This paper is a discussion presented August 13, 1981 at the American Statistical Association Annual Meeting in Detroit of an invited paper by John Geweke entitled 'The Measurement of Linear Dependence and Feedback Between Multiple Time Series'. It shows how the results presented by Geweke can be derived and clarified using the approaches to multiple time series modeling published in Parzen (1967), (1969), (1977), and Parzen and Newton (1979).

Topics: DTIC Archive, Parzen,Emanuel, TEXAS A AND M UNIV COLLEGE STATION INST OF STATISTICS, *TIME SERIES...

New methods for scaling square, nonnegative matrices to doubly stochastic form are described. A generalized version of the convergence theorem in SINKHORN and KNOPP 1967 is proved and applied to show convergence for these new methods. Tests indicate that one of the new methods has significantly better average and worst-case behavior than the Sinkhorn/Knopp methods; for one of the 3X3 examples in MARSHALL and OLKIN 1968, SK requires 130 times as many operations as the new algorithm to achieve...

Topics: DTIC Archive, Parlett, B N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The purpose of this investigation was to compare the results obtained from three modal prediction techniques. The first technique was an algorithm developed by Whaley for lightly damped structures (Method 1). Results using this algorithm were extracted from a thesis by Glenesk. The second method was the finite element method using NASTRAN (Method 2). The final method was the recovery of unloaded mass and stiffness matrices from the general matrix-vector differential equation of modal analysis...

Topics: DTIC Archive, Atkinson,Frank Broderick, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF...

In this paper, we present a class of iterative descent methods for solving large, sparse, nonsymmetric systems of linear equations whose coefficient matrices have positive-definite symmetric parts. Such problems commonly arise from the discretization of non-self-adjoint elliptic partial differential equations. The methods we consider are modelled after the conjugate gradient method. They require no estimation of parameters and their rate of convergence appears to depend on the spectrum of A...

Topics: DTIC Archive, Elman,Howard C, YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE, *ITERATIONS, *LINEAR...

In this paper, we present a class of iterative descent methods for solving large, sparse, nonsymmetric systems of linear equations whose coefficient matrices have positive-definite symmetric parts. Such problems commonly arise from the discretization of non-self-adjoint elliptic partial differential equations. The methods we consider are modelled after the conjugate gradient method. They require no estimation of parameters and their rate of convergence appears to depend on the spectrum of A...

Topics: DTIC Archive, Elman,Howard C, YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE, *ITERATIONS, *LINEAR...

A software package of major image processing functions is provided with illustrative computer results based on real imagery. (Author)

Topics: DTIC Archive, Yen,Chihsung, SOUTHEASTERN MASSACHUSETTS UNIV NORTH DARTMOUTH DEPT OF ELECTRICAL...

The research developed, implemented, and evaluated traditional matrix and graph algorithms at large scale to allow an analyst with domain insight to explore more interactively the properties of large, e.g., consisting of millions or billions of nodes, social and information networks. Depending on the situation, these larger networks may not fit on a single machine. Although we considered traditional matrix and graph algorithms, e.g., regression and low-rank matrix approximation, we took a...

Topics: DTIC Archive, Saunders, Michael, Stanford University Stanford United States, algorithms, social...

This project considers a class of general quadratic optimization problems involving both integer and continuous variables. These problems are strongly motivated by applications in optimal and dynamic resource management, cardinality constrained quadratic programs, and the matrix completion problems with non-convex regularity. The project addresses a fundamental question how to efficiently solve these problems, such as to find a provably high quality approximate solution or to fast find a local...

Topics: DTIC Archive, Ye,Yinyu, Stanford University Stanford United States, Nonlinear programming, convex...

This technical report is an accumulation of work performed in 2015 and 2016 under SSC Pacific's Naval Innovative Science and Engineering (NISE) Program. This research on Wireless Power Control has provided key information on power-rate trade-offs, gain matrices, quality-of-service issues, and the performance of various wireless power control algorithms.

Topics: DTIC Archive, Lauff,Sarah, Space and Naval Warfare Systems Center Pacific San Diego United States,...

Exploiting the latent structure in many real-world signals can dramatically increase algorithmic robustness to both noise and missing data. The theory of compressed sensing shows that if a signal of interest is sparse --- well-approximated by some small subset of a dictionary of basis elements --- then the signal can be acquired from a reduced number of measurements and reconstructed using efficient convex programming techniques. However, the standard compressed sensing theory is valid only for...

Topics: DTIC Archive, Ward,Rachel A, University of Texas at Austin Austin United States, Approximation...

Recent years have seen exciting new developments in mathematics and computer science, which have opened up new domains of application for computational mathematics. These come with new challenges, for which new approaches and tools must be and are being developed. Machine learning and compressive sensing are two typical examples; they draw not only from traditional linear algebra based numerical analysis or approximation theory, but also from information theory, graph theory, the geometry of...

Topics: DTIC Archive, Singer,Amit, Princeton University Princeton United States, INFORMATION THEORY,...

We present a very efficient semi-supervised graph-based algorithm for classification of high-dimensional data that is motivated by the MBO method of Garcia-Cardona (2014) and derived using the similarity graph. Our procedure is an elegant combination of heat kernel page rank and the MBO method applied to study semi-supervised problems. The timing of our algorithm is highly dependent on how quickly the page rank can be computed; we use two different yet very efficient approaches to calculate the...

Topics: DTIC Archive, Merkurjev,Ekatherina, University of California, Los Angeles Los Angeles United...

Topics: DTIC Archive, Warnke,Scott D, Naval Postgraduate School Monterey United States, algorithms,...

Advective diffusion of passive tracers by fluid flow plays a key role in the transport of salt, heat, buoys and markers in geophysical flows, in the dispersion of pollutants and trace gases in the atmosphere, and even in the motion of sea ice floes influenced by winds and ocean currents. The long time, large scale behavior of such systems is equivalent to an enhanced diffusion process with an effective diffusivity tensor D. Over twenty five years ago, a Stieltjes integral representation for the...

Topics: DTIC Archive, Murphy,N B, University of California at Irvine Irvine United States, eigenvalues,...

Computing the Singular Value Decomposition (SVD) of 3 x 3 matrices is commonplace in 3D computational mechanics and computer graphics applications. We present a C ++ implementation of implicit symmetric QR SVD with Wilkinson shift. The method is fast and robust in both float and double precisions. We also perform a benchmark test to study the performance compared to other popular algorithms.

Topics: DTIC Archive, Gast,Theodore, University of California, Los Angeles Los Angeles United States,...

This report describes a polarization modulated link and the associated polarization dependent loss, including theory. The general system is discussed as well as the details for measuring and calculating polarization dependent loss in the system. A set of experiments are presented that looks at non-ideal alignment of the polarization modulation arc. In addition to the theory for polarization distortion and a compensation technique, the system is investigated when only partially compensated for...

Topics: DTIC Archive, NAVAL RESEARCH LAB WASHINGTON DC OPTICAL SCIENCES DIV, *DIRECT CURRENT, *FIBER...

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on...

Topics: NASA Technical Reports Server (NTRS), MOLECULAR SPECTROSCOPY, LINE SPECTRA, RAMAN SPECTRA, REMOTE...

In order to make computing on encrypted data more practical to use and more secure from attack, it is necessary to discover, develop, and understand the mathematics on which it is based and the mathematics that can be used to attack it. The security of homomorphic encryption schemes is based on the presumed difficulty of mathematics problems about lattices. Discovering and fully exploring algorithms to solve these mathematical problems allow computing on encrypted data to be performed with...

Topics: DTIC Archive, CALIFORNIA UNIV IRVINE, *COMPUTER NETWORK SECURITY, *CRYPTOGRAPHY, *LATTICE DYNAMICS,...

The COxSwAIN project focuses on building an image and video compression scheme that can be implemented in a small or low-power satellite. To do this, we used Compressive Sensing, where the compression is performed by matrix multiplications on the satellite and reconstructed on the ground. Our paper explains our methodology and demonstrates the results of the scheme, being able to achieve high quality image compression that is robust to noise and corruption.

Topics: NASA Technical Reports Server (NTRS), COMMUNICATION SATELLITES, SIGNAL PROCESSING, IMAGING...

The major goals of this project include three components: First, we want to characterize the optimal number of measurements that are needed to identify any problematic component of a connected complex system. Second, we aim to provide constructive methods to generate those measurements. Finally, we would like to test these theoretical results by numerical simulations. All three goals have been essentially met. More concretely, for goal number 1, we have shown the lower bound of number of...

Topics: DTIC Archive, CORNELL UNIV ITHACA NY, *MATRICES(MATHEMATICS), *NETWORK ARCHITECTURE, *STATISTICAL...

We derive a CUR approximate matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix A, such a factorization provides a low rank approximate decomposition of the form A nearly equal to CUR, where C and R are subsets of the columns and rows of A, and U is constructed to make CUR a good approximation. Given a low-rank singular value decomposition A nearly equal to VSWT , the DEIM procedure uses V and W to select the columns and rows of A that form C and...

Topics: DTIC Archive, RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS,...

Briefing Charts

Topics: DTIC Archive, Langhoff, P W, AFRL/RQRP Edwards AFB United States, Atoms, Molecules, Hamiltonian...

There are a number of NP-hard optimization problems where the search space can be characterized as an elementary landscape. For these search spaces the evaluation function is an eigenfunction of the Laplacian matrix that describes the neighborhood structure of the search space. Problems such as the Traveling Salesman Problem (TSP) and Graph Coloring are elementary. Problems such as MAX-kSAT are a superposition of k elementary landscapes. This research has exploited statistical and mathematical...

Topics: DTIC Archive, COLORADO STATE UNIV FORT COLLINS, *COMBINATORIAL ANALYSIS, *OPTIMIZATION,...

We perform a comparison of mass conservation properties of the continuous (CG) and discontinuous (DG) Galerkin methods on non-conforming, dynamically adaptive meshes for two atmospheric test cases. The two methods are implemented in a unified way which allows for a direct comparison of the non-conforming edge treatment. We outline the implementation details of the non-conforming direct stiffness summation algorithm for the CG method and show that the mass conservation error is similar to the DG...

Topics: DTIC Archive, NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS, *ATMOSPHERICS,...

Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains. Traditionally, neuronal sequences have been interpreted as noisy manifestations of neuronal templates (i.e., orderings), ignoring much richer structure contained in the sequences. This paper introduces a new tool for understanding neuronal sequences: the bias matrix....

Topics: DTIC Archive, Roth,Zachary J, Pennsylvania State University University Park, Sequences...

No abstract available

Topics: NASA Technical Reports Server (NTRS), SPACE DEBRIS, COLLISIONS, PROBABILITY THEORY, POSITION...

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or...

Topics: NASA Technical Reports Server (NTRS), SPACE DEBRIS, COLLISIONS, PROBABILITY THEORY, POSITION...

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing...

Topics: NASA Technical Reports Server (NTRS), PROBABILITY THEORY, POSITION ERRORS, COVARIANCE, ERROR...

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise...

Topics: NASA Technical Reports Server (NTRS), ORBIT DETERMINATION, STATE ESTIMATION, COVARIANCE, MATRICES...

Graphs naturally represent information ranging from links between webpages to friendships in social networks, to connections between neurons in our brains. These graphs often span billions of nodes and interactions between them. Within this deluge of interconnected data, how can we find the most important structures and summarize them? How can we efficiently visualize them? How can we detect anomalies that indicate critical events, such as an attack on a computer system, disease formation in...

Topics: DTIC Archive, CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE, *DATA MINING, *GRAPHS,...

This work introduces estimation of disturbance covariance matrices for radar STAP. In particular, we first exploit physically inspired constraints, both the structure of the disturbance covariance and importantly the knowledge of the clutter rank to yield a new rank constrained maximum likelihood (RCML) estimator of clutter/disturbance covariance. We demonstrate that the rank-constrained estimation problem can in fact be cast in the framework of a tractable convex optimization problem, and...

Topics: DTIC Archive, PENNSYLVANIA STATE UNIV STATE COLLEGE, *ADAPTIVE SYSTEMS, *NOISE JAMMERS, *RADAR...

This project has developed and analyzed new mathematical algorithms to substantially reduce the complexity of simulating and optimizing parametrically dependent systems and to support decision-making under uncertainty. Specifically, this research has advanced the state of the art in reduced order modeling based on projections and on the discrete empirical interpolation method (DEIM) for nonlinear systems, developed new adaptive sampling methods for optimization of systems with uncertain inputs,...

Topics: DTIC Archive, RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS, *COMPUTER AIDED...

This proposal will work towards the eventual realization of a long term goal of developing, waveforms and other radar resources, scheduling of those resources, and the processing of target returns to provide high performance detection and tracking using resource agility for a realizable radar system.

Topics: DTIC Archive, MELBOURNE UNIV PARKVILLE (AUSTRALIA), *RADAR TRACKING, *SEARCH RADAR, *TARGET...

The world of vehicle design is a fast-paced iterative environment that demand s efficiency in the simulation of suspension loads. Toward that end, a computationally efficient, linear, planar, quasi-static tire model is developed in this work that accurately predicts a tire s lower-frequency, reasonably large amplitude, nonlinear stiffness relationship. Hamilton s principle is used to derive the axisymmetric and circumferentially isotropic stiffness equation which is discretized into segments to...

Topics: DTIC Archive, ARMY TANK AUTOMOTIVE RESEARCH DEVELOPMENT AND ENGINEERING CENTER WARREN MI, *TIRES,...

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the...

Topics: NASA Technical Reports Server (NTRS), DISCRETE FUNCTIONS, FOURIER TRANSFORMATION, VECTOR SPACES,...

In the third and final year of research on magneto-electric conversion of optical energy to electricity, several major project objectives were achieved in the areas of theory and experiment. This was chiefly the result of a breakthrough in understanding the reported enhancement of magneto-electric scattering and switching to computer codes based on Matlab to improve both the speed of computations and the time required to acquire data. On the theoretical front, a dressed state approach was...

Topics: DTIC Archive, MICHIGAN UNIV ANN ARBOR, *ENERGY CONVERSION, *NONLINEAR OPTICS, *SPINTRONICS,...

The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in Rd, the objective is to minimize the sum of the smallest 50% squared residuals (or more generally any given fraction). There exist practical heuristics for computing the linear LTS estimator, but they provide no guarantees on the accuracy of the final...

Topics: DTIC Archive, MARYLAND UNIV COLLEGE PARK DEPT OF COMPUTER SCIENCE, *LEAST SQUARES METHOD, *LINEAR...

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and...

Topics: NASA Technical Reports Server (NTRS), DIFFERENTIAL EQUATIONS, WALSH FUNCTION, ALGORITHMS, PARTIAL...

An advanced form of background subtraction is presented and applied to aeroacoustic wind tunnel data. A variant of this method has seen use in other fields such as climatology and medical imaging. The technique, based on an eigenvalue decomposition of the background noise cross-spectral matrix, is robust against situations where isolated background auto-spectral levels are measured to be higher than levels of combined source and background signals. It also provides an alternate estimate of the...

Topics: NASA Technical Reports Server (NTRS), BACKGROUND NOISE, SUBTRACTION, AEROACOUSTICS, WIND TUNNEL...

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor...

Topics: NASA Technical Reports Server (NTRS), ENGINE MONITORING INSTRUMENTS, GAS TURBINE ENGINES,...

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor...

Topics: NASA Technical Reports Server (NTRS), KALMAN FILTERS, PERFORMANCE PREDICTION, FAULT DETECTION,...

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted batch least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. The proposed empirical state error covariance...

Topics: NASA Technical Reports Server (NTRS), STATE ESTIMATION, ALGORITHMS, COVARIANCE, ERROR ANALYSIS,...

This thesis explores the power of interactivity in unsupervised machine learning problems. Interactive algorithms employ feedback-driven measurements to reduce data acquisition costs and consequently enable statistical analysis in otherwise intractable settings. Unsupervised learning methods are fundamental tools across a variety of domains, and interactive procedures promise to broaden the scope of statistical analysis. We develop interactive learning algorithms for three unsupervised...

Topics: DTIC Archive, CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE, *LEARNING MACHINES,...

Tor is a communications infrastructure widely used for unfettered and anonymous access to Internet websites. Tor is also used to access sites on the .onion virtual domain. The focus of .onion use and discussion has traditionally been on the offering of hidden services, services that separate their reachability from the identification of their IP addresses. We argue that Tor's onion system can be used to provide an entirely separate benefit: basic website authentication. We also argue that not...

Topics: DTIC Archive, NAVAL RESEARCH LAB WASHINGTON DC, *COMMUNICATIONS TRAFFIC, *COMPUTER NETWORK...

A central goal of genetics is to learn how the genotype of an organism determines its phenotype. We address the implicit problem of predicting the association of genes with phenotypes or traits. Our primary goal is to develop pragmatic data analytic methods for linking specific genes to traits and diseases, especially polygenic traits, which are the most challenging. We are also interested in developing theoretical guarantees for the methods. In the past, we have developed predictive methods...

Topics: DTIC Archive, TEXAS UNIV AT AUSTIN, *BIOMEDICAL INFORMATION SYSTEMS, *DISEASE VECTORS, *NETWORK...

Program termination analysis is an important task in logic and computer science. While determining if a program terminates is known to be undecidable in general, there has been a significant amount of attention given to finding sufficient and computationally practical conditions to prove termination. One such method takes a program and builds from it a matrix weighted digraph. These are directed graphs whose edges are labeled by square matrices with entries in {-1,0,1}, equipped with a...

Topics: NASA Technical Reports Server (NTRS), MATRICES (MATHEMATICS), THEOREM PROVING, GRAPH THEORY,...

Hyperspectral IR profiles can be assimilated in GSI as a separate observation other than radiosondes with only changes to tables in the fix directory. Assimilation of profiles does produce changes to analysis fields and evidenced by: Innovations larger than +/-2.0 K are present and represent where individual profiles impact the final temperature analysis.The updated temperature analysis is colder behind the cold front and warmer in the warm sector. The updated moisture analysis is modified more...

Topics: NASA Technical Reports Server (NTRS), RADIOSONDES, ERROR ANALYSIS, ASSIMILATION, COLD FRONTS,...

In this thesis we focus on the problem of entanglement in an important class of states, called X-states, that we will introduce. Our study led us to an algebraic formula for the value of multipartite entanglement for X-states. We will take advantage of this formula to further explore the connection of entanglement and mixedness in multipartite systems and study the dynamics of entanglement in open systems. We introduce the entanglement, its definition, and the properties of good measures of...

Topics: DTIC Archive, ROCHESTER UNIV NY, *MATRICES(MATHEMATICS), ALGEBRA, DYNAMICS, FORMULATIONS, FOULING,...

This research is a continuation of part of what was shown at the last AIRS Science Team Meeting in the talk Improved Water Vapor and Ozone Profiles in SRT AIRS Version-6.X and the AIRS February 11, 2015 NetMeeting Further improvements in water vapor and ozone profiles compared to Version-6.AIRS Version-6 was finalized in late 2012 and is now operational. Version-6 contained many significant improvements in retrieval methodology compared to Version-5. However, Version-6 retrieval methodology...

Topics: NASA Technical Reports Server (NTRS), BRIGHTNESS TEMPERATURE, WATER VAPOR, OZONE, CLIMATOLOGY,...

Principal Component Analysis (PCA) has been shown effective for reducing thermographic NDE data. While a reliable technique for enhancing the visibility of defects in thermal data, PCA can be computationally intense and time consuming when applied to the large data sets typical in thermography. Additionally, PCA can experience problems when very large defects are present (defects that dominate the field-of-view), since the calculation of the eigenvectors is now governed by the presence of the...

Topics: NASA Technical Reports Server (NTRS), COMPOSITE MATERIALS, THERMOGRAPHY, TEMPERATURE EFFECTS, DATA...