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The Mars Climate Sounder (MCS) onboard the Mars Reconnaissance Orbiter is the latest of a series of investigations devoted to improving the understanding of current Martian climate. MCS is a nine‐channel passive midinfrared and far‐infrared filter radiometer designed to measure thermal emission in limb and on‐planet geometries from which vertical profiles of atmospheric temperature, water vapor, dust, and condensates can be retrieved. Here we describe the algorithm that is used to retrieve atmospheric profiles from MCS limb measurements for delivery to the Planetary Data System. The algorithm is based on a modified Chahine method and uses a fast radiative transfer scheme based on the Curtis‐Godson approximation. It retrieves pressure and vertical profiles of atmospheric temperature, dust opacity, and water ice opacity. Water vapor retrievals involve a different approach and will be reported separately. Pressure can be retrieved to a precision of 1–2% and is used to establish the vertical coordinate. Temperature profiles are retrieved over a range from 5–10 to 80–90 km altitude with a typical altitude resolution of 4–6 km and a precision between 0.5 and 2 K over most of this altitude range. Dust and water ice opacity profiles also achieve vertical resolutions of about 5 km and typically have precisions of 10−4–10−5 km−1 at 463 cm−1 and 843 cm−1, respectively. Examples of temperature profiles as well as dust and water ice opacity profiles from the first year of the MCS mission are presented, and atmospheric features observed during periods employing different MCS operational modes are described. An intercomparison with historical temperature measurements from the Mars Global Surveyor mission shows good agreement.

Calculations have been made of the new Rice University gamma ray astronomical telescope, over the energy interval 0.1 MeV-5.0MeV. A computer program, ACCEPT, was used and simulations performed on the Rice University's AS-9000 mainframe. For gamma ray fluxes at 3.5 g cm$\\sp{-2}$ atmospheric depth over Palestine, Texas, efficiency curves for the principal detector have been obtained. Energy deposition profiles have been calculated and compared to previous simulations and observations. The study shows the simulation code ACCEPT to be more machine dependent than previously believed.

This paper evaluates the first 15 months of the Ozone Mapping and Profiler Suite (OMPS) Sensor Data Record (SDR) acquired by the nadir sensors and processed by the National Oceanic and Atmospheric Administration Interface Data Processing Segment. The evaluation consists of an inter-comparison with a similar satellite instrument, an analysis using a radiative transfer model, and an assessment of product stability. This is in addition to the evaluation of sensor calibration and the Environment Data Record product that are also reported in this Special Issue. All these are parts of synergetic effort to provide comprehensive assessment at every level of the products to ensure its quality. It is found that the OMPS nadir SDR quality is satisfactory for the current Provisional maturity. Methods used in the evaluation are being further refined, developed, and expanded, in collaboration with international community through the Global Space-based Inter-Calibration System, to support the upcoming long-term monitoring.

Distribution-free tests such as the Wilcoxon rank sum test are popular for testing the equality of two univariate distributions. Among the important reasons for their popularity are the striking results of Hodges-Lehmann (1956) and Chernoff-Savage (1958), where the authors show that the asymptotic (Pitman) relative efficiency of Wilcoxon's test with respect to Student's \\(t\\)-test, under location-shift alternatives, never falls below \\(0.864\\) (with the identity score) and \\(1\\) (with the Gaussian score) respectively, despite the former being exactly distribution-free for all sample sizes. Motivated by these results, we propose and study a large family of exactly distribution-free multivariate rank-based two-sample tests by leveraging the theory of optimal transport. First, we propose distribution-free analogs of the Hotelling \\(T^2\\) test (the natural multidimensional counterpart of Student's \\(t\\)-test) and show that they satisfy Hodges-Lehmann and Chernoff-Savage-type efficiency lower bounds over natural sub-families of multivariate distributions, despite being entirely agnostic to the underlying data generating mechanism -- making them the first multivariate, nonparametric, exactly distribution-free tests that provably achieve such efficiency lower bounds. As these tests are derived from Hotelling \\(T^2\\), naturally they are not universally consistent (same as Wilcoxon's test). To overcome this, we propose exactly distribution-free versions of the celebrated kernel maximum mean discrepancy test and the energy test. These tests are indeed universally consistent under no moment assumptions, exactly distribution-free for all sample sizes, and have non-trivial Pitman efficiency. We believe this trifecta of properties hasn't yet been proven for any existing test in the literature.

Given a set \\(P\\) of \\(n\\) points in the plane, in general position, denote by \\(N_\\Delta(P)\\) the number of empty triangles with vertices in \\(P\\). In this paper we investigate by how much \\(N_\\Delta(P)\\) changes if a point \\(x\\) is removed from \\(P\\). By constructing a graph \\(G_P(x)\\) based on the arrangement of the empty triangles incident on \\(x\\), we transform this geometric problem to the problem of counting triangles in the graph \\(G_P(x)\\). We study properties of the graph \\(G_P(x)\\) and, in particular, show that it is kite-free. This relates the growth rate of the number of empty triangles to the famous Ruzsa-Szemerédi problem.

We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian \\(H_N(\\sigma) = \\sigma^T J \\sigma\\), where the coupling matrix \\(J\\) is drawn from certain symmetric orthogonally invariant ensembles. Our derivation relates the annealed free energy of these models to a spherical integral, and expresses the limit of the free energy in terms of the limiting spectral measure of the coupling matrix \\(J\\). As an application, we derive the limiting free energy of the Random Orthogonal Model (ROM) at high temperatures, which confirms non-rigorous calculations of Marinari et al. (1994). Our methods also apply to other well-known models of disordered systems, including the SK and Gaussian Hopfield models.