Multidimensional Arrays Research Articles

Considerations of an efficiency-intelligent geo-localised mobile application for personalised SME market predictions

The few applications used by Small and Medium Scale Enterprises (SMEs’) businesses lack efficiency and the appropriate intelligence to save them from price instability, inventory carrying costs, excess inventory, wrong decision making, inaccurate monitoring of stock levels, etc. through predictive analytics. The study explored various Artificial Intelligence Machine Learning (AI/ML) models and data structure array types that could be used with the day-to-day local weather conditions of low and high temperatures to predict market parameters and aid SMEs with predictive data to use for combating wrong decision-making, inaccurate business monitoring and excess inventory, etc. Among the ML models explored included sequential minimal optimisation, iterative reweighted least-squares, Fan-Chen-Lin support vector regression, linear regression newton method and multivariate linear regression Ordinary least squares for a multivariate linear regression and logistic regression. The models were compiled using visual C# and Accord.Net libraries. Multivariate linear regression Ordinary least squares models recorded the least predictive accuracy loss, for the test quantity prediction test samples, and varying acceptable square loss values, for usage in geo-localised mobile intelligent systems for SME predictions due to their favourable scores. The jagged array overall performed better than the multi-dimensional array on some time and space complexity tests. This work is contributing to the body of knowledge by evaluatively suggesting better data structures and ML models for building intelligent systems in Xamarin forms using C# and small data for the model training for applications in mobile phone systems that will aid SMEs’ in adjusting spending and sales targets.

SERS as a Probe of Surface Chemistry Enabled by Surface-Accessible Plasmonic Nanomaterials.

ConspectusWhen the size of materials is reduced, their volume decreases much faster than their surface area, which in the most extreme case leads to 2D nanomaterials which are "all surface". Since atoms at the surface have free energies, electronic states, and mobility which are very different from bulk atoms, nanomaterials that have large surface-to-volume ratios can display remarkable new properties compared to their bulk counterparts. More generally, the surface is where nanomaterials interact with their environment, which in turn places surface chemistry at the heart of catalysis, nanotechnology, and sensing applications. Understanding and utilizing nanosurfaces are not possible without appropriate spectroscopic and microscopic characterization techniques. An emerging technique in this area is surface-enhanced Raman spectroscopy (SERS), which utilizes the interaction between plasmonic nanoparticles and light to enhance the Raman signals of molecules near the nanoparticles' surfaces. SERS has the great advantage that it can provide detailed in situ information on surface orientation and binding between molecules and the nanosurface. A long-standing dilemma that has limited the applications of SERS in surface chemistry studies is the choice between surface-accessibility and plasmonic activity. More specifically, the synthesis of metal nanomaterials with strong plasmonic and SERS-enhancing properties typically involves the use of strongly adsorbing modifier molecules, but these modifiers also passivate the surface of the product material, which prevents the general application of SERS in the analysis of weaker molecule-metal interactions.In this Account, we discuss our efforts in the development of modifier-free synthetic approaches to synthesize surface-accessible, plasmonic nanomaterials for SERS. We start by discussing the definition of "modifiers" and "surface-accessibility", especially in the context of surface chemistry studies in SERS. As a general rule of thumb, the chemical ligands on surface-accessible nanomaterials should be easily displaceable by a wide range of target molecules relevant to potential applications. We then introduce modifier-free approaches for the bottom-up synthesis of colloidal nanoparticles, which are the basic building blocks for nanotechnology. Following this, we introduce modifier-free interfacial self-assembly approaches developed by our group that allow the creation of multidimensional plasmonic nanoparticle arrays from different types of nanoparticle-building blocks. These multidimensional arrays can be further combined with different types of functional materials to form surface-accessible multifunctional hybrid plasmonic materials. Finally, we demonstrate applications for surface-accessible nanomaterials as plasmonic substrates for SERS studies of surface chemistry. Importantly, our studies revealed that the removal of modifiers led to not only significantly enhanced properties but also the observation of new surface chemistry phenomena that had been previously overlooked or misunderstood in the literature. Realizing the current limitations of modifier-based approaches provides new perspectives in manipulating molecule-metal interactions in nanotechnology and can have significant implications in the design and synthesis of the next generation of nanomaterials.

Determining Body Condition of Dairy Cows for Early Diagnosis of Physiological Diseases

The paper points out the problem with automated diagnostics of body condition in dairy cattle, including ketosis. The conducted research is aimed at determining the possibility for non-contact automated diagnostics of the cattle physiological state on a daily basis. (Research purpose) To develop an algorithm for complex operational diagnostics of the physiological state of dairy cows by their live weight and body condition. (Materials and methods) Field data were collected in 2021-2022 on the FSUE Grigoryevskoye (Yaroslavl Region), Istra Cheese Factory and Lenin Dairy State Farm (Moscow Region). A commercial 3D ToF (Time-of-Flight) camera O3D303 was used. The 3D camera is capable of calculating and displaying the Point Cloud space as a multidimensional array. The program received 144 images, 136 images passed the filtering stage, 6 images did not detect the areas of interest, because of the high level of image noise, and the sacrum was not detected. 62 cows were subject to research. (Results and discussion) The sample and the dependence are proved to be representative as the Pearson correlation coefficient equals R=0.849, which shows a strong linear relationship between the body condition score and live weight. It was determined that in 24 percent of cases the body condition score is less than the least normal one. An algorithm was developed to help veterinarians to detect the animals that need additional examination. (Conclusions) It was found that the developed algorithm helps to quickly detect ketosis in dairy cows and automatically diagnose physiological diseases at an early stage, without additional labor and monetary costs.

Поиск предикторов токсичности иммунотерапии при помощи дискриминантного анализа

Immune-mediated adverse events in therapy with checkpoint inhibitors can be severe and even fatal. The identification of indicators that will allow predicting the toxicity of immunotherapy is an urgent task. In this work, an attempt was made to determine the predictors of immunotherapy toxicity using the discriminant analysis method. The meaning of discriminant analysis is to convert a multidimensional array into a one-dimensional indicator based on training samples to predict whether observations belong to groups. After the calculations were made by the program, 2 out of 7 analyzed indicators were selected: CPS and the number of lymphocytes before the start of therapy. Both independent indicators included in the prognostic model are directly related to the value of the discriminant function: an increase in both CPS values and the number of lymphocytes leads to an increase in the likelihood of autoimmune manifestations. The sensitivity of the model was 100%, the specificity was 75%. Based on the constructed model, it is possible to create a calculator that allows predicting the risk of developing immune-mediated complications in a particular patient, according to his laboratory data.

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits such as one- and two-dimensional Su-Schrieffer-Heeger circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite $LC$ circuits. Through the method of images, we study how resonance modes in a multidimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally reduced expressions for the impedance in three dimensions and above.

SIGEST

The SIGEST article in this issue is “Nonlinear Perron--Frobenius Theorems for Nonnegative Tensors,” by Antoine Gautier, Francesco Tudisco, and Matthias Hein. Most computational and applied mathematicians will be aware of the results that Perron published in 1907 about the eigensystems of positive matrices, which were then extended by Frobenius in 1912 to the case of nonnegative matrices. This theory has impacted many areas of mathematics, including graph theory, Markov chains, and matrix computation, and it forms a fundamental component in the analysis of a range of models in areas such as demography, economics, wireless networking, and search engine optimization. Our SIGEST article, which first appeared in SIAM Journal on Matrix Analysis and Applications in 2019, extends Perron--Frobenius theory in two directions. First, the authors generalize from matrices to multidimensional arrays. This ties in with one of SIAM Review's most highly cited offerings: •Tensor decompositions and applications, T. G. Kolda and B. W. Bader, SIAM Review, 51 (3) (2009), pp. 455--500. It may also be viewed as extending the theory from graphs to hypergraphs---objects that are currently of much interest, as evidenced by several recent SIAM Review articles, including •Hypergraph cuts with general splitting functions, N. Veldt, A. R. Benson and J. Kleinberg, SIAM Review, 64 (3) (2022), pp. 650--685. By studying this higher-order setting, the authors open up new applications in network science, computer vision, and machine learning. The second major direction of the article is to develop and study nonlinear versions of the underlying spectral problems, and corresponding extensions of the traditional power method. This makes available new classes of iterations for which a comprehensive and satisfactory convergence theory is available. In preparing this SIGEST version, the authors have included new material. The introduction has been extended, and section 2 has been added to provide nontrivial examples of tensor eigenvalue problems in applications, including problems from computer vision and optimal transport. Moreover, subsection 4.1 includes a new nonlinear Perron--Frobenius theorem (Theorem 4.4) that builds on the previously known results in Theorems 4.2. and 4.3.

FPGA-based parallel implementation to classify Hyperspectral images by using a Convolutional Neural Network

Thanks to its richness in extractable features, Hyperspectral images (HSI) find an accelerated use in medical, industrial, agricultural, and environmental fields. In this paper, we present a wavelet-based reduction technique that creates a Hypercube containing the most significant features extracted from the original HSI and representing a multi-dimensional array that is utilized for training a Convolutional Neural Network (CNN), which is designed here to classify different types of surfaces or materials. The performance of this approach is tested and proved using two distinct datasets. Then, we compare the same approach with the PCA, a widely used reduction method. The most important contribution of this paper is the implementation of an FPGA-based parallel accelerator to train the same suggested CNN in only 10% of the computational time compared to the classical CPU-based techniques. The Microblaze will be explained and exploited here to play the role of an embedded microprocessor.

Multidimensional query processing algorithm by dimension transformation

Multidimensional query processing is an important access pattern for multidimensional scientific data. We propose an in-memory multidimensional query processing algorithm for dense data using a higher-dimensional array. We developed a new array system namely a Converted two-dimensional Array (C2A) of a multidimensional array of dimension n (n > 2) where the n dimensions are transformed into 2 dimensions. Using the C2A, we design and analyze less complex algorithms that show improve performance for data locality and cache miss rate. Therefore, improved performance for data retrieval is achieved. We demonstrate algorithms for single key and range key queries for both Traditional Multidimensional Array(TMA) and C2A. We also compare the performance of both schemes. The cost of index computation gets high when the number of dimensions increases in a TMA but the proposed C2A based algorithm shows less computation cost. The cache miss rate is also lower for in C2A based algorithm than TMA based algorithm. Theoretical and experimental results show that the performance of C2A based algorithm outperforms the TMA-based algorithms.

Photo-Activated Direct Catalytic Oxidation of Gaseous Benzene with a Cu-Connected Serial Heterojunction Array of Co3 O4 /Cux O/Foam Cu Assembled via Layer upon Layer Oxidation.

The foam copper (FCu) has been first used as a promising supporting material to prepare a photo-activated catalyst of Co3 O4 /Cux O/FCu, in which the fine Co3 O4 particles are inlayed on the Cux O nanowires to form a Z-type heterojunction array connected by substrate Cu. The prepared samples have been used as a photo-activated catalyst to directly decompose gaseous benzene and the optimized Co3 O4 /Cux O/FCu demonstrates a 99.5% removal efficiency and 100% mineralizing rate within 15min in benzene concentration range from 350 to 4000ppm under simulate solar light irradiation. To track the reactive mechanism, a series of MOx /Cux O/FCu (M = Mn, Fe, Co, Ni, Cu, Zn) is prepared and a novel photo-activated direct catalytic oxidation route is proposed based on the comparative investigation of material properties. Moreover, the approach grew in situ via layer upon layer oxidation on FCu dedicates to the extra lasting reusability and the easy accessibility in the diverse situations. This work provides a novel strategy for the preparation of Cu connected series multidimensional heterojunction array and a promising application for the quick abatement of the high-leveled concentration gaseous benzene and its derivatives from the industrial discharged flow or the accident scene's leakage.

Scalar Measures of Volatility and Dependence for the Multivariate Models with Applications to Asian Financial Markets

The variance–covariance matrix is a multi-dimensional array of numbers, containing information about the individual variabilities and the pairwise linear dependence of a set of variables. However, the matrix itself is difficult to represent in a concise way, particularly in the context of multivariate autoregressive conditional heteroskedastic models. The common practice is to report the plots of k(k−1)/2 time-varying pairwise conditional covariances, where k is the number of markets (or assets) considered; thus, when k=10, there will be 45 graphs. We suggest a scalar measure of overall variabilities (and dependences) by summarizing all the elements in a variance–covariance matrix into a single quantity. The determinant of the covariance matrix Σ, called the generalized variance, can be used as a measure of overall spread of the multivariate distribution. Similarly, the positive square root of the determinant |R| of the correlation matrix, called the scatter coefficient, will be a measure of linear independence among the random variables, while collective correlation+(1−|R|)1/2 will be an overall measure of linear dependence. In an empirical application to the six Asian market returns, these statistics perform the intended roles successfully. In addition, these are shown to be able to reveal and explain the empirical facts that cannot be uncovered by the traditional methods. In particular, we show that both the contagion and interdependence (among the national equity markets) are present and could be quantitatively measured in contrast to previous studies, which revealed only market interdependence.

Commodity market profiling methodology

The article considers the methodology of commodity markets research, which includes the assessment of the volume and structure of supply and demand according to a wide range of indicators. The information on formation of system representations of markets on the basis of segmentation of markets, marketing profiling of markets and their clients is generalized. The market profiling approach is discussed in depth. This approach consists in the representation of the market as a multidimensional array of data on the type of goods, price ranges, the distribution of buyers and sellers by region, industry and other characteristics on the basis of available reliable, but incomplete data. The article considers the problem of obtaining reliable data to determine their reliable sources and organization of data collection in the framework of consulting services. The relevance of the task of forming the correct sample for consulting markets research, which provides in conjunction with data from public sources, a representative representation of the commodity market. Specific features of commodity markets, which causes the variability of approaches to the market dependence on imports, the share of direct deliveries, transport channels of supply and other factors have been considered; features of profiling in the express-analysis of commodity markets have been determined. As an example of practical realization of commodity markets profiling methodology, the market of hot-rolled stainless steel sheets with thickness of 2.0–13.0 mm and width up to 1600 mm is considered. This market is characterized by high import dependence and, therefore, the Federal Customs Service database was used as a source of information for it. Market profiling, performed in accordance with the proposed methodology, provided detailed information on the distribution of imports and consumption of individual groups of stainless steel sheets. Estimates of the commodity market obtained as a result of the study using market profiling have been verified by independent consulting studies.

Mean Convergence and Weak Laws of Large Numbers for Multidimensional Arrays of Random Elements

Mean Convergence and Weak Laws of Large Numbers for Multidimensional Arrays of Random Elements

КРИТЕРІАЛЬНІ ПОКАЗНИКИ ЯКОСТІ ОБРОБКИ МУЛЬТИСЕНСОРНОЇ ІНФОРМАЦІЇ В УМОВАХ ДЕСТАБІЛІЗУЮЧИХ ВПЛИВІВ

The approach to determining the criterion indicators of the quality of digital information processing in the multi-sensor information-controlled system of the car under the influence of destabilizing factors is considered. It was established that the process of processing information that enters the information-controlled system in digital form from various sensors involves the calculation of discrete convolutions of matrices of relevant operators and arrays of initial data. This process includes procedures for forming an array of responses to the observed information flow, an array of responses to the restored (restored) information flow, and forming conditions for restoration (restoration) of the observed information flow. The approach to assessing the quality of digital information processing in terms of determining subjective and objective assessments and methods of obtaining them is analyzed. The basis of these methods is the procedure of direct inversion of the estimated correlation matrix of random realizations of the observed multidimensional information process. Systems with an inverse operator for processing a multidimensional information array are quite sensitive to destabilizing influences: to random perturbations of the coefficients of the recovery (processing) operator and internal noise of the system along with internal system perturbations. The need to take into account destabilizing influences in the process of processing digital information in the car's information-controlled system necessitates the development of a general methodology for studying the influence of destabilizing factors on the quality of image processing. Based on the application of inverse synthesis methods, analytical expressions for criterion quality indicators of digital image processing are proposed, which are not limited to the upper limit of quality assessment and allow analytical evaluation and quantitative determination of the quality level of discrete images restored by direct inversion at the stage of system synthesis. Keywords: car, information-controlled system, image, restoration, restoration operator, criterion indicators, multisensory information, quality of information processing. internal noise, destabilizing factors.

Static and Streaming Tucker Decomposition for Dense Tensors

Given a dense tensor, how can we efficiently discover hidden relations and patterns in static and online streaming settings? Tucker decomposition is a fundamental tool to analyze multidimensional arrays in the form of tensors. However, existing Tucker decomposition methods in both static and online streaming settings have limitations of efficiency since they directly deal with large dense tensors for the result of Tucker decomposition. In a static setting, although few static methods have tried to reduce their time cost by sampling tensors, sketching tensors, and efficient matrix operations, there remains a need for an efficient method. Moreover, streaming versions of Tucker decomposition are still time-consuming to deal with newly arrived tensors. We propose D-Tucker and D-TuckerO, efficient Tucker decomposition methods for large dense tensors in static and online streaming settings, respectively. By decomposing a given large dense tensor with randomized singular value decomposition, avoiding the reconstruction from SVD results, and carefully determining the order of operations, D-Tucker and D-TuckerO efficiently obtain factor matrices and core tensor. Experimental results show that D-Tucker achieves up to 38.4 × faster running times, and requires up to 17.2 × less space than existing methods while having similar accuracy. Furthermore, D-TuckerO is up to 6.1× faster than existing streaming methods for each newly arrived tensor while its running time is proportional to the size of the newly arrived tensor, not the accumulated tensor.

Non-negative low-rank approximations for multi-dimensional arrays on statistical manifold

Although low-rank approximation of multi-dimensional arrays has been widely discussed in linear algebra, its statistical properties remain unclear. In this paper, we use information geometry to uncover a statistical picture of non-negative low-rank approximations. First, we treat each input array as a probability distribution using a log-linear model on a poset, where a structure of an input array is realized as a partial order. We then describe the low-rank condition of arrays as constraints on parameters of the model and formulate the low-rank approximation as a projection onto a subspace that satisfies such constraints, where parameters correspond to coordinate systems of a statistical manifold. Second, based on information-geometric analysis of low-rank approximation, we point out the unexpected relationship between the rank-1 non-negative low-rank approximation and mean-field approximation, a well-established method in physics that uses a one-body problem to approximate a many-body problem. Third, our theoretical discussion leads to a novel optimization method of non-negative low-rank approximation, called Legendre Tucker rank reduction. Because the proposed method does not use the gradient method, it does not require tuning parameters such as initial position, learning rate, and stopping criteria. In addition, the flexibility of the log-linear model enables us to treat the problem of non-negative multiple matrix factorization (NMMF), a variant of low-rank approximation with shared factors. We find the best rank-1 NMMF formula as a closed form and develop a rapid rank-1 NMF method for arrays with missing entries based on the closed form, called A1GM.

Sepsis heterogeneity.

Sepsis is a life-threatening organ dysfunction caused by a dysregulated host response to infection, with extremely high mortality. Notably, sepsis is a heterogeneous syndrome characterized by a vast, multidimensional array of clinical and biologic features, which has hindered advances in the therapeutic field beyond the current standards. We used PubMed to search the subject-related medical literature by searching for the following single and/or combination keywords: sepsis, heterogeneity, personalized treatment, host response, infection, epidemiology, mortality, incidence, age, children, sex, comorbidities, gene susceptibility, infection sites, bacteria, fungi, virus, host response, organ dysfunction and management. We found that host factors (age, biological sex, comorbidities, and genetics), infection etiology, host response dysregulation and multiple organ dysfunctions can all result in different disease manifestations, progression, and response to treatment, which make it difficult to effectively treat and manage sepsis patients. Herein, we have summarized contributing factors to sepsis heterogeneity, including host factors, infection etiology, host response dysregulation, and multiple organ dysfunctions, from the key elements of pathogenesis of sepsis. An in-depth understanding of the factors that contribute to the heterogeneity of sepsis will help clinicians understand the complexity of sepsis and enable researchers to conduct more personalized clinical studies for homogenous patients.

Tensor Factorization and Attention-Based CNN-LSTM Deep-Learning Architecture for Improved Classification of Missing Physiological Sensors Data

One of the essential issues for efficient control of prosthesis is the accurate classification of target movements hidden in electroencephalography (EEG) and electromyography (EMG) signals. However, in the presence of missing data in acquired signals, the classification accuracy degrades significantly as the amount of missing data increases, reducing the control performance of the prosthesis. This research proposes a framework based on tensor (multidimensional array) factorization and attention-based convolutional neural network (CNN)-long short-term memory (LSTM) deep learning (DL) for recovering missing data and performing classification of target movements, respectively. To recover missing data in tensor factorization, Canonical/Polyadic Weighted OPTimization (CP-WOPT) is employed, and its performance is compared to state-of-the-art factorization methods, whereas the performance of CNN-LSTM-attention layer (Attn) is compared to state-of-the-art machine learning and DL classifiers. Results show that CNN-LSTM-Attn obtained the mean classification accuracy of 98%, 83%, and 90% on complete (0% missing data), partially complete (10% to 50% missing data), and tensor-recovered real-world EEG and EMG data, respectively, demonstrating the applicability of the proposed framework.

Eigenproblem of tensors - a geometrical viewpoint

The classical eigenproblem focuses on eigenvalues and eigenvectors of linear operators acting on a vector space. The matrix representation of the problem has been extended towards multidimensional arrays, with various applications. Another extension addresses invariant subspaces of multilinear operators in Banach spaces. The generalization of the eigenproblem for tensors is still a challenging issue. We investigate eigenproblems of supersymmetric tensors on Riemannian manifolds, emerging from the initial proper definitions, with the proposed extensions.

Methods of Dimensions Reduction in Text Processing Algorithms

Paper describes methods of dimensionality reduction widely used in artificial intelligence in general, and in computer linguistics in particular, such as Non-negative matrix factorization and Singular value decomposition from the point of use in methods of Latent Semantic Analysis and Method of Principal Components. Advantages and disadvantages of each method are given. The computational complexity was investigated and a comparison of performance on dense and sparse matrices of different sizes was made. It is proposed to use them to reduce the dimensionality also of multidimensional linguistic data arrays.

Decomposed CNN for Sub-Nyquist Tensor-Based 2-D DOA Estimation

Direction-of-arrival (DOA) estimation using sub-Nyquist tensor signals benefits from enhanced performance by extracting structural angular information with multi-dimensional sparse arrays. Although convolutional neural network (CNN) has been employed to achieve efficient DOA estimation in challenging conditions, conventional methods demand excessive memory storage and computation power to process sub-Nyquist tensor statistics. In this letter, we propose a decomposed CNN for sub-Nyquist tensor-based 2-D DOA estimation, where an augmented coarray tensor is derived and used as the network input. To compress convolution kernels for efficient coarray tensor propagation, we develop a convolution kernel decomposition approach. This enables the acquisition of canonical polyadic (CP) factors containing compressed parameters. Performing decomposable convolution between the coarray tensor and the CP factors leads to resource-efficient DOA estimation. Our simulation results indicate that the proposed method conserves system resources while maintaining competitive performance.