The Experts below are selected from a list of 7518 Experts worldwide ranked by ideXlab platform

V V Belokurov - One of the best experts on this subject based on the ideXlab platform.

E T Shavgulidze - One of the best experts on this subject based on the ideXlab platform.

Nirmalya Ghosh - One of the best experts on this subject based on the ideXlab platform.

  • comparative study of differential matrix and extended Polar Decomposition formalisms for Polarimetric characterization of complex tissue like turbid media
    Journal of Biomedical Optics, 2012
    Co-Authors: Satish Kumar, Harsh Purwar, Razvigor Ossikovski, Alex I Vitkin, Nirmalya Ghosh
    Abstract:

    Development of methodologies for quantification/unique interpretation of the intrinsic Polarimetry char- acteristics of biological tissues are important for various applications involving tissue characterization/diagnosis. A detailed comparative evaluation of the Polar Decomposition and the differential matrix Decomposition of Mueller matrices for extraction/quantification of the intrinsic Polarimetry characteristics (with special emphasis on linear retardance δ, optical rotation Ψ and dePolarization Δ parameters was performed, because these are the most pro- minent tissue Polarimetry effects) from complex tissue-like turbid media exhibiting simultaneous scattering and Polarization effects. The results suggest that for media exhibiting simultaneous linear retardance and optical rotation Polarization events, the use of retarder Polar Decomposition with its associated analysis which assumes sequential occurrence of these effects, results in systematic underestimation of δ and overestimation of Ψ parameters. Analy- tical relationships between the Polarization parameters (δ, Ψ) extracted from both the retarder Polar Decomposition and the differential matrix Decomposition for either simultaneous or sequential occurrence of the linear retardance and optical rotation effects were derived. The self-consistency of both Decompositions is validated on experimental Mueller matrices recorded from tissue-simulating phantoms (whose Polarization properties are controlled, known a-priori, and exhibited simultaneously) of increasing biological complexity. Additional theoretical validation tests were performed on Monte Carlo-generated Mueller matrices from analogous turbid media exhibiting simultaneous dePolarization (Δ), linear retardance (δ) and optical rotation (Ψ) effects. After successful evaluation, the potential advantage of the differential matrix Decomposition over the Polar Decomposition formalism was explored for mon- itoring of myocardial tissue regeneration following stem cell therapy. © 2012 Society of Photo-Optical Instrumentation Engineers

  • Polar Decomposition of 3 x 3 mueller matrix a tool for quantitative tissue Polarimetry
    Optics Express, 2006
    Co-Authors: M K Swami, Nirmalya Ghosh, Sandeep Manhas, P Buddhiwant, Abha Uppal, P K Gupta
    Abstract:

    The Polarization properties of any medium are completely described by the sixteen element Mueller matrix that relates the Polarization parameters of the light incident on the medium to that emerging from it. Measurement of all the elements of the matrix requires a minimum of sixteen measurements involving both linear and circularly Polarized light. However, for many diagnostic applications, it would be useful if the Polarization parameters can be quantified with linear Polarization measurements alone. In this paper, we present a method based on Polar Decomposition of Mueller matrix for quantification of the Polarization parameters of a scattering medium using the nine element (3 x 3) Mueller matrix that requires linear Polarization measurements only. The methodology for Decomposition of the 3 x 3 Mueller matrix is based on the previously developed Decomposition process for sixteen element (4 x 4) Mueller matrix but with an assumption that the dePolarization of linearly Polarized light due to scattering is independent of the orientation angle of the incident linear Polarization vector. Studies conducted on various scattering samples demonstrated that this assumption is valid for a turbid medium like biological tissue where the dePolarization of linearly Polarized light primarily arises due to the randomization of the field vector's direction as a result of multiple scattering. For such medium, Polar Decomposition of 3 x 3 Mueller matrix can be used to quantify the four independent Polarization parameters namely, the linear retardance (delta ), the circular retardance (psi), the linear dePolarization coefficient (Delta) and the linear diattenuation (d) with reasonable accuracy. Since this approach requires measurements using linear Polarizers only, it considerably simplifies measurement procedure and might find useful applications in tissue diagnosis using the retrieved Polarization parameters.

Dalal Sukkari - One of the best experts on this subject based on the ideXlab platform.

  • Leveraging Task-Based Polar Decomposition Using PARSEC on Massively Parallel Systems
    2019
    Co-Authors: Dalal Sukkari, Hatem Ltaief, David Keyes, Mathieu Faverge
    Abstract:

    This paper describes how to leverage a task-based implementation of the Polar Decomposition on massively parallel systems using the PARSEC dynamic runtime system. Based on a formulation of the iterative QR Dynamically-Weighted Halley (QDWH) algorithm, our novel implementation reduces data traffic while exploiting high concurrency from the underlying hardware architecture. First, we replace the most time-consuming classical QR factorization phase with a new hierarchical variant, customized for the specific structure of the matrix during the QDWH iterations. The newly developed hierarchical QR for QDWH exploits not only the matrix structure, but also shortens the length of the critical path to maximize hardware occupancy. We then deploy PARSEC to seamlessly orchestrate, pipeline, and track the data dependencies of the various linear algebra building blocks involved during the iterative QDWH algorithm. PARSEC enables to overlap communications with computations thanks to its asynchronous scheduling of fine-grained computational tasks. It employs look-ahead techniques to further expose parallelism, while actively pursuing the critical path. In addition, we identify synergistic opportunities between the task-based QDWH algorithm and the PARSEC framework. We exploit them during the hierarchical QR factorization to enforce a locality-aware task execution. The latter feature permits to minimize the expensive inter-node communication, which represents one of the main bottlenecks for scaling up applications on challenging distributed-memory systems. We report numerical accuracy and performance results using well and ill-conditioned matrices. The benchmarking campaign reveals up to 2X performance speedup against the existing state-of-the-art implementation for the Polar Decomposition on 36,864 cores.

  • massively parallel Polar Decomposition on distributed memory systems
    Parallel Computing, 2019
    Co-Authors: Hatem Ltaief, Dalal Sukkari, Yuji Nakatsukasa, Aniello Esposito, David E Keyes
    Abstract:

    The authors thank Cray Inc. and Intel Corp. in the context of the Cray Center of Excellence and Intel Parallel Computing Center awarded to the Extreme Computing Research Center (ECRC) at KAUST. The authors also thank Mustafa Abduljabbar from ECRC for his help to further enhance the general features of the code. For computer time, this research used Shaheen supercomputer hosted at the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST).

  • asynchronous task based Polar Decomposition on single node manycore architectures
    IEEE Transactions on Parallel and Distributed Systems, 2018
    Co-Authors: Dalal Sukkari, Hatem Ltaief, Mathieu Faverge, David E Keyes
    Abstract:

    This paper introduces the first asynchronous, task-based formulation of the Polar Decomposition and its corresponding implementation on manycore architectures. Based on a new formulation of the iterative $QR$ dynamically-weighted Halley algorithm (QDWH) for the calculation of the Polar Decomposition, the proposed implementation replaces the original and hostile LU factorization for the condition number estimator by the more adequate $QR$ factorization to enable software portability across various architectures. Relying on fine-grained computations, the novel task-based implementation is also capable of taking advantage of the identity structure of the matrix involved during the QDWH iterations, which decreases the overall algorithmic complexity. Furthermore, the artifactual synchronization points have been weakened compared to previous implementations, unveiling look-ahead opportunities for better hardware occupancy. The overall QDWH-based Polar Decomposition can then be represented as a directed acyclic graph (DAG), where nodes represent computational tasks and edges define the inter-task data dependencies. The StarPU dynamic runtime system is employed to traverse the DAG, to track the various data dependencies and to asynchronously schedule the computational tasks on the underlying hardware resources, resulting in an out-of-order task scheduling. Benchmarking experiments show significant improvements against existing state-of-the-art high performance implementations (i.e., Intel MKL and Elemental) for the Polar Decomposition on latest shared-memory vendors’ systems (i.e., Intel Haswell/Broadwell/Knights Landing, NVIDIA K80/P100 GPUs and IBM Power8), while maintaining high numerical accuracy.

  • Asynchronous Task-Based Polar Decomposition on Manycore Architectures
    2016
    Co-Authors: Dalal Sukkari, Hatem Ltaief, Mathieu Faverge, David Keyes
    Abstract:

    This paper introduces the first asynchronous, task-based implementation of the Polar Decomposition on manycore architectures. Based on a new formulation of the iterative QR dynamically-weighted Halley algorithm (QDWH) for the calculation of the Polar Decomposition, the proposed implementation replaces the original and hostile LU factorization for the condition number estimator by the more adequate QR factorization to enable software portability across various architectures. Relying on fine-grained computations, the novel task-based implementation is also capable of taking advantage of the identity structure of the matrix involved during the QDWH iterations, which decreases the overall algorithmic complexity. Furthermore, the artifactual synchronization points have been severely weakened compared to previous implementations, unveiling look-ahead opportunities for better hardware occupancy. The overall QDWH-based Polar Decomposition can then be represented as a directed acyclic graph (DAG), where nodes represent computational tasks and edges define the inter-task data dependencies. The StarPU dynamic runtime system is employed to traverse the DAG, to track the various data dependencies and to asynchronously schedule the computational tasks on the underlying hardware resources, resulting in an out-of-order task scheduling. Benchmarking experiments show significant improvements against existing state-of-the-art high performance implementations (i.e., Intel MKL and Elemental) for the Polar Decomposition on latest shared-memory vendors' systems (i.e., Intel Haswell/Broadwell/Knights Landing, NVIDIA K80/P100 GPUs and IBM Power8), while maintaining high numerical accuracy.

  • high performance Polar Decomposition on distributed memory systems
    European Conference on Parallel Processing, 2016
    Co-Authors: Dalal Sukkari, Hatem Ltaief, David E Keyes
    Abstract:

    The Polar Decomposition of a dense matrix is an important operation in linear algebra. It can be directly calculated through the singular value Decomposition SVD or iteratively using the QR dynamically-weighted Halley algorithm QDWH. The former is difficult to parallelize due to the preponderant number of memory-bound operations during the bidiagonal reduction. We investigate the latter scenario, which performs more floating-point operations but exposes at the same time more parallelism, and therefore, runs closer to the theoretical peak performance of the system, thanks to more compute-bound matrix operations. Profiling results show the performance scalability of QDWH for calculating the Polar Decomposition using around 9200 MPI processes on well and ill-conditioned matrices of 100i¾źKi¾ź$$\times $$i¾ź100i¾źK problem size. We study then the performance impact of the QDWH-based Polar Decomposition as a pre-processing step toward calculating the SVD itself. The new distributed-memory implementation of the QDWH-SVD solver achieves up to five-fold speedup against current state-of-the-art vendor SVD implementations.

George Haller - One of the best experts on this subject based on the ideXlab platform.

  • dynamic rotation and stretch tensors from a dynamic Polar Decomposition
    Journal of The Mechanics and Physics of Solids, 2016
    Co-Authors: George Haller
    Abstract:

    Abstract The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the Polar Decomposition of the deformation gradient. Beyond its well-known merits, the Polar rotation tensor also has a lesser known dynamical inconsistency: it does not satisfy the fundamental superposition principle of rigid-body rotations over adjacent time intervals. As a consequence, the Polar rotation diverts from the observed mean material rotation of fibers in fluids, and introduces a purely kinematic memory effect into computed material rotation. Here we derive a generalized Polar Decomposition for linear processes that yields a unique, dynamically consistent rotation component, the dynamic rotation tensor, for the deformation gradient. The left dynamic stretch tensor is objective, and shares the principal strain values and axes with its classic Polar counterpart. Unlike its classic Polar counterpart, however, the dynamic stretch tensor evolves in time without spin. The dynamic rotation tensor further decomposes into a spatially constant mean rotation tensor and a dynamically consistent relative rotation tensor that is objective for planar deformations. We also obtain simple expressions for dynamic analogues of Cauchy's mean rotation angle that characterize a deforming body objectively.