Multidimensional Arrays Research Articles

Multi-dimensional and large-sized optical phased array for space laser communication

In this study, we propose a novel multi-dimensional and large-sized optical phased array theory for space laser communication that addresses the theoretical limitations of the conventional optical phased array. We theoretically analyzed the principle of this phased array technology. The results of simulation and laboratory experiment clearly showed it can realize the large scanning angle and high optical gain required for communication. The novel optical phased array theory is of great significance to the revolution of miniaturization and networking in the field of space laser communication.

Bayesian Dynamic Tensor Regression

High- and multi-dimensional array data are becoming increasingly available. They admit a natural representation as tensors and call for appropriate statistical tools. We propose a new linear autoregressive tensor process (ART) for tensor-valued data, that encompasses some well-known time series models as special cases. We study its properties and derive the associated impulse response function. We exploit the PARAFAC low-rank decomposition for providing a parsimonious parameterization and develop a Bayesian inference allowing for shrinking effects. We apply the ART model to time series of multilayer networks and study the propagation of shocks across nodes, layers and time.

Особенности разработки программных продуктов с использованием массивов в объектно-ориентированной среде

The features of software development using static and dynamic arrays in the C ++ Builder object-oriented environment are considered. The syntax of various options for creating static and dynamic arrays in the C ++ Builder language is considered in detail. Examples of working with static and dynamic arrays in C ++ Builder developed by the authors and the corresponding algorithms are presented in the form of block diagrams, program codes and program interfaces. Examples of program development are given using one-dimensional and multidimensional arrays. Examples of memory allocation are given for dynamic arrays. The choice of the required method for solving the problem is substantiated, taking into account the available input data and taking into account the expected results, as well as the peculiarities of their obtaining and processing. The external specification and the main features of the solution of the assigned tasks are considered. The development of algorithms and programs for solving problems using arrays in the C ++ Builder environment is the basis for solving engineering and technical problems using software on a computer. The proposed approaches can be used in practice, since the algorithms outlined in the work will serve as a complex example in solving the set engineering and technical problems.

A general framework for tensor screening through smoothing

Screening is an important technique for analyzing high-dimensional data. Most screening tools have been developed for vectors and are marginal in the sense that each variable is evaluated individually at a time. Many multi-dimensional arrays (tensors) are generated nowadays. In addition to being high-dimensional, these data further have the tensor structure that should be exploited for more efficient analysis. Variables adjacent to each other in a tensor tend to be important or unimportant at the same time. Such information is ignored by marginal screening methods. In this article, we propose a general framework for tensor screening called smoothed tensor screening (STS). STS combines the strength of current marginal screening methods with tensor structural information by aggregating the information of its adjacent variables when evaluating one variable. STS is widely applicable since the statistical utility used in screening can be chosen based on the underlying model or data type of the responses and predictors. Moreover, we establish the SURE screening property for STS under mild conditions. Numerical studies demonstrate that STS has better performance than marginal screening methods.

Trainable Subspaces for Low Rank Tensor Completion: Model and Analysis

With the help of auxiliary data, tensor completion may better recover a low rank multidimensional array from limited observation entries. Most existing methods, including coupled matrix-tensor factorization and coupled tensor rank minimization, mainly focus on how to extract and incorporate subspace or directly use auxiliary data for tensor completion. They are either sensitive to a given rank or lack of physical interpretations of subspace information. In addition, the shared subspace information receives little attention in current tensor completion methods, especially there is no analysis of its impact on sample complexity. In this paper, we propose to extract shared subspace information from auxiliary data and incorporate the learned subspace for tensor completion. Specifically, dictionary learning is employed to get the useful subspace from auxiliary data in the first step. Then an optimization model for low rank tensor completion incorporates the learned subspace by assuming that the recovered tensor is composed of two low rank components, where one shares the subspace information with auxiliary data and the other is outside the shared space. Based on this optimization model, we make a quantitative analysis to illustrate the effect of subspace information on sample complexity, and provide theoretical insights into the usefulness of subspace information. Finally, experiments on simulated data are conducted to validate the theoretical analysis on the impact of subspace information. Experiments in two real-world applications including color image and multispectral image recovery show that the proposed method outperforms state-of-the-art ones in terms of prediction accuracy and CPU time.

3-D Array Image Data Completion by Tensor Decomposition and Nonconvex Regularization Approach

Various image datasets appear naturally in the form of multi-dimensional arrays (hypermatrices), called tensors. Image with incomplete entries, which often can be formulated as the low-rank tensor completion problem, is practically important in order to process large size 3D array images both efficiently and effectively. To make the low-rank approximation being tractable, most current approaches make use of the lower convex envelope of tensor multi-rank function for the approximation. Due to the gap between the rank function and its lower convex envelope, the adoption of tensor nuclear norm may lead to the approximation of the corresponding tensor tubal-rank being insufficient. In this paper, we introduce a new nonconvex regularization approach, which can better capture the low-rank characteristics than the convex approach. By transforming the original problem to the Fourier domain, we formulate an equivalent optimization problem with more transparent tensor rank characteristics, whose explicit solution can be obtained under our framework. A minimization algorithm, associated with the augmented Lagrangian multipliers and the nonconvex regularizer, is established and is shown to be feasible. The constructed sequence converges to the desirable Karush-Kuhn-Tucker point, which is mathematically validated in detail. Extensive experimental results demonstrate that our proposed approach outperforms the existing state-of-the-art convex approaches consistently.

Theoretical Foundations of an Algorithm of Visualization of a Set of Points of a Multidimensional Space for Use in Anthropotechnical Decision Support Systems

Active usage of data collections by experts and decision makers tasked with preparing decision alternatives is an essential characteristic of effectiveness of an anthropotechnic system. In many cases such data analysis may require a standalone visual analysis that implies projection of a multidimensional array of data onto a lower-dimensional space. The article below presents the results of developing the theoretical foundation of such algorithm that is oriented towards an interactive analysis procedure.

Multi-Dimensional Data Compression and Query Processing in Array Databases

In recent times, the production of multidimensional data in various domains and their storage in array databases has witnessed a sharp increase; this rapid growth in data volumes necessitates compression in array databases. However, existing compression schemes used in array databases are general-purpose and not designed specifically for the databases. They could degrade query performance with complex analytical tasks, which incur huge computing costs. Thus, a compression scheme that considers the workflow of array databases is required. This study presents a compression scheme, SEACOW, for storing and querying multidimensional array data. The scheme is specially designed to be efficient for both dimension-based and value-based exploration. It considers data access patterns for exploration queries and embeds a synopsis, which can be utilized as an index, in the compressed array. In addition, we implement an array storage system, namely MSDB, to perform experiments. We evaluate query performance on real scientific datasets and compared it with those of existing compression schemes. Finally, our experiments demonstrate that SEACOW provides high compression rates compared to existing compression schemes, and the synopsis improves analytical query processing performance.

Adaptive Protection Scheme for FREEDM Microgrid Based on Convolutional Neural Network and Gorilla Troops Optimization Technique

Microgrids (MGs) suffer from unpredictable faults on the feeders for various random reasons. These faults could obstruct the stability of the MG operation and damage the components. Moreover, many uncertainties elements affect the MG’s response to faults, such as faults’ types and locations and resistances, MG operation modes, DG penetration levels, load variations, and system topologies. Therefore, fault detection, classification, and location are vital for the MGs as they provide rapid restoration and protect the components. This paper proposes an adaptive protection (AP) scheme for the future renewable electric energy delivery and management (FREEDM) system. The proposed scheme is based on the convolution neural network (CNN), in which the measured current and voltage at buses are processed in multidimensional arrays for the images’ identification and classification. The gorilla troops optimization (GTO) technique has been used to improve the CNN by acquiring the optimal architecture and hyperparameters of the proposed CNN. The proposed protection scheme can detect the system fault, classify the fault type, and determine the fault location using three proposed CNN-GTO protection scheme models. A communication channel has been performed to transfer the data, information, and tripping signals between the different devices in the FREEDM system. The proposed method is tested using a hypothetical FREEDM microgrid system under different fault conditions. The results show that the proposed CNN-GTO models can detect, classify, and location feeder faults in the FREEDM system with high accuracy. A comparison with the existing schemes such as Support vector machine, Fuzzy logic, conventional CNN, and wavelet-based CNN is performed. The optimized CNN-based GTO models can achieve an overall accuracy for fault detection, classification, and location of 99.37, 99, and 98.2%, respectively.

КОНТРОЛЬ ЦЕЛОСТНОСТИ ДАННЫХ НА ОСНОВЕ ПРАВИЛ ПОСТРОЕНИЯ КОДОВ С НЕРАВНОЙ ЗАЩИТОЙ СИМВОЛОВ

Information and analytical systems for various purposes are considered, the functioning of which is based on the processing of large multidimensional arrays of information in the conditions of destructive effects of an attacker and environmental disturbances. For such operating conditions, one of the most urgent tasks is the organization of secure data storage with a limited resource of the systems under consideration, ensuring the identity of the data from the operator who sent them for storage and from the decision-maker when requesting their use. A subsystem of data integrity control based on the use of redundant coding is proposed, in which the data to be protected is presented in the form of blocks, pre-grouped according to the criterion of “information value” to ensure the possibility of timeliness and correctness of a decision by the user of the system. The use of redundant coding in the developed subsystem is based on the rules for constructing codes with unequal character protection, which makes it possible to reduce the introduced redundancy of control information at given different levels of security of groups of data blocks processed in information and analytical systems.

Searching Monotone Arrays: A Survey

Given a monotone ordered multi-dimensional real array A and a real value k, an important question in computation is to establish if k is a member of A by sequentially searching A by comparing k with some of its entries. This search problem and its known results are surveyed, including the case when A has sizes not necessarily equal. Worst case search algorithms for various types of arrays of finite dimension and sizes are reported. Each algorithm has order strictly less than the product of the sizes of the array. Present challenges and open problems in the area are also presented.

Towards virtual modelling environments for functional–structural plant models based on Jupyter notebooks: application to the modelling of mango tree growth and development

Abstract Functional–structural plant models (FSPMs) are powerful tools to explore the complex interplays between plant growth, underlying physiological processes and the environment. Various modelling platforms dedicated to FSPMs have been developed with limited support for collaborative and distributed model design, reproducibility and dissemination. With the objective to alleviate these problems, we used the Jupyter project, an open-source computational notebook ecosystem, to create virtual modelling environments for plant models. These environments combined Python scientific modules, L-systems formalism, multidimensional arrays and 3D plant architecture visualization in Jupyter notebooks. As a case study, we present an application of such an environment by reimplementing V-Mango, a model of mango tree development and fruit production built on interrelated processes of architectural development and fruit growth that are affected by temporal, structural and environmental factors. This new implementation increased model modularity, with modules representing single processes and the workflows between them. The model modularity allowed us to run simulations for a subset of processes only, on simulated or empirical architectures. The exploration of carbohydrate source–sink relationships on a measured mango branch architecture illustrates this possibility. We also proposed solutions for visualization, distant distributed computation and parallel simulations of several independent mango trees during a growing season. The development of models on locations far from computational resources makes collaborative and distributed model design and implementation possible, and demonstrates the usefulness and efficiency of a customizable virtual modelling environment.

Theoretical Framework for Determination of Linear Structures in Multidimensional Geodynamic Data Arrays

The article addresses the issue of clustering of multidimensional data arrays with a noise using the methods of discrete mathematical analysis (DMA clustering). The theory of DMA clustering through the logical densities calculus is detailed, and the new algorithm Linear Discrete Perfect Sets (LDPS) is described. The main objective of the LDPS algorithm is to identify linearly stretched anomalies in a multidimensional array of geo-spatial data (geophysical fields, geochemistry, satellite images, local topography, maps of recent crustal movements, seismic monitoring data, etc.). These types of anomalies are associated with tectonic structures in the upper part of the Earth’s crust and pose the biggest threat for integrity of the isolation properties of the geological environment, including in regions of high-level radioactive waste disposal. The main advantage of the LDPS algorithm as compared to other cluster analysis algorithms that may be used in arrays with a noise is that it is more focused on searching for clusters that are linear. The LDPS algorithm can apply not only in the analysis of spatial natural objects and fields but also to elongated lineament structures.

Bayesian Tensor Response Regression with an Application to Brain Activation Studies

This article proposes a novel Bayesian implementation of regression with multi-dimensional array (tensor) response on scalar covariates. The recent emergence of complex datasets in various disciplines presents a pressing need to devise regression models with a tensor valued response. This article considers one such application of detecting neuronal activation in fMRI experiments in presence of tensor valued brain images and scalar predictors. The overarching goal in this application is to identify spatial regions (voxels) of a brain activated by an external stimulus. In such and related applications, we propose to regress responses from all cells (or voxels in brain activation studies) together as a tensor response on scalar predictors, accounting for the structural information inherent in the tensor response. To estimate model parameters with proper cell specific shrinkage, we propose a novel multiway stick breaking shrinkage prior distribution on tensor structured regression coefficients, enabling identification of cells which are related to the predictors. The major novelty of this article lies in the theoretical study of the contraction properties for the proposed shrinkage prior in the tensor response regression when the number of cells grows faster than the sample size. Specifically, estimates of tensor regression coefficients are shown to be asymptotically concentrated around the true sparse tensor in L2-sense under mild assumptions. Various simulation studies and analysis of a brain activation data empirically verify desirable performance of the proposed model in terms of estimation and inference on cell-level parameters.

Semiconductor metal oxide sensor for hydrogen sulphide operating under non-stationary temperature conditions

The aim of the work was to create a selective gas sensor for hydrogen sulphide. As a result of adding ammonia to the zinc acetate solution, centrifuging the obtained zinc hydroxide and subsequent calcination, a polydisperse zinc oxide powder with a grain size of 5–50 nm was obtained. The material was characterized using X-ray phase analysis and transmission electron microscopy. Subsequently, silver nitrate and terpeniol were added to the zinc oxide nanopowder to form a paste. The gas-sensitive material was obtained by applying the resulting paste on a special dielectric substrate and subsequent calcination, as a result of which the terpeniol burned out, and the silver nitrate turned into an oxide (the mass fraction of the silver was 3%). A non-stationary temperature mode for the operation of the sensor was selected, in which, after rapidheating of the sensor to 450 °C (2 seconds), slow (13 seconds) cooling to 100 °C occurred. Each subsequent heating-cooling cycle with a total period of 15 seconds began immediately after the end of the previous cycle. The use of an unsteady temperature mode in combination with the selection of the composition of the gas-sensitive layer made it possible to obtain a response of 200 for a hydrogen sulphide concentration of 1 ppm. Along with an increase in sensitivity, a significant increase in selectivity was also observed. The cross-sensitivity for the determination of hydrogen sulphide and other reducing gases (CO, NH3, H2) was more than three orders of magnitude. Thus, this sensor can be used to detect hydrogen sulphide even in the presence of interfering components. The use of highly selective sensors in the tasks of qualitative andquantitative analysis can significantly simplify the calibration in comparison with “electronic nose” devices. Devices based on highly selective sensors do not require the use of mathematical methods for processing multidimensional data arrays.

Application research of pulse signal physiology and pathology feature mining in the field of disease diagnosis

This experiment is based on the principle of traditional Chinese medicine (TCM) pulse diagnosis, the human pulse signal collected by the sensor is organized into a dataset, and the algorithms are designed to apply feature extraction. After denoising, smoothing and eliminating baseline drift of the photoelectric sensors pulse data of several groups of subjects, we designed three algorithms to describe the difference between the two-dimensional images of the pulse data of normal people and patients with chronic diseases. Convert the calculated feature values into multi-dimensional arrays, enter the decision tree (DT) to balance the differences in human physiological conditions, then train in the support vector machine kernel method (SVM-KM) classifier. Experimental results show that the application of these feature mining algorithms to disease detection greatly improves the reliability of TCM diagnosis.

Processing and visualization of the results of parametric numerical calculations

In modern problems of mathematical modeling in computational gas dynamics, it is increasingly necessary to implement parametric studies. In these cases, the key factors of the problem under consideration vary with the chosen step within the given ranges. Calculations of this kind can be effectively carried out by constructing a generalized computational experiment. A generalized computational experiment is a computational technology that combines the solution of mathematical modeling problems, parallel technologies, and visual analytics technologies. The results of a generalized computational experiment are multidimensional arrays, where the dimension of the arrays corresponds to the number of key factors. Processing and visual presentation of such arrays requires solving a number of separate tasks. The processing and visual presentation of the results are carried out for target functionals represented as a function of many variables. The report presents an examples of solving specific processing and visualization problems based on the implemented generalized computational experiment for 3D cone in supersonic flow.

Controlling and Restoring the Integrity of Multi-Dimensional Data Arrays through Cryptocode Constructs

Controlling and Restoring the Integrity of Multi-Dimensional Data Arrays through Cryptocode Constructs

Gap-Filling of NDVI Satellite Data Using Tucker Decomposition: Exploiting Spatio-Temporal Patterns

Remote sensing satellite images in the optical domain often contain missing or misleading data due to overcast conditions or sensor malfunctioning, concealing potentially important information. In this paper, we apply expectation maximization (EM) Tucker to NDVI satellite data from the Iberian Peninsula in order to gap-fill missing information. EM Tucker belongs to a family of tensor decomposition methods that are known to offer a number of interesting properties, including the ability to directly analyze data stored in multidimensional arrays and to explicitly exploit their multiway structure, which is lost when traditional spatial-, temporal- and spectral-based methods are used. In order to evaluate the gap-filling accuracy of EM Tucker for NDVI images, we used three data sets based on advanced very-high resolution radiometer (AVHRR) imagery over the Iberian Peninsula with artificially added missing data as well as a data set originating from the Iberian Peninsula with natural missing data. The performance of EM Tucker was compared to a simple mean imputation, a spatio-temporal hybrid method, and an iterative method based on principal component analysis (PCA). In comparison, imputation of the missing data using EM Tucker consistently yielded the most accurate results across the three simulated data sets, with levels of missing data ranging from 10 to 90%.

Some laws of large numbers for arrays of random upper semicontinuous functions

The aim of this paper is to investigate some laws of large numbers for multidimensional arrays of level-wise negatively associated and level-wise pairwise negatively dependent random upper semicontinuous functions under various settings. We also provide some Rosenthal's type and Hájek-Rényi's type maximal inequalities for multi-dimensional structure. Our results are extensions of corresponding ones in the literature.