High-dimensional Research Articles

Unambiguous discrimination of general quantum operations

The discrimination of quantum operations has long been an intriguing challenge, with theoretical research notably advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related to the discrimination of quantum states, and proof-of-principle demonstrations of the latter have already been realized using optical photons. However, the experimental demonstration of discriminating general quantum operations, including both unitary and nonunitary operations, has remained elusive. In general quantum systems, especially those with high dimensions, the preparation of arbitrary quantum states and the implementation of arbitrary quantum operations and generalized measurements are nontrivial tasks. Here, we experimentally demonstrate the optimal unambiguous discrimination of up to six displacement operators and the unambiguous discrimination of nonunitary quantum operations. Our results demonstrate powerful tools for experimental research in quantum information processing and are expected to stimulate a wide range of valuable applications in the field of quantum sensing.

Machine Learning in Genomics: Applications in Whole Genome Sequencing, Whole Exome Sequencing, Single-Cell Genomics, and Spatial Transcriptomics

The application of machine learning (ML) to genomics has transformed the process of analyzing and interpreting large-scale, complex datasets, leading to important breakthroughs in our knowledge of biological systems. This review provides a comprehensive overview of ML applications in key genomic areas: Whole Genome Sequencing (WGS), Whole Exome Sequencing (WES), single-cell genomics, and spatial transcriptomics. In WGS and WES, ML techniques are employed for variant calling, genome-wide association studies, rare variant analysis, and the prediction of pathogenicity. In single-cell genomics, ML facilitates clustering, trajectory inference, and cell type identification, while in spatial transcriptomics, it aids in deciphering spatial patterns of gene expression and tissue heterogeneity. This review further explores the application of ML in related omics fields, including proteomics, transcriptomics, metagenomics, epigenomics, and microbiome research. These applications encompass protein structure prediction, functional annotation, microbial community profiling, and the analysis of epigenetic modifications. We address the challenges caused by high dimensionality, variability in the data, and the requirement for interpretable machine learning models when dealing with genomic data. Emerging technologies like explainable AI and federated learning are highlighted for their potential to address these challenges. Additionally, the review addresses ethical considerations, data privacy issues, and the necessity for standardized protocols in ML applications. This comprehensive examination underscores the transformative impact of ML in genomics and highlights its potential to drive future innovations in personalized medicine and biological research.

How Analysis Can Teach Us the Optimal Way to Design Neural Operators

This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to enhance the stability, convergence, generalization, and computational efficiency of neural operators. We revisit key theoretical insights, including stability in high dimensions, exponential convergence, and universality of neural operators. Based on these insights, we provide detailed design recommendations, each supported by mathematical proofs and citations. Our contributions offer a systematic methodology for developing next-gen neural operators with improved performance and reliability.

Spectral Diffusion of MMT Model with Condensate in Two or Higher Dimensions

Spectral Diffusion of MMT Model with Condensate in Two or Higher Dimensions

Greenland Wind-Wave Bivariate Dynamics by Gaidai Natural Hazard Spatiotemporal Evaluation Approach

The current work presents a case study for the state-of-the-art multimodal risk assessment approach, which is especially appropriate for environmental wind-wave dynamic systems that are either directly physically observed or numerically modeled. High dimensionality of the wind-wave environmental system and cross-correlations between its primary dimensions or components make it quite challenging for existing reliability methods. The primary goal of this investigation has been the application of a novel multivariate hazard assessment methodology to a combined windspeed and correlated wave-height unfiltered/raw dataset, which was recorded in 2024 by in situ NOAA buoy located southeast offshore of Greenland. Existing hazard/risk assessment methods are mostly limited to univariate or at most bivariate dynamic systems. It is well known that the interaction of windspeeds and corresponding wave heights results in a multimodal, nonstationary, and nonlinear dynamic environmental system with cross-correlated components. Alleged global warming may represent additional factor/covariate, affecting ocean windspeeds and related wave heights dynamics. Accurate hazard/risk assessment of in situ environmental systems is necessary for naval, marine, and offshore structures that operate within particular offshore/ocean zones of interest, susceptible to nonstationary ocean weather conditions. Benchmarking of the novel spatiotemporal multivariate reliability approach, which may efficiently extract relevant information from the underlying in situ field dataset, has been the primary objective of the current work. The proposed multimodal hazard/risk evaluation methodology presented in this study may assist designers and engineers to effectively assess in situ environmental and structural risks for multimodal, nonstationary, nonlinear ocean-driven wind-wave-related environmental/structural systems. The key result of the presented case study lies within the demonstration of the methodological superiority, compared to a popular bivariate copula reliability approach.

Model-Based Sequential Design of Experiments with Machine Learning for Aerospace Systems

Traditional experimental design methods often face challenges in handling complex aerospace systems due to the high dimensionality and nonlinear behavior of such systems, resulting in nonoptimal experimental designs. To address these challenges, machine learning techniques can be used to further increase the application areas of modern Bayesian Optimal Experimental Design (BOED) approaches, enhancing their efficiency and accuracy. The proposed method leverages neural networks as surrogate models to approximate the underlying physical processes, thereby reducing computational costs and allowing for full differentiability. Additionally, the use of reinforcement learning enables the optimization of sequential designs and essential real-time capability. Our framework is validated by optimizing experimental designs that are used for the efficient characterization of turbopumps for liquid propellant rocket engines. The reinforcement learning approach yields superior results in terms of the expected information gain related to a sequence of 15 experiments, exhibiting mean performance increases of 9.07% compared to random designs and 6.47% compared to state-of-the-art approaches. Therefore, the results demonstrate significant improvements in experimental efficiency and accuracy compared to conventional methods. This work provides a robust framework for the application of advanced BOED methods in aerospace testing, with implications for broader engineering applications.

Review of Recent Advances in Remote Sensing and Machine Learning Methods for Lake Water Quality Management

This review examines the integration of remote sensing technologies and machine learning models for efficient monitoring and management of lake water quality. It critically evaluates the performance of various satellite platforms, including Landsat, Sentinel-2, MODIS, RapidEye, and Hyperion, in assessing key water quality parameters including chlorophyll-a (Chl-a), turbidity, and colored dissolved organic matter (CDOM). This review highlights the specific advantages of each satellite platform, considering factors like spatial and temporal resolution, spectral coverage, and the suitability of these platforms for different lake sizes and characteristics. In addition to remote sensing platforms, this paper explores the application of a wide range of machine learning models, from traditional linear and tree-based methods to more advanced deep learning techniques like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and generative adversarial networks (GANs). These models are analyzed for their ability to handle the complexities inherent in remote sensing data, including high dimensionality, non-linear relationships, and the integration of multispectral and hyperspectral data. This review also discusses the effectiveness of these models in predicting various water quality parameters, offering insights into the most appropriate model–satellite combinations for different monitoring scenarios. Moreover, this paper identifies and discusses the key challenges associated with data quality, model interpretability, and integrating remote sensing imagery with machine learning models. It emphasizes the need for advancements in data fusion techniques, improved model generalizability, and the developing robust frameworks for integrating multi-source data. This review concludes by offering targeted recommendations for future research, highlighting the potential of interdisciplinary collaborations to enhance the application of these technologies in sustainable lake water quality management.

Empowering Urdu sentiment analysis: an attention-based stacked CNN-Bi-LSTM DNN with multilingual BERT

Sentiment analysis (SA) as a research field has gained popularity among the researcher throughout the globe over the past 10 years. Deep neural networks (DNN) and word vector models are employed nowadays and perform well in sentiment analysis. Among the different deep neural networks utilized for SA globally, Bi-directional long short-term memory (Bi-LSTM), BERT, and CNN models have received much attention. Even though these models can process a wide range of text types, Because DNNs treat different features the same, using these models in the feature learning phase of a DNN model leads to the creation of a feature space with very high dimensionality. We suggest an attention-based, stacked, two-layer CNN-Bi-LSTM DNN to overcome these glitches. After local feature extraction, by applying stacked two-layer Bi-LSTM, our proposed model extracted coming and outgoing sequences by seeing sequential data streams in backward and forward directions. The output of the stacked two-layer Bi-LSTM is supplied to the attention layer to assign various words with varying values. A second Bi-LSTM layer is constructed atop the initial layer in the suggested network to increase performance. Various experiments have been conducted to evaluate the effectiveness of our proposed model on two Urdu sentiment analysis datasets named as UCSA-21 and UCSA, and an accuracies of 83.12% and 78.91% achieved, respectively.

Evolutionary Optimization with a Simplified Helper Task for High-Dimensional Expensive Multiobjective Problems

In recent years, surrogate-assisted evolutionary algorithms (SAEAs) have been sufficiently studied for tackling computationally expensive multiobjective optimization problems (EMOPs), as they can quickly estimate the qualities of solutions by using surrogate models to substitute for expensive evaluations. However, most existing SAEAs only show promising performance for solving EMOPs with no more than 10 dimensions, and become less efficient for tackling EMOPs with higher dimensionality. Thus, this article proposes a new SAEA with a simplified helper task for tackling high-dimensional EMOPs. In each generation, one simplified task will be generated artificially by using random dimension reduction on the target task (i.e., the target EMOPs). Then, two surrogate models are trained for the helper task and the target task, respectively. Based on the trained surrogate models, evolutionary multitasking optimization is run to solve these two tasks so that the experiences of solving the helper task can be transferred to speed up the convergence of tackling the target task. Moreover, an effective model management strategy is designed to select new promising samples for training the surrogate models. When compared to five competitive SAEAs on four well-known benchmark suites, the experiments validate the advantages of the proposed algorithm on most test cases.

Parameterized hypercomplex convolutional network for accurate protein backbone torsion angle prediction

Predicting the backbone torsion angles corresponding to each residue of a protein from its amino acid sequence alone is a challenging problem in computational biology. Existing torsion angle predictors mainly use profile features, which are generated by performing time-consuming multiple sequence alignments, for torsion angle prediction. Compared with traditional profile features, embedding features from pretrained protein language models have significant advantages in prediction performance and computational speed. However, embedding features usually have higher dimensions and different embedding features have significantly different dimensions. To this end, we design a novel parameter-efficient deep torsion angle predictor, PHAngle, specifically for embedding features. PHAngle is a parameterized hypercomplex convolutional network consisting of parameterized hypercomplex linear and convolutional layers whose weight parameters can be characterized as the sum of Kronecker products. Experimental results on six benchmark test sets including TEST2016, TEST2018, TEST2020_HQ, CASP12, CASP13 and CASP-FM demonstrate that PHAngle achieves the state-of-the-art torsion angle performance with the fewest parameters compared to the nine existing methods. The source code and datasets are available at https://github.com/fengtuan/PHAngle.

Comparison the Performances for Distributed Machine Learning: Evidence from XGboost and DNN

Abstract. As a matter of fact, distributed machine learning approaches are widely adopted to enhance the training speed. The purpose of this study is to compare the performance of distributed machine learning models, specifically XGBoost and Deep Neural Networks (DNNs), using a telecommunications customer dataset. The dataset consists of 320,000 samples and 25 features and the analysis focuses on model performance under different data heterogeneity conditions. According to the analysis, XGBoost achieves excellent performance, rapidly reaching a high AUC of 97.7% with a minimal number of iterations, proving its effectiveness on structured, small and medium-sized datasets. In contrast, DNN struggled with this dataset and failed to outperform XGBoost due to its low dimensionality and small size. The paper also discusses the main limitations, including the lack of model diversity, the low dimensionality of the dataset, and the problem of model interpretability, especially for DNN. The results suggest that XGBoost is more suited to small and structured datasets, whereas DNN excels at high dimensionality and complex datasets. Future research should focus on improving model diversity, tuning, and addressing interpretability challenges.

A unified framework for the analysis of accuracy and stability of a class of approximate Gaussian filters for the Navier–Stokes equations

Abstract Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is important in many geophysical and engineering applications. In these cases, nonlinearities, high (or infinite) dimensionality of the state space, and sparse observations pose key challenges for deriving efficient and accurate data assimilation (DA) techniques. A number of DA algorithms used commonly in practice, such as the Ensemble Kalman Filter (EnKF) or Ensemble Square Root Kalman Filter (EnSRKF), suffer from serious drawbacks such as catastrophic filter divergence and filter instability. The analysis of stability and accuracy of these DA schemes has thus far focused either on finite-dimensional dynamics, or on complete observations in case of infinite-dimensional dissipative systems. We develop a unified framework for the analysis of several well-known and empirically efficient DA techniques derived from various Gaussian approximations of the Bayesian filtering schemes for geophysical-type dissipative dynamics with quadratic nonlinearities. We establish rigorous results on (time-asymptotic) accuracy and stability of these algorithms with general covariance and observation operators. The accuracy and stability results for EnKF and EnSRKF for dissipative PDEs are, to the best of our knowledge, completely new in this general setting. It turns out that a hitherto unexploited cancellation property involving the ensemble covariance and observation operators and the concept of covariance localization in conjunction with covariance inflation play a pivotal role in the accuracy and stability for EnKF and EnSRKF. Our approach also elucidates the links, via determining functionals, between the approximate-Bayesian and control-theoretic approaches to DA. We consider the ‘model’ dynamics governed by the two-dimensional incompressible Navier–Stokes equations (NSEs) and observations given by noisy measurements of averaged volume elements or spectral/modal observations of the velocity field. In this setup, several continuous-time DA techniques, namely the so-called 3DVar, EnKF and EnSRKF reduce to a stochastically forced NSEs. For the first time, we derive conditions for accuracy and stability of EnKF and EnSRKF. The derived bounds are given for the limit supremum of the expected value of the L 2 norm and of the H 1 Sobolev norm of the difference between the approximating solution and the actual solution as the time tends to infinity. Moreover, our analysis reveals an interplay between the resolution of the observations (roughly, the ‘richness’ of the observation space) associated with the observation operator underlying the DA algorithms and covariance inflation and localization which are employed in practice for improved filter performance.

GraphPCA: a fast and interpretable dimension reduction algorithm for spatial transcriptomics data

The rapid advancement of spatial transcriptomics technologies has revolutionized our understanding of cell heterogeneity and intricate spatial structures within tissues and organs. However, the high dimensionality and noise in spatial transcriptomic data present significant challenges for downstream data analyses. Here, we develop GraphPCA, an interpretable and quasi-linear dimension reduction algorithm that leverages the strengths of graphical regularization and principal component analysis. Comprehensive evaluations on simulated and multi-resolution spatial transcriptomic datasets generated from various platforms demonstrate the capacity of GraphPCA to enhance downstream analysis tasks including spatial domain detection, denoising, and trajectory inference compared to other state-of-the-art methods.

Incremental Classification for High-Dimensional EEG Manifold Representation Using Bidirectional Dimensionality Reduction and Prototype Learning.

In brain-computer interface (BCI) systems, symmetric positive definite (SPD) manifold within Riemannian space has been frequently utilized to extract spatial features from electroencephalogram (EEG) signals. However, the intrinsic high dimensionality of SPD matrices introduces too much computational burden to hinder the real-time applications of such BCI, especially in handling dynamic tasks, like incremental learning. Directly reducing the dimensionality of SPD matrices with conventional dimensionality reduction (DR) methods will alter the fundamental properties of SPD matrices. Moreover, current DR methods for incremental learning always necessitate retaining old data to update their representations under new mapping. To this end, a bidirectional two-dimensional principal component analysis for SPD manifold (B2DPCA-SPD) is proposed to reduce the dimensionality of SPD matrices, in such way that the reduced matrices remain on SPD manifold. Afterwards, the B2DPCA-SPD is extended to adapt to incremental learning tasks without saving old data. The incremental B2DPCA-SPD can be seamlessly integrated with the matrix-formed growing neural gas network (MF-GNG) to achieve an incremental EEG classification, where the new low-dimensional representations of the prototypes in old classifiers can be easily recalculated with the updated projection matrix. Extensive experiments are conducted on two public datasets to perform the EEG classification. The results demonstrate that our method significantly reduces computation time by 38.53% and 35.96%, and outperforms conventional methods in classification accuracy by 4.21% to 19.59%.

SYSAI for System Health Management - a Statistical Framework for the Analysis of Diagnosis Systems

On-board failure diagnosis and health management systems (HMS) are crucial for the operation of complex autonomous aerospace systems. False alarms (false positives, FPs) or false negatives (FNs) can lead to lower system performance or even loss of mission or the autonomous vehicle. Therefore, a careful verification and validation (V&V) is important. Due to the high dimensionality of the system’s state space, however, exhaustive testing of the HMS is usually not possible. In this paper, we present how our SYSAI (System Analysis for Systems with AI components) framework can support intelligent analysis and testing of HMS on the system level. SYSAI’s capabilities to efficiently explore high-dimensional state and parameter spaces and to identify diagnosability regions and their boundaries, makes a comprehensive analysis of the diagnosis system possible and can provide feedback to the designer. We will illustrate our approach using the ADAPT (Advanced Diagnostics and Prognostics Testbed) redundant power storage and distribution system.

Well Pattern optimization as a planning process using a novel developed optimization algorithm

Determination of optimum well location and operational settings for existing and new wells is crucial for maximizing production in field development. These optimum conditions depend on geological and petrophysical factors, fluid flow regimes, and economic variables. However, conducting numerous simulations for various parameters can be time-consuming and costly. Also, due to the high dimension of the possible solutions, there is still no general approach to address this problem. The application of searching algorithm as a general approach to solve such problems has received much attention in recent years. In this study, the efficiency, and reliability of genetic algorithm, particle swarm optimization and in particular a newly developed algorithm was analyzed and compared. The novelty of this work is the integrated algorithm, which improves searching performance by leveraging the memorizing characteristics of the particle swarm optimization algorithm to enhance genetic algorithm efficiency. In traditional genetic algorithms, solutions lacking adequate qualifications are deleted from the algorithmic process; however, the new algorithm provides these solutions with additional opportunities to prove themselves by acquiring new velocities from particle swarm optimization. The results indicate that while the genetic algorithm and particle swarm optimization do not guarantee optimal outcomes, the newly developed algorithm outperforms both methods. This performance was tested across various scenarios focused on well pattern optimization, highlighting its innovative contribution to the field development.

Phase transitions of ice VIII-VII-X: A potential energy landscape perspective

Water ice, an archetypal molecular system, exhibits a complex phase diagram characterized by numerous phase transitions under varying pressure-temperature conditions. However, it remains a significant challenge to theoretical modeling of these transitions owing to the high dimensionality in representing the potential energy landscapes (PEL) of ice crystalline phases. In an attempt to deeply understand the mechanisms of phase transitions between ice VII, VIII, and X, a graph-based stationary-point network was employed to simplify the representation of the PEL and locally constructed the PEL of ice at different pressures by our developed high-index saddle dynamic scheme. The stationary-point networks at 40 and 80 GPa indicate a pronounced flattened PEL of ice over a wide range of pressure (up to at least 80 GPa), where multiple structures (i.e., local minima) are energetically degenerate with phase VIII and separated by low-energy barriers (∼10 meV/atom at 40 GPa). These features indicate the disordered VII phase is more favorable at finite temperatures, in agreement with previous experimental observations. Additionally, we demonstrated that the PEL topology undergoes a fundamental alteration at higher pressures, with a single funnel emerging at 120 GPa, facilitating the crystallization of phase X. This work serves as a proof of concept for using the stationary-point network to explicitly represent the PEL, highlighting their potential in elucidating complex phase transitions. Published by the American Physical Society 2024

Identification of a Novel Biomarker Panel for Breast Cancer Screening

Breast cancer remains a major public health concern, and early detection is crucial for improving survival rates. Metabolomics offers the potential to develop non-invasive screening and diagnostic tools based on metabolic biomarkers. However, the inherent complexity of metabolomic datasets and the high dimensionality of biomarkers complicates the identification of diagnostically relevant features, with multiple studies demonstrating limited consensus on the specific metabolites involved. Unlike previous studies that rely on singular feature selection techniques such as Partial Least Square (PLS) or LASSO regression, this research combines supervised and unsupervised machine learning methods with random sampling strategies, offering a more robust and interpretable approach to feature selection. This study aimed to identify a parsimonious and robust set of biomarkers for breast cancer diagnosis using metabolomics data. Plasma samples from 185 breast cancer patients and 53 controls (from the Cooperative Human Tissue Network, USA) were analyzed. This study also overcomes the common issue of dataset imbalance by using propensity score matching (PSM), which ensures reliable comparisons between cancer and control groups. We employed Univariate Naïve Bayes, L2-regularized Support Vector Classifier (SVC), Principal Component Analysis (PCA), and feature engineering techniques to refine and select the most informative features. Our best-performing feature set comprised 11 biomarkers, including 9 metabolites (SM(OH) C22:2, SM C18:0, C0, C3OH, C14:2OH, C16:2OH, LysoPC a C18:1, PC aa C36:0 and Asparagine), a metabolite ratio (Kynurenine-to-Tryptophan), and 1 demographic variable (Age), achieving an area under the ROC curve (AUC) of 98%. These results demonstrate the potential for a robust, cost-effective, and non-invasive breast cancer screening and diagnostic tool, offering significant clinical value for early detection and personalized patient management.

Using cross-domain knowledge augmentation to explore comorbidity in electronic health records data

Research concentrating on specific diseases or employing single datasets, such as medical histories and thematic data, has garnered considerable attention. However, there has been limited investigation into comorbidities. Although some ad-hoc methods have been utilized in the medical field, there is a scarcity of systematic approaches to address this challenge. The task of expressing patient features using heterogeneous and cross-domain data presents considerable difficulties. Directly mapping this data into a matrix frequently results in issues such as high dimensionality, sparsity, redundancy, and noise. Additionally, given the critical role of supervisory information in medicine, acquiring accurate information is paramount. To address these issues, we propose an enhanced clustering method that capitalizes on cross-domain knowledge augmentation. This method can iteratively learn clustering outcomes and cross-domain knowledge. The cross-domain knowledge matrix produced by our approach can be interpreted as a measure of similarity between instances across domains. We validate our proposed model in real-world electronic health records (EHR) data, and achieve significant performance improvement compared to the baseline method, successfully completing the task of exploring comorbidity. Due to the privacy of EHR data, we also conduct extensive experiments on the publicly available datasets DBLP and UCI. The experimental results show that our algorithm is superior to the baseline algorithm and has strong generality.

Comparison of methods measuring electrical conductivity in coastal aquifers

Coastal aquifers, the transition zone between freshwater and saltwater, show large salinity contrasts in the subsurface. Salinity is a key parameter to understand coastal groundwater flow dynamics and consequently also geochemical and microbial processes. For mapping porewater salinity, a variety of methods exists, mainly using electrical conductivity as a proxy. We investigate methods including hydrological/geochemical (well sampling, fluid logger) as well as geophysical method (direct push, geoelectrics) utilising measurements near the high-water line of a high-energy beach at the North Sea island of Spiekeroog. We compare the methods, discuss their benefits and limitations and assess their spatial and temporal resolution. One key to enable a comparison is the estimation of formation factors transforming bulk conductivity measured by geophysical tools in to fluid conductivities obtained from direct measurements. We derive depth-dependent formation factors derived from time-series measurements of fluid loggers and a vertical electrode installation. Using these formation factors, the vertical electrode chain proves to provide reliable salinities at high spatial and temporal dimension. Direct-push profiling data provide the highest vertical resolution. However, a careful calibration is needed to allow for salinity quantification. On the other hand, electrical resistivity tomography (ERT) exhibits the lowest spatial resolution, but can image two-dimensional salinity distributions. We found ERT to fit very well to all other methods, but the data analysis should be aimed at salinities instead of bulk conductivities, i.e. including formation factors and temperature models into the inversion process.