How well can we estimate a sparse vector?

The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the sensing/design matrix being used and regardless of the estimation procedure. This lower bound very nearly matches the known upper bound one gets by taking a random projection of the sparse vector followed by an $\ell_1$ estimation procedure such as the Dantzig selector. In this sense, compressive sensing techniques cannot essentially be improved

Engineering and fabrication cost considerations for cryogenic wind tunnel models

Design and fabrication cost drivers for cryogenic transonic wind tunnel models are defined. The major cost factors for wind tunnel models are model complexity, tolerances, surface finishes, materials, material validation, and model inspection. The cryogenic temperatures require the use of materials with relatively high fracture toughness but at the same time high strength. Some of these materials are very difficult to machine, requiring extensive machine hours which can add significantly to the manufacturing costs. Some additional engineering costs are incurred to certify the materials through mechanical tests and nondestructive evaluation techniques, which are not normally required with conventional models. When instrumentation such as accelerometers and electronically scanned pressure modules is required, temperature control of these devices needs to be incorporated into the design, which requires added effort. Additional thermal analyses and subsystem tests may be necessary, which also adds to the design costs. The largest driver to the design costs is potentially the additional static and dynamic analyses required to insure structural integrity of the model and support system

Integrated oxygen recovery system

Life Systems has conceptualized an innovative Integrated Oxygen Recovery System (IORS) applicable to advanced mission air revitalization. The IORS provides the capability to electrochemically generate metabolic oxygen (O2) and recover O2 from the space habitat atmosphere via a carbon dioxide (CO2) reduction process within a single assembly. To achieve this capability, the IORS utilizes a Solid Metal Cathode (SMC) water electrolysis unit that simultaneously serves as the Sabatier CO2 reduction reactor. The IORS enables two major life support systems currently baselined in closed loop air revitalization systems to be combined into one smaller, less complex system. This concept reduces fluidic and electrical interface requirements and eliminates a hydrogen (H2) interface. Life Systems is performing an evaluation of the IORS process directed at demonstrating performance and quantifying key physical characteristics including power, weight, and volume. The results of the checkout, shakedown, and initial parametric tests are summarized

Removing noise from pyrosequenced amplicons

Background In many environmental genomics applications a homologous region of DNA from a diverse sample is first amplified by PCR and then sequenced. The next generation sequencing technology, 454 pyrosequencing, has allowed much larger read numbers from PCR amplicons than ever before. This has revolutionised the study of microbial diversity as it is now possible to sequence a substantial fraction of the 16S rRNA genes in a community. However, there is a growing realisation that because of the large read numbers and the lack of consensus sequences it is vital to distinguish noise from true sequence diversity in this data. Otherwise this leads to inflated estimates of the number of types or operational taxonomic units (OTUs) present. Three sources of error are important: sequencing error, PCR single base substitutions and PCR chimeras. We present AmpliconNoise, a development of the PyroNoise algorithm that is capable of separately removing 454 sequencing errors and PCR single base errors. We also introduce a novel chimera removal program, Perseus, that exploits the sequence abundances associated with pyrosequencing data. We use data sets where samples of known diversity have been amplified and sequenced to quantify the effect of each of the sources of error on OTU inflation and to validate these algorithms

Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page