scholarly journals Hierarchical approach for deriving a reproducible unblocked LU factorization

2019 ◽  
Vol 33 (5) ◽  
pp. 791-803 ◽  
Author(s):  
Roman Iakymchuk ◽  
Stef Graillat ◽  
David Defour ◽  
Enrique S Quintana-Ortí
Keyword(s):  
High Performance ◽  
Iterative Refinement ◽  
Inner Product ◽  
Lu Factorization ◽  
Stable Algorithm ◽  
Partial Pivoting ◽  
The Matrix ◽  
Level 1 ◽  
Matrix Vector ◽  
Product Vector

We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we build upon Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via iterative refinement. Following a bottom-up approach, we finally construct a reproducible unblocked implementation of the LU factorization for GPUs, which accommodates partial pivoting for stability and can be eventually integrated in a high performance and stable algorithm for the (blocked) LU factorization.

scholarly journals Computing the sparse matrix vector product using block-based kernels without zero padding on processors with AVX-512 instructions

2018 ◽  
Vol 4 ◽  
pp. e151 ◽  
Author(s):  
Bérenger Bramas ◽  
Pavel Kus
Keyword(s):  
Open Source ◽  
High Performance ◽  
Sparse Matrix ◽  
Assembly Language ◽  
Memory Storage ◽  
Vector Product ◽  
Zero Padding ◽  
The Matrix ◽  
Block Based ◽  
Matrix Vector

The sparse matrix-vector product (SpMV) is a fundamental operation in many scientific applications from various fields. The High Performance Computing (HPC) community has therefore continuously invested a lot of effort to provide an efficient SpMV kernel on modern CPU architectures. Although it has been shown that block-based kernels help to achieve high performance, they are difficult to use in practice because of the zero padding they require. In the current paper, we propose new kernels using the AVX-512 instruction set, which makes it possible to use a blocking scheme without any zero padding in the matrix memory storage. We describe mask-based sparse matrix formats and their corresponding SpMV kernels highly optimized in assembly language. Considering that the optimal blocking size depends on the matrix, we also provide a method to predict the best kernel to be used utilizing a simple interpolation of results from previous executions. We compare the performance of our approach to that of the Intel MKL CSR kernel and the CSR5 open-source package on a set of standard benchmark matrices. We show that we can achieve significant improvements in many cases, both for sequential and for parallel executions. Finally, we provide the corresponding code in an open source library, called SPC5.

Morphology of High-Performance Rigid-Rod Polymer Fibers and Molecular Composites

1989 ◽  
Vol 47 ◽  
pp. 338-339
Author(s):  
W.W. Adams ◽  
S. J. Krause
Keyword(s):  
Tensile Strength ◽  
High Performance ◽  
Liquid Crystalline ◽  
Molecular Level ◽  
Synergistic Effects ◽  
Tensile Modulus ◽  
Commercial Development ◽  
The Matrix ◽  
Molecular Composites ◽  
Rigid Rod

Rigid-rod polymers such as PBO, poly(paraphenylene benzobisoxazole), Figure 1a, are now in commercial development for use as high-performance fibers and for reinforcement at the molecular level in molecular composites. Spinning of liquid crystalline polyphosphoric acid solutions of PBO, followed by washing, drying, and tension heat treatment produces fibers which have the following properties: density of 1.59 g/cm3; tensile strength of 820 kpsi; tensile modulus of 52 Mpsi; compressive strength of 50 kpsi; they are electrically insulating; they do not absorb moisture; and they are insensitive to radiation, including ultraviolet. Since the chain modulus of PBO is estimated to be 730 GPa, the high stiffness also affords the opportunity to reinforce a flexible coil polymer at the molecular level, in analogy to a chopped fiber reinforced composite. The objectives of the molecular composite concept are to eliminate the thermal expansion coefficient mismatch between the fiber and the matrix, as occurs in conventional composites, to eliminate the interface between the fiber and the matrix, and, hopefully, to obtain synergistic effects from the exceptional stiffness of the rigid-rod molecule. These expectations have been confirmed in the case of blending rigid-rod PBZT, poly(paraphenylene benzobisthiazole), Figure 1b, with stiff-chain ABPBI, poly 2,5(6) benzimidazole, Fig. 1c A film with 30% PBZT/70% ABPBI had tensile strength 190 kpsi and tensile modulus of 13 Mpsi when solution spun from a 3% methane sulfonic acid solution into a film. The modulus, as predicted by rule of mixtures, for a film with this composition and with planar isotropic orientation, should be 16 Mpsi. The experimental value is 80% of the theoretical value indicating that the concept of a molecular composite is valid.

scholarly journals Simplified and Rapid Determination of Primaquine and 5,6-Orthoquinone Primaquine by UHPLC-MS/MS: Its Application to a Pharmacokinetic Study

Molecules ◽  
2021 ◽  
Vol 26 (14) ◽  
pp. 4357
Author(s):  
Waritda Pookmanee ◽  
Siriwan Thongthip ◽  
Jeeranut Tankanitlert ◽  
Mathirut Mungthin ◽  
Chonlaphat Sukasem ◽  
...  
Keyword(s):  
Pharmacokinetic Study ◽  
High Performance ◽  
Rapid Determination ◽  
Active Metabolites ◽  
Chromatography Tandem Mass Spectrometry ◽  
Accuracy And Precision ◽  
The Matrix ◽  
Liquid Chromatography Tandem Mass ◽  
Isocratic Mode

The method for the determination of primaquine (PQ) and 5,6-orthoquinone primaquine (5,6-PQ), the representative marker for PQ active metabolites, via CYP2D6 in human plasma and urine has been validated. All samples were extracted using acetonitrile for protein precipitation and analyzed using the ultra-high-performance liquid chromatography–tandem mass spectrometry (UHPLC-MS/MS) system. Chromatography separation was carried out using a Hypersil GOLDTM aQ C18 column (100 × 2.1 mm, particle size 1.9 μm) with a C18 guard column (4 × 3 mm) flowed with an isocratic mode of methanol, water, and acetonitrile in an optimal ratio at 0.4 mL/min. The retention times of 5,6-PQ and PQ in plasma and urine were 0.8 and 1.6 min, respectively. The method was validated according to the guideline. The linearity of the analytes was in the range of 25–1500 ng/mL. The matrix effect of PQ and 5,6-PQ ranged from 100% to 116% and from 87% to 104% for plasma, and from 87% to 89% and from 86% to 87% for urine, respectively. The recovery of PQ and 5,6-PQ ranged from 78% to 95% and form 80% to 98% for plasma, and from 102% to from 112% to 97% to 109% for urine, respectively. The accuracy and precision of PQ and 5,6-PQ in plasma and urine were within the acceptance criteria. The samples should be kept in the freezer (−80 °C) and analyzed within 7 days due to the metabolite stability. This validated UHPLC-MS/MS method was beneficial for a pharmacokinetic study in subjects receiving PQ.

Selecting optimal SpMV realizations for GPUs via machine learning

2021 ◽  
pp. 109434202199073
Author(s):  
Ernesto Dufrechou ◽  
Pablo Ezzatti ◽  
Enrique S Quintana-Ortí
Keyword(s):  
Machine Learning ◽  
Sparse Matrix ◽  
Machine Learning Techniques ◽  
Optimal Method ◽  
Learning Techniques ◽  
General Rules ◽  
Machine Learning Approach ◽  
The Matrix ◽  
Time And Energy ◽  
Matrix Vector

More than 10 years of research related to the development of efficient GPU routines for the sparse matrix-vector product (SpMV) have led to several realizations, each with its own strengths and weaknesses. In this work, we review some of the most relevant efforts on the subject, evaluate a few prominent routines that are publicly available using more than 3000 matrices from different applications, and apply machine learning techniques to anticipate which SpMV realization will perform best for each sparse matrix on a given parallel platform. Our numerical experiments confirm the methods offer such varied behaviors depending on the matrix structure that the identification of general rules to select the optimal method for a given matrix becomes extremely difficult, though some useful strategies (heuristics) can be defined. Using a machine learning approach, we show that it is possible to obtain unexpensive classifiers that predict the best method for a given sparse matrix with over 80% accuracy, demonstrating that this approach can deliver important reductions in both execution time and energy consumption.

scholarly journals Development and Validation of a Sensitive, Specific and Reproducible UPLC-MS/MS Method for the Quantification of OJT007, A Novel Anti-Leishmanial Agent: Application to a Pharmacokinetic Study

2021 ◽  
Vol 18 (9) ◽  
pp. 4624
Author(s):  
Maria Rincon Nigro ◽  
Jing Ma ◽  
Ololade Tosin Awosemo ◽  
Huan Xie ◽  
Omonike Arike Olaleye ◽  
...  
Keyword(s):  
Formic Acid ◽  
High Performance ◽  
Leishmania Major ◽  
Internal Standard ◽  
Gradient Elution ◽  
Rat Plasma ◽  
The Matrix ◽  
Liquid Chromatography Tandem Mass ◽  
Positive Mode ◽  
Acquity Uplc

OJT007 is a methionine aminopeptidase 1 (MetAP1) inhibitor with potent anti-proliferative effects against Leishmania Major. In order to study its pharmacokinetics as a part of the drug development process, a sensitive, specific, and reproducible ultra-high performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) method was developed and validated. Voriconazole was used as the internal standard to generate standard curves ranging from 5 to 1000 ng/mL. The separation was achieved using a UPLC system equipped with an Acquity UPLC BEH C18 column (2.1 × 50 mm, 1.7 μm) with 0.1% formic acid in acetonitrile and 0.1% formic acid in water as the mobile phase under gradient elution at a flow rate of 0.4 mL/min. The mass analysis was performed with a 4000 QTRAP® mass spectrometer using multiple-ion reaction monitoring (MRM) in the positive mode, with the transition of m/z 325 → m/z 205 for OJT007 and m/z 350 → m/z 101 for voriconazole. The intra- and inter-day precision and accuracy were within ±15%. The mean extraction recovery and the matrix effect were 95.1% and 7.96%, respectively, suggesting no significant matrix interfering with the quantification of the drug in rat plasma. This study was successfully used for the pharmacokinetic evaluation of OJT007 using the rat as an animal model.

scholarly journals Behaviour of UHPFRCs in compression under high stress-rates

2018 ◽  
Vol 183 ◽  
pp. 02005
Author(s):  
Ezio Cadoni ◽  
Matteo Dotta ◽  
Daniele Forni
Keyword(s):  
Reinforced Concrete ◽  
Mechanical Behaviour ◽  
High Performance ◽  
High Stress ◽  
Slight Reduction ◽  
Fibre Reinforcement ◽  
Fibre Reinforced Concrete ◽  
Dynamic Event ◽  
The Matrix ◽  
High Performance Fibre

The paper presents the results obtained on cylindrical Ultra High Performance Fibre Reinforced Concrete specimens with diameter of 30mm and a height of 60mm under compression at high stress rate (1.7–2.3 TPa/s). Four different percentages of fibre reinforcement are considered (1, 2, 3, and 4% fibre content) and compared with the results of the matrix (UHPC). A slight reduction of the strength and fracture time with the introduction of fibres is observed. The experimental results are analysed and discussed with the intent to better understand the mechanical behaviour of UHPFRC materials in case of dynamic event under service loading conditions.

scholarly journals Development and Application of a Novel Pluri-Residue Method to Determine Polar Pesticides in Fruits and Vegetables through Liquid Chromatography High Resolution Mass Spectrometry

Foods ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 553
Author(s):  
Lorena Manzano-Sánchez ◽  
José Antonio Martínez-Martínez ◽  
Irene Domínguez ◽  
José Luis Martínez Vidal ◽  
Antonia Garrido Frenich ◽  
...  
Keyword(s):  
Liquid Chromatography ◽  
High Resolution ◽  
High Performance ◽  
Fruits And Vegetables ◽  
High Resolution Mass Spectrometry ◽  
Stationary Phases ◽  
Mean Values ◽  
Polar Pesticides ◽  
Relative Standard ◽  
The Matrix

Nowadays, highly polar pesticides are not included in multiresidue methods due to their physico-chemical characteristics and therefore, specific analytical methodologies are required for their analysis. Laboratories are still looking for a pluri-residue method that encompasses the largest number of polar pesticides. The aim of this work was the simultaneous determination of ethephon, 2-hydroxyethylphosphonic acid (HEPA), fosetyl aluminum, glyphosate, aminomethylphosphonic acid (AMPA), N-acetyl-glyphosate and N-acetyl-AMPA in tomatoes, oranges, aubergines and grapes. For that purpose, an ultra high performance liquid chromatography (UHPLC) coupled to a high resolution single mass spectrometer Orbitrap-MS were used. Different stationary phases were evaluated for chromatographic separation, and among them, the stationary phase Torus DEA provided the best separation of the selected compounds. The QuPPe method was used for the extraction of the analytes, but slight modifications were needed depending on the matrix. The developed method was validated, observing matrix effect in all matrices. Intra- and inter-day precision were estimated, and relative standard deviation were lower than 19%. Recoveries were satisfactory, and mean values ranged from 70% to 110%. Limits of quantification were between 25 and 100 µg kg−1. Finally, the analytical method was applied to different fruits and vegetables (oranges, tomatoes, aubergines and grapes).

scholarly journals MATRIX THEORY, HILBERT SCHEME AND INTEGRABLE SYSTEM

1998 ◽  
Vol 13 (34) ◽  
pp. 2731-2742 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Hilbert Scheme ◽  
Matrix Theory ◽  
Fock Space ◽  
Homology Class ◽  
Orthogonal Basis ◽  
Inner Product ◽  
Virasoro Symmetry ◽  
Hilbert Scheme Of Points ◽  
The Matrix ◽  
Boson Fock Space

We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relates the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These bases can be related to the eigenfunctions of Calogero–Sutherland (CS) equation and the deformation parameter of MNS is identified with coupling of CS system. We discuss the structure of Virasoro symmetry in this model.

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