Higher Dimensional Arrays Research Articles

Practical Screening Method for Cancer Gene Diagnosis -How to Choose Cancer and Normal Patients by four Principles

We developed a new theory of discriminant analysis (Theory1). Physicians can use it for practical medical diagnoses. Only Revised IP Optimal-LDF (RIP) obtains the minimum number of misclassification (MNM). RIP can discriminate linearly separable data (LSD) theoretically. It discriminated against 169 microarrays with two classes and found that 169 MNMs are zero and LSD. It can split high-dimensional arrays into many small LSD with less than n (patient’s number) genes that are the candidates of multivariate oncogenes. We completed a new theory of high-dimensional gene data analysis (Theory2). A 100-fold Cross-Validation (Method1) can rank all candidates for the importance of diagnosis. Thus, if physicians firstly use Theory2 as the screening method, they can start their medical studies with the correct small sizes of candidates. This paper analyzes four arrays in detail and proposes correctly choosing cancer and normal patients using four principles.

Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics.

Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.

Programming Language Selection for The Development of Deep Learning Library

Recently, deep learning has become very successful in various applications, leading to an increasing need for software tools to keep up with the rapid pace of innovation in deep learning research. As a result, we suggested the development of a software library related to deep learning that would be useful for researchers and practitioners in academia and industry for their research endeavors. The programming language is the core of deep learning library development, so this paper describes the selection stage to find the most suitable programming language for developing a deep learning library based on two criteria, including coverage on many projects and the ability to handle high-dimensional array processing. We addressed the comparison of programming languages with two approaches. First, we looked for the most demanding programming languages for AI Jobs by conducting a data-driven approach against the data gathered from several Job-Hunting Platforms. Then, we found the findings that imply Python, C++, and Java as the top three. After that, we compared the three most widely used programming languages by calculating interval time to three different programs that contain an array of exploitation processes. Based on the result of the experiments that were executed in the computer terminal, Java outperformed Python and C++ in two of the three experiments conducted with 5,4047 milliseconds faster than C++ and 231,1639 milliseconds faster than Python to run quick sort algorithm for arrays that contain 100.000 integer values.

Planar matrices and arrays of Feynman diagrams

Recently, planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of k = 3 biadjoint amplitudes. Planar collections are one-dimensional arrays of metric trees satisfying an induced planarity and compatibility condition. In this work, we introduce planar matrices of Feynman diagrams as the objects that compute k = 4 biadjoint amplitudes. These are symmetric matrices of metric trees satisfying compatibility conditions. We introduce two notions of combinatorial bootstrap techniques for finding collections from Feynman diagrams and matrices from collections. As applications of the first, we find all 693, 13 612 and 346 710 collections for (k, n) = (3, 7), (3, 8) and (3, 9), respectively. As applications of the second kind, we find all 90 608 and 30 659 424 planar matrices that compute (k, n) = (4, 8) and (4, 9) biadjoint amplitudes, respectively. As an example of the evaluation of matrices of Feynman diagrams, we present the complete form of the (4, 8) and (4, 9) biadjoint amplitudes. We also start a study of higher-dimensional arrays of Feynman diagrams, including the combinatorial version of the duality between (k, n) and (n − k, n) objects.

Retrieval of Missing Remotely Sensed Tropospheric NO2 Data Using Tensor Completion

Missing values in remotely sensed satellite data present a significant challenge for accurate analysis and interpretation of environmental data. Factors such as dead pixel values or cloud coverage can lead to significant gaps in datasets, degrading its overall quality and value. Tensor completion utilizes high-dimensional arrays known as tensors and their low-rank decompositions to recover missing values. This paper demonstrates the application and value of applying Tensor Completion to enhance remotely sensed Nitrogen-Dioxide satellite data and proposes an algorithm for its use. An efficient and accurate recovery method is proposed by leveraging relationships within the tensor and by employing suitable tensor decomposition methods. The proposed algorithm will enhance the analysis, interpretation, and utilization of satellite data. The algorithm is validated on real-world satellite datasets and its superiority demonstrated against existing alternate data recovery methods such as IDW and Kriging.

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.

Attention-Oriented Deep Multi-Task Hash Learning

Hashing has wide applications in image retrieval at large scales due to being an efficient approach to approximate nearest neighbor calculation. It can squeeze complex high-dimensional arrays via binarization while maintaining the semantic properties of the original samples. Currently, most existing hashing methods always predetermine the stable length of hash code before training the model. It is inevitable for these methods to increase the computing time, as the code length converts, caused by the task requirements changing. A single hash code fails to reflect the semantic relevance. Toward solving these issues, we put forward an attention-oriented deep multi-task hash learning (ADMTH) method, in which multiple hash codes of varying length can be simultaneously learned. Compared with the existing methods, ADMTH is one of the first attempts to apply multi-task learning theory to the deep hashing framework to generate and explore multi-length hash codes. Meanwhile, it embeds the attention mechanism in the backbone network to further extract discriminative information. We utilize two common available large-scale datasets, proving its effectiveness. The proposed method substantially improves retrieval efficiency and assures the image characterizing quality.

Coverage and Capacity of Terahertz Cellular Networks With Joint Transmission

Beamforming with high dimensional antenna arrays provides the gain needed to enable high bandwidth communication in the sub-terahertz (THz) band. The resulting narrow beams, however, come at the cost of increased sensitivity to beam alignment errors. A potential remedy to this problem is to introduce a form a macrodiversity through non-coherent joint transmission (NC-JT). We employ a stochastic geometry framework to analyze the performance of a THz network employing user-centric base station clustering and NC-JT. We derive semi-closed form lower bounds for the coverage probability and ergodic capacity experienced by a typical user in the network. Our model includes THz networks without joint transmission as a special case. Overall, our analysis indicates that joint transmission from a few base stations improves coverage and capacity by mitigating the impact of beam misalignment. Moreover, in certain settings, NC-JT is a more efficient usage a network access points compared to the non-cooperative case, and reduces the sensitivity of coverage and capacity to the choice of user beamwidth.

Prediction of contact resistance between copper blocks under cyclic load based on deep learning algorithm

This paper establishes a data-driven Neural Network (NN) framework. The contact resistance of T2 copper blocks with different roughnesses is predicted by deep learning at room temperature and cyclic loading. The contact resistance problem can be regarded as a regression problem of mapping the high-dimensional array space of multiple variables to the contact resistance. This paper measures the contact resistance of copper blocks with different surface roughnesses under loading and unloading states and obtains the original dataset required by the algorithm. The data characteristics include three surface topography parameters, number of cyclic loads, loading and unloading conditions, and load magnitude, with the data labeled contact resistance. This paper compares the results of the NN model and Holm model results to verify the NN model’s effectiveness. The comparison results show that the prediction results of the NN are consistent with the predictions of the Holm model. After training and debugging, the root mean square error of the multiple hidden layers neural network test set is 6.81%, showing a good prediction effect. In conclusion, the deep learning algorithm provides a new way for fast and accurate prediction of the relationship between T2 copper blocks and contact resistance under cyclic loading times and unloading states.

Adapting reservoir computing to solve the Schrödinger equation.

Reservoir computing is a machine learning algorithm that excels at predicting the evolution of time series, in particular, dynamical systems. Moreover, it has also shown superb performance at solving partial differential equations. In this work, we adapt this methodology to integrate the time-dependent Schrödinger equation, propagating an initial wavefunction in time. Since such wavefunctions are complex-valued high-dimensional arrays, the reservoir computing formalism needs to be extended to cope with complex-valued data. Furthermore, we propose a multi-step learning strategy that avoids overfitting the training data. We illustrate the performance of our adapted reservoir computing method by application to four standard problems in molecular vibrational dynamics.

Deep Learning Methods Capture Non-Linear Brain Aging Patterns Underlying Alzheimer’s Disease and Resilience

The current era of multi-omics data collection has enabled researchers to obtain exceptionally comprehensive profiling of disease subjects. However, exceptionally high dimensionality can ultimately be an obstacle to biological insight. Previously, we presented a method in which penalized regression of methylation principal components reduces noise and improves prediction of age, disease, and Alzheimer’s Disease (AD) pathophysiology. However, strictly linear methods may overly simplify the complex epigenetic aging landscape. We hypothesized that non-linear deep learning methods could identify molecular signatures that better reflect individual resilience to AD. Through the use of an autoencoder to represent high dimensional methylation array data, and supplemental machine learning methods, we connect latent nonlinear representations of the brain to aging, resilience, and indications of AD. In particular, resultant age-predicting representations of methylation were correlated with enrichment of methylation regions and biological pathways. Contextualized within AD pathology, this work provides valuable, ongoing insight into resilience in AD.

Integrating Audio Signal Processing and Deep Learning Algorithms for Gait Pattern Classification in Brazilian Gaited Horses

This study focused on assessing the usefulness of using audio signal processing in the gaited horse industry. A total of 196 short-time audio files (4 s) were collected from video recordings of Brazilian gaited horses. These files were converted into waveform signals (196 samples by 80,000 columns) and divided into training (N = 164) and validation (N = 32) datasets. Twelve single-valued audio features were initially extracted to summarize the training data according to the gait patterns (Marcha Batida—MB and Marcha Picada—MP). After preliminary analyses, high-dimensional arrays of the Mel Frequency Cepstral Coefficients (MFCC), Onset Strength (OS), and Tempogram (TEMP) were extracted and used as input information in the classification algorithms. A principal component analysis (PCA) was performed using the 12 single-valued features set and each audio-feature dataset—AFD (MFCC, OS, and TEMP) for prior data visualization. Machine learning (random forest, RF; support vector machine, SVM) and deep learning (multilayer perceptron neural networks, MLP; convolution neural networks, CNN) algorithms were used to classify the gait types. A five-fold cross-validation scheme with 10 repetitions was employed for assessing the models' predictive performance. The classification performance across models and AFD was also validated with independent observations. The models and AFD were compared based on the classification accuracy (ACC), specificity (SPEC), sensitivity (SEN), and area under the curve (AUC). In the logistic regression analysis, five out of the 12 audio features extracted were significant (p < 0.05) between the gait types. ACC averages ranged from 0.806 to 0.932 for MFCC, from 0.758 to 0.948 for OS and, from 0.936 to 0.968 for TEMP. Overall, the TEMP dataset provided the best classification accuracies for all models. The most suitable method for audio-based horse gait pattern classification was CNN. Both cross and independent validation schemes confirmed that high values of ACC, SPEC, SEN, and AUC are expected for yet-to-be-observed labels, except for MFCC-based models, in which clear overfitting was observed. Using audio-generated data for describing gait phenotypes in Brazilian horses is a promising approach, as the two gait patterns were correctly distinguished. The highest classification performance was achieved by combining CNN and the rhythmic-descriptive AFD.

Functional Modeling of High-Dimensional Data: A Manifold Learning Approach

This paper introduces stringing via Manifold Learning (ML-stringing), an alternative to the original stringing based on Unidimensional Scaling (UDS). Our proposal is framed within a wider class of methods that map high-dimensional observations to the infinite space of functions, allowing the use of Functional Data Analysis (FDA). Stringing handles general high-dimensional data as scrambled realizations of an unknown stochastic process. Therefore, the essential feature of the method is a rearrangement of the observed values. Motivated by the linear nature of UDS and the increasing number of applications to biosciences (e.g., functional modeling of gene expression arrays and single nucleotide polymorphisms, or the classification of neuroimages) we aim to recover more complex relations between predictors through ML. In simulation studies, it is shown that ML-stringing achieves higher-quality orderings and that, in general, this leads to improvements in the functional representation and modeling of the data. The versatility of our method is also illustrated with an application to a colon cancer study that deals with high-dimensional gene expression arrays. This paper shows that ML-stringing is a feasible alternative to the UDS-based version. Also, it opens a window to new contributions to the field of FDA and the study of high-dimensional data.

Effective Tensor Sketching via Sparsification

In this article, we investigate effective sketching schemes via sparsification for high dimensional multilinear arrays or tensors. More specifically, we propose a novel tensor sparsification algorithm that retains a subset of the entries of a tensor in a judicious way, and prove that it can attain a given level of approximation accuracy in terms of tensor spectral norm with a much smaller sample complexity when compared with existing approaches. In particular, we show that for a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> th order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {d}\times \cdots \times {d}$ </tex-math></inline-formula> cubic tensor of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stable rank</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {r}_{ {s}}$ </tex-math></inline-formula> , the sample size requirement for achieving a relative error <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> is, up to a logarithmic factor, of the order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {r}_{ {s}}^{1/2} {d}^{ {k}/2} /\varepsilon $ </tex-math></inline-formula> when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> is relatively large, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {r}_{ {s}} {d} /\varepsilon ^{2}$ </tex-math></inline-formula> and essentially optimal when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> is sufficiently small. It is especially noteworthy that the sample size requirement for achieving a high accuracy is of an order independent of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> . To further demonstrate the utility of our techniques, we also study how higher order singular value decomposition (HOSVD) of large tensors can be efficiently approximated via sparsification.

Statistical Channel Modelling of Millimetre Waves at 28 GHz and 73 GHz Frequency Signals Using MIMO Antennas

To meet the demand of high spectrum requirement and high-speed wireless communication in future, millimetre waves (mm-Wave) can play a very important role for it. Millimetre waves starting from 30 GHz and ending at 300 GHz can solve the problems like high throughput, faster data rates and capacity. Millimetre waves can help to achieve higher gain by using high dimensional antenna array technology. Beamforming and spatial multiplexing are very famous techniques that can help to increase the gain when antenna arrays are used. Channel modelling plays a very important role in determining the possibility of deploying the wireless communication system. In this research paper, the major challenges regarding the mm-Wave channel modelling are identified and the statistical behaviour of mm-Wave channel at 28GHz and 73 GHz is explained with the help of NYUSIM software. The power loss, power delay profile and path loss, angle of arrival and departure are simulated in this work. These simulations are performed using multiple antennas configuration along with considering the effect of atmospheric impairments like rain, humidity and temperature.

Robust Low-tubal-rank Tensor Recovery from Binary Measurements

Low-rank tensor recovery (LRTR) is a natural extension of low-rank matrix recovery (LRMR) to high-dimensional arrays, which aims to reconstruct an underlying tensor X from incomplete linear measurements [Formula: see text]. However, LRTR ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of [Formula: see text]. We still hope to recover X from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed-the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real n1×n2×n3 tensor X with tubal rank r from m random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor λ:=m/((n1+n2)n3r). To improve the convergence rate, we develop a new quantization scheme under which the convergence rate can be accelerated to an exponential function of λ. Numerical experiments verify our results, and the applications to real-world data demonstrate the promising performance of the proposed methods.

Technique of Gene Expression Profiles Extraction Based on the Complex Use of Clustering and Classification Methods.

In this paper, we present the results of the research concerning extraction of informative gene expression profiles from high-dimensional array of gene expressions considering the state of patients’ health using clustering method, ML-based binary classifiers and fuzzy inference system. Applying of the proposed stepwise procedure can allow us to extract the most informative genes taking into account both the subtypes of disease or state of the patient’s health for further reconstruction of gene regulatory networks based on the allocated genes and following simulation of the reconstructed models. We used the publicly available gene expressions data as the experimental ones which were obtained using DNA microarray experiments and contained two types of patients’ gene expression profiles—the patients with lung cancer tumor and healthy patients. The stepwise procedure of the data processing assumes the following steps—in the beginning, we reduce the number of genes by removing non-informative genes in terms of statistical criteria and Shannon entropy; then, we perform the stepwise hierarchical clustering of gene expression profiles at hierarchical levels from 1 to 10 using the SOTA (Self-Organizing Tree Algorithm) clustering algorithm with correlation distance metric. The quality of the obtained clustering was evaluated using the complex clustering quality criterion which is considered both the gene expression profiles distribution relative to center of the clusters where these gene expression profiles are allocated and the centers of the clusters distribution. The result of this stage execution was a selection of the optimal cluster at each of the hierarchical levels which corresponded to the minimum value of the quality criterion. At the next step, we have implemented a classification procedure of the examined objects using four well known binary classifiers—logistic regression, support-vector machine, decision trees and random forest classifier. The effectiveness of the appropriate technique was evaluated based on the use of ROC (Receiver Operating Characteristic) analysis using criteria, included as the components, the errors of both the first and the second kinds. The final decision concerning the extraction of the most informative subset of gene expression profiles was taken based on the use of the fuzzy inference system, the inputs of which are the results of the appropriate single classifiers operation and the output is the final solution concerning state of the patient’s health. To our mind, the implementation of the proposed stepwise procedure of the informative gene expression profiles extraction create the conditions for the increasing effectiveness of the further procedure of gene regulatory networks reconstruction and the following simulation of the reconstructed models considering the subtypes of the disease and/or state of the patient’s health.

Haery: A Hadoop Based Query System on Accumulative and High-Dimensional Data Model for Big Data

Column-oriented stores, known for their scalability and flexibility, are a common NoSQL database implementation and are increasingly used in big data management. In column-oriented stores, a “full-scan” query strategy is inefficient and the search space can be reduced if data is well partitioned or indexed; however, there is no pre-defined schema for building and maintaining partitions and indexes at lower cost. We leverage an accumulative and high-dimensional data model, a sophisticated linearization algorithm, and an efficient query algorithm, to solve the challenge of how a pre-defined and well-partitioned data model can be applied to flexible and time-varied key-value data. We adapt a high-dimensional array as the data model to partition the key-value data without additional storage and massive calculation; improve the Z-order linearization algorithm, which map multidimensional data to one dimension while preserving locality of the data points, for flexibility; efficiently build an expansion mechanism for the data model to support time-varied data. The result is Haery, a column-oriented store, based on a distributed file system and computing framework. In experiments, Haery is compared with Hive, HBase, Cassandra, MongoDB, PostgresXL, and HyperDex in terms of query performance. With results indicating Haery on average performs 4.57x, 4.23x, 3.55x, 1.79x, 1.82x, and 120.6x faster, respectively.

Multilingual Transformer-Based Personality Traits Estimation

Intelligent agents have the potential to understand personality traits of human beings because of their every day interaction with us. The assessment of our psychological traits is a useful tool when we require them to simulate empathy. Since the creation of social media platforms, numerous studies dealt with measuring personality traits by gathering users’ information from their social media profiles. Real world applications showed how natural language processing combined with supervised machine learning algorithms are effective in this field. These applications have some limitations such as focusing on English text only and not considering polysemy in text. In this paper, we propose a multilingual model that handles polysemy by analyzing sentences as a semantic ensemble of interconnected words. The proposed approach processes Facebook posts from the myPersonality dataset and it turns them into a high-dimensional array of features, which are then exploited by a deep neural network architecture based on transformer to perform regression. We prove the effectiveness of our work by comparing the mean squared error of our model with existing baselines and the Kullback–Leibler divergence between the relative data distributions. We obtained state-of-the-art results in personality traits estimation from social media posts for all five personality traits.

Two-Dimensional $Z$-Complementary Array Code Sets Based on Matrices of Generating Polynomials

The unprecedented elevation of wireless technologies produces the ever-increasing requirement for higher-dimensional array sets with preferable correlation properties and more flexible parameters. In this paper, we investigate new two-dimensional $Z$ -complementary array code sets (2D-ZCACSs) with unimodular arrays, which are more preferable in ultra wideband communication system to improve its performance than 2D mutually orthogonal complementary array set. We first introduce a new idea of 2D $Z$ -paraunitary (2D-ZPU) matrices by extending our previous concept of 1D-ZPU matrices. Then, we show that there exists an equivalence between a 2D-ZCACS and 2D-ZPU matrix when the former is expressed as a matrix with 2D generating polynomial entries. In the 2D generating matrix, each column corresponds to a 2D $Z$ -complementary array code and two distinct columns correspond to 2D $Z$ -complementary array mates. Finally, we propose a new construction method of unimodular 2D-ZCACSs with the aid of higher-dimensional $z$ -transforms and the theory of ZPU matrices.