Sampling and reconstruction of operators

We study the recovery of operators with bandlimited Kohn-Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as operator sampling. Kailath, and later Kozek and the authors have shown that operator sampling is possible if the symbol of the operator is bandlimited to a set with area less than one. In this paper we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions. We give necessary and sufficient conditions on the sampling rate that depend on size and geometry of the bandlimiting set. Moreover, we show that under mild geometric conditions, classes of operators bandlimited to an unknown set of area less than one-half permit sampling and reconstruction. A similar result considering unknown sets of area less than one was independently achieved by Heckel and Boelcskei. Operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly-time-varying impulse response. The results in this paper are rooted in work by Bello and Kailath in the 1960s.Comment: Submitted to IEEE Transactions on Information Theor

Weyl-Heisenberg Wavelet Expansions: Existence and Stability in Weighted Spaces

The theory of wavelets can be used to obtain expansions of vectors in certain spaces. These expansions are like Fourier series in that each vector can be written in terms of a fixed collection of vectors in the Banach space and the coefficients satisfy a "Plancherel Theorem" with respect to some sequence space. In Weyl-Heisenberg expansions, the expansion vectors (wavelets) are translates and modulates of a single vector (the analyzing vector) . The thesis addresses the problem of the existence and stability of Weyl-Heisenberg expansions in the space of functions square-integrable with respect to the measure w(x) dx for a certain class of weights w. While the question of the existence of such expansions is contained in more general theories, the techniques used here enable one to obtain more general and explicit results. In Chapter 1, the class of weights of interest is defined and properties of these weights proven. In Chapter 2, it is shown that Weyl-Heisenberg expansions exist if the analyzing vector is locally bounded and satisfies a certain global decay condition. In Chapter 3, it is shown that these expansions persist if the translations and modulations are not taken at regular intervals but are perturbed by a small amount. Also, the expansions are stable if the analyzing vector is perturbed. It is also shown here that under more general assumptions, expansions exist if translations and modulations are taken at any sufficiently dense lattice of points. Like orthonormal bases, the coefficients in Weyl-Heisenberg expansions can be formed by the inner product of the vector being expanded with a collection of wavelets generated by a transformed version of the analyzing vector. In Chapter 4, it is shown that this transformation preserves certain decay and smoothness conditions and a formula for this transformation is given. In Chapter 5, results on Weyl-Heisenberg expansions in the space of square-integrable functions are presented

Hormonal Signaling Induced in Soybean by Lysobacter enzymogenes Strain C3

The biological control bacterium Lysobacter enzymogenes strain C3 has been shown to suppress fungal diseases by producing a suite of lytic enzymes and antimicrobial secondary metabolites. Previous studies have found that C3, when applied to grass and cereal plants, also is capable of inducing local and systemic resistance against fungal pathogens. It is unknown, however, whether the bacterium has the ability to induce resistance in dicots and what signaling pathways are involved. This study assessed the ability of C3 to trigger local and systemic induced resistance responses in soybean (Glycine max ‘Williams82’) by analyzing relative expression of salicylic acid (SA), jasmonic acid (JA), and ethylene pathway genes using qPCR. The first set of experiments determined that foliar treatments with C3 induced all three defense hormone pathways in the treated leaves. Upstream marker genes Allene Oxide Synthase (AOS) and Aminocyclopropane-1-carboxylic acid Synthase (ACS) for jasmonate and ethylene pathways respectively, were upregulated by C3 treatment, indicating activation of these pathways. Downstream marker genes Pathogenesis Related Proteins 1 (PR1) and Pathogenesis Related Proteins 3 (PR3) for the SA and JA/ET pathways, respectively, were also upregulated by C3 treatment. The second set of experiments involved C3 treatment applications to soybean roots and measuring changes in transcription of PR genes in the foliage. Systemic induction of PR1 and PR3 was not observed after root treatment. This is the first study to provide evidence of a biocontrol bacteria inducing three hormone pathways upon application to soybean foliage. The ability of C3 to induce systemic resistance in dicots after root treatment remains unclear. Advisor: Gary Yue

Nancy and Hegel: philosophies of community, singularity and relational being

This thesis will develop the claim made by Nancy in the essay “Shattered Love” that it is possible to read Hegel’s Elements of the Philosophy of Right and The Phenomenology of Spirit, for the expositions they offer on relational being, despite, for Nancy, their dialectical structure. I will argue that for Nancy, the situations that Hegel calls Self-Consciousness and The State are better understood as Singularity and Community respectively, both of which are relations to be experienced not works to be achieved, and which furthermore are the same relation, the same situation of Being. Hegel’s project of dialectical assimilation, I will argue, can be seen therefore as one that tries to convert this problematic multiple non-presentable Being into a singular identity which does have presence. Whilst the current Nancy scholarship acknowledges Nancy’s preoccupation with Hegel’s philosophy as evidenced by Nancy’s two books on Hegel, there is at present no study in the secondary literature on Nancy’s reception of Hegel’s philosophy generally, let alone with a specific focus on community and social being. This thesis therefore will seek to offer a trajectory of Nancy’s reception of Hegel’s philosophy, covering both Nancy’s works on Hegel, The Speculative Remark and The Restlessness of the Negative and the two most well-known works specifically concerned with community and social being, The Inoperative Community and Being Singular Plural. Additionally, it will seek to positon Nancy’s reception of Hegel against a backdrop of the receptions of Marx, various French Twentieth Century receptions and also a selection of those from the Analytic tradition. In conclusion, following a reading of Nancy’s essay, “The Surprise of The Event” I argue that Hegel misses what Nancy calls the very “event-ness” of the situations of Community and Singularity with the consequence that he ends up with sundered instances or moments rather than the movement he wishes for. Finally, I will argue that Nancy’s response to the problem of trying to preserve the event-ness of event is to provoke a situation of simultaneous separation and connection, or to give it for Nancy its proper name, wonder

Delay-Coordinates Embeddings as a Data Mining Tool for Denoising Speech Signals

In this paper we utilize techniques from the theory of non-linear dynamical systems to define a notion of embedding threshold estimators. More specifically we use delay-coordinates embeddings of sets of coefficients of the measured signal (in some chosen frame) as a data mining tool to separate structures that are likely to be generated by signals belonging to some predetermined data set. We describe a particular variation of the embedding threshold estimator implemented in a windowed Fourier frame, and we apply it to speech signals heavily corrupted with the addition of several types of white noise. Our experimental work seems to suggest that, after training on the data sets of interest,these estimators perform well for a variety of white noise processes and noise intensity levels. The method is compared, for the case of Gaussian white noise, to a block thresholding estimator

Sandia National Laboratories, California Air Quality Program : annual report.

The annual program report provides detailed information about all aspects of the SNL/CA Air Quality Program. It functions as supporting documentation to the SNL/CA Environmental Management System Program Manual. The program report describes the activities undertaken during the past year, and activities planned in future years to implement the Air Quality Program, one of six programs that supports environmental management at SNL/CA

Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur

Stochastic variability in X-ray emission from the black hole binary GRS 1915+105

We examine stochastic variability in the dynamics of X-ray emission from the black hole system GRS 1915+105, a strongly variable microquasar commonly used for studying relativistic jets and the physics of black hole accretion. The analysis of sample observations for 13 different states in both soft (low) and hard (high) energy bands is performed by flicker-noise spectroscopy (FNS), a phenomenological time series analysis method operating on structure functions and power spectrum estimates. We find the values of FNS parameters, including the Hurst exponent, flicker-noise parameter, and characteristic time scales, for each observation based on multiple 2,500-second continuous data segments. We identify four modes of stochastic variability driven by dissipative processes that may be related to viscosity fluctuations in the accretion disk around the black hole: random (RN), power-law (1F), one-scale (1S), and two-scale (2S). The variability modes are generally the same in soft and hard energy bands of the same observation. We discuss the potential for future FNS studies of accreting black holes.Comment: 25 pages, 3 figures, 2 tables; to be published in "The Astronomical Journal

Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory

Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BigDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program deMon2k for the calculation of electronic absorption spectra of N2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BigDFT than for deMon2k. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BigDFT, while all virtual orbitals are included in TD-DFT calculations in deMon2k. As a reality check, we report the x-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1,2-a]pyridin-3-amine