Basis Of Singular Value Decomposition Research Articles

Sensor Selection With Cost Constraints for Dynamically Relevant Bases

We consider cost-constrained sparse sensor selection for full-state reconstruction, applying a well-known greedy algorithm to dynamical systems for which the usual singular value decomposition (SVD) basis may not be available or preferred. We apply the cost-modified, column-pivoted QR decomposition to a physically relevant basis—the pivots correspond to sensor locations, and these locations are penalized with a heterogeneous cost function. In considering different bases, we are able to account for the dynamics of the particular system, yielding sensor arrays that are nearly Pareto optimal in sensor cost and performance in the chosen basis. This flexibility extends our framework to include actuation and dynamic estimation, and to select sensors without training data. We provide three examples from the physical and engineering sciences and evaluate sensor selection in three dynamically relevant bases: truncated balanced modes for control systems, dynamic mode decomposition (DMD) modes, and a basis of analytic modes. We find that these bases all yield effective sensor arrays and reconstructions for their respective systems. When possible, we compare to results using an SVD basis and evaluate tradeoffs between methods.

Position detection method of linear motor mover based on extended phase correlation algorithm

This study aims to explain the real-time and high-precision requirements of linear motor mover position detection. A new sub-pixel displacement estimation based on an extended phase correlation algorithm (PCA) is proposed and applied to measure the position of the linear motor mover. This extended PCA is on the basis of singular value decomposition (SVD), which is a novel application in position measurement of the linear motor mover. First, two adjacent stripe images are captured by a high-speed camera installed in the linear motor. Second, an improved Hanning (flap-top) window function is added to the input fence images to suppress the edge effect and spectral aliasing, before the discrete Fourier transform (DFT). Next, phase correlation matrix is acquired by PCA, and using SVD technique to calculate approximate rank-one matrix for subsequent phase unwrapping. Then, weighted-phase unwrap algorithm is applied to acquire the real horizontal phase data. Finally, least-squares method is utilised to linearly fit the real phase data and to obtain sub-pixel displacement of the linear motor mover. Experiments show that the detection accuracy is 1/100 pixel, and the position measurement of linear motor mover is fast and effective.

A secure image sharing scheme based on SVD and Fractional Fourier Transform

Outsourcing multimedia contents to cloud servers without obscuring may lead to an increase in security breaches that might discourage the end users from exploiting the multiple facilities provided by the cloud-based architecture. To secure the content and still be capable enough to provide the cloud services, many homomorphic encryption based schemes are being proposed in the literature. In this article, secured image outsourcing and ownership verification service in a cloud environment on the basis of singular value decomposition (SVD) and Fractional Fourier Transform (FrFT) has been proposed. It disseminates the image information via Shamir secret sharing scheme to create multiple obfuscated shares that reveal no information about the image. To assert the ownership in the encrypted domain at the receiver end, an owner specific information is embedded into some of the shares based on the secret keys. The secret information can be extracted either directly from the cloud servers or obtained after recovery of the cover media. Different attack scenarios have been analyzed considering the possibilities of the attacks that may be attempted by intruders once the information is outsourced to the cloud servers. The proposed scheme was found to be robust against various attacks, hence proving its efficacy.

Learning discriminative singular value decomposition representation for face recognition

Face representation is a critical step in face recognition. Recently, singular value decomposition (SVD) based representation methods have attracted researchers׳ attentions for their power of alleviating the facial variations. The SVD representation reveals that the SVD basis set is important for the recognition purpose and the corresponding singular values (SVs) are regulated to form a more effective representation image. However, there exists a common problem in the existing SVD based representation methods: they all empirically make a rule to regulate the SVs, which is obviously not optimal in theory. To address this problem, in this paper, we propose a novel method named learning discriminative singular value decomposition representation (LDSVDR) for face recognition. We build an individual SVD basis set for each image and then learn a common set of SVs by taking account of the information in the basis sets according to a discriminant criterion across the training images. The proposed model is solved by sequential quadratic programming (SQP) method. Extensive experiments are conducted on three popular face databases and the results demonstrate the effectiveness of our method when dealing with variations of illumination, occlusion, disguise and face sketch recognition task.

Methods for analysis of size-exclusion chromatography-small-angle X-ray scattering and reconstruction of protein scattering.

Size-exclusion chromatography in line with small-angle X-ray scattering (SEC-SAXS) has emerged as an important method for investigation of heterogeneous and self-associating systems, but presents specific challenges for data processing including buffer subtraction and analysis of overlapping peaks. This paper presents novel methods based on singular value decomposition (SVD) and Guinier-optimized linear combination (LC) to facilitate analysis of SEC-SAXS data sets and high-quality reconstruction of protein scattering directly from peak regions. It is shown that Guinier-optimized buffer subtraction can reduce common subtraction artifacts and that Guinier-optimized linear combination of significant SVD basis components improves signal-to-noise and allows reconstruction of protein scattering, even in the absence of matching buffer regions. In test cases with conventional SAXS data sets for cytochrome c and SEC-SAXS data sets for the small GTPase Arf6 and the Arf GTPase exchange factors Grp1 and cytohesin-1, SVD-LC consistently provided higher quality reconstruction of protein scattering than either direct or Guinier-optimized buffer subtraction. These methods have been implemented in the context of a Python-extensible Mac OS X application known as Data Evaluation and Likelihood Analysis (DELA), which provides convenient tools for data-set selection, beam intensity normalization, SVD, and other relevant processing and analytical procedures, as well as automated Python scripts for common SAXS analyses and Guinier-optimized reconstruction of protein scattering.

Temperature Control for Extractive Dividing-Wall Column with an Adjustable Vapor Split: Methylal/Methanol Azeotrope Separation

In our previous work, the extractive dividing-wall column (EDWC) was proved to be a promising energy-saving method for methylal/methanol azeotrope separation because it offered about an 8.3% energy saving over the corresponding conventional extractive distillation columns. We also have explored two effective composition control structures for the stabilization of the EDWC previously. However, the composition control needs online composition analyzers which are usually expensive, require high maintenance, and introduce large lags. Therefore, it is highly desirable to avoid the use of composition analyzers to economically gain this energy-saving potential. In this work, the use of temperature control instead of composition control for the EDWC process is investigated to overcome the above drawbacks. Several control structures are developed on the basis of singular value decomposition (SVD) analysis. Two temperature control structures with an adjustable vapor split are proposed first. Dynamic simulations sho...

Interpolation in waveform space: Enhancing the accuracy of gravitational waveform families using numerical relativity

Matched filtering for the identification of compact object mergers in gravitational wave antenna data involves the comparison of the data stream to a bank of template gravitational waveforms. Typically the template bank is constructed from phenomenological waveform models, since these can be evaluated for an arbitrary choice of physical parameters. Recently it has been proposed that singular value decomposition (SVD) can be used to reduce the number of templates required for detection. As we show here, another benefit of SVD is its removal of biases from the phenomenological templates along with a corresponding improvement in their ability to represent waveform signals obtained from numerical relativity (NR) simulations. Using these ideas, we present a method that calibrates a reduced SVD basis of phenomenological waveforms against NR waveforms in order to construct a new waveform approximant with improved accuracy and faithfulness compared to the original phenomenological model. The new waveform family is given numerically through the interpolation of the projection coefficients of NR waveforms expanded onto the reduced basis and provides a generalized scheme for enhancing phenomenological models.

Improved maximum entropy analysis with an extended search space

The standard implementation of the Maximum Entropy Method (MEM) follows Bryan [1] and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time [2]. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.

Rare De Novo Germline Copy-Number Variation in Testicular Cancer

Although heritable factors are an important determinant of risk of early-onset cancer, the majority of these malignancies appear to occur sporadically without identifiable risk factors. Germline de novo copy-number variations (CNVs) have been observed in sporadic neurocognitive and cardiovascular disorders. We explored this mechanism in 382 genomes of 116 early-onset cancer case-parent trios and unaffected siblings. Unique de novo germline CNVs were not observed in 107 breast or colon cancer trios or controls but were indeed found in 7% of 43 testicular germ cell tumor trios; this percentage exceeds background CNV rates and suggests a rare de novo genetic paradigm for susceptibility to some human malignancies.

Adaptive wave field synthesis

Wave field synthesis (WFS) is a sound field reproduction technology which assumes that the reproduction environment is anechoic. A real reproduction space reduces the objective accuracy of WFS. This research involves the improvement of WFS performance by active noise control and adaptive filters. Simulations of sound field reproduction in a three-dimensional space show the physical possibility of progressive sound field reproduction in a closed space on the basis of optimal control of the reproduction errors at a sensor array. The proposed solution is adaptive wave field synthesis (AWFS). The originality of AWFS is the combination of the minimization of the reproduction error along with a penalty for any departure from the WFS solution. AWFS is theoretically analyzed on the basis of singular value decomposition. This suggests that the AWFS underlying mechanism is independent radiation mode control. Two adaptive algorithms for AWFS are developed. An experimental AWFS system is tested in different rooms (hemi-anechoic, laboratory, reverberant). It shows that AWFS performs better than WFS: AWFS significantly reduces the room effects on sound field reproduction. The algorithm based on independent radiation mode control contributes to the enlargement of the effective reproduction region. The thesis is written in French and in English.

Hydrophobic Distal Pocket Affects NO−Heme Geminate Recombination Dynamics in Dehaloperoxidase and H64V Myoglobin

The recombination dynamics of NO with dehaloperoxidase (DHP) from Amphitrite ornata following photolysis were measured by femtosecond time-resolved absorption spectroscopy. Singular value decomposition (SVD) analysis reveals two important basis spectra. The first SVD basis spectrum reports on the population of photolyzed NO molecules and has the appearance of the equilibrium difference spectrum between the deoxy and NO forms of DHP. The first basis time course has two kinetic components with time constants of tau(11) approximately 9 ps and tau(12) approximately 50 ps that correspond to geminate recombination. The fast geminate process tau(11) arises from a contact pair with the heme iron in a bound state with S = 3/2 spin. The slow geminate process tau(12) corresponds to the recombination from a more remote docking site >3 A from the heme iron with the greater barrier corresponding to a S = 5/2 spin state. The second SVD basis spectrum represents a time-dependent Soret band shift indicative of heme photophysical processes and protein relaxation with time constants of tau(21) approximately 3 ps and tau(22) approximately 17 ps, respectively. A comparison between the more rapid rate constant of the slow geminate phase in DHP-NO and horse heart myoglobin (HHMbNO) or sperm whale myoglobin (SWMbNO) suggests that protein interactions with photolyzed NO are weaker in DHP than in the wild-type MbNOs, consistent with the hydrophobic distal pocket of DHP. The slower protein relaxation rate tau(22) in DHP-NO relative to HHMbNO implies less effective trapping in the docking site of the distal pocket and is consistent with a greater yield for the fast geminate process. The trends observed for DHP-NO also hold for the H64V mutant of SWMb (H64V MbNO), consistent with a more hydrophobic distal pocket for that protein as well. We examine the influence of solution viscosity on NO recombination by varying the glycerol content in the range from 0% to 90% (v/v). The dominant effect of increasing viscosity is the increase of the rate of the slow geminate process, tau(12), coupled with a population decrease of the slow geminate component. Both phenomena are similar to the effect of viscosity on wild-type Mb due to slowing of protein relaxation resulting from an increased solution viscosity and protein surface dehydration.

Accuracy of spectrum estimate in fluorescence spectral microscopy with spectral filters

We establish the accuracy of the spectrum that is estimated with an inexpensive fluorescence spectral microscope utilizing a small set of spectral filters [Soriano et al, Opt. Exp. 10, 1458–1464 (2002)]. The spectrum at an arbitrary image location of the fluorescent sample is estimated as a linear superposition of basis spectra that are derived by singular value decomposition (SVD) or principal component analysis (PCA) from a spectral library of fluorescence spectra. Estimation performance is analyzed as a function of library statistics, filter selection and sequencing, minimum negativity constraint and signal to noise ratio (SNR) of fluorescence image. We consider image SNR degradations that arise from weakening of image intensity, additive Gaussian noise, intensity-dependent Poisson noise and quantization errors. The recovery of specific spectral features like spectral resolution, general similarity and peak alignments, is assessed using Linfoot’s criteria of fidelity, structural content, and correlation. We found that estimation with SVD basis spectra is more robust against image noise than that with PCA basis spectra. However for high SNR images, accurate estimation is achieved more quickly with PCA basis spectra and with better response to the application of minimum negativity constraint.

Photoinduced electron transfer in the cytochrome c/cytochrome c oxidase complex using thiouredopyrenetrisulfonate-labeled cytochrome c. Optical multichannel detection.

Intramolecular electron transfer in the electrostatic cytochrome c oxidase/cytochrome c complex was investigated using a novel photoactivatable dye. Laser photolysis of thiouredopyrenetrisulfonate (TUPS), covalently linked to cysteine 102 on yeast iso-1-cytochrome c, generates a triplet state of the dye, which donates an electron to cytochrome c, followed by electron transfer to cytochrome c oxidase. Time-resolved optical absorption difference spectra were collected at delay times from 100 ns to 200 ms between 325 and 650 nm. On the basis of singular value decomposition (SVD) and multiexponential fitting, three apparent lifetimes were resolved. A sequential kinetic mechanism is proposed from which the microscopic rate constants and spectra of the intermediates were determined. The triplet state of TUPS donates an electron to cytochrome c with a forward rate constant of approximately 2.0 x 10(4) s(-1). A significant fraction of the triplet returns back to the ground state on a similar time scale. The reduction of cytochrome c is followed by faster electron transfer from cytochrome c to Cu(A), with the equilibrium favoring the reduced cytochrome c. Subsequently, Cu(A) equilibrates with heme a with an apparent rate constant of approximately 1 x 10(4) s(-1). On a millisecond time scale, the oxidized TUPS returns to the ground state and heme a becomes reoxidized. The extracted intermediate spectra are in excellent agreement with model spectra of the postulated intermediates, supporting the proposed mechanism.