When weak identification is a concern researchers frequently calculate confidence sets in two steps, first assessing the strength of identification and then, on the basis of this initial assessment, deciding whether to use an identification-robust confidence set. Unfortunately, two-step procedures of this sort can generate highly misleading confidence sets, and we demonstrate that two-step conf...

ethan kohlberg, the jewish orientalist and specialist on shi‘a, sees the distortion in holy scriptures, including quran, inevitable. from his point of view, some quranic verses confirm this point. his second proof is the history of the quran and the time when its whole text was written down. in his viewpoint,   hadiths which prove that the quran had been written down in abu bakr’s time ore orie...

A novel algorithm is proposed in this paper to solve blind source separation of post-nonlinear convolutive mixtures of non-stationary sources. Both convolutive mixing and post-nonlinear distortion are included in the proposed model. Based on the generalized Expectation-Maximization (EM) algorithm, the Maximum Likelihood (ML) approach is developed to estimate the parameters in the model. A set o...

We study embedding a subset K of the unit sphere to the Hamming cube {−1,+1}m . We characterize the tradeoff between distortion and sample complexity m in terms of the Gaussian width ω(K) of the set. For subspaces and several structured-sparse sets we show that Gaussian maps provide the optimal tradeoff m ∼ δω(K), in particular for δ distortion one needs m ≈ δd where d is the subspace dimension...

In 1959, Rényi proposed the information dimension and the d-dimensional entropy to measure the information content of general random variables. This paper proposes a generalization of information dimension to stationary stochastic processes by defining the information dimension rate as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer...

A new lossy variant of the Fixed-Database Lempel–Ziv coding algorithm for encoding at a fixed distortion level is proposed, and its asymptotic optimality and universality for memoryless sources (with respect to bounded single-letter distortion measures) is demonstrated: As the database size m increases to infinity, the expected compression ratio approaches the rate-distortion function. The comp...

Suppose A is a finite set, let P be a discrete distribution on A, and let M be an arbitrary “mass” function on A. We give a precise characterization of the most efficient way in which An can be almost-covered using spheres of a fixed radius. An almost-covering is a subset Cn of An, such that the union of the spheres centered at the points of Cn has probability close to one with respect to the p...

Given a space Y in X, a cycle in Y may be filled with a chain in two ways: either by restricting the chain to Y or by allowing it to be anywhere in X. When the pair (G, H) acts on (X, Y ), we define the k–volume distortion function of H in G to measure the large-scale difference between the volumes of such fillings. We show that these functions are quasi-isometry invariants, and thus independen...

Sixteen isomers of heterometallic germanium clusters have been analysed in this review. There are two types of isomerism, distortion (x 15) and cis – trans (x 1) and cis – isomer contains two crystallographically independent molecules. Distortion isomers, differing only by degree of distortion in Ge – L, Ge – M (M = metal) distances and L – Ge L (L = ligand) angles. The data are discussed with ...