Linear Algebraic Model Research Articles

PyBEST: Improved functionality and enhanced performance

PyBEST: Improved functionality and enhanced performance

Compartment-based reconstruction of 3D acquisition-weighted 31 P cardiac magnetic resonance spectroscopic imaging at 7 T: A reproducibility study.

Even at 7 T, cardiac 31 P magnetic resonance spectroscopic imaging (MRSI) is fundamentally limited by low signal-to-noise ratio (SNR), leading to long scan times and poor temporal and spatial resolutions. Compartment-based reconstruction algorithms such as magnetic resonance spectroscopy with linear algebraic modeling (SLAM) and spectral localization by imaging (SLIM) may improve SNR or reduce scan time without changes to acquisition. Here, we compare the repeatability and SNR performance of these compartment-based methods, applied to three different acquisition schemes at 7 T. Twelve healthy volunteers were scanned twice. Each scan session consisted of a 6.5-min 3D acquisition-weighted (AW) cardiac 31 P phase encode-based MRSI acquisition and two 6.5-min truncated k-space acquisitions with increased averaging (4 × 4 × 4 central k-space phase encodes and fractional SLAM [fSLAM] optimized k-space phase encodes). Spectra were reconstructed using (i) AW Fourier reconstruction; (ii) AW SLAM; (iii) AW SLIM; (iv) 4 × 4 × 4 SLAM; (v) 4 × 4 × 4 SLIM; and (vi) fSLAM acquisition-reconstruction combinations. The phosphocreatine-to-adenosine triphosphate (PCr/ATP) ratio, the PCr SNR, and spatial response functions were computed, in addition to coefficients of reproducibility and variability. Using the compartment-based reconstruction algorithms with the AW 31 P acquisition resulted in a significant increase in SNR compared with previously published Fourier-based MRSI reconstruction methods while maintaining the measured PCr/ATP ratio and improving interscan reproducibility. The alternative acquisition strategies with truncated k-space performed no better than the common AW approach. Compartment-based spectroscopy approaches provide an attractive reconstruction method for cardiac 31 P spectroscopy at 7 T, improving reproducibility and SNR without the need for a dedicated k-space sampling strategy.

Neuroscience Scaffolded by Informatics: A Raging Interdisciplinary Field

Following breakthrough achievements in molecular neurosciences, the current decade witnesses a trend toward interdisciplinary and multimodal development. Supplementation of neurosciences with tools from computer science solidifies previous knowledge and sets the ground for new research on “big data” and new hypothesis-free experimental models. In this Special Issue, we set the focus on informatics-supported interdisciplinary neuroscience accomplishments symmetrically combining wet-lab and clinical routines. Video-tracking and automated mitosis detection in vitro, the macromolecular modeling of kinesin motion, and the unsupervised classification of the brain’s macrophage activation status share a common denominator: they are energized by machine and deep learning. Essential clinical neuroscience questions such as the estimated risk of brain aneurysm rupture and the surgical outcome of facial nerve transplantation are addressed in this issue as well. Precise and rapid evaluation of complex clinical data by deep learning and data mining dives deep to reveal symmetrical and asymmetrical features beyond the abilities of human perception or the limits of linear algebraic modeling. This editorial opts to motivate researchers from the wet lab, computer science, and clinical environments to join forces in reshaping scientific platforms, share and converge high-quality data on public platforms, and use informatics to facilitate interdisciplinary information exchange.

Measurements Of The Thickness Of Liquid Films Utilising Total Reflection Of A Laser Beam At The Phase Boundary

In this work, a measurement technique for measuring liquid film thickness based on the total reflection of a laser is investigated. The thickness of liquid films is a key parameter in modeling certain two-phase flow regimes like annular or slug flow. Its measurement usually requires extensive optical or mechanical access to the flow. However, in situations where optical access is limited and radical modifications on the measurement object are impossible, e.g. in an operating fuel cell, these conventional techniques are not easily applicable. A key feature of the technique presented in this work is that it requires no modifications other than an optical access at the surface on which the liquid film of interest is deposited on. A laser beam is introduced through a prism to the optical access and consequently the liquid film in an angle that causes the beam to be totally internally reflected at the free surface of the film. An imprint of the reflected beam, which leaves the optical access again through the prism, is captured on a scope. If the thickness of the film changes, the laser beam’s optical path changes with it, causing a displacement of its imprint on the scope. This displacement is a direct measure for the film thickness. In this work, a three dimensional linear algebra model describing the experimental setup is presented and used to derive the basic working principle. It is successfully shown in a proof of concept study that the measurement technique correctly estimates the thickness of a static liquid film deposited on a prism in combination with a cross-correlation based image processing routine. To understand the restrictions of the measurement technique, the most important error sources with regards to the measurement of dynamic film flows are discussed using a mixed analytical and numerical approach based on the previously derived working model. The technique is likely applicable to dynamic film flows. However, concerns regarding high measurement uncertainty caused by curved free surfaces demand further investigation.

An Implicit Algebraic Turbulence Closure Scheme for Atmospheric Boundary Layer Simulation

Abstract Turbulence parameterization plays a critical role in the simulation of many weather regimes. For challenging cases such as the stratocumulus-capped boundary layer (SCBL), traditional schemes can produce unrealistic results even when a fine large-eddy-simulation (LES) resolution is used. Here we present an implicit generalized linear algebraic subfilter-scale model (iGLASS) to better represent unresolved turbulence in the simulation of the atmospheric boundary layer, at both standard LES and so-called terra incognita (TI) resolutions. The latter refers to a range of model resolutions where turbulent eddies are only partially resolved, and therefore the simulated processes are sensitive to the representation of unresolved turbulence. iGLASS is based on the truncated conservation equations of subfilter-scale (SFS) fluxes, but it integrates the full equations of the SFS turbulence kinetic energy and potential energy to retain “memory” of the SFS turbulence. Our evaluations suggest iGLASS can perform significantly better than traditional eddy-diffusivity models and exhibit skills comparable to the dynamic reconstruction model (DRM). For a neutral boundary layer case run at LES resolution, the simulation using iGLASS exhibits a wind profile that reasonably matches the similarity-theory solution. For an SCBL case with 5-m vertical resolution, iGLASS maintains more realistic cloud water profiles and boundary layer structure than traditional schemes. The SCBL case is also tested at TI resolution, and iGLASS also exhibits superior performance. iGLASS permits significant backscatter, whereas traditional models allow forward scatter (diffusion) only. As a physics-based approach, iGLASS appears to be a viable alternative for turbulence parameterization.

Revisiting the universal linear algebraic model for the characteristic two case

Abstract In [3], a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes ([6]). This formalism was independent from the underlying field, providing an extension and general approach to other fields, such as finite fields. Some steps were taken even for the characteristic 2 case. In this article, we undertake the study of the characteristic 2 case in more detail. In particular, the concept of virtual quadratic spaces is used ([4]), and a similar result is achieved for finite fields of characteristic 2 as for other fields. Some differences from the non-characteristic 2 case are also pointed out.

Enhanced hyperpolarized chemical shift imaging based on a priori segmented information.

The purpose of the study was to develop an approach for improving the resolution and sensitivity of hyperpolarized 13 C MRSI based on a priori anatomical information derived from featured, water-based 1 H images. A reconstruction algorithm exploiting 1 H MRI for the redefinition of the 13 C MRSI anatomies was developed, based on a modification of the spectroscopy with linear algebraic modeling (SLAM) principle. To enhance 13 C spatial resolution and reduce spillover effects without compromising SNR, this model was extended by endowing it with a search allowing smooth variations in the 13 C MR intensity within the targeted regions of interest. Experiments were performed in vitro on enzymatic solutions and in vivo on rodents, based on the administration of 13 C-enriched hyperpolarized pyruvate and urea. The spectral images reconstructed for these substrates and from metabolic products based on predefined 1 H anatomical compartments using the new algorithm, compared favorably with those arising from conventional Fourier-based analyses of the same data. The new approach also delivered reliable kinetic 13 C results, for the kind of processes and timescales usually targeted by hyperpolarized MRSI. A simple, flexible strategy is introduced to boost the sensitivity and resolution provided by hyperpolarized 13 C MRSI, based on readily available 1 H MR information.

Ultrafast compartmentalized relaxation time mapping with linear algebraic modeling

To dramatically accelerate compartmental-average longitudinal (T1 ) and transverse (T2 ) relaxation measurements using the minimal-acquisition linear algebraic modeling (SLAM) method, and to validate it in phantoms and humans. Relaxation times were imaged at 3 Tesla in phantoms, in the abdomens of six volunteers, and in six brain tumor patients using standard inversion recovery and multi-spin-echo sequences. k-space was fully sampled to provide reference T1 and T2 measurements, and SLAM was performed using a limited set of phase encodes from central k-space. Anatomical compartments were segmented on scout images post-acquisition, and SLAM reconstruction was implemented using two algorithms. Compartment-average T1 and T2 measurements were determined retroactively from fully sampled data sets, and proactively from SLAM data sets at acceleration factors of up to 16. Values were compared with reference measurements. The compartment's localization properties were analyzed using the discrete spatial response function. At 16-fold acceleration, compartment-average SLAM T1 measurements agreed with the full k-space compartment-average results to within 0.0% ± 0.7%, 1.4% ± 3.4%, and 0.5% ± 2.9% for phantom, abdominal, and brain T1 measurements, respectively. The corresponding T2 measurements agreed within 0.2% ± 1.9%, 0.9% ± 7.9%, and 0.4% ± 5.8%, respectively. SLAM can dramatically accelerate relaxation time measurements when compartmental or lesion-average values can suffice, or when standard relaxometry is precluded by scan-time limitations. Magn Reson Med 79:286-297, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Describing the Information Spreading on a Small-world Network Based on State Space

The investigation about the information spreading in a network has been described by the ODE dynamic system excellently. It has given a direct explanation to the statistic tendency on result. However it doesn’t give enough information about the individual state. The investigation on the topology of a network can helpful to deal with the problem. The paper build a linear algebra model, which give a relationship between the ODE function groups and the graph topology. The model also give the distribution of the information in a network at the time of t. It is also satisfied with ODE in terms of statistical trendency.

Unleashing GPU acceleration for symmetric band linear algebra kernels and model reduction

Linear algebra operations arise in a myriad of scientific and engineering applications and, therefore, their optimization is targeted by a significant number of high performance computing research ...

Steady and unsteady numerical simulations of the flow in the Tokke Francis turbine model, at three operating conditions

This work investigates the flow in the scale model of the high-head Tokke Francis turbine at part load, best efficiency point and high load, as a contribution to the first Francis-99 workshop. The work is based on the FOAM-extend CFD software, which is a recent fork of the OpenFOAM CFD software that contains new features for simulations in rotating machinery. Steady-state mixing plane RANS simulations are conducted, with an inlet before the guide vanes and an outlet after the draft tube. Different variants of the k-ϵ and k-ω turbulence models are used and a linear explicit algebraic Reynolds stress model is implemented. Sliding grid URANS simulations, using a general grid interface coupling, are performed including the entire turbine geometry, from the inlet to the spiral casing to the outlet of the draft tube. For the unsteady simulations, the k-ω SSTF model is implemented and used in addition to the standard k-ϵ model. Both the steady and unsteady simulations give good predictions of the pressure distribution in the turbine compared to the experimental results. The velocity profiles at the runner outlet are well predicted at off-design conditions. A strong swirl is however obtained at best efficiency point, which is not observed in the experiments. While the steady-state simulations strongly overestimate the efficiency, the unsteady simulations give good predictions at best efficiency point (error of 1.16%) with larger errors at part load (10.67%) and high load (2.72%). Through the use of Fourier decomposition, the pressure fluctuations in the turbine are analysed, and the main rotor-stator interaction frequencies are predicted correctly at all operating conditions.

Epilepsy Treatment Simplified through Mobile Ketogenic Diet Planning.

The Ketogenic Diet (KD) is an effective, alternative treatment for refractory epilepsy. This high fat, low protein and carbohydrate diet mimics the metabolic and hormonal changes that are associated with fasting. To maximize the effectiveness of the KD, each meal is precisely planned, calculated, and weighed to within 0.1 gram for the average three-year duration of treatment. Managing the KD is time-consuming and may deter caretakers and patients from pursuing or continuing this treatment. Thus, we investigated methods of planning KD faster and making the process more portable through mobile applications. Nutritional data was gathered from the United States Department of Agriculture (USDA) Nutrient Database. User selected foods are converted into linear equations with n variables and three constraints: prescribed fat content, prescribed protein content, and prescribed carbohydrate content. Techniques are applied to derive the solutions to the underdetermined system depending on the number of foods chosen. The method was implemented on an iOS device and tested with varieties of foods and different number of foods selected. With each case, the application's constructed meal plan was within 95% precision of the KD requirements. In this study, we attempt to reduce the time needed to calculate a meal by automating the computation of the KD via a linear algebra model. We improve upon previous KD calculators by offering optimal suggestions and incorporating the USDA database. We believe this mobile application will help make the KD and other dietary treatment preparations less time consuming and more convenient.

A Blind Calibration Scheme Exploiting Mutual Calibration Relationships for a Dense Mobile Sensor Network

In sensor-based measurement systems, the sensor calibrations are crucial to obtain the correct measured values. In this paper, we propose a new blind calibration scheme for a massive mobile sensor network. The mutual calibration relationships between colocated sensors are utilized in a densely deployed sensor network. We model the calibration relationships in a linear algebraic model, and derive an equivalent Laplacian matrix. By just solving the Laplacian linear equation, we can determine how much each sensor has to be calibrated. The proposed calibration scheme is explained as a generalized extension of the simple mean model scheme to the mobile sensor network. Theoretical analysis and simulation results show that the proposed linear algebraic model improves the accuracy of the simple mean model by nearly σdrift2/σnoise2 times at maximum, in terms of mean square error, where usually σdrift ≫ σnoise. In addition, we show the feasibility of our scheme on human movements, by applying the scheme to the Levy-walk model in the simulation. The most important advantages of our scheme are that the calibration model is straightforward and that the solution is simply obtained with a matrix inversion.

Modeling Digital Switching Circuits with Linear Algebra

Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transfer functions is ubiquitous in many areas of engineering and their rich background in linear systems theory and signal processing is easily applied to digital switching circuits with this model. The common tasks of circuit simulation and justification are specific examples of the application of the linear algebraic model and are described in detail. The advantages offered by the new model as compa ed to traditional methods are emphasized throughout the book. Furthermore, the new approach is easily generalized to other types of information processing circuits such as those based upon multiple-valued or quantum logic; thus providing a unifying mathematical framework common to each of these areas. Modeling Digital Switching Circuits with Linear Algebra provides a blend of theoretical concepts and practical issues involved in implementing the method for circuit design tasks. Data structures are described and are shown to not require any more resources for representing the underlying matrices and vectors than those currently used in modern electronic design automation (EDA) tools based on the Boolean model. Algorithms are described that perform simulation, justification, and other common EDA tasks in an efficient manner that are competitive with conventional design tools. The linear algebraic model can be used to implement common EDA tasks directly upon a structural netlist thus avo ding the intermediate step of transforming a circuit description into a representation of a set of switching functions as is commonly the case when conventional Boolean techniques are used. Implementation results are provided that empirically demonstrate the practicality of the linear algebraic model.

Periodicity Domains and the Transit of Venus

A transit of Venus occurs when it passes directly between the Earth and the Sun. A straightforward linear algebraic model for the orbits of Earth and Venus—essentially using one parameter, namely, the relative angular velocity σ of Venus—is powerful enough to generate respectable transit year predictions. We generalize, allowing σ to vary; uncover an algebraic analog for predicting transits; and show that time cycles for transits are what they are because each σ is sufficiently close to a suitably simple rational number, which for Venus is 13/8, and which in turn induces a modulo 8 shuffling of successive transit years by a factor of 3.

Efficient Target Detection from Hyperspectral Images Based On Removal of Signal Independent and Signal Dependent Noise

In our proposed system the random noise present in hyper spectral image is removed by means of tensor based decomposition methods. The noises present in hyper spectral images are classified into two categories namely: signal independent noise and signal dependent noise. The noises present in the hyper spectral images have dependence on the noise variance of the signal. The input image is separated into seven different frequency bands and noise is added into some of those bands. The corresponding peak signal to noise ratio was calculated for each band based on mean square error value. In our project we are using GUI tool in MATLAB to enable user friendly approach in noise removal. The overall system comprises of three types of algorithm namely: parallel factor analysis (PARAFAC), hyper spectral noise estimation (HYNE) and multidimensional Wiener filter (MWF).The first one, named as the PARAFACSI–PARAFACSD method, uses a multi linear algebra model, PARAFAC decomposition, twice to remove SI and SD noise, respectively. The second one is a combination of the multiple-linear-regression-based approach termed as the HYNE method and PARAFAC decomposition, which is named as the HYNE-PARAFAC method. The last one combines the MWF method and PARAFAC decomposition and is named as the MWF-PARAFAC method. SI noise is removed from the original image by PARAFAC decomposition, HYNE method, or MWF method based on the property of SI Noise. SD components can be further reduced by PARAFAC decomposition due to its own statistical property.

Span Programs are Equivalent to Quantum Query Algorithms

Span programs form a linear-algebraic model of computation that is studied to prove classical lower bounds. Quantum query complexity is a coherent generalization for quantum algorithms of decision-tree complexity. It is characterized by a semidefinite program known as the general adversary bound. We connect these classical and quantum models by proving that for any boolean function, the optimal “witness size” of a span program equals the general adversary bound. Therefore, span program witness size and quantum query complexity are equivalent measures. In particular, quantum algorithms can be designed based on span programs.

Highly-accelerated quantitative 2D and 3D localized spectroscopy with linear algebraic modeling (SLAM) and sensitivity encoding

Noninvasive magnetic resonance spectroscopy (MRS) with chemical shift imaging (CSI) provides valuable metabolic information for research and clinical studies, but is often limited by long scan times. Recently, spectroscopy with linear algebraic modeling (SLAM) was shown to provide compartment-averaged spectra resolved in one spatial dimension with many-fold reductions in scan-time. This was achieved using a small subset of the CSI phase-encoding steps from central image k-space that maximized the signal-to-noise ratio. Here, SLAM is extended to two- and three-dimensions (2D, 3D). In addition, SLAM is combined with sensitivity-encoded (SENSE) parallel imaging techniques, enabling the replacement of even more CSI phase-encoding steps to further accelerate scan-speed. A modified SLAM reconstruction algorithm is introduced that significantly reduces the effects of signal nonuniformity within compartments. Finally, main-field inhomogeneity corrections are provided, analogous to CSI. These methods are all tested on brain proton MRS data from a total of 24 patients with brain tumors, and in a human cardiac phosphorus 3D SLAM study at 3T. Acceleration factors of up to 120-fold versus CSI are demonstrated, including speed-up factors of 5-fold relative to already-accelerated SENSE CSI. Brain metabolites are quantified in SLAM and SENSE SLAM spectra and found to be indistinguishable from CSI measures from the same compartments. The modified reconstruction algorithm demonstrated immunity to maladjusted segmentation and errors from signal heterogeneity in brain data. In conclusion, SLAM demonstrates the potential to supplant CSI in studies requiring compartment-average spectra or large volume coverage, by dramatically reducing scan-time while providing essentially the same quantitative results.

Optical attenuation of plasmonic nanocomposites within photonic devices

Plasmonic nanostructures enable microscopic optical manipulation such as light trapping in photonic devices. However, integration of embedded nanostructures into photonic devices has been limited by tractability of nanoscale and microscale descriptions in device architectures. This work uses a linear algebraic model to distinguish geometric optical responses of nanoparticles integrated into dielectric substrates interacting with macroscopic back-reflectors from absorptive and nonlinear plasmonic effects. Measured transmission, reflection, and attenuation (losses) from ceramic and polymer composites supporting two- and three-dimensional distributions of gold nanoparticles, respectively, are predictable using the model. A unique equilateral display format correlates geometric optical behavior and attenuation to nanoparticle density and back-reflector opacity, allowing intuitive, visual specification of density and opacity necessary to obtain a particular optical performance. The model and display format are useful for facile design and integration of plasmonic nanostructures into photonic devices for light manipulation.

Cost allocation for outside sources replacing service departments

The validity of the linear algebra model to solve the reciprocal service department cost allocation problem has been widely recognized since Kaplan’s seminal paper in The Accounting Review in 1973 [2]. In a manufacturing company, certain departments can be characterized as production departments and others as service departments. Examples of service departments are purchasing, computing services, repair and maintenance, security, food services etc. The costs of such service departments must be allocated to the production departments, which in turn will allocate them to the product. We shall determine the exact price that should be paid to external suppliers of the same services currently supplied by the service departments. We shall also prove that once the costs of services allocated to each production department is obtained, then they will stay the same even if some of the service departments are replaced by outside sources.