Current Search: Matrices (x)
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Title
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A simplified Jacobian representation for robot manipulators.
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Creator
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Alewine, Neal Jon., Florida Atlantic University, Roth, Zvi S.
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Abstract/Description
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Central to many manipulator positional control schemes is a requirement to invert the forward kinematic equations which model the given manipulator. It is shown in this thesis that for manipulator types where a common wrist center exists, a simplified Jacobian form is feasible and its inversion can be used in place of inverse kinematic solutions for positional control. The Jacobian simplification is obtained by decoupling of the wrist member from the positional member, resulting in a Jacobian...
Show moreCentral to many manipulator positional control schemes is a requirement to invert the forward kinematic equations which model the given manipulator. It is shown in this thesis that for manipulator types where a common wrist center exists, a simplified Jacobian form is feasible and its inversion can be used in place of inverse kinematic solutions for positional control. The Jacobian simplification is obtained by decoupling of the wrist member from the positional member, resulting in a Jacobian inversion involving the solution of two sets of three equations with three unknowns. Within the development of the alternate Jacobian form, a technique for substituting incremental rotations with incremental translations is introduced yielding better insight into the Jacobian structure. A requirement for small moves is validated with a discussion of a proposed positional control strategy and a comprehensive example is presented as a summary of the results.
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Date Issued
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1988
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PURL
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http://purl.flvc.org/fcla/dt/14477
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Subject Headings
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Robots, Manipulators (Mechanism), Matrices
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Format
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Document (PDF)
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Title
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LONESUM MATRICES AND ACYCLIC ORIENTATIONS: ENUMERATION AND ASYMPTOTICS.
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Creator
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Khera, Jessica, Lundberg, Erik, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
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Abstract/Description
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An acyclic orientation of a graph is an assignment of a direction to each edge in a way that does not form any directed cycles. Acyclic orientations of a complete bipartite graph are in bijection with a class of matrices called lonesum matrices, which can be uniquely reconstructed from their row and column sums. We utilize this connection and other properties of lonesum matrices to determine an analytic form of the generating function for the length of the longest path in an acyclic...
Show moreAn acyclic orientation of a graph is an assignment of a direction to each edge in a way that does not form any directed cycles. Acyclic orientations of a complete bipartite graph are in bijection with a class of matrices called lonesum matrices, which can be uniquely reconstructed from their row and column sums. We utilize this connection and other properties of lonesum matrices to determine an analytic form of the generating function for the length of the longest path in an acyclic orientation on a complete bipartite graph, and then study the distribution of the length of the longest path when the acyclic orientation is random. We use methods of analytic combinatorics, including analytic combinatorics in several variables (ACSV), to determine asymptotics for lonesum matrices and other related classes.
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Date Issued
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2021
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PURL
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http://purl.flvc.org/fau/fd/FA00013716
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Subject Headings
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Matrices, Combinatorial analysis, Graph theory
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Format
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Document (PDF)
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Title
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Blind source separation using a spatial fourth-order cumulant matrix-pencil.
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Creator
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Dishman, John Fitzgerald., Florida Atlantic University, Aalo, Valentine A., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
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Abstract/Description
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The research presented investigates the use of cumulants in conjunction with a spectral estimation technique of the signal subspace to perform the blind separation of statistically independent signals with low signal-to-noise ratios under a narrowband assumption. A new blind source separation (BSS) algorithm is developed that makes use of the generalized eigen analysis of a matrix pencil defined on two similar spatial fourth-order cumulant matrices. The algorithm works in the presence of...
Show moreThe research presented investigates the use of cumulants in conjunction with a spectral estimation technique of the signal subspace to perform the blind separation of statistically independent signals with low signal-to-noise ratios under a narrowband assumption. A new blind source separation (BSS) algorithm is developed that makes use of the generalized eigen analysis of a matrix pencil defined on two similar spatial fourth-order cumulant matrices. The algorithm works in the presence of spatially and/or temporally correlated noise and, unlike most existing higher-order BSS techniques, is based on a spectral estimation technique rather than a closed loop optimization of a contrast function, for which the convergence is often problematic. The dissertation makes several contributions to the area of blind source separation. These include: (1) Development of a robust blind source separation technique that is based on higher-order cumulant based principle component analysis that works at low signal-to-noise ratios in the presence of temporally and/or spatially correlated noise. (2) A novel definition of a spatial fourth-order cumulant matrix suited to blind source separation with non-equal gain and/or directional sensors. (3) The definition of a spatial fourth-order cumulant matrix-pencil using temporal information. (4) The concept of separation power efficiency (SPE) as a measure of the algorithm's performance. Two alternative definitions for the spatial fourth-order cumulant matrix that are found in the literature are also presented and used by the algorithm for comparison. Additionally, the research contributes the concept of wide sense equivalence between matrix-pencils to the field of matrix algebra. The algorithm's performance is verified by computer simulation using realistic digital communications signals in white noise. Random mixing matrices are generated to ensure the algorithm's performance is independent of array geometry. The computer results are promising and show that the algorithm works well down to input signal-to-noise ratios of -6 dB, and using as few as 250 x 103 samples.
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Date Issued
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2001
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PURL
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http://purl.flvc.org/fcla/dt/11963
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Subject Headings
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Matrix pencils, Adaptive signal processing, Matrices
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Format
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Document (PDF)
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Title
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CHARACTERIZATIONS OF LINEAR ISOMETRIES ON COMPLEX SEQUENCE SPACES.
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Creator
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Babun Codorniu, Omar, Zhang, Xiao-Dong, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
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Abstract/Description
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An operator acting on a Banach space is called an isometry if it preserves the norm of the space. An interesting problem is to determine the form or structure of linear isometries on Banach spaces. This can be done in some instances. This dissertation presents several theorems that provide necessary and sufficient conditions for some linear operators acting on finite and infinite dimensional sequence spaces of complex numbers to be isometries. In all cases, the linear isometries have the form...
Show moreAn operator acting on a Banach space is called an isometry if it preserves the norm of the space. An interesting problem is to determine the form or structure of linear isometries on Banach spaces. This can be done in some instances. This dissertation presents several theorems that provide necessary and sufficient conditions for some linear operators acting on finite and infinite dimensional sequence spaces of complex numbers to be isometries. In all cases, the linear isometries have the form of a permutation of the elements of the sequences in the given space, with each component of each sequence multiplied by a complex number of absolute value 1.
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Date Issued
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2019
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PURL
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http://purl.flvc.org/fau/fd/FA00013354
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Subject Headings
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Banach spaces, Isometrics (Mathematics), Matrices, Linear operators, Normed linear spaces
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Format
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Document (PDF)
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Title
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On the Laplacian and fractional Laplacian in exterior domains, and applications to the dissipative quasi-geostrophic equation.
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Creator
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Kosloff, Leonardo., Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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In this work, we develop an extension of the generalized Fourier transform for exterior domains due to T. Ikebe and A. Ramm for all dimensions n>2 to study the Laplacian, and fractional Laplacian operators in such a domain. Using the harmonic extension approach due to L. Caffarelli and L. Silvestre, we can obtain a localized version of the operator, so that it is precisely the square root of the Laplacian as a self-adjoint operator in L2 with DIrichlet boundary conditions. In turn, this...
Show moreIn this work, we develop an extension of the generalized Fourier transform for exterior domains due to T. Ikebe and A. Ramm for all dimensions n>2 to study the Laplacian, and fractional Laplacian operators in such a domain. Using the harmonic extension approach due to L. Caffarelli and L. Silvestre, we can obtain a localized version of the operator, so that it is precisely the square root of the Laplacian as a self-adjoint operator in L2 with DIrichlet boundary conditions. In turn, this allowed us to obtain a maximum principle for solutions of the dissipative two-dimensional quasi-geostrophic equation the exterior domain, which we apply to prove decay results using an adaptation of the Fourier Splitting method of M.E. Schonbek.
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Date Issued
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2012
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PURL
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http://purl.flvc.org/FAU/3355570
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Subject Headings
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Fluid dynamics, Data processing, Laplacian matrices, Attractors (Mathematics), Differential equations, Partial
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Format
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Document (PDF)
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Title
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Sparse Coding and Compressed Sensing: Locally Competitive Algorithms and Random Projections.
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Creator
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Hahn, William E., Barenholtz, Elan, Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
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Abstract/Description
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For an 8-bit grayscale image patch of size n x n, the number of distinguishable signals is 256(n2). Natural images (e.g.,photographs of a natural scene) comprise a very small subset of these possible signals. Traditional image and video processing relies on band-limited or low-pass signal models. In contrast, we will explore the observation that most signals of interest are sparse, i.e. in a particular basis most of the expansion coefficients will be zero. Recent developments in sparse...
Show moreFor an 8-bit grayscale image patch of size n x n, the number of distinguishable signals is 256(n2). Natural images (e.g.,photographs of a natural scene) comprise a very small subset of these possible signals. Traditional image and video processing relies on band-limited or low-pass signal models. In contrast, we will explore the observation that most signals of interest are sparse, i.e. in a particular basis most of the expansion coefficients will be zero. Recent developments in sparse modeling and L1 optimization have allowed for extraordinary applications such as the single pixel camera, as well as computer vision systems that can exceed human performance. Here we present a novel neural network architecture combining a sparse filter model and locally competitive algorithms (LCAs), and demonstrate the networks ability to classify human actions from video. Sparse filtering is an unsupervised feature learning algorithm designed to optimize the sparsity of the feature distribution directly without having the need to model the data distribution. LCAs are defined by a system of di↵erential equations where the initial conditions define an optimization problem and the dynamics converge to a sparse decomposition of the input vector. We applied this architecture to train a classifier on categories of motion in human action videos. Inputs to the network were small 3D patches taken from frame di↵erences in the videos. Dictionaries were derived for each action class and then activation levels for each dictionary were assessed during reconstruction of a novel test patch. We discuss how this sparse modeling approach provides a natural framework for multi-sensory and multimodal data processing including RGB video, RGBD video, hyper-spectral video, and stereo audio/video streams.
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Date Issued
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2016
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PURL
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http://purl.flvc.org/fau/fd/FA00004713, http://purl.flvc.org/fau/fd/FA00004713
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Subject Headings
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Artificial intelligence, Expert systems (Computer science), Image processing -- Digital techniques -- Mathematics, Sparse matrices
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Format
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Document (PDF)