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Journal articles on the topic 'Multidimensional array'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Lu, Meng, Marius Appel, and Edzer Pebesma. "Multidimensional Arrays for Analysing Geoscientific Data." ISPRS International Journal of Geo-Information 7, no. 8 (August 3, 2018): 313. http://dx.doi.org/10.3390/ijgi7080313.

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Geographic data is growing in size and variety, which calls for big data management tools and analysis methods. To efficiently integrate information from high dimensional data, this paper explicitly proposes array-based modeling. A large portion of Earth observations and model simulations are naturally arrays once digitalized. This paper discusses the challenges in using arrays such as the discretization of continuous spatiotemporal phenomena, irregular dimensions, regridding, high-dimensional data analysis, and large-scale data management. We define categories and applications of typical array operations, compare their implementation in open-source software, and demonstrate dimension reduction and array regridding in study cases using Landsat and MODIS imagery. It turns out that arrays are a convenient data structure for representing and analysing many spatiotemporal phenomena. Although the array model simplifies data organization, array properties like the meaning of grid cell values are rarely being made explicit in practice.

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Holm, A., W. Wu, H. S. Slaastad, L. Goullart, and D. Carrillo. "Multidimensional antibody array analysis." New Biotechnology 27 (April 2010): S74. http://dx.doi.org/10.1016/j.nbt.2010.01.211.

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3

Rogozovskyi, Oleg A. "Multidimensional array signal processing with multidimensional matrix operations." Journal of the Acoustical Society of America 105, no. 2 (February 1999): 1253. http://dx.doi.org/10.1121/1.426010.

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4

Fitzgerald, Steven M., and Rodney R. Oldehoeft. "Update-in-Place Analysis for True Multidimensional Arrays." Scientific Programming 5, no. 2 (1996): 147–60. http://dx.doi.org/10.1155/1996/493673.

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Applicative languages have been proposed for defining algorithms for parallel architectures because they are implicitly parallel and lack side effects. However, straightforward implementations of applicative-language compilers may induce large amounts of copying to preserve program semantics. The unnecessary copying of data can increase both the execution time and the memory requirements of an application. To eliminate the unnecessary copying of data, the Sisal compiler uses both build-in-place and update-in-place analyses. These optimizations remove unnecessary array copy operations through compile-time analysis. Both build-in-place and update-in-place are based on hierarchical ragged arrays, i.e., the vector-of-vectors array model. Although this array model is convenient for certain applications, many optimizations are precluded, e.g., vectorization. To compensate for this deficiency, new languages, such as Sisal 2.0, have extended array models that allow for both high-level array operations to be performed and efficient implementations to be devised. In this article, we introduce a new method to perform update-in-place analysis that is applicable to arrays stored either in hierarchical or in contiguous storage. Consequently, the array model that is appropriate for an application can be selected without the loss of performance. Moreover, our analysis is more amenable for distributed memory and large software systems.

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5

Edwards, H. Carter, Daniel Sunderland, Vicki Porter, Chris Amsler, and Sam Mish. "Manycore Performance-Portability: Kokkos Multidimensional Array Library." Scientific Programming 20, no. 2 (2012): 89–114. http://dx.doi.org/10.1155/2012/917630.

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Large, complex scientific and engineering application code have a significant investment in computational kernels to implement their mathematical models. Porting these computational kernels to the collection of modern manycore accelerator devices is a major challenge in that these devices have diverse programming models, application programming interfaces (APIs), and performance requirements. The Kokkos Array programming model provides library-based approach to implement computational kernels that are performance-portable to CPU-multicore and GPGPU accelerator devices. This programming model is based upon three fundamental concepts: (1) manycore compute devices each with its own memory space, (2) data parallel kernels and (3) multidimensional arrays. Kernel execution performance is, especially for NVIDIA® devices, extremely dependent on data access patterns. Optimal data access pattern can be different for different manycore devices – potentially leading to different implementations of computational kernels specialized for different devices. The Kokkos Array programming model supports performance-portable kernels by (1) separating data access patterns from computational kernels through a multidimensional array API and (2) introduce device-specific data access mappings when a kernel is compiled. An implementation of Kokkos Array is available through Trilinos [Trilinos website, http://trilinos.sandia.gov/, August 2011].

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LI, Jiang, Yusuke ATSUMARI, Hiromasa KUBO, Yuichi OGISHIMA, Satoru YOKOTA, Hakaru TAMUKOH, and Masatoshi SEKINE. "A Multidimensional Configurable Processor Array — Vocalise." IEICE Transactions on Information and Systems E98.D, no. 2 (2015): 313–24. http://dx.doi.org/10.1587/transinf.2014edp7219.

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7

Flesch, Aime, and An Nguyen-Dinh. "Stack based multidimensional ultrasonic transducer array." Journal of the Acoustical Society of America 115, no. 5 (2004): 1865. http://dx.doi.org/10.1121/1.1757128.

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8

King, James E. "Number concepts in animals: A multidimensional array." Behavioral and Brain Sciences 11, no. 4 (December 1988): 590. http://dx.doi.org/10.1017/s0140525x00053565.

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9

Moran, Mark L., Roy J. Greenfield, Steven A. Arcone, and Allan J. Delaney. "Multidimensional GPR array processing using Kirchhoff migration." Journal of Applied Geophysics 43, no. 2-4 (March 2000): 281–95. http://dx.doi.org/10.1016/s0926-9851(99)00065-8.

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10

Chun-Yuan Lin, Jen-Shiuh Liu, and Yeh-Ching Chung. "Efficient representation scheme for multidimensional array operations." IEEE Transactions on Computers 51, no. 3 (March 2002): 327–45. http://dx.doi.org/10.1109/12.990130.

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11

Amir, Amihood, and Gad M. Landau. "Fast parallel and serial multidimensional approximate array matching." Theoretical Computer Science 81, no. 1 (April 1991): 97–115. http://dx.doi.org/10.1016/0304-3975(91)90318-v.

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12

Zhao, Yihong, Prasad M. Deshpande, and Jeffrey F. Naughton. "An array-based algorithm for simultaneous multidimensional aggregates." ACM SIGMOD Record 26, no. 2 (June 1997): 159–70. http://dx.doi.org/10.1145/253262.253288.

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13

Mao, Jinpeng, Yuexiang Lu, Ning Chang, Jiaoe Yang, Sichun Zhang, and Yueying Liu. "Multidimensional colorimetric sensor array for discrimination of proteins." Biosensors and Bioelectronics 86 (December 2016): 56–61. http://dx.doi.org/10.1016/j.bios.2016.06.040.

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14

Min, Xiang, Wang Zhuwen, and Qi Xinghua. "Comparison and research of multidimensional analysis for array acoustic logging in fractured formations." Interpretation 8, no. 3 (June 13, 2020): SL89—SL102. http://dx.doi.org/10.1190/int-2019-0212.1.

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Currently, array acoustic logging data processing is mainly achieved by calculating only the velocity variation of each component wave. This provides a little formation information; thus, it is difficult to identify all fractures. We have analyzed the array acoustic logging signals by combining their times, frequencies, or amplitudes. First, we decomposed the array acoustic logging signals into main and secondary signals by improving the singular value decomposition. We then analyzed the characteristics of the array acoustic logging signals in fractured formations and compared them using three multidimensional analysis methods: the 2D Fourier transform, the 2D wavelet transform, and the Choi-Williams distribution. The results showed that the frequency characteristics of the compressional waves (P-waves), shear waves (S-waves), and Stoneley waves in the [Formula: see text]-[Formula: see text] domain of the fracture formations can be obtained by the 2D Fourier transform method. The multiresolution time characteristics of these waves can be realized by the 2D wavelet transform method, and their time-frequency characteristics can be observed via the Choi-Williams distribution. The times, frequencies, and amplitudes of the P-waves, S-waves, and Stoneley waves change from the tight formation to the fractured formation. The three methods introduced here can comprehensively use eight arrays, time, frequency, or amplitude to improve the information usage rate of array acoustic logging and provide new ways to interpret it.

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15

Meng, Lili, Jingchao Zhu, Ruixin Bian, Bojie Xu, Zhongxue Tang, Yu Zhang, and Huan Liu. "Multidimensional Aligned Nanowires Array: Toward Bendable and Stretchable Strain Sensors." Coatings 11, no. 8 (August 16, 2021): 975. http://dx.doi.org/10.3390/coatings11080975.

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Micropatterns based on the oriented nanowires have attracted research interests for their unique physicochemical advantages in various applications of electric microdevices. Here, we proposed a facile fibrous dewetting strategy by spreading and dewetting of the silver nanowire (AgNW) solution on the vertical aligned carbon nanotube array (ACNTs) for preparing multidimensional aligned nanowires array, based on the elastocapillary coalescence. The unidirectional shrinking of the liquid film on the top of ACNTs happens during the dewetting process, as a result of the elastocapillary coalescence of ACNTs, which drives the AgNWs aligned along normal direction of liquid film shrinkage on the top of ACNTs. Thus, a multidimensional aligned NWs array was prepared, composing of the horizontally oriented NWs of top layer and vertical ACNT bundles of under layer connected by CNT yarns. A bendable flexible electrode was prepared using the as-prepared multidimensional aligned nanowires array, showing high stability during bending cycles (1800 cycles). Moreover, the multidimensional aligned nanowires array is also applicable for fabricating strain sensors, which show stable resistance response under strain. We envision that the as-developed approach shed new light on easy manufacture NW-based micropatterns.

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Aminev, A. M., A. V. Gilev, D. Yu Grishin, V. E. Zaytsev, and V. N. Sergeev. "Automated active phased array control stand software." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 4 (December 30, 2019): 93–102. http://dx.doi.org/10.38013/2542-0542-2019-4-93-102.

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The study suggests using a software platform for multidimensional data cubes in automated active phased array control stands. The application of the platform greatly facilitates and accelerates the display and analysis of very large volumes of data coming from large-aperture active phased arrays during the measurement process, so that the end user can make spontaneous data requests. The study shows the prospects of using this platform for radar systems as a whole.

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Lachikhina, A. B., and K. N. Soldatov. "COORDINATE SYSTEM FOR REPRESENTATION OF MULTIDIMENSIONAL DATA." Issues of radio electronics, no. 11 (November 20, 2018): 40–44. http://dx.doi.org/10.21778/2218-5453-2018-11-40-44.

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Visualization of analyzing multidimensional data is often required in order to improve perception and visibility. The purpose of this research is a multidimensional array of data representation. It is proposed to use a three-dimensional model as a tool. The methods used to represent an array of data with more than three dimensions are presented. The principle of constructing a multidimensional array cell is considered. An example of the constructed hypercube cell is given. The formulas for calculating the number of faces of the figure, the number of triangles that can be built through points, the number of internal triangles are obtained. The approach of visualization of aggregates is described. The use of color gradation to improve the convenience of perception of the cell in the analysis of the cube cells. It is concluded that the proposed model allows us to perceive each cell as an independent data element in the construction of charts for the analyzed indicators.

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., Dattatray V. Meshram. "UNSTRUCTURED MULTIDIMENSIONAL ARRAY MULTIMEDIA RETRIVAL MODEL BASED XML DATABASE." International Journal of Research in Engineering and Technology 01, no. 03 (March 25, 2012): 302–6. http://dx.doi.org/10.15623/ijret.2012.0103018.

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19

Currie, I. D., M. Durban, and P. H. C. Eilers. "Generalized linear array models with applications to multidimensional smoothing." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68, no. 2 (April 2006): 259–80. http://dx.doi.org/10.1111/j.1467-9868.2006.00543.x.

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20

Krijkamp, Eline M., Fernando Alarid-Escudero, Eva A. Enns, Petros Pechlivanoglou, M. G. Myriam Hunink, Alan Yang, and Hawre J. Jalal. "A Multidimensional Array Representation of State-Transition Model Dynamics." Medical Decision Making 40, no. 2 (January 28, 2020): 242–48. http://dx.doi.org/10.1177/0272989x19893973.

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Cost-effectiveness analyses often rely on cohort state-transition models (cSTMs). The cohort trace is the primary outcome of cSTMs, which captures the proportion of the cohort in each health state over time (state occupancy). However, the cohort trace is an aggregated measure that does not capture information about the specific transitions among health states (transition dynamics). In practice, these transition dynamics are crucial in many applications, such as incorporating transition rewards or computing various epidemiological outcomes that could be used for model calibration and validation (e.g., disease incidence and lifetime risk). In this article, we propose an alternative approach to compute and store cSTMs outcomes that capture both state occupancy and transition dynamics. This approach produces a multidimensional array from which both the state occupancy and the transition dynamics can be recovered. We highlight the advantages of the multidimensional array over the traditional cohort trace and provide potential applications of the proposed approach with an example coded in R to facilitate the implementation of our method.

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Arce-Nazario, Rafael A., and José Ortiz-Ubarri. "Multidimensional Costas Arrays and Their Enumeration Using GPUs and FPGAs." International Journal of Reconfigurable Computing 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/196761.

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The enumeration of two-dimensional Costas arrays is a problem with factorial time complexity and has been solved for sizes up to 29 using computer clusters. Costas arrays of higher dimensionality have recently been proposed and their properties are beginning to be understood. This paper presents, to the best of our knowledge, the first proposed implementations for enumerating these multidimensional arrays in GPUs and FPGAs, as well as the first discussion of techniques to prune the search space and reduce enumeration run time. Both GPU and FPGA implementations rely on Costas array symmetries to reduce the search space and perform concurrent explorations over the remaining candidate solutions. The fine grained parallelism utilized to evaluate and progress the exploration, coupled with the additional concurrency provided by the multiple instanced cores, allowed the FPGA (XC5VLX330-2) implementation to achieve speedups of up to 30× over the GPU (GeForce GTX 580).

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Jain, Rajashree, and G. S. Mani. "Solving “Antenna Array Thinning Problem” Using Genetic Algorithm." Applied Computational Intelligence and Soft Computing 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/946398.

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Thinning involves reducing total number of active elements in an antenna array without causing major degradation in system performance. Dynamic thinning is the process of achieving this under real-time conditions. It is required to find a strategic subset of antenna elements for thinning so as to have its optimum performance. From a mathematical perspective this is a nonlinear, multidimensional problem with multiple objectives and many constraints. Solution for such problem cannot be obtained by classical analytical techniques. It will be required to employ some type of search algorithm which can lead to a practical solution in an optimal. The present paper discusses an approach of using genetic algorithm for array thinning. After discussing the basic concept involving antenna array, array thinning, dynamic thinning, and application methodology, simulation results of applying the technique to linear and planar arrays are presented.

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23

DI COSMO, ROBERTO, and SUSANNA PELAGATTI. "A CALCULUS FOR DENSE ARRAY DISTRIBUTIONS." Parallel Processing Letters 13, no. 03 (September 2003): 377–88. http://dx.doi.org/10.1142/s0129626403001355.

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We introduce a very simple, yet powerful, distribution calculus aimed at describing different strategies that can be used to distribute (ie, partition and replicate) multidimensional dense arrays over a set of processors, like what is done in the implementation of the P3L Map skeleton. We give a formal semantics, that allows to prove equations between distributions, and we show how to associate a cost to such distributions, allowing to choose between semantically equivalent distribution strategies.

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Gorinevsky, D., and G. Stein. "Structured uncertainty analysis of robust stability for multidimensional array systems." IEEE Transactions on Automatic Control 48, no. 9 (September 2003): 1557–68. http://dx.doi.org/10.1109/tac.2003.816980.

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Birchfield, S. T., and A. Subramanya. "Microphone array position calibration by basis-point classical multidimensional scaling." IEEE Transactions on Speech and Audio Processing 13, no. 5 (September 2005): 1025–34. http://dx.doi.org/10.1109/tsa.2005.851893.

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Ertug, O. "Asymptotic Ergodic Capacity of Multidimensional Vector-Sensor Array MIMO Channels." IEEE Transactions on Wireless Communications 7, no. 9 (September 2008): 3297–300. http://dx.doi.org/10.1109/twc.2008.070324.

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27

Tamura, Yasutaka, Osamu Akasaka, and Mitsuru Okada. "Wavefront Generation Using a Dense Array and Multidimensional ΔΣ Modulation." Japanese Journal of Applied Physics 36, Part 1, No. 5B (May 30, 1997): 3053–56. http://dx.doi.org/10.1143/jjap.36.3053.

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28

Broomhead, D. S., R. Jones, J. G. McWhirter, and T. J. Shepherd. "Systolic array for nonlinear multidimensional interpolation using radial basis functions." Electronics Letters 26, no. 1 (January 4, 1990): 7–9. http://dx.doi.org/10.1049/el:19900005.

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Men, Baiyong, Xiaodong Ju, Junqiang Lu, and Wenxiao Qiao. "A synchronous serial bus for multidimensional array acoustic logging tool." Journal of Geophysics and Engineering 13, no. 6 (November 11, 2016): 974–83. http://dx.doi.org/10.1088/1742-2132/13/6/974.

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LIU, XIAOJIAN, and LEONARD T. BRUTON. "PARALLEL COMPUTING IN MULTIDIMENSIONAL RECURSIVE FILTERING." International Journal of High Speed Electronics and Systems 04, no. 02 (June 1993): 219–43. http://dx.doi.org/10.1142/s0129156493000108.

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This paper introduces and generalizes a number of multidimensional (MD) recursive parallel filter algorithms, which are based on the principles of orthogonal and diagonal computing, respectively. Efficient software and hardware implementation methods for the proposed parallel algorithms are presented. In particular, it is shown that systolic array implementations can be achieved for MD parallel filter structures that are locally interconnected and have a critical path of 1 multiplication plus 1 addition. In this way, the proposed parallel filters are easily able to perform real-time processing at video rates.

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SAOUDI, A., and M. NIVAT. "PARALLEL ALGORITHMS FOR MULTIDIMENSIONAL IMAGE TEMPLATE MATCHING." International Journal of Pattern Recognition and Artificial Intelligence 08, no. 02 (April 1994): 457–64. http://dx.doi.org/10.1142/s021800149400022x.

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This paper presents efficient and optimal parallel algorithms for multidimensional image template matching on CREW PRAM model. For an Nd image and an Md window, we present an optimal (respectively efficient) algorithm which runs in O(log(M)) time with O(Md×Nd/log(M) processors (respectively O(Md×Nd)). We also present efficient and optimal algorithms for solving the multidimensional array and pattern matching.

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Hong, Mun-Gwan, Woojoo Lee, Peter Nilsson, Yudi Pawitan, and Jochen M. Schwenk. "Multidimensional Normalization to Minimize Plate Effects of Suspension Bead Array Data." Journal of Proteome Research 15, no. 10 (September 12, 2016): 3473–80. http://dx.doi.org/10.1021/acs.jproteome.5b01131.

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Vanpoucke, F. J., P. B. Boermans, and J. H. Frijns. "Assessing the Placement of a Cochlear Electrode Array by Multidimensional Scaling." IEEE Transactions on Biomedical Engineering 59, no. 2 (February 2012): 307–10. http://dx.doi.org/10.1109/tbme.2011.2173198.

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Lin Zi-Yang, Fu Zhe, Liu Li-Xin, Hu Tao, Qu Jun-Le, Guo Bao-Ping, and Niu Han-Ben. "Information processing of multidimensional simultaneity fluorescence with two-photon array excitation." Acta Physica Sinica 55, no. 12 (2006): 6701. http://dx.doi.org/10.7498/aps.55.6701.

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Van Thanh, Le. "On theLP-convergence for multidimensional arrays of random variables." International Journal of Mathematics and Mathematical Sciences 2005, no. 8 (2005): 1317–20. http://dx.doi.org/10.1155/ijmms.2005.1317.

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For ad-dimensional array of random variables{Xn,n∈ℤ+d}such that{|Xn|p,n∈ℤ+d}is uniformly integrable for some0<p<2, theLp-convergence is established for the sums(1/|n|1/p) (∑j≺n(Xj−aj)), whereaj=0if0<p<1, andaj=EXjif1≤p<2.

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Amundsen, Lasse, Luc T. Ikelle, and Lars E. Berg. "Multidimensional signature deconvolution and free‐surface multiple elimination of marine multicomponent ocean‐bottom seismic data." GEOPHYSICS 66, no. 5 (September 2001): 1594–604. http://dx.doi.org/10.1190/1.1486770.

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This paper presents a wave‐equation method for multidimensional signature deconvolution (designature) and elimination of free‐surface related multiples (demultiple) in four‐component (4C) ocean‐bottom seismic data. The designature/demultiple method has the following characteristics: it preserves primary amplitudes while attenuating free‐surface related multiples; it requires no knowledge of the sea floor‐parameters and the subsurface; it requires information only of the local density and acoustic wave propagation velocity just above the sea floor; it accommodates source arrays; and no information (except location) of the physical source array, its volume, and its radiation characteristics (wavelet) is required. Designature is an implicit part of the demultiple process; hence, the method is capable of transforming recorded reflection data excited by any source array below the sea surface into free‐surface demultipled data that would be recorded from a point source with any desired signature. In addition, the incident wavefield is not subtracted from the data prior to free‐surface demultiple; hence, separation of incident and scattered fields is not an issue as it is for most other free‐surface demultiple schemes. The designature/demultiple algorithm can be divided into two major computational steps. First, a multidimensional deconvolution operator, inversely proportional to the time derivative of the downgoing part of the normal component of the particle velocity just above the sea floor, is computed. Second, an integral equation is solved to find any component of the designatured, free‐surface demultipled multicomponent field. When the geology is horizontally layered, the designature and free‐surface demultiple scheme greatly simplifies and lends itself toward implementation in the τ‐p domain or frequency‐wavenumber domain as deterministic deconvolution of common shot gathers (or common receiver gathers when source array variations are negligible).

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Wang, Junxiang, Ping Huang, and Dingjie Xu. "Joint DOA and DOD Estimation Based on Tensor Subspace with Partially Calibrated Bistatic MIMO Radar." International Journal of Antennas and Propagation 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/4370637.

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A joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation algorithm based on tensor subspace approach for partially calibrated bistatic multiple-input multiple-output (MIMO) radar is proposed. By exploiting the multidimensional structure of the received data, a third-order measurement tensor is constructed. Consequently, the tensor-based signal subspace is achieved using the higher-order singular value decomposition (HOSVD). To achieve accurate DOA estimation with partially calibrated array, a closed-form solution is provided to estimate the gain-phase uncertainties of the transmit and receive arrays by modeling the imperfections of the arrays. Simulation results demonstrate the effectiveness of the proposed calibration algorithm.

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Imtiaz, A., C. Cornou, P.-Y. Bard, and M. Hobiger. "Diffracted wavefield decomposition and multidimensional site effects in the Argostoli valley, Greece." Geophysical Journal International 224, no. 3 (November 5, 2020): 1849–69. http://dx.doi.org/10.1093/gji/ggaa529.

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SUMMARY Effects of seismic ground motion induced by surface geology and geometry are known to be associated with the generation of a substantial proportion of surface waves. As a consequence, surface waves significantly contribute to ground-motion variability and site amplification. There is a growing body of literature recognizing that an understanding of physical patterns of the wavefield crossing a site is the key aspect to characterize and quantify them. However, this task remains technically challenging due to the complexity of such effects as well as the limitations of geophysical investigations, especially in case of small sedimentary valleys. The present study attempts to investigate the waves propagating across two 2-D dense seismic arrays from a number of earthquakes and explore the extent to which they are contributing to the multidimensional site effects. The arrays were deployed in the small-size, shallow alluvial valley of Koutavos-Argostoli, located in Cephalonia Island, Greece, and consisted of three-component velocimeters with interstation distances ranging from 5 to 160 m. A set of 46 earthquakes, with magnitudes between 2 and 5 and epicentral distances up to 200 km, was analysed by using an advanced seismic array processing technique, MUSIQUE. The phase velocity, backazimuth and energy of the dominant waves crossing the array were extracted, and their identification as Love or prograde/retrograde Rayleigh waves was obtained. The results clearly indicate a predominance of scattered surface waves (up to 60 per cent of total energy), mainly from the closest valley edges, above the fundamental frequency (∼1.5 Hz) of the valley. Love waves dominate the low-frequency wavefield (<3 Hz) while Rayleigh waves dominate some high-frequency bands. An excellent consistency is observed, in a given frequency range, among the dominance of the type of diffracted surface waves, group velocities estimated from the ground velocity structure and site amplification. The outcomes of this research provide a better understanding of the contribution of edge-diffracted surface waves and the 2-D/3-D site amplification at small and shallow alluvium valleys like Argostoli. The method applied here can be used to calibrate and validate 3-D models for simulating seismic ground motion.

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Stergiopoulos, Stergios, and Amar C. Dhanantwari. "High resolution 3D ultrasound imaging system deploying a multidimensional array of sensors and method for multidimensional beamforming sensor signals." Journal of the Acoustical Society of America 113, no. 5 (2003): 2399. http://dx.doi.org/10.1121/1.1584206.

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Hucul, D., M. Yeo, W. K. Hensinger, J. Rabchuk, S. Olmschenk, and C. Monroe. "On the transport of atomic ions in linear and multidimensional ion trap arrays." Quantum Information and Computation 8, no. 6&7 (July 2008): 501–78. http://dx.doi.org/10.26421/qic8.6-7-1.

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Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.

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Azharul Hasan, K. M., Tatsuo Tsuji, and Ken Higuchi. "A Parallel Implementation Scheme of Relational Tables Based on Multidimensional Extendible Array." International Journal of Data Warehousing and Mining 2, no. 4 (October 2006): 66–85. http://dx.doi.org/10.4018/jdwm.2006100104.

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Harris, Michael J., Jochem O. Struppe, Benjamin J. Wylie, Ann E. McDermott, and Lynmarie K. Thompson. "Multidimensional Solid-State Nuclear Magnetic Resonance of a Functional Multiprotein Chemoreceptor Array." Biochemistry 55, no. 26 (June 24, 2016): 3616–24. http://dx.doi.org/10.1021/acs.biochem.6b00234.

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Jiun-In Guo, Chi-Min Liu, and Chein-Wei Jen. "A novel CORDIC-based array architecture for the multidimensional discrete Hartley transform." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 42, no. 5 (May 1995): 349–55. http://dx.doi.org/10.1109/82.386175.

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Agusil, Juan Pablo, Núria Torras, Marta Duch, Jaume Esteve, Lluïsa Pérez-García, Josep Samitier, and José A. Plaza. "Highly Anisotropic Suspended Planar-Array Chips with Multidimensional Sub-Micrometric Biomolecular Patterns." Advanced Functional Materials 27, no. 13 (February 22, 2017): 1605912. http://dx.doi.org/10.1002/adfm.201605912.

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Lingenfelter, A., and D. Liu. "Multidimensional tensor array analysis of multiphase flow during a hydrodynamic ram event." Journal of Physics: Conference Series 656 (December 3, 2015): 012116. http://dx.doi.org/10.1088/1742-6596/656/1/012116.

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Hales, Riley Chad, Everett James Nelson, Gustavious P. Williams, Norman Jones, Daniel P. Ames, and J. Enoch Jones. "The Grids Python Tool for Querying Spatiotemporal Multidimensional Water Data." Water 13, no. 15 (July 29, 2021): 2066. http://dx.doi.org/10.3390/w13152066.

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Abstract:

Scientific datasets from global-scale earth science models and remote sensing instruments are becoming available at greater spatial and temporal resolutions with shorter lag times. Water data are frequently stored as multidimensional arrays, also called gridded or raster data, and span two or three spatial dimensions, the time dimension, and other dimensions which vary by the specific dataset. Water engineers and scientists need these data as inputs for models and generate data in these formats as results. A myriad of file formats and organizational conventions exist for storing these array datasets. The variety does not make the data unusable but does add considerable difficulty in using them because the structure can vary. These storage formats are largely incompatible with common geographic information system (GIS) software. This introduces additional complexity in extracting values, analyzing results, and otherwise working with multidimensional data since they are often spatial data. We present a Python package which provides a central interface for efficient access to multidimensional water data regardless of the file format. This research builds on and unifies existing file formats and software rather than suggesting entirely new alternatives. We present a summary of the code design and validate the results using common water-related datasets and software.

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Gomes, Paulo R. B., André L. F. de Almeida, João Paulo C. L. da Costa, João C. M. Mota, Daniel Valle de Lima, and Giovanni Del Galdo. "Tensor-Based Methods for Blind Spatial Signature Estimation in Multidimensional Sensor Arrays." International Journal of Antennas and Propagation 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/1615962.

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The estimation of spatial signatures and spatial frequencies is crucial for several practical applications such as radar, sonar, and wireless communications. In this paper, we propose two generalized iterative estimation algorithms to the case in which a multidimensional (R-D) sensor array is used at the receiver. The first tensor-based algorithm is anR-D blind spatial signature estimator that operates in scenarios where the source’s covariance matrix is nondiagonal and unknown. The second tensor-based algorithm is formulated for the case in which the sources are uncorrelated and exploits the dual-symmetry of the covariance tensor. Additionally, a new tensor-based formulation is proposed for anL-shaped array configuration. Simulation results show that our proposed schemes outperform the state-of-the-art matrix-based and tensor-based techniques.

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Maeda, Michiharu, Hiromi Miyajima, and Noritaka Shigei. "Parallel Learning Model and Topological Measurement for Self-Organizing Maps." Journal of Advanced Computational Intelligence and Intelligent Informatics 11, no. 3 (March 20, 2007): 327–34. http://dx.doi.org/10.20965/jaciii.2007.p0327.

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The parallel learning model we propose for self-organizing maps (SOMs) uses reference vectors for simultaneously given multiple input and introduces a topological measurement of ordering for reference vectors in a multidimensional array. We term the parallel SOM algorithm parallel learning and the criterion of ordering the twist index. Parallel learning simultaneously updates reference vectors corresponding to individual input when multiple input is prepared. The twist index is the criterion for evaluating multidimensional ordering of the topological array for reference vectors. When the parallel degree changes for a SOM, the topology preserving map (TPM) for post-learning is evaluated using the twist index. Although adaptation generally yields different results for single and multiple input given at each step in neural networks, parallel learning in SOMs produces results almost the same as sequential learning. Discussing the formation rate of TPMs and average distortion, we examine the effectiveness of our approach through numerical experiments.

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Liu, Haicheng, Peter van Oosterom, Chengfang Hu, and Wen Wang. "Managing Large Multidimensional Array Hydrologic Datasets: A Case Study Comparing NetCDF and SciDB." Procedia Engineering 154 (2016): 207–14. http://dx.doi.org/10.1016/j.proeng.2016.07.449.

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Kosaka, Hideo, Mikihiro Kajita, and Yoshimasa Sugimoto. "Multidimensional VCSEL-array push/pull module fabricated using the self-alignment mounting technique." IEEE Transactions on Components, Packaging, and Manufacturing Technology: Part B 21, no. 4 (November 1998): 471–78. http://dx.doi.org/10.1109/tcpmb.1998.730433.

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