Multivariate Density Estimation and Visualization

This chapter examines the use of flexible methods to approximate an unknown density function, and techniques appropriate for visualization of densities in up to four dimensions. The statistical analysis of data is a multilayered endeavor. Data must be carefully examined and cleaned to avoid spurious findings. A preliminary examination of data by graphical means is useful for this purpose. Graphical exploration of data was popularized by Tukey (1977) in his book on exploratory data analysis (EDA). Modern data mining packages also include an array of graphical tools such as the histogram, which is the simplest example of a density estimator. Exploring data is particularly challenging when the sample size is massive or if the number of variables exceeds a handful. In either situation, the use of nonparametric density estimation can aid in the fundamental goal of understanding the important features hidden in the data. In the following sections, the algorithms and theory of nonparametric density estimation will be described, as well as descriptions of the visualization of multivariate data and density estimates. For simplicity, the discussion will assume the data and functions are continuous. Extensions to discrete and mixed data are straightforward. --

Wave techniques for noise modeling and measurement

The noise wave approach is applied to analysis, modeling, and measurement applications. Methods are presented for the calculation of component and network noise wave correlation matrices. Embedding calculations, relations to two-port figures-of-merit, and transformations to traditional representations are discussed. Simple expressions are derived for MESFET and HEMT noise wave parameters based on a linear equivalent circuit. A noise wave measurement technique is presented and experimentally compared with the conventional method

Expert system verification and validation study. ES V/V guidelines/workshop conference summary

The intent of the workshop was to start moving research on the verification and validation (V&V) of knowledge based systems (KBSs) in the direction of providing tangible 'products' that a KBS developer could use. In the near term research will focus on identifying the kinds of experiences encountered during KBS development of 'real' KBSs. These will be stored in a repository and will serve as the foundation for the rest of the activities described here. One specific approach to be pursued is 'benchmarking'. With this approach, a KBS developer can use either 'canned' KBSs with seeded errors or existing KBSs with known errors to evaluate a given tool's ability to satisfactorily identify errors

Werner state structure and entanglement classification

We present applications of the representation theory of Lie groups to the analysis of structure and local unitary classification of Werner states, sometimes called the {\em decoherence-free} states, which are states of $n$ quantum bits left unchanged by local transformations that are the same on each particle. We introduce a multiqubit generalization of the singlet state, and a construction that assembles these into Werner states.Comment: 9 pages, 2 figures, minor changes and corrections for version

Maximum stabilizer dimension for nonproduct states

Composite quantum states can be classified by how they behave under local unitary transformations. Each quantum state has a stabilizer subgroup and a corresponding Lie algebra, the structure of which is a local unitary invariant. In this paper, we study the structure of the stabilizer subalgebra for n-qubit pure states, and find its maximum dimension to be n-1 for nonproduct states of three qubits and higher. The n-qubit Greenberger-Horne-Zeilinger state has a stabilizer subalgebra that achieves the maximum possible dimension for pure nonproduct states. The converse, however, is not true: we show examples of pure 4-qubit states that achieve the maximum nonproduct stabilizer dimension, but have stabilizer subalgebra structures different from that of the n-qubit GHZ state.Comment: 6 page

Infusing Training into the Documentation and Culture of Ares I Upper Stage Design and Manufacturing

In roughly two years time, Marshall Space Flight Center's (MSFC) Mission Operations Laboratory (MOL) has incubated a personnel training and certification program for about 1000 learners and multiple phases of the Ares I Upper Stage (US) project. Previous MOL-developed training programs focused on about 100 learners with a focus on operations, and had enough full-time training staff to develop courseware and provide training administration. This paper discusses 1) how creation of a broad, structured training program unfolded as feedback from more narrowly defined tasks, 2) how training philosophy, development methods, and administration are being simplified and tailored so that many Upper Stage organizations can grow their own training yet maintain consistency, accountability, and traceability across the project, and 3) possibilities for interfacing with the production contractor's training system and staff

How to Boost Engineering Support Via Web 2.0 - Seeds for the Ares Project...and/or Yours?

The Mission Operations Laboratory (MOL) at Marshall Space Flight Center (MSFC) is responsible for Engineering Support capability for NASA s Ares launch system development. In pursuit of this, MOL is building the Ares Engineering and Operations Network (AEON), a web-based portal intended to provide a seamless interface to support and simplify two critical activities: a) Access and analyze Ares manufacturing, test, and flight performance data, with access to Shuttle data for comparison. b) Provide archive storage for engineering instrumentation data to support engineering design, development, and test. A mix of NASA-written and COTS software provides engineering analysis tools. A by-product of using a data portal to access and display data is access to collaborative tools inherent in a Web 2.0 environment. This paper discusses how Web 2.0 techniques, particularly social media, might be applied to the traditionally conservative and formal engineering support arena. A related paper by the author [1] considers us