Dimension Reduction Procedure Research Articles

Planar anisotropic CPT-odd systems: A field theoretical approach

The primary objective of this study is to introduce field-theoretical tools into the realm of physical properties within planar systems exhibiting possible anisotropic features. This goal is achieved by fitting a specific field-theoretical model to simulate the presence of such a system. The proposed approach enables the investigation of in-plane physical phenomena using analytic methods. Specifically, our focus is on phenomena related to stationary point-like field sources that can mimic defects in material layers. We employ a dimensional reduction procedure on the well-known Carroll–Field–Jackiw model to derive a planar theory. This theory includes an electromagnetic sector governed by Maxwell-Chern–Simons electrodynamics, a scalar sector described by a massless Klein–Gordon field, and a mixed sector where the background vector controls the interactions between the scalar and gauge fields. Across all sectors of this planar theory, we explore physical phenomena arising from interactions with external sources. Specifically, we analyze perturbative effects up to second order in the background vector, examining contributions from both electric and scalar planar charges as well as Dirac points.

Advanced Image Analytics for Mobile Robot-Based Condition Monitoring in Hazardous Environments: A Comprehensive Thermal Defect Processing Framework.

In hazardous environments like mining sites, mobile inspection robots play a crucial role in condition monitoring (CM) tasks, particularly by collecting various kinds of data, such as images. However, the sheer volume of collected image samples and existing noise pose challenges in processing and visualizing thermal anomalies. Recognizing these challenges, our study addresses the limitations of industrial big data analytics for mobile robot-generated image data. We present a novel, fully integrated approach involving a dimension reduction procedure. This includes a semantic segmentation technique utilizing the pre-trained VGG16 CNN architecture for feature selection, followed by random forest (RF) and extreme gradient boosting (XGBoost) classifiers for the prediction of the pixel class labels. We also explore unsupervised learning using the PCA-K-means method for dimension reduction and classification of unlabeled thermal defects based on anomaly severity. Our comprehensive methodology aims to efficiently handle image-based CM tasks in hazardous environments. To validate its practicality, we applied our approach in a real-world scenario, and the results confirm its robust performance in processing and visualizing thermal data collected by mobile inspection robots. This affirms the effectiveness of our methodology in enhancing the overall performance of CM processes.

(2+δ)-dimensional theory of the electromechanics of lipid membranes: Electrostatics.

The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects are relevant for many biological processes, such as the propagation of action potentials in axons and the activation of mechanically gated ion channels. Currently, a theoretical framework describing the electromechanical behavior of arbitrarily curved and deforming lipid membranes does not exist. Purely mechanical models commonly treat lipid membranes as two-dimensional surfaces, ignoring their finite thickness. While holding analytical and numerical merit, this approach cannot describe the coupling of lipid membranes to electric fields and is thus unsuitable for electromechanical models. In a sequence of articles, we derive an effective surface theory of the electromechanics of lipid membranes, called the (2+δ)-dimensional theory, which has the advantages of surface descriptions while accounting for finite thickness effects. The present article proposes a generic dimension reduction procedure relying on low-order spectral expansions. This procedure is applied to the electrostatics of lipid membranes to obtain the (2+δ)-dimensional theory that captures potential differences across and electric fields within lipid membranes. This model is tested on different geometries relevant for lipid membranes, showing good agreement with the corresponding three-dimensional electrostatics theory.

Data driven assessment of rock mass quality in red-bed hilly area: a case study of Guang’an city, SW China

The evaluation of geological suitability for urban underground space (UUS) development is an indispensable prerequisite for its optimal utilization. As the actual carrier of underground facilities, the evaluation of rock mass quality plays a crucial role in assessing geological suitability. However, it is notable that the evaluation of rock mass quality has regrettably remained somewhat marginalized within the broader framework of the geological suitability assessment in recent years. The selection of pertinent indicators for the evaluation of rock mass quality inherently presents an appreciable degree of subjectivity. Predominantly subjective evaluation methods continue to dominate the field, while the application of objective algorithms, such as unsupervised clustering, remains in its nascent stage. Furthermore, there is a lack of comprehensive investigations into distinct combinations of attributes. This limitation confines the broader applicability of the evaluation outcomes in the context of urban underground space. Within this study, we meticulously amassed rock core test data from over 40 boreholes of engineering geological significance within the urban planning ambit of Guang'An City. Utilizing the K-means unsupervised clustering algorithm and the Principal Component Analysis (PCA) algorithm. We successfully conducted an unsupervised clustering procedure with nine distinct physical and mechanical attributes. This yielded an aggregation into five discernible clusters. Building upon the derived clustering outcomes, a stratification of rock mass quality was effectuated into three distinct tiers: Level 1 (characterized by pure sandstone), Level 2 (primarily dominated by sandstone), and Level 3 (denoting fair conditions predominantly influenced by mudstone). This structured stratification facilitates a relatively objective and comprehensive evaluation of rock mass quality within the context of the red-bed hilly terrain. In the course of this analytical trajectory, we conducted a dissection of the clustering efficacy. For strongly correlated attributes, we propose a preliminary dimensionality reduction procedure prior to the clustering endeavor. Moreover, we recommend intervals of 10 m for the stratified evaluation in red bed hilly urban terrains.

Self-identified barriers to health services among migrants 50 years of age or older: population-based survey study of Russian speakers in Finland

BackgroundThe compounded effect of a migratory background and ageing increases the risk of unequal medical treatment opportunities. The aim of this article is to investigate the social determinants of barriers to health services.MethodsThe study uses population-based survey data of Russian-speaking migrants (50 + years) residing in Finland (n = 1082, 57% of men, mean age 63 years). Multiple correspondence analysis was performed as a dimension reduction procedure on six barriers to health services. Multiple ordinary least-squares linear regression was used for the predicted score of the barriers as an outcome variable.ResultsMost of the sociodemographic characteristics were not associated with barriers to health services, except gender, as women tended to face more disadvantages. Migration-related factors, such as the need for interpreters for health services and experienced discrimination, were associated with an increased likelihood of reporting barriers to health services. Using the internet as a primary source of health information was associated with more access barriers to health services.ConclusionsMigrants 50 years of age or older face multiple barriers to health services. Given that the healthcare needs increase with age, addressing this issue becomes crucial, necessitating improved access to health services for older migrants.

Sparse random hypergraphs: non-backtracking spectra and community detection

Abstract We consider the community detection problem in a sparse $q$-uniform hypergraph $G$, assuming that $G$ is generated according to the Hypergraph Stochastic Block Model (HSBM). We prove that a spectral method based on the non-backtracking operator for hypergraphs works with high probability down to the generalized Kesten–Stigum detection threshold conjectured by Angelini et al. (2015, Spectral detection on sparse hypergraphs. In: 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, pp. 66–73). We characterize the spectrum of the non-backtracking operator for the sparse HSBM and provide an efficient dimension reduction procedure using the Ihara–Bass formula for hypergraphs. As a result, community detection for the sparse HSBM on $n$ vertices can be reduced to an eigenvector problem of a $2n\times 2n$ non-normal matrix constructed from the adjacency matrix and the degree matrix of the hypergraph. To the best of our knowledge, this is the first provable and efficient spectral algorithm that achieves the conjectured threshold for HSBMs with $r$ blocks generated according to a general symmetric probability tensor.

Neuroguard:Unveiling the Strength of Lightfooted Anomaly Detection with Swift-Net Neural Networks in Countering Network Threats

In the dominion of cybersecurity, the prime tasks revolve around recognizing and moderating network breaches. This research paper impacts the widely recognized CICIDS2017 dataset to conduct a complete evaluation and comparison of numerous deep learning and machine learning representations designed for Anomaly-detection by the analysis of a diverse array of algorithms, spanning from traditional methodologies like logistic regression to more modern advances such as K-Nearest Neighbors (KNN) and state-of-the-art Swift-Net neural networks. The research also delves into the realism of employing dimensionality reduction and feature selection procedures, remarkably Principal Component Analysis (PCA) in addition with Gaussian Mixture Models (GMM). The implications of this consideration are substantial for the enhancement of network security with an emphasis of the efficiency of PCA and GMM in facilitating data visualization, enabling a deeper understanding of network behavior. Moreover, the paper highlights the potential of Swift-Net for real-time threat detection, signifying its relevance in the evolving cybersecurity environment. As the cybersecurity domain undergoes constant transformation, this research serves as a valuable reserve, paving the way for more effective Anomaly detection techniques and the employment of efficient network security solutions. These outcomes offer acute insights to reinforce network safety.

Model building by coset space dimensional reduction scheme using eight-dimensional coset spaces

We investigate the twelve-dimensional gauge-Higgs unification models with an eight- dimensional coset space as the extra space. For each model, we apply the coset space dimensional reduction procedure and examine the particle contents of the resulting four-dimensional theory. All combinations of inputs to the procedure are exhaustively analyzed under several assumptions. As a result, some twelve-dimensional SO(18) gauge theories lead to models of the SO(10) × U(1) grand unified theory in four dimensions, where fermions of the Standard Model appear in multiple generations along with scalars that may break the electroweak symmetry. The representations of the obtained scalars and fermions are summarized.

Depression, anxiety, and burnout in academia: topic modeling of PubMed abstracts

The problem of mental health in academia is increasingly discussed in literature, and to extract meaningful insights from the growing amount of scientific publications, text mining approaches are used. In this study, BERTopic, an advanced method of topic modeling, was applied to abstracts of 2,846 PubMed articles on depression, anxiety, and burnout in academia published in years 1975–2023. BERTopic is a modular technique comprising a text embedding method, a dimensionality reduction procedure, a clustering algorithm, and a weighing scheme for topic representation. A model was selected based on the proportion of outliers, the topic interpretability considerations, topic coherence and topic diversity metrics, and the inevitable subjectivity of the criteria was discussed. The selected model with 27 topics was explored and visualized. The topics evolved differently with time: research papers on students' pandemic-related anxiety and medical residents' burnout peaked in recent years, while publications on psychometric research or internet-related problems are yet to be presented more amply. The study demonstrates the use of BERTopic for analyzing literature on mental health in academia and sheds light on areas in the field to be addressed by further research.

Brain Tumor Detection and Multi Classification Using GNB-Based Machine Learning Approach

In an abnormal tissue called a brain tumor, the cells of the tumor reproduce quickly. if no control over tumor cell growth. The difficulties involved in identifying and treating brain tumors Machine learning is the most technologically sophisticated tool for classification and detection, implementing reliable state-of-the-art A.I. as well as neural network classification techniques, the use of this technology in early diagnosis detection of brain tumors can be accomplished successfully. it is well known that the segmentation method is capable of helping simply destroy the brain's abnormal tumor regions In order to segment and categorize brain tumors, this study suggests a multimodal approach involving machine learning and medical assistance. Noise can be seen in MRI images. To make the method for eliminating noise from images easier, a geometric mean is used later. The algorithms used to segment an image into smaller pieces are fuzzy c-means algorithms. Detection of a specific area of interest is made simpler by segmentation. The dimension reduction procedure is carried out using the GLCM. Photographic features are extracted using the GLCM algorithm. Then, using a variety of ML techniques, like as CNN, ANN, SVM, Gaussian NB, and Adaptive Boosting, the photos are categorized. The Gaussian NB method performs more effectively with regard to the identification and classification of brain tumors. The plasterwork work achieved 98.80 percent accuracy using GNB, RBF SVM.

The impact of ROI extraction method for MEG connectivity estimation: Practical recommendations for the study of resting state data.

Magnetoencephalography and electroencephalography (M/EEG) seed-based connectivity analysis typically requires regions of interest (ROI)-based extraction of measures. M/EEG ROI-derived source activity can be treated in different ways. For instance, it is possible to average each ROI's time series prior to calculating connectivity measures. Alternatively one can compute connectivity maps for each element of the ROI, prior to dimensionality reduction to obtain a single map. The impact of these different strategies on connectivity estimation is still unclear.Here, we address this question within a large MEG resting state cohort (N=113) and simulated data. We consider 68 ROIs (Desikan-Kiliany atlas), two measures of connectivity (phase locking value-PLV, and its imaginary counterpart- ciPLV), and three frequency bands (theta 4-8 Hz, alpha 9-12 Hz, beta 15-30 Hz). We consider four extraction methods: (i) mean, or (ii) PCA of the activity within the ROI before computing connectivity, (iii) average, or (iv) maximum connectivity after computing connectivity for each element of the seed. Connectivity outputs from these extraction strategies are then compared with hierarchical clustering, followed by direct contrasts across extraction methods. Finally, the results are validated by using a set of realistic simulations.We show that ROI-based connectivity maps vary remarkably across strategies in both connectivity magnitude and spatial distribution. Dimensionality reduction procedures conducted after computing connectivity are more similar to each-other, while PCA before approach is the most dissimilar to other approaches. Although differences across methods are consistent across frequency bands, they are influenced by the connectivity metric and ROI size. Greater differences were observed for ciPLV than PLV, and in larger ROIs. Realistic simulations confirmed that after aggregation procedures are generally more accurate but have lower specificity (higher rate of false positive connections). Although computationally demanding, after dimensionality reduction strategies should be preferred when higher sensitivity is desired. Given the remarkable differences across aggregation procedures, caution is warranted in comparing results across studies applying different extraction methods.

On the challenges of predicting treatment response in Hodgkin’s Lymphoma using transcriptomic data

BackgroundDespite the advancements in multiagent chemotherapy in the past years, up to 10% of Hodgkin’s Lymphoma (HL) cases are refractory to treatment and, after remission, patients experience an elevated risk of death from all causes. These complications are dependent on the treatment and therefore an increase in the prognostic accuracy of HL can help improve these outcomes and control treatment-related toxicity. Due to the low incidence of this cancer, there is a lack of works comprehensively assessing the predictability of treatment response, especially by resorting to machine learning (ML) advances and high-throughput technologies.MethodsWe present a methodology for predicting treatment response after two courses of Adriamycin, Bleomycin, Vinblastine and Dacarbazine (ABVD) chemotherapy, through the analysis of gene expression profiles using state-of-the-art ML algorithms. We work with expression levels of tumor samples of Classical Hodgkin’s Lymphoma patients, obtained through the NanoString’s nCounter platform. The presented approach combines dimensionality reduction procedures and hyperparameter optimization of various elected classifiers to retrieve reference predictability levels of refractory response to ABVD treatment using the regulatory profile of diagnostic tumor samples. In addition, we propose a data transformation procedure to map the original data space into a more discriminative one using biclustering, where features correspond to discriminative putative regulatory modules.ResultsThrough an ensemble of feature selection procedures, we identify a set of 14 genes highly representative of the result of an fuorodeoxyglucose Positron Emission Tomography (FDG-PET) after two courses of ABVD chemotherapy. The proposed methodology further presents an increased performance against reference levels, with the proposed space transformation yielding improvements in the majority of the tested predictive models (e.g. Decision Trees show an improvement of 20pp in both precision and recall).ConclusionsTaken together, the results reveal improvements for predicting treatment response in HL disease by resorting to sophisticated statistical and ML principles. This work further consolidates the current hypothesis on the structural difficulty of this prognostic task, showing that there is still a considerable gap to be bridged for these technologies to reach the necessary maturity for clinical practice.

Main conjectures for higher rank nearly ordinary families – I

In this article, we present the first half of our project on the Iwasawa theory of higher rank Galois deformations over deformations rings of arbitrary dimension. We develop a theory of Coleman maps for a very general class of coefficient rings, devise a dimension reduction procedure for locally restricted Euler systems and finally, put these into use in order to prove a divisibility in a 3-variable main conjecture for nearly ordinary families of Rankin-Selberg convolutions.

Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing.

Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardware-efficient ansätze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.

The electromechanics of lipid membranes: A dimensionally-reduced theory.

Lipid membranes separate the interior and exterior of a biological cell and its organelles. Their viscous-elastic material behavior gives rise to intriguing lipid membrane dynamics. However, lipid membrane dynamics are also affected by the presence of an electric field. For instance, lipid vesicles deform into prolates, oblates, and other shapes and even form pores when an electric field is applied. Furthermore, varying ionic concentrations across the boundary and within the interior of cells and organelles expose lipid membranes to electric fields in physiological conditions. Thus, understanding the electromechanics of lipid membranes is essential for many biological and experimental processes, such as the propagation of action potentials and the electroformation of lipid vesicles. Studying the electromechanics of lipid membranes on long lengths- and timescales requires a continuum physics framework. While continuum models are well-established for the pure mechanics of lipid membranes, a continuum model that captures the coupling between mechanical deformations and electric fields is currently missing. Capturing the effects of electric fields requires resolving the electric potential through the thickness of the lipid membrane. Current continuum approaches, however, treat lipid membranes as two-dimensional manifolds, making them unsuitable for describing the electromechanics of lipid membranes. Thus, we propose a new dimension reduction procedure for differential equations on thin bodies. Using this approach, we derive new surface theories for the electrostatics and mechanics of lipid membranes. Combining them, we obtain a novel continuum model for the electromechanics of lipid membranes. After discussing the new model, we apply it to a fluctuating lipid membrane in an external electric field and demonstrate the effect of accounting for the finite thickness of lipid membranes.

A co-kurtosis based dimensionality reduction method for combustion datasets

Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermo-chemical state space based on eigenvectors of co-variance of the data, could fail to capture information regarding important localized chemical dynamics, such as the formation of ignition kernels, appearing as extreme-valued samples in a dataset. In this paper, we propose an alternate dimensionality reduction procedure, co-kurtosis PCA (CoK-PCA), wherein the required principal vectors are computed from a high-order joint statistical moment, namely the co-kurtosis tensor, which may better identify directions in the state space that represent stiff dynamics. We first demonstrate the potential of the proposed CoK-PCA method using a synthetically generated dataset that is representative of typical combustion simulations. Thereafter, we characterize and contrast the accuracy of CoK-PCA against PCA for datasets representing spontaneous ignition of premixed ethylene-air in a simple homogeneous reactor and ethanol-fueled homogeneous charged compression ignition (HCCI) engine. Specifically, we compare the low-dimensional manifolds in terms of reconstruction errors of the original thermo-chemical state, and species production and heat release rates computed from the linearly reconstructed state. The latter – a comparison of species production and heat release rates – is a more rigorous assessment of the accuracy of dimensionality reduction. We find that, for the simplistic linear reconstruction, the co-kurtosis based reduced manifold represents the original thermo-chemical state more accurately than PCA, especially in the regions where chemical reactions are important.

Spectral imaging and chemometrics applied at phenotyping in seed science studies: a systematic review

AbstractThe evaluation of the genetic quality of a seed lot is crucial for the quality control process in its production and commercialization, as well as in the identification of superior genotypes and the verification of the correct crossing in plant breeding programmes. Current techniques, based on the identification of seed morphological characteristics, require skilled analysts, while biochemical methods are time-consuming and costly. The application of spectral imaging analysis, which combines digital imaging with spectroscopy, is gaining ground as a fast, accurate and non-destructive method. The success of this technique is closely linked to chemometric techniques, which use statistical and mathematical tools in data processing. The aim of the work was to evaluate the main procedures in terms of spectral image analysis and chemometric procedures applied in seed phenotyping and its practical application. A systematic review was conducted using the PRISMA methodology, in which a total of 1304 articles were identified and screened to the inclusion of 44 articles pertaining to the scope. It was concluded that spectral image analysis has a high ability to classify seeds of different genotypes (93.33%) in a range of situations: between cultivars; hybrids and progenitors; and hybrids and lines, as well as in the separation of coated seeds. Accurate classification can be obtained by different strategies, such as the choice of the equipment type, the spectrum range and extra features, guided by the characteristics of the species, as well as in the choice of algorithms and dimensionality reduction procedures for the optimization of models when there is a large amount of data. Despite the fact that the practical application of this technique in seed phenotyping still needs to be developed for use in laboratories with large volumes of analyses, lots, genotypes and harvests. Research has been accelerated to overcome the practical challenges of this method, as seen in works using model update algorithms, online classification systems, and real-time classification maps. Thus, there are strong indications that the application of multispectral image analysis will reach the routine of seed analysis laboratories.

A flexible predictive density combination for large financial data sets in regular and crisis periods

A flexible predictive density combination is introduced for large financial data sets which allows for model set incompleteness. Dimension reduction procedures that include learning allocate the large sets of predictive densities and combination weights to relatively small subsets. Given the representation of the probability model in extended nonlinear state-space form, efficient simulation-based Bayesian inference is proposed using parallel dynamic clustering as well as nonlinear filtering, implemented on graphics processing units. The approach is applied to combine predictive densities based on a large number of individual US stock returns of daily observations over a period that includes the Covid-19 crisis period. Evidence on dynamic cluster composition, weight patterns and model set incompleteness gives valuable signals for improved modelling. This enables higher predictive accuracy and better assessment of uncertainty and risk for investment fund management.

Tensor Train Random Projection

This work proposes a Tensor Train Random Projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a Tensor Train (TT) representation with TT-ranks equal to one. Based on the tensor train format, this random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires fewer storage costs with little loss in accuracy, compared with existing methods. We provide a theoretical analysis of the bias and the variance of TTRP, which shows that this approach is an expected isometric projection with bounded variance, and we show that the scaling Rademacher variable is an optimal choice for generating the corresponding TT-cores. Detailed numerical experiments with synthetic datasets and the MNIST dataset are conducted to demonstrate the efficiency of TTRP.

Stress-based dimensional reduction and dual-mixed hp finite elements for elastic plates

Starting from the linearized weak forms of the kinematic equation and the angular momentum balance equation of three-dimensional non-linear elasticity, a stressbased dimensional reduction procedure is presented for elastic plates. After expanding the three-dimensional non-symmetric stress tensor into power series with respect to the thickness coordinate, the translational equilibrium equations, written in terms of the expanded stress coefficients, are satisfied by introducing first-order stress functions. The symmetry of the stress field is satisfied in a weak sense by applying the material rotations as Lagrangian multipliers. The seven-field plate model developed in this way employs unmodified three-dimensional strain-stress relations. On the basis of the dimensionally reduced plate model derived, a new dual-mixed plate bending finite element model is developed and presented. The numerical performance of the hp-version plate elements is investigated through the solutions of standard plate bending problems. It is shown that the modeling error of the stress-based plate model in the energy norm is better than that of the displacement-based Kirchhoff- and Reissner-Mindlin plate models. The numerical solutions and their comparisons to reference solutions indicate that the dual-mixed hp elements are free from locking problems, in either the energy norm or the stress computations, both for h- and p-extensions, and the results obtained for the stresses are accurate and reliable even for extremely thin plates.