We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including SPH and grid methods with fixed, deformable or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gas dynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of two. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to about 10%, and the ratio of specific kinetic to thermal energies of the gas agree to about 5%. Various factors contribute to the spread in calculated cluster properties, including differences in the internal timing of the simulations. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modelled.

ObjectiveTo estimate the prevalence of diagnosed total diabetes, type 1 diabetes, and type 2 diabetes in the US general population and the proportions of each among US adults with a diagnosis of diabetes.DesignNationwide, population based, cross sectional survey.SettingNational Health Interview Survey, 2016 and 2017.ParticipantsAdults aged 20 years or older (n=58 186), as a nationally representative sample of the civilian, non-institutionalized US population.Main outcome measuresPrevalence of diagnosed diabetes, type 1 diabetes, and type 2 diabetes in the US general population, and the proportions of each subtype in participants with a diagnosis of diabetes.ResultsAmong the 58 186 included adults, 6317 had received a diagnosis of diabetes. The weighted prevalence of diagnosed diabetes, type 1 diabetes, and type 2 diabetes among US adults was 9.7% (95% confidence interval 9.4% to 10.0%), 0.5% (0.5% to 0.6%), and 8.5% (8.2% to 8.8%), respectively. Type 1 diabetes was more prevalent among adults with lower education level, and type 2 diabetes was more prevalent among older adults, men, and those with lower educational level, lower family income level, and higher body mass index (BMI). Among adults with a diagnosis of diabetes, the weighted percentage of type 1 and type 2 diabetes was 5.6% (4.9% to 6.4%) and 91.2% (90.4% to 92.1%), respectively. The percentage of type 1 diabetes was higher among younger adults (age 20-44 years), non-Hispanic white people, those with higher education level, and those with lower BMI, whereas the percentage of type 2 diabetes was higher among older adults (age ≥65 years), non-Hispanic Asians, those with lower education level, and those with higher BMI.ConclusionThis study provided benchmark estimates on the national prevalence of diagnosed type 1 diabetes (0.5%) and type 2 diabetes (8.5%) among US adults. Among US adults with diagnosed diabetes, type 1 and type 2 diabetes accounted for 5.6% and 91.2%, respectively.

Key Points Question What are the long-term trends in prevalence of attention-deficit/hyperactivity disorder among US children and adolescents over the past 2 decades? Findings In this study of data from 186 457 children and adolescents aged 4 to 17 years from the National Health Interview Survey, a nationwide, population-based, cross-sectional survey conducted annually from 1997 to 2016, the estimated prevalence of diagnosed attention-deficit/hyperactivity disorder in US children and adolescents increased from 6.1% in 1997-1998 to 10.2% in 2015-2016. Meaning Among US children and adolescents, the estimated prevalence of diagnosed attention-deficit/hyperactivity disorder increased significantly between 1997 and 2016.

Abstract-In this paper, we present a concise and coherent analysis of the constrained`1 minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary, while leads to strong results. In particular, it is shown that the sparse recovery problem can be solved via`1 minimization under weaker conditions than what is known in the literature. A key technical tool is an elementary inequality, called Shifting Inequality, which, for a given nonnegative decreasing sequence, bounds the`2 norm of a subsequence in terms of the`1 norm of another subsequence by shifting the elements to the upper end.Index Terms-1 minimization, restricted isometry property, shifting inequality, sparse recovery.

This article considers constrained ℓ 1 minimization methods for the recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaussian noise. A unified and elementary treatment is given in these noise settings for two ℓ 1 minimization methods: the Dantzig selector and ℓ 1 minimization with an ℓ 2 constraint. The results of this paper improve the existing results in the literature by weakening the conditions and tightening the error bounds. The improvement on the conditions shows that signals with larger support can be recovered accurately. This paper also establishes connections between restricted isometry property and the mutual incoherence property. Some results of Candes, Romberg and Tao (2006) and Donoho, Elad, and Temlyakov (2006) are extended.

Abstract-This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is derived under the mutual incoherence condition in the case of Gaussian noise.Index Terms-1 minimization, compressed sensing, mutual incoherence, oracle inequality, sparse recovery.

In this paper we show that if the restricted isometry constant δ k of the compressed sensing matrix satisfies δ k < 0.307, then k-sparse signals are guaranteed to be recovered exactly via ℓ 1 minimization when no noise is present and k-sparse signals can be estimated stably in the noisy case. It is also shown that the bound cannot be substantively improved. An explicitly example is constructed in which δ k = k−1 2k−1 < 0.5, but it is impossible to recover certain k-sparse signals.

We describe an automated method for detecting clusters of galaxies in imaging and redshift galaxy surveys. The adaptive matched Ðlter (AMF) method utilizes galaxy positions, magnitudes, andÈwhen availableÈphotometric or spectroscopic redshifts to Ðnd clusters and determine their redshift and richness. The AMF can be applied to most types of galaxy surveys, from two-dimensional (2D) imaging surveys, to multiband imaging surveys with photometric redshifts of any accuracy (2.5 dimensional to three-dimensional (3D) redshift surveys. The AMF can also be utilized in the selection of [21 2 D]), clusters in cosmological N-body simulations. The AMF identiÐes clusters by Ðnding the peaks in a cluster likelihood map generated by convolving a galaxy survey with a Ðlter based on a model of the cluster and Ðeld galaxy distributions. In tests on simulated 2D and data with a magnitude limit of 21 2 D r@ B 23.5, clusters are detected with an accuracy of *z B 0.02 in redshift and D10% in richness to z [ 0.5. Detecting clusters at higher redshifts is possible with deeper surveys. In this paper we present the theory behind the AMF and describe test results on synthetic galaxy catalogs.