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We study a simple “horizon model” for the problem of recovering an image from noisy data; in this model the image has an edge with $\alpha$-Hölder regularity. Adopting the viewpoint of computational harmonic analysis, we develop an overcomplete collection of atoms called wedgelets, dyadically organized indicator functions with a variety of locations, scales and orientations. The wedgelet representation provides nearly optimal representations of objects in the horizon model, as measured by minimax description length. We show how to rapidly compute a wedgelet approximation to noisy data by finding a special edgelet-decorated recursive partition which minimizes a complexity-penalized sum of squares. This estimate, using sufficient subpixel resolution, achieves nearly the minimax mean-squared error in the horizon model. In fact, the method is adaptive in the sense that it achieves nearly the minimax risk for any value of the unknown degree of regularity of the horizon, $1 \leq \alpha \leq 2$. Wedgelet analysis and denoising may be used successfully outside the horizon model. We study images modelled as indicators of star-shaped sets with smooth boundaries and show that complexity-penalized wedgelet partitioning achieves nearly the minimax risk in that setting also.

Abstract In recent decades, the warming in the Arctic has been much faster than in the rest of the world, a phenomenon known as Arctic amplification. Numerous studies report that the Arctic is warming either twice, more than twice, or even three times as fast as the globe on average. Here we show, by using several observational datasets which cover the Arctic region, that during the last 43 years the Arctic has been warming nearly four times faster than the globe, which is a higher ratio than generally reported in literature. We compared the observed Arctic amplification ratio with the ratio simulated by state-of-the-art climate models, and found that the observed four-fold warming ratio over 1979–2021 is an extremely rare occasion in the climate model simulations. The observed and simulated amplification ratios are more consistent with each other if calculated over a longer period; however the comparison is obscured by observational uncertainties before 1979. Our results indicate that the recent four-fold Arctic warming ratio is either an extremely unlikely event, or the climate models systematically tend to underestimate the amplification.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSynthesis and characterization of nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor nanocrystallitesC. B. Murray, D. J. Norris, and M. G. BawendiCite this: J. Am. Chem. Soc. 1993, 115, 19, 8706–8715Publication Date (Print):September 1, 1993Publication History Published online1 May 2002Published inissue 1 September 1993https://pubs.acs.org/doi/10.1021/ja00072a025https://doi.org/10.1021/ja00072a025research-articleACS PublicationsRequest reuse permissionsArticle Views65449Altmetric-Citations7838LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts

The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory [similar to that introduced by Schneider (1977)] is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

We report the theoretical discovery of a class of 2D tight-binding models containing nearly flatbands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Because of the similarity with 2D continuum Landau levels, these topologically nontrivial nearly flatbands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flatband aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.

We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is fast and continuous, but biased. The bias of the LASSO may prevent consistent variable selection. Subset selection is unbiased but computationally costly. The MC+ has two elements: a minimax concave penalty (MCP) and a penalized linear unbiased selection (PLUS) algorithm. The MCP provides the convexity of the penalized loss in sparse regions to the greatest extent given certain thresholds for variable selection and unbiasedness. The PLUS computes multiple exact local minimizers of a possibly nonconvex penalized loss function in a certain main branch of the graph of critical points of the penalized loss. Its output is a continuous piecewise linear path encompassing from the origin for infinite penalty to a least squares solution for zero penalty. We prove that at a universal penalty level, the MC+ has high probability of matching the signs of the unknowns, and thus correct selection, without assuming the strong irrepresentable condition required by the LASSO. This selection consistency applies to the case of p≫n, and is proved to hold for exactly the MC+ solution among possibly many local minimizers. We prove that the MC+ attains certain minimax convergence rates in probability for the estimation of regression coefficients in ℓr balls. We use the SURE method to derive degrees of freedom and Cp-type risk estimates for general penalized LSE, including the LASSO and MC+ estimators, and prove their unbiasedness. Based on the estimated degrees of freedom, we propose an estimator of the noise level for proper choice of the penalty level. For full rank designs and general sub-quadratic penalties, we provide necessary and sufficient conditions for the continuity of the penalized LSE. Simulation results overwhelmingly support our claim of superior variable selection properties and demonstrate the computational efficiency of the proposed method.

Solar wind fluctuations are commonly regarded as a superposition of MHD waves, primarily in the Alfvén mode. These MHD fluctuations are frequently assumed to possess “slab” or isotropic symmetry, particularly in the development of models of the propagation of cosmic rays throughout the heliosphere. There are, however, several long‐standing problems with either of these choices. One problem is that the mean free path for pitch angle scattering of cosmic rays in the heliosphere is apparently longer than can be accounted for by using either assumption about the statistical symmetry of the fluctuations. Another problem is the prediction of WKB theory that the direction of minimum variance should tend to lie along the radial direction rather than along the mean magnetic field as is observed. Motivated by laboratory plasma experiments, a series of two‐dimensional MHD simulations, recent theoretical work, and extensive analyses of solar wind data, we suggest that there is a third possible viewpoint with potentially important implications for solar wind studies. From this perspective we suggest that solar wind fluctuations contain a subpopulation that have wave vectors nearly transverse to both the mean magnetic field and the fluctuations about the mean. For this quasi‐two‐dimensional component the direction of minimum variance lies along the mean magnetic field, density fluctuations are small and anticorrelated with | B |, the total pressure at small scales is nearly constant, and pitch angle scattering by resonant wave‐particle interactions is suppressed.

We demonstrate very high efficiency electrophosphorescence in organic light-emitting devices employing a phosphorescent molecule doped into a wide energy gap host. Using bis(2-phenylpyridine)iridium(III) acetylacetonate [(ppy)2Ir(acac)] doped into 3-phenyl-4(1′-naphthyl)-5-phenyl-1,2,4-triazole, a maximum external quantum efficiency of (19.0±1.0)% and luminous power efficiency of (60±5) lm/W are achieved. The calculated internal quantum efficiency of (87±7)% is supported by the observed absence of thermally activated nonradiative loss in the photoluminescent efficiency of (ppy)2Ir(acac). Thus, very high external quantum efficiencies are due to the nearly 100% internal phosphorescence efficiency of (ppy)2Ir(acac) coupled with balanced hole and electron injection, and triplet exciton confinement within the light-emitting layer.

A purely statistical origin of hierarchical density structure in pressureless and nearly pressureless turbulent flows without self-gravity is proposed. It is argued that hydrodynamic (Navier-Stokes) flows with rms Mach numbers M<SUB>rms</SUB> ≫ 1, like the cold interstellar medium or some cosmological flows, have a nearly pressureless behavior, except perhaps in a small fraction of the volume. Assuming that in these flows the density field can be considered as a random variable in time with an associated probability distribution function (pdf), a condition on the pdf for the spontaneous development of hierarchical structure is proposed. The condition is essentially a requirement that the joint probability of a succession of n constructively interfering relative density fluctuations of amplitude a be larger than the probability of a single, large fluctuation of the same final amplitude a . An analytic form for this condition is derived, under the assumption that the density pdf is scale- invariant, and three important functional forms of the pdf (a power-law, a lognormal, and an exponential distribution) are tested according to this criterion. It is found that development of hierarchical structure should always be expected for the lognormal and exponential distributions at large values of n and/or a, but is parameter-dependent in the case of the power law. The assumption of a scale-invariant density pdf is motivated (but not rigorously proved) by the scale invariance of the pressureless hydrodynamic equations with negligible self-gravity, and a numerical simulation of a compressible turbulent flow in two dimensions in a transonic regime (M ∼ 1) is used to test this and other secondary assumptions. The density field developed by the simulation clearly exhibits at least three levels of hierarchical nesting. The density statistics, albeit obscured by the limited resolution, which limits the feasible density contrasts, are shown to be consistent with the hypotheses. A discussion on the degree to which the dynamics of two- and three-dimensional flows may differ from one another in the compressible case is given. Finally, a remark is made that the hierarchical structure produced by this mechanism in turbulent compressible flows is transient although statistically stationary. This should be the case of all non-self-gravitating clouds in the cold interstellar medium and of small-scale structures in cosmological flows.

Abstract The observed rapid loss of thick multiyear sea ice over the last 7 years and the September 2012 Arctic sea ice extent reduction of 49% relative to the 1979–2000 climatology are inconsistent with projections of a nearly sea ice‐free summer Arctic from model estimates of 2070 and beyond made just a few years ago. Three recent approaches to predictions in the scientific literature are as follows: (1) extrapolation of sea ice volume data, (2) assuming several more rapid loss events such as 2007 and 2012, and (3) climate model projections. Time horizons for a nearly sea ice‐free summer for these three approaches are roughly 2020 or earlier, 2030 ± 10 years, and 2040 or later. Loss estimates from models are based on a subset of the most rapid ensemble members. It is not possible to clearly choose one approach over another as this depends on the relative weights given to data versus models. Observations and citations support the conclusion that most global climate model results in the CMIP5 archive are too conservative in their sea ice projections. Recent data and expert opinion should be considered in addition to model results to advance the very likely timing for future sea ice loss to the first half of the 21st century, with a possibility of major loss within a decade or two.

We point out two simple but instructive possibilities to modify the tri-bimaximal neutrino mixing ansatz, such that leptonic CP violation can naturally be incorporated into the resultant scenarios of nearly tri-bimaximal flavor mixing. The consequences of two new ansaetze on solar, atmospheric and reactor neutrino oscillations are analyzed. We also discuss an interesting approach to construct lepton mass matrices under permutation symmetry, from which one may derive another nearly tri-bimaximal neutrino mixing scenario with no intrinsic CP violation in neutrino oscillations.

A first-order autoregressive process, $Y_t = \beta Y_{t - 1} + \epsilon_t$, is said to be nearly nonstationary when $\beta$ is close to one. The limiting distribution of the least-squares estimate $b_n$ for $\beta$ is studied when $Y_t$ is nearly nonstationary. By reparameterizing $\beta$ to be $1 - \gamma/n, \gamma$ being a fixed constant, it is shown that the limiting distribution of $\tau_n = (\sum^n_{t = 1}Y^2_{t - 1})^{1/2}(b_n - \beta)$ converges to $\mathscr{L}(\gamma)$ which is a quotient of stochastic integrals of standard Brownian motion. This provides a reasonable alternative to the approximation of the distribution of $\tau_n$ proposed by Ahtola and Tiao (1984).

Angle-resolved photoemission and x-ray diffraction experiments show that multilayer epitaxial graphene grown on the SiC(0001) surface is a new form of carbon that is composed of effectively isolated graphene sheets. The unique rotational stacking of these films causes adjacent graphene layers to electronically decouple leading to a set of nearly independent linearly dispersing bands (Dirac cones) at the graphene K point. Each cone corresponds to an individual macroscale graphene sheet in a multilayer stack where AB-stacked sheets can be considered as low density faults.

Challenges in cultivating microorganisms have limited the phylogenetic diversity of currently available microbial genomes. This is being addressed by advances in sequencing throughput and computational techniques that allow for the cultivation-independent recovery of genomes from metagenomes. Here, we report the reconstruction of 7,903 bacterial and archaeal genomes from >1,500 public metagenomes. All genomes are estimated to be ≥50% complete and nearly half are ≥90% complete with ≤5% contamination. These genomes increase the phylogenetic diversity of bacterial and archaeal genome trees by >30% and provide the first representatives of 17 bacterial and three archaeal candidate phyla. We also recovered 245 genomes from the Patescibacteria superphylum (also known as the Candidate Phyla Radiation) and find that the relative diversity of this group varies substantially with different protein marker sets. The scale and quality of this data set demonstrate that recovering genomes from metagenomes provides an expedient path forward to exploring microbial dark matter.