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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...

Airborne suspended particulate matter is an important marker of air quality. The term 'particulates' includes organic and inorganic matter, nitrogen compounds, sulphur compounds, polycyclic aromatic hydrocarbons (PAHs), several heavy metals, and radionuclides. The health risks from the 'classic' pollutants sulfur dioxide, nitrogen dioxide, ozone, carbon monoxide, and particulates have been comprehensively reviewed. Alarming levels of non-classic pollutants like the PAHs have been reported globally. PAHs have been found in placental tissues of women and in umbilical cord blood samples from newborn babies. The damaged DNA in cord blood is a indication of the fate of these pollutants in the environment. Hence, a need exists for a comprehensive investigation of the human health-related aspects of exposure to particulates and PAHs in the urban environment. This paper reviews the literature on PAHs in conjunction with particulate matter on a global perspective.

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Effective collaboration in data science can leverage domain expertise from each team member and thus improve the quality and efficiency of the work. Computational notebooks give data scientists a convenient interactive solution for sharing and keeping track of the data exploration process through a combination of code, narrative text, visualizations, and other rich media. In this paper, we report how synchronous editing in computational notebooks changes the way data scientists work together compared to working on individual notebooks. We first conducted a formative survey with 195 data scientists to understand their past experience with collaboration in the context of data science. Next, we carried out an observational study of 24 data scientists working in pairs remotely to solve a typical data science predictive modeling problem, working on either notebooks supported by synchronous groupware or individual notebooks in a collaborative setting. The study showed that working on the synchronous notebooks improves collaboration by creating a shared context, encouraging more exploration, and reducing communication costs. However, the current synchronous editing features may lead to unbalanced participation and activity interference without strategic coordination. The synchronous notebooks may also amplify the tension between quick exploration and clear explanations. Building on these findings, we propose several design implications aimed at better supporting collaborative editing in computational notebooks, and thus improving efficiency in teamwork among data scientists.