The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2N x 2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our N x N phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space.Comment: 60 pages; minor corrections and additional references in v2 and v3; improved historical introduction in v4; references to quantum error correction in v5; v6 corrects the value quoted for the number of similarity classes for N=
Marine plastic debris floating on the ocean surface is a major environmental problem. However, its distribution in the ocean is poorly mapped, and most of the plastic waste estimated to have entered the ocean from land is unaccounted for. Better understanding of how plastic debris is transported from coastal and marine sources is crucial to quantify and close the global inventory of marine plastics, which in turn represents critical information for mitigation or policy strategies. At the same time, plastic is a unique tracer that provides an opportunity to learn more about the physics and dynamics of our ocean across multiple scales, from the Ekman convergence in basin-scale gyres to individual waves in the surfzone. In this review, we comprehensively discuss what is known about the different processes that govern the transport of floating marine plastic debris in both the open ocean and the coastal zones, based on the published literature and referring to insights from neighbouring fields such as oil spill dispersion, marine safety recovery, plankton connectivity, and others. We discuss how measurements of marine plastics (both in situ and in the laboratory), remote sensing, and numerical simulations can elucidate these processes and their interactions across spatio-temporal scales. Environ. Res. Lett. 15 (2020) 023003 E van Sebille et al Environ. Res. Lett. 15 (2020) 023003 E van Sebille et al References Acha E M, Mianzan H W, Iribarne O, Gagliardini D A, Lasta C and Daleo P 2003 The role of the Rı́o de la Plata bottom salinity front in accumulating debris Mar. Pollut. Bull. 46 197-202 Acha E M, Piola A, Iribarne O and Mianzan H 2015 Ecological Processes at Marine Fronts: Oases in the Ocean (Berlin: Springer) Aliani S and Molcard A 2003 Hitch-hiking on floating marine debris: macrobenthic species in the Western Mediterranean Sea Hydrobiologia 503 59-67 Allen J 1985 Principles of Physical Sedimentology (Berlin: Springer) Alpers W 1985 Theory of radar imaging of internal waves Nature 314 245-7 Alsina J M and Cáceres I 2011 Sediment suspension events in the inner surf and swash zone. Measurements in large-scale and high-energy wave conditions Coast. Eng. 58
5285 Port Royal Road Springfield, VA 22161 (703) 487-4650 g* Printed on paper containing at least 50% wastepaper, including 10% postconsumer waste c: Foreword Airfoils for wind turbines have been selected by comparing data from different wind tunnels, tested under different conditions, making it difficult to make accurate comparisons. Most wind tunnel data sets do not contain airfoil performance in stall commonly experienced by turbines operating in the field. Wind turbines commonly experience extreme roughness for which there is very little data. Finally, recent tests have shown that dynamic stall is a common occurrence for most wind turbines operating in yawed, stall or turbulent conditions. Very little dynamic stall data exists for the airfoils of interest to a wind turbine designer. In summary, very little airfoil performance data exists which is appropriate for wind turbine design. Recognizing the need for a wind turbine airfoil performance data base, the National Renewable Energy Laboratory (NREL), funded by the US. Department of Energy, awarded a contract to Ohio State University (OSU) to conduct a wind tunnel test program. Under this program, OSU tested a series of popular wind turbine airfoils. A standard test matrix was developed to assure that each airfoil was tested under the same conditions. The test matrix was developed in partnership with industry and is intended to include all of the operating conditions experienced by wind turbines. These conditions include airfoil performance at high angles of attack, rough leading edge (bug simulation), steady and unsteady angles of attack. Special care has been taken to report as much of the test conditions and raw data as practical so that designers can make their own comparisons and focus on details of the data relevant to their design goals. Some of the airfoil coordinates are proprietary to NREL or an industry partner. To protect the information which defines the exact shape of the airfoil, the coordinates have not been included in the report. Instructions on how to obtain these coordinates may be obtained by contacting C.P. (Sandy) Butterfeld at NREL.
Elevated concentrations of albumin in the urine, albuminuria, are a hallmark of diabetic kidney disease and are associated with an increased risk for end-stage renal disease and cardiovascular events. To gain insight into the pathophysiological mechanisms underlying albuminuria, we conducted meta-analyses of genome-wide association studies and independent replication in up to 5,825 individuals of European ancestry with diabetes and up to 46,061 without diabetes, followed by functional studies. Known associations of variants in CUBN, encoding cubilin, with the urinary albumin-to-creatinine ratio (UACR) were confirmed in the overall sample (P = 2.4 × 10−10). Gene-by-diabetes interactions were detected and confirmed for variants in HS6ST1 and near RAB38/CTSC. Single nucleotide polymorphisms at these loci demonstrated a genetic effect on UACR in individuals with but not without diabetes. The change in the average UACR per minor allele was 21% for HS6ST1 (P = 6.3 × 10–7) and 13% for RAB38/CTSC (P = 5.8 × 10−7). Experiments using streptozotocin-induced diabetic Rab38 knockout and control rats showed higher urinary albumin concentrations and reduced amounts of megalin and cubilin at the proximal tubule cell surface in Rab38 knockout versus control rats. Relative expression of RAB38 was higher in tubuli of patients with diabetic kidney disease compared with control subjects. The loci identified here confirm known pathways and highlight novel pathways influencing albuminuria.
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