multidimensional arrays have proven to be useful in watermarking, therefore interest in this subject has increased in the previous years along with the number of publications. For one dimensional arrays (sequences), l...
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ISBN:
(纸本)9781467383080
multidimensional arrays have proven to be useful in watermarking, therefore interest in this subject has increased in the previous years along with the number of publications. For one dimensional arrays (sequences), linear complexity is regarded as standard measure of complexity. Although linear complexity of sequences has been widely studied, only recently, we have extended it to the study of multidimensional arrays. In this paper, we show that the concept of multidimensional linear complexity is a powerful tool, by examining the results for selected constructs. We have obtained the linear complexity of logartihmic Moreno-Tirkel arrays and we show that they show high multidimensional linear complexity. Finally, we explicitly provide the minimal generators for quadratic Moreno-Tirkel arrays. The results show that these techniques are effective in finding the multidimensional linear complexity of the constructions, representing only a small fraction of the applicability of multidimensional linear complexity. The study of multidimensional arrays provides new ways to understand sequences and set the basis for forthcoming proof of the three years old conjectures related with CDMA sequences.
Reshuffling elements of a multidimensional array according to an index operation traditionally requires an auxiliary buffer of the same size as the original array. Here, we describe a new in-place algorithm using vaca...
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Reshuffling elements of a multidimensional array according to an index operation traditionally requires an auxiliary buffer of the same size as the original array. Here, we describe a new in-place algorithm using vacancy tracking cycles with minimum memory access which eliminates the buffer array and the related copy-back, speeding up the reshuffle significantly for large arrays. The algorithm can be paralleiized using a multithread approach on shared-memory multiprocessor computers. On distributed-memory multiprocessor computers, the index reshuffle of distributed multidimensional arrays amounts to a remapping of processor domains and is carried out using the in-place local algorithm combined with a global exchange algorithm. Implementation and test results on GRAY T3E and IBM SP indicate the effectiveness of the algorithm.
The robust Capon beamformer has been shown to alleviate the problem of signal cancellation resulting from steering vector errors, caused, for example, by calibration and/or angle-of-arrival (AOA) errors, which would, ...
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The robust Capon beamformer has been shown to alleviate the problem of signal cancellation resulting from steering vector errors, caused, for example, by calibration and/or angle-of-arrival (AOA) errors, which would, otherwise, seriously degrade the performance of an adaptive beamformer. Here, we examine robust Capon beamforming of multidimensional arrays, where robustness to AOA errors is needed in both azimuth and elevation. It is shown that the commonly used spherical uncertainty sets are unable to control robustness in each of these directions independently. Here, we instead propose the use of flat ellipsoidal sets to control the AOA uncertainty. To also allow for other errors, such as calibration errors, we combine these flat ellipsoids with a higher dimension error ellipsoid. Computationally efficient automatic techniques for estimating the necessary uncertainty sets are derived, and the proposed methods are evaluated using both simulated data and experimental underwater acoustic measurements, clearly showing the benefits of the technique.
This extended abstract describes the prototype of a mul-tidimensional array interface that sits on top of Arkouda, a Python-based productivity layer for distributed array and dataframe computations [1] . Arkouda suppo...
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ISBN:
(纸本)9781665423694
This extended abstract describes the prototype of a mul-tidimensional array interface that sits on top of Arkouda, a Python-based productivity layer for distributed array and dataframe computations [1] . Arkouda support has focused on 1-D arrays, offering an interface similar to Numpy (Python’s de facto standard sequential library for array processing) and using a Chapel-based backend for distributed execution. Motivated by tensor computations, we are exploring extensions of Arkouda to support multiway (\"N-D\") array objects. The goal of our prototype is not to claim a fully-featured, high-performance implementation but rather to initiate a broader discussion with the Arkouda community about whether and how to pursue such an extension. (For a practical, high-performance drop-in replacement for Numpy with distributed GPU support, see Legate [2] , among other efforts [3] – [6] .)
In this paper we propose a simple strategy for memory management of multidimensional arrays whose entries are known to be invariant under a special permutation group P of the coordinates. The group P is not known in a...
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In this paper we propose a simple strategy for memory management of multidimensional arrays whose entries are known to be invariant under a special permutation group P of the coordinates. The group P is not known in advance and is entered as a parameter of the procedure. The strategy is to obtain a partition of LΔn, the relevant lattice of positive integer points in Rn, into parts which behaves well under the action of P. The partition is controlled by a hierarchy of combinatorial objects, forming a tree. The leaves of this tree are identified with some vertices of a digraph encoding special decreasing sequences. Both this digraph and the leaf-identified tree, denoted LΔn/P, are instances of Nijenhuis-Wilf combinatorial families. The members of L Δn/P become maximal paths in L Δn/P. This fact enables the quick computation of the address rΔP(δ), for δ ∈ L Δn/P.
The lack of direct support for multidimensional arrays in Java(TM) has been recognized as a major deficiency in the language's applicability to numerical computing. It has been shown that, when augmented with mult...
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The lack of direct support for multidimensional arrays in Java(TM) has been recognized as a major deficiency in the language's applicability to numerical computing. It has been shown that, when augmented with multidimensional arrays, Java can achieve very high-performance for numerical computing through the use of compiler techniques and efficient implementations of aggregate array operations. Three approaches have been discussed in the literature for extending Java with support for multidimensional arrays: class libraries that implement these structures;extending the Java language with new syntactic constructs for multidimensional arrays that are directly translated to bytecode;and relying on the Java Virtual Machine to recognize those arrays of arrays that are being used to simulate multidimensional arrays. This paper presents a balanced presentation of the pros and cons of each technique in the areas of functionality, language and virtual machine impact, implementation effort, and effect on performance. We show that the best choice depends on the relative importance attached to the different metrics, and thereby provide a common ground for a rational discussion and comparison of the techniques. Copyright (C) 2003 John Wiley Sons, Ltd.
A novel higher-dimensional definition for Costas arrays is introduced. This definition works for arbitrary dimensions and avoids some limitations of previous definitions. Some non-existence results are presented for m...
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A novel higher-dimensional definition for Costas arrays is introduced. This definition works for arbitrary dimensions and avoids some limitations of previous definitions. Some non-existence results are presented for multidimensional Costas arrays preserving the Costas condition when the array is extended periodically throughout the whole space. In particular, it is shown that three-dimensional arrays with this property must have the least possible order;extending an analogous two-dimensional result by H. Taylor. Said result is conjectured to extend for Costas arrays of arbitrary dimensions.
This paper describes ExaShark, a hybrid n-dimensional array toolkit offered as a high-level library for scientists to compute large-scale simulations. It offers a global-array-like interface while its runtime can be c...
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This paper describes ExaShark, a hybrid n-dimensional array toolkit offered as a high-level library for scientists to compute large-scale simulations. It offers a global-array-like interface while its runtime can be configured to use shared memory threading techniques, inter-node distribution techniques, or combinations of both. ExaShark takes advantage of the latest HPC technologies, helping to scale to future generation systems. It has been used to develop several scientific applications including stencil codes, solvers, and matrix factorization algorithms. These applications are used to demonstrate that it improves on the state of the art by providing a user-friendly, generic API without sacrificing performance.
The linear complexity of a sequence is an important parameter for many applications, especially those related to information security, and hardware implementation. It is desirable to develop a corresponding measure an...
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The linear complexity of a sequence is an important parameter for many applications, especially those related to information security, and hardware implementation. It is desirable to develop a corresponding measure and theory for multidimensional arrays that are consistent with those of sequences. In this paper we use Grobner bases to develop a theory for analyzing the multidimensional linear complexity of general periodic arrays. We also analyze arrays constructed using the method of composition and establish tight bounds for their multidimensional linear complexity.
Short-lag spatial coherence (SLSC) imaging has demonstrated improved performance over conventional B-mode ultrasound imaging. Previous work has evaluated the performance of SLSC using 2-D matrix arrays in simulation a...
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Short-lag spatial coherence (SLSC) imaging has demonstrated improved performance over conventional B-mode ultrasound imaging. Previous work has evaluated the performance of SLSC using 2-D matrix arrays in simulation and in vivo studies across various levels of subaperture beamforming, demonstrating improved contrast-to-noise ratio (CNR) and speckle signal-to-noise ratio (SNR) over 1-D arrays. This work explores the application of SLSC imaging in 1.5-D and 1.75-D arrays to quantify the impacts of elevation element count, mirroring, and Fresnel element spacing on SLSC image quality. Through simulation and in vivo studies, increased elevation element count was shown to improve CNR and speckle SNR relative to 1-D SLSC and B-mode images. Elevation mirroring (1.5-D) was shown to force the inclusion of long lags into the SLSC calculation, introducing additional decorrelation and reducing image quality relative to 1.75-D arrays with individually connected elements. These results demonstrate the effectiveness of SLSC imaging in 1.5-D and 1.75-D arrays.
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