Adaptive variance function estimation in heteroscedastic nonparametric regression

We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. The estimator is shown to achieve the optimal adaptive rate of convergence under the pointwise squared error simultaneously over a range of smoothness classes. The estimator is also adaptively within a logarithmic factor of the minimax risk under the global mean integrated squared error over a collection of spatially inhomogeneous function classes. Numerical implementation and simulation results are also discussed.Comment: Published in at http://dx.doi.org/10.1214/07-AOS509 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A knowledge base browser using hypermedia

A hypermedia system is being developed to browse CLIPS (C Language Integrated Production System) knowledge bases. This system will be used to help train flight controllers for the Mission Control Center. Browsing this knowledge base will be accomplished either by having navigating through the various collection nodes that have already been defined, or through the query languages

Covariate-assisted ranking and screening for large-scale two-sample inference

Two-sample multiple testing has a wide range of applications. The conventionalpractice first reduces the original observations to a vector of p-values and then chooses a cutoffto adjust for multiplicity. However, this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures.We introduce a new framework fortwo-sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power. A data-driven multiple-testing procedure is developed by employinga covariate-assisted ranking and screening (CARS) approach that optimally combines the informationfrom both the primary and the auxiliary variables. The proposed CARS procedureis shown to be asymptotically valid and optimal for false discovery rate control. The procedureis implemented in the R package CARS. Numerical results confirm the effectiveness of CARSin false discovery rate control and show that it achieves substantial power gain over existingmethods. CARS is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection

New Bounds for Restricted Isometry Constants

In this paper we show that if the restricted isometry constant $\delta_k$ of the compressed sensing matrix satisfies $$\delta_k < 0.307,$$ then $k$-sparse signals are guaranteed to be recovered exactly via $\ell_1$ 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 $\delta_{k}=\frac{k-1}{2k-1} < 0.5$, but it is impossible to recover certain $k$-sparse signals

PRICE TRANSMISSION, MARKET POWER AND RETURNS TO SCALE: A NOTE

In this paper, we aim to model the vertical relation between retailers and suppliers in the food industry whereby retailers exercise seller power in their relation with consumers and buyer power in their relation with producers. We then evaluate the degree of price transmission, relative to the perfectly competitive benchmark, from the farm to the retail sector assuming a supply shock. With the view to evaluating the impact of market power's interaction with industry technology on the degree of price transmission, we assume industry technology to be characterized by variable input proportions and non-constant returns to scale. Our model predicts that, relative to that which obtains when markets are perfectly competitive and industry technology is characterized by constant returns to scale, the degree of price transmission when market power and industry technology interact cannot be unambiguously determined.price transmission, returns to scale, market power

Entanglement tongue and quantum synchronization of disordered oscillators

We study the synchronization of dissipatively-coupled van der Pol oscillators in the quantum limit, when each oscillator is near its quantum ground state. Two quantum oscillators with different frequencies exhibit an entanglement tongue, which is the quantum analogue of an Arnold tongue. It means that the oscillators are entangled in steady state when the coupling strength is greater than a critical value, and the critical coupling increases with detuning. An ensemble of many oscillators with random frequencies still exhibits a synchronization phase transition in the quantum limit, and we analytically calculate how the critical coupling depends on the frequency disorder. Our results can be experimentally observed with trapped ions or neutral atoms.Comment: 11 pages, 5 figure