Nonparametric Regression, Confidence Regions and Regularization

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in that region where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest non-asymptotic confidence bounds which are less informative but conceptually much simpler

Modality, Runs, Strings and Wavelets

The paper considers the problem of non-parametric regression with emphasis on controlling the number of local extrema. Two methods, the run method and the taut string-wavelet method, are introduced and analysed on standard test beds. It is shown that the number and location of local extreme values are consistently estimated.Rates of convergence are proved for both methods. The run method has a slow rate but can withstand blocks as well as a high proportion of isolated outliers. The rate of convergence of the taut string-wavelet method is almost optimal and the method is extremely sensitive being able to detect very low power peaks. Section 1 contains a short introduction with special reference to modality. The run method is described in Section 2 and the taut string-wavelet method in Section 3. Low power peaks are considered in Section 4. Section 5 contains a short conclusion and the proofs are given in Section 6

Parameter Estimation from Improved Measurements of the Cosmic Microwave Background from QUaD

We evaluate the contribution of cosmic microwave background (CMB) polarization spectra to cosmological parameter constraints. We produce cosmological parameters using high-quality CMB polarization data from the ground-based QUaD experiment and demonstrate for the majority of parameters that there is significant improvement on the constraints obtained from satellite CMB polarization data. We split a multi-experiment CMB data set into temperature and polarization subsets and show that the best-fit confidence regions for the ΛCDM six-parameter cosmological model are consistent with each other, and that polarization data reduces the confidence regions on all parameters. We provide the best limits on parameters from QUaD EE/BB polarization data and we find best-fit parameters from the multi-experiment CMB data set using the optimal pivot scale of k_p = 0.013 Mpc^(–1) to be {h^2Ω_c, h^2Ω_b, H_0, A_s, n_s, τ} = {0.113, 0.0224, 70.6, 2.29 × 10^(–9), 0.960, 0.086}

Circadian regulation of lipid mobilization in white adipose tissues.

In mammals, a network of circadian clocks regulates 24-h rhythms of behavior and physiology. Circadian disruption promotes obesity and the development of obesity-associated disorders, but it remains unclear to which extent peripheral tissue clocks contribute to this effect. To reveal the impact of the circadian timing system on lipid metabolism, blood and adipose tissue samples from wild-type, Clock Delta 19, and Bmall(-/-) circadian mutant mice were subjected to biochemical assays and gene expression profiling. We show diurnal variations in lipolysis rates and release of free fatty acids (FFAs) and glycerol into the blood correlating with rhythmic regulation of two genes encoding the lipolysis pacemaker enzymes, adipose triglyceride (TG) lipase and hormone-sensitive lipase, by self-sustained adipocyte clocks. Circadian clock mutant mice show low and nonrhythmic FFA and glycerol blood content together with decreased lipolysis rates and increased sensitivity to fasting. Instead circadian clock disruption promotes the accumulation of TGs in white adipose tissue (WAT), leading to increased adiposity and adipocyte hypertrophy. In summary, circadian modulation of lipolysis rates regulates the availability of lipid-derived energy during the day, suggesting a role for WAT clocks in the regulation of energy homeostasis

A massive, distant proto-cluster at z=2.47 caught in a phase of rapid formation?

Numerical simulations of cosmological structure formation show that the Universe's most massive clusters, and the galaxies living in those clusters, assemble rapidly at early times (2.5 < z < 4). While more than twenty proto-clusters have been observed at z > 2 based on associations of 5-40 galaxies around rare sources, the observational evidence for rapid cluster formation is weak. Here we report observations of an asymmetric, filamentary structure at z = 2.47 containing seven starbursting, submillimeter-luminous galaxies and five additional AGN within a comoving volume of 15000 Mpc$^{3}$. As the expected lifetime of both the luminous AGN and starburst phase of a galaxy is ~100 Myr, we conclude that these sources were likely triggered in rapid succession by environmental factors, or, alternatively, the duration of these cosmologically rare phenomena is much longer than prior direct measurements suggest. The stellar mass already built up in the structure is $\sim10^{12}M_{\odot}$ and we estimate that the cluster mass will exceed that of the Coma supercluster at $z \sim 0$. The filamentary structure is in line with hierarchical growth simulations which predict that the peak of cluster activity occurs rapidly at z > 2.Comment: 7 pages, 3 figures, 2 tables, accepted in ApJL (small revisions from previous version