In compressed sensing, one takes n < N samples of an N-dimensional vector x 0 using an n × N matrix A, obtaining undersampled measurements y = Ax 0 . For random matrices with independent standard Gaussian entries, it is known that, when x 0 is k-sparse, there is a precisely determined phase transition: for a certain region in the (k/n,n/N)-phase diagram, convex optimization min || x || 1 subject to y = Ax, x ∈ X N typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property-with the same phase transition location-holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to X N for four different sets X ∈ {[0, 1], R + , R, C}, and the results establish our finding for each of the four associated phase transitions.sparse recovery | universality in random matrix theory equiangular tight frames | restricted isometry property | coherence C ompressed sensing aims to recover a sparse vector x 0 ∈ X N from indirect measurements y = Ax 0 ∈ X n with n < N, and therefore, the system of equations y = Ax 0 is underdetermined. Nevertheless, it has been shown that, under conditions on the sparsity of x 0 , by using a random measurement matrix A with Gaussian i.i.d entries and a nonlinear reconstruction technique based on convex optimization, one can, with high probability, exactly recover x 0 (1, 2). The cleanest expression of this phenomenon is visible in the large n; N asymptotic regime. We suppose that the object x 0 is k-sparse-has, at most, k nonzero entries-and consider the situation where k ∼ ρn and n ∼ δN. Fig. 1A depicts the phase diagram ðρ; δ; Þ ∈ ð0; 1Þ 2 and a curve ρ*ðδÞ separating a success phase from a failure phase. Namely, if ρ < ρ*ðδÞ, then with overwhelming probability for large N, convex optimization will recover x 0 exactly; however, if ρ > ρ*ðδÞ, then with overwhelming probability for large N convex optimization will fail. [Indeed, Fig. 1 depicts four curves ρ*ðδjXÞ of this kind for X ∈ f½0; 1; R + ; R; Cg-one for each of the different types of assumptions that we can make about the entries of x 0 ∈ X N (details below).]How special are Gaussian matrices to the above results? It was shown, first empirically in ref. 3 and recently, theoretically in ref. 4, that a wide range of random matrix ensembles exhibits precisely the same behavior, by which we mean the same phenomenon of separation into success and failure phases with the same phase boundary. Such universality, if exhib...

The competitive oxidation of a mixture of two alcohols by less than an equivalent amount of oxidant under the conditions developed by Swern (reaction of the alcohol at 4 0 "C with Me2SClCCl-(4) generated from (COC1)2 and Me2S0 in CH2C12 followed by reaction with Et3N) shows significant selectivity, with crowded alcohols and those bearing electron-withdrawing substituents being less reactive. Experiments in which the order of mixing of the alcohols and the oxidant are changed and the time of reaction varied establish that the process involves initial fast formation of a mixture of alkoxydimethylsulfonium ions ROSMe2+ (l), which equilibrate at a slower rate with the residual alcohols. Addition of Et3N rapidly converts the existing mixture of 1 to carbonyl products. Intramolecular and intermolecular H / D isotope effects are consistent with this mechanistic scheme. In a practical application of these reactivity principles the steroid 33 with a crowded 11P-OH group was oxidized smoothly in 58% yield to the 11-ketone 34, whereas the Sa-fluoro substituent present in 36 inhibited the reaction, and ketone was formed in only 5% yield. (10) Corey, E. J.; Kim, C. U.; Takeda, M.

Our study provides the first evidence that overexpression of CARP, which is thought to act as a transcriptional co-repressor, may deteriorate contractile function of the heart tissue. Furthermore, beta-adrenoceptor stimulation and activation of PKA and CaMK have been identified as mechanisms that induce expression of CARP in cardiomyocytes.

The application of ZPs to phase aberration correction was shown to be beneficial for adaptive focusing of transcranial ultrasound. The skull-based phase aberrations were found to be well approximated by the number of ZP modes representing only a fraction of the number of elements in the hemispherical transducer. Implementing the initial phase aberration estimate together with Zernike-based algorithm can be used to improve the robustness and can potentially greatly increase the viability of MR-ARFI-based focusing for a clinical transcranial MRgFUS therapy.

Multiple-echo spiral imaging significantly improves MR thermometry efficiency, enabling multiple-slice monitoring. Optimizing multiple specialized sequences provides better performance than can be achieved by any single sequence. Magn Reson Med 78:508-517, 2017. © 2016 International Society for Magnetic Resonance in Medicine.