Highly Robust Error Correction by Convex Programming

This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x ∈ ℝ^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by arbitrary gross errors, and when in addition, all the entries of the codeword are contaminated by smaller errors (e.g., quantization errors). We show that if one encodes the information as Ax where A ∈ ℝ^(m x n) (m ≥ n) is a suitable coding matrix, there are two decoding schemes that allow the recovery of the block of n pieces of information x with nearly the same accuracy as if no gross errors occurred upon transmission (or equivalently as if one had an oracle supplying perfect information about the sites and amplitudes of the gross errors). Moreover, both decoding strategies are very concrete and only involve solving simple convex optimization programs, either a linear program or a second-order cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well

Highly robust error correction by convex programming

This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x in R^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by arbitrary gross errors, and when in addition, all the entries of the codeword are contaminated by smaller errors (e.g. quantization errors). We show that if one encodes the information as Ax where A is a suitable m by n coding matrix (m >= n), there are two decoding schemes that allow the recovery of the block of n pieces of information x with nearly the same accuracy as if no gross errors occur upon transmission (or equivalently as if one has an oracle supplying perfect information about the sites and amplitudes of the gross errors). Moreover, both decoding strategies are very concrete and only involve solving simple convex optimization programs, either a linear program or a second-order cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well.Comment: 23 pages, 2 figure

Metamodel-based model conformance and multiview consistency checking

Model-driven development, using languages such as UML and BON, often makes use of multiple diagrams (e.g., class and sequence diagrams) when modeling systems. These diagrams, presenting different views of a system of interest, may be inconsistent. A metamodel provides a unifying framework in which to ensure and check consistency, while at the same time providing the means to distinguish between valid and invalid models, that is, conformance. Two formal specifications of the metamodel for an object-oriented modeling language are presented, and it is shown how to use these specifications for model conformance and multiview consistency checking. Comparisons are made in terms of completeness and the level of automation each provide for checking multiview consistency and model conformance. The lessons learned from applying formal techniques to the problems of metamodeling, model conformance, and multiview consistency checking are summarized

NASA SBIR abstracts of 1991 phase 1 projects

The objectives of 301 projects placed under contract by the Small Business Innovation Research (SBIR) program of the National Aeronautics and Space Administration (NASA) are described. These projects were selected competitively from among proposals submitted to NASA in response to the 1991 SBIR Program Solicitation. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 301, in order of its appearance in the body of the report. Appendixes to provide additional information about the SBIR program and permit cross-reference of the 1991 Phase 1 projects by company name, location by state, principal investigator, NASA Field Center responsible for management of each project, and NASA contract number are included

NASA SBIR abstracts of 1990 phase 1 projects

The research objectives of the 280 projects placed under contract in the National Aeronautics and Space Administration (NASA) 1990 Small Business Innovation Research (SBIR) Phase 1 program are described. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses in response to NASA's 1990 SBIR Phase 1 Program Solicitation. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 280, in order of its appearance in the body of the report. The document also includes Appendixes to provide additional information about the SBIR program and permit cross-reference in the 1990 Phase 1 projects by company name, location by state, principal investigator, NASA field center responsible for management of each project, and NASA contract number

The NASA SBIR product catalog

The purpose of this catalog is to assist small business firms in making the community aware of products emerging from their efforts in the Small Business Innovation Research (SBIR) program. It contains descriptions of some products that have advanced into Phase 3 and others that are identified as prospective products. Both lists of products in this catalog are based on information supplied by NASA SBIR contractors in responding to an invitation to be represented in this document. Generally, all products suggested by the small firms were included in order to meet the goals of information exchange for SBIR results. Of the 444 SBIR contractors NASA queried, 137 provided information on 219 products. The catalog presents the product information in the technology areas listed in the table of contents. Within each area, the products are listed in alphabetical order by product name and are given identifying numbers. Also included is an alphabetical listing of the companies that have products described. This listing cross-references the product list and provides information on the business activity of each firm. In addition, there are three indexes: one a list of firms by states, one that lists the products according to NASA Centers that managed the SBIR projects, and one that lists the products by the relevant Technical Topics utilized in NASA's annual program solicitation under which each SBIR project was selected

Phase Stability and Segregation in Alloy 22 Base Metal and Weldments

The current design of the waste disposal containers relies heavily on encasement in a multi-layered container, featuring a corrosion barrier of Alloy 22, a Ni-Cr-Mo-W based alloy with excellent corrosion resistance over a wide range of conditions. The fundamental concern from the perspective of the Yucca Mountain Project, however, is the inherent uncertainty in the (very) long-term stability of the base metal and welds. Should the properties of the selected materials change over the long service life of the waste packages, it is conceivable that the desired performance characteristics (such as corrosion reistance) will become compromised, leading to premature failure of the system. To address this, we will study the phase stability and solute segregation characteristics of Alloy 22 base metal and welds. A better understanding of the underlying microstructural evolution tendencies, and their connections with corrosion behavior will (in turn) produce a higher confidence in the extrapolated behavior of the container materials over time periods that are not feasibly tested in a laboratory. Additionally, the knowledge gained here may potentially lead to cost savings through development of safe and realistic design constraints and model assumptions throughout the entire disposal system

MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems

CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ's solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This understanding motivates us to design a MINRES-like algorithm to compute minimum-length solutions to singular symmetric systems. MINRES uses QR factors of the tridiagonal matrix from the Lanczos process (where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned systems (singular or not), MINRES-QLP can give more accurate solutions than MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better estimates of the solution and residual norms, the matrix norm, and the condition number.Comment: 26 pages, 6 figure

A Pluto thermal model

The recent discovery of nitrogen on Pluto suggests that Pluto's volatile cycles may be similar to those on Neptune's moon Triton. Here, we report the first results of our efforts to apply a thermal model that we developed to study the seasonal nitrogen cycle on Triton to the case of Pluto. The model predicts volatile behavior as a function of time to calculate frost deposit depth, polar cap boundaries, temperature of the frost and substrate, and atmospheric pressure, assuming nitrogen frost deposits in solid-vapor equilibrium with nitrogen in the atmosphere