The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Aminoacid zwitterions in solution : Geometric, energetic, and vibrational analysis using density functional theory-continuum model calculations

Glycine and alanine aminoacids chemistry in solution is explored using a hybrid three parameters density functional (B3PW91) together with a continuum model. Geometries, energies, and vibrational spectra of glycine and alanine zwitterions are studied at the B3PW91/6-31+G∗∗ level and the results compared with those obtained at the HF and MP2/6-31+G∗∗ levels. Solvents effects are incorporated by means of an ellipsoidal cavity model with a multipolar expansion (up to sixth order) of the solute’s electrostatic potential. Our results confirm the validity of the B3PW91 functional for studying aminoacid chemistry in solution. Taking into account the more favorable scaling behavior of density functional techniques with respect to correlated ab initio methods these studies could be extended to larger [email protected] ; [email protected]

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $\ell_1$-constraints, using a gradient method, with projection on $\ell_1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page

A reassessment of Kelmayisaurus petrolicus, a large theropod dinosaur from the Early Cretaceous of China

The Early Cretaceous fossil record of large−bodied theropods from Asia is poor, hindering comparison of Asian predatory dinosaur faunas with those from other continents. One of the few large Asian theropod specimens from this interval is a partial skull (maxilla and dentary) from the Lianmugin Formation (?Valanginian–Albian), the holotype of Kelmayisaurus petrolicus. Most authors have either considered this specimen as an indeterminate basal tetanuran or a nomen dubium. Weredescribe K. petrolicus and note that it possesses a single autapomorphy (a deep accessory groove on the lateral surface of the anterior dentary), as well as a unique combination of characters that differentiates it from other theropods, affirming its validity. A phylogenetic analysis recovers K. petrolicus as a basal carcharodontosaurid, which is supported by various features: very deep interdental plates (a carcharodontosaurid synapomorphy), fused interdental plates (present in carchardontosaurids and a limited number of other theropods), and the absence of diagnostic features of other clades of large−bodied theropods such as abelisaurids, megalosauroids, and coelurosaurs. As such, Kelmayisaurus is the second known carcharodontosaurid from Asia, and further evidence that this clade represented a global radiation of large−bodied predators during the Early–mid Cretaceous

Sorting Via Screening Versus Signaling: A Theoretic and Experimental Comparison

Similar to Kübler et al. (2008, GEB 64, p. 219-236), we compare sorting in games with asymmetric incomplete information theoretically and experimentally. Rather than distinguishing two very different sequential games, we use the same game format and capture the structural difference of screening and signaling only via their payoff specification. The experiment thus relies on the same verbal instructions. Although the equilibrium outcomes coincide, greater efficiency losses off the equilibrium play due to sorting under signaling, compared to screening, is predicted and confirmed experimentally

Identification of tissue-specific microRNAs from mouse

MicroRNAs (miRNAs) are a new class of noncoding RNAs, which are encoded as short inverted repeats in the genomes of invertebrates and vertebrates [1, 2]. It is believed that miRNAs are modulators of target mRNA translation and stability, although most target mRNAs remain to be identified. Here we describe the identification of 34 novel miRNAs by tissue- specific cloning of approximately 21-nucleotide RNAs from mouse. Almost all identified miRNAs are conserved in the human genome and are also frequently found in nonmammalian vertebrate genomes, such as pufferfish. In heart, liver, or brain, it is found that a single, tissue-specifically expressed miRNA dominates the population of expressed miRNAs and suggests a role for these miRNAs in tissue specification or cell lineage decisions. Finally, a miRNA was identified that appears to be the fruitfly and mammalian ortholog of C. elegans lin-4 stRNA