeholder and citizen and their application, and hopes to continue this conversation with the researcher-practitioner community

From risk to fairness

Kadcyla is a drug that extends the life of breast cancer patients by an average of 6 mo. It also happens to be incredibly expensive. The United Kingdom’s National Health Service sparked controversy when it refused to provide this drug to patients, citing its low cost effectiveness. Cases like this raise the question of how societies should make distributive decisions. Should we maximize utility or should we aim to improve the lives of the least fortunate, even if doing so is costly for everyone else? The influential philosopher John Rawls tackled this dilemma by framing fair distributive decisions as a kind of gamble (1). Rawls famously argued that we should choose the kind of society we would all prefer if our choice was made from behind a “veil of ignorance” — that is, under conditions of complete uncertainty about where we would end up. He held that people should make such choices by following a risk-averse “maximin” strategy of maximizing the minimum possible outcome for themselves and others. Echoing Rawls’s theory, new research by Kameda et al. (2) links risk and fairness by showing that preferences about risk and about distribution may arise from common psychological and neural substrates

KPZ in one dimensional random geometry of multiplicative cascades

We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When the random variables generating the cascade are exponentials of Gaussians, the well known KPZ formula of Knizhnik, Polyakov and Zamolodchikov from quantum gravity appears. This note was inspired by the recent work of Duplantier and Sheffield proving a somewhat different version of the KPZ formula for Liouville gravity. In contrast with the Liouville gravity setting, the one dimensional multiplicative cascade framework facilitates the determination of the Hausdorff dimension, rather than some expected box count dimension.Comment: 14 page