What the Sine-of-a-Sum Example Tells Us About Sums of Separable Functions and Canonical Tensor Decompositions

Chemometric tools combined with excitation-emission matrix fluorescence for the identification and quantification of adulterations in Pequi oil.

Artificial emotional intelligence is a sub-domain of human–computer interaction research that aims to develop deep learning models capable of detecting and interpreting human emotional states through various modalities. A major challenge in this domain is identifying meaningful correlations between heterogeneous modalities—for example, between audio and visual data—due to their distinct temporal and spatial properties. Traditional fusion techniques used in multimodal learning to combine data from different sources often fail to adequately capture meaningful and less computational cross-modal interactions, and struggle to adapt to varying modality reliability. Following a review of the relevant literature, this study adopts an experimental research method to develop and evaluate a mathematical cross-modal fusion model, thereby addressing a gap in the extant research literature. The framework uses the Tucker tensor decomposition to analyse the multi-dimensional array of data into a set of matrices to support the integration of temporal features from audio and spatiotemporal features from visual modalities. A cross-attention mechanism is incorporated to enhance cross-modal interaction, enabling each modality to attend to the relevant information from the other. The efficacy of the model is rigorously evaluated on three publicly available datasets and the results conclusively demonstrate that the proposed fusion technique outperforms conventional fusion methods and several more recent approaches. The findings break new ground in this field of study and will be of interest to researchers and developers in artificial emotional intelligence.

ABSTRACTPreterm birth is a syndrome that is triggered by diverse biological pathways and presents with many comorbid diseases. Although twin studies reveal a substantial heritable component, the genetic mechanisms of preterm birth remain poorly understood. We hypothesize that refining the preterm birth phenotype will reveal sub-phenotypes associated with distinct genetic risk factors and potential treatments. Here, we leverage rich longitudinal data from electronic health records (EHRs) from over 60,000 individuals from two clinical sites. Using tensor decomposition, we uncover several latent factors (LFs) that capture coherent combinations of comorbidities (e.g., metabolic, inflammatory, and mental health) and temporal trajectories of preterm and term births. Similar LFs are discovered between the two sites, underscoring their interpretability. Machine learning models trained on LFs accurately predict preterm birth and perform comparably to models trained on the full EHR data. Integrating genome-wide genotyping for >2,200 individuals, we find robust associations of preterm birth risk with high polygenic burden for cardiovascular disease, type 2 diabetes and body mass index. Using LFs, we discover that these genetic signals are strongly and specifically associated with different subsets of the preterm birth cohort. For example, the polygenic diabetes risk is associated with a LF characterized by relevant metabolic disorders. In summary, our study integrates latent phenotypes discovered from large EHR datasets with genetic data to predict preterm birth risk, uncover disease subtypes and comorbidities that drive genetic associations, and delineate the mechanisms underlying the heterogeneity of this complex trait.

Currently, Kronecker Matrix–Matrix Multiplication play a crucial role in many advanced applications across science and engineering, such as Quantum Computing (Tensor Representation of Quantum States, Quantum Gate Construction), Machine Learning and Data Science (Kernel Methods, Tensor Decompositions), and Signal and Image Processing (Multi-dimensional Filtering, Compression Algorithms). However, the implementation of the Kronecker Matrix–Matrix Multiplication increasingly relies on systems with enhanced computational capabilities. Specifically, current implementations expend large amounts of external memory and requires a large number of processing units to perform this operation. As is commonly acknowledged, cutting-edge high-performance computing schemes still faces limitations in terms of energy and performance due to the bottleneck in data transfer between processing units and memory. To mitigate this limitation, memory processing units (MPUs) enable direct computation on in-memory data, reducing latency and eliminating the need for data transfer. On the other hand, spiking neural P systems, with their inherent parallelism and distributed processing capabilities, are therefore well-suited as foundational components for implementing such memory architectures efficiently. From the mathematical point of view, we present for the first time a neural, synaptic, and dendritic model to support the Kronecker Matrix–Matrix multiplication. To this end, the proposed spiking neural P system with their cutting-edge variants, such as anti-spikes, communication on request, synaptic weights, and dendritic–axonal delays, facilitates the creation of neural memory cells and spike-based routers. Hence, these elements potentially allow the design of novel processing memory architectures that markedly enhance data transfer efficiency between computational units and memory.

With the widespread application of multi-view data across various domains, multi-view unsupervised feature selection (MUFS) has achieved remarkable progress in both feature selection (FS) and missing-view completion. However, existing MUFS methods typically rely on centralized servers, which not only fail to meet privacy requirements in distributed settings but also suffer from suboptimal FS quality and poor convergence. To overcome these challenges, we propose a novel federated incomplete MUFS method (Fed-IMUFS), which integrates a fractional Sparsity-Guided Whale Optimization Algorithm (SGWOA) and Tensor Alternating Learning (TAL). Within this federated learning framework, each client performs local optimization in two stages: in the first stage, SGWOA introduces an L2,1 proximal projection to enforce row-sparsity in the FS weight matrix, while fractional-order dynamics and fractal-inspired elite kernel injection mechanisms enhance global search ability, yielding a discriminative and stable weight matrix; in the second stage, based on the obtained weight matrix, an alternating optimization framework with tensor decomposition is employed to iteratively complete missing views while simultaneously optimizing low-dimensional representations to preserve cross-view consistency, with the objective function gradually minimized until convergence. During federated training, the server employs an aggregation and distribution strategy driven by normalized mutual information, where clients upload only their local weight matrices and quality indicators, and the server adaptively fuses them into a global FS matrix before distributing it back to clients. This process achieves consistent FS across clients while safeguarding data privacy. Comprehensive evaluations on CEC2022 and several incomplete multi-view datasets confirm that Fed-IMUFS outperforms state-of-the-art methods, delivering stronger global optimization capability, higher-quality feature selection, faster convergence, and more effective handling of missing views.

The accurate and efficient treatment of electron-electron interactions remains a central challenge in electronic structure theory. Post-Hartree-Fock (HF) methods are often hindered by high computational costs, primarily due to the need to compute four-index electron repulsion integrals. To address this issue, low-rank approaches, such as tensor hyper-contraction (THC) and interpolative separable density fitting, have been developed to accelerate the computation of HF exchange and dynamic correlation energies in post-HF frameworks. Nevertheless, these methods remain inefficient for molecular systems, mainly because of the quartic-scaling computational cost associated with constructing the THC kernel with respect to the number of basis functions. In this work, we present a new algorithm, named block tensor decomposition (BTD), based on a dual-grid scheme. By integrating Hilbert sorting with pivoted Cholesky decomposition, BTD generates compact and non-redundant interpolative grids, achieving formal O(N3) scaling for kernel building. Key parameters of the method are optimized via differential evolution, ensuring an effective balance between computational efficiency and accuracy. We further demonstrate the application of BTD in scaled opposite-spin second-order Møller-Plesset perturbation theory, where sparse mapping in real space enables O(N2) scaling for both electron correlation and exchange evaluations. Test examples show that BTD is a robust, low-scaling framework for accurate electronic structure calculations in molecular systems.

Accurate traffic flow prediction is vital for intelligent transportation systems, yet strong spatiotemporal coupling and multi-scale dynamics make modelling difficult. Existing methods often rely on static adjacency and short input windows, limiting adaptation to time-varying spatial relations and long-term patterns. To address these issues, we propose the Pre-trained Trend-aware Dynamic Graph Convolutional Network (PT-TDGCN), a two-stage framework. In the pre-training stage, a Transformer-based masked autoencoder learns segment-level temporal representations from historical sequences. In the prediction stage, three designs are integrated: (1) dynamic graph learning parameterized by tensor decomposition; (2) convolutional trend-aware attention that adds 1D convolutions to capture local trends while preserving global context; and (3) spatial graph convolution combined with lightweight fusion projection for aligning pre-trained, spatial, and temporal representations. Extensive experiments on four real-world datasets demonstrated that PT-TDGCN consistently outperformed 14 baseline models, achieving superior predictive accuracy and robustness.

A parametric reduced-order model based on tensor decomposition for unstructured mesh data

ABSTRACT Sparse tensors have become prevalent data structures in multiple applications, such as medical imaging and machine learning, making operations that decompose them, that is, creating smaller structures that retain most of the original information, essential. Two of the most commonly used tensor decomposition methods are the Canonical Polyadic and Tucker Decomposition, with the most time‐consuming operations being the MTTKRP and TTM‐chain, respectively. Modern computing platforms combine multiple devices with different architectures to achieve unprecedented levels of performance, creating an environment where portability is as important as performance. To tackle this challenge, this work proposes SYCL‐based MTTKRP and TTM‐chain approaches for sparse tensors, which are portable to any CPU or GPU, extending previous literature by handling mode‐4 and mode‐5 tensors and tackling the TTM‐chain operation as a whole, allowing for further optimizations. The experimental results show that the proposed approaches present linear to superlinear scalability as the problem size grows and outperform the portable state‐of‐the‐art by 4.9× on average.

Protein secondary structure prediction is a fundamental task in bioinformatics, crucial for understanding protein function and guiding drug discovery. Traditional regression and ensemble models show limited performance due to their inability to capture nonlinear dependencies and sequential features of protein sequences. To address these challenges, this study proposes a hybrid model that integrates the Sparrow Search Algorithm (SSA) with Deep Neural Networks (DNN). SSA optimizes the initialization and hyperparameters of DNN, improving convergence and generalization. Furthermore, Online Low-rank Subspace Tracking by Tensor Decomposition (OLSTEC) is incorporated to exploit multi-dimensional correlations among sequence, evolutionary, and physicochemical features. Experimental results demonstrate that the SSA-DNN framework achieves superior accuracy over regression baselines, and the addition of OLSTEC further improves test accuracy to 36.82% with a Macro-F1 score of 0.1555. These findings highlight the advantages of combining metaheuristic optimization with tensor decomposition for large-scale protein structure prediction.

In this paper, we intend to define complexity related to the self-gravitating composition in a new way by assuming the formalism of [Formula: see text] theory. The irrotational spherically static space-time associated with a spatially anisotropic fluid is contemplated in this regard along with the orthogonal decomposition of Riemann tensor by assuming the formalism related to modified field equations and the conservation law. We perceive [Formula: see text] as a complexity factor out of all the determined structural scalars, which includes the features of anisotropic pressure and the compelling appearance of the energy density. The correction terms related to [Formula: see text] theory are essential for deriving some particular results for the Tolman mass, Weyl scalar, and complexity factor. Furthermore, the scalars determined in our case study are employed to derive the result for the complexity factor and the restriction of the diminishing complexity is considered to calculate the solutions related to certain models. A self-gravitational fluid with non-uniform energy density and anisotropic pressure exhibits ultimate complexity. However, these fluids might have no complexity if the impacts of anisotropic pressure and non-uniformity in energy density are canceled due to the appearance of correction values associated with [Formula: see text] theory.

We introduce an innovative recursive tensor decomposition method that draws inspiration from quantum chemical theories. This approach integrates ideas such as natural occupation numbers and natural basis, much like natural orbitals, and employs truncations that parallel the excitation-level truncations in the linear expansions of configuration interaction theory. The framework features recursive algorithms that combine linear expansion with natural basis transformations at each step, ensuring convergence to the original tensor. Consequently, a numerical technique is developed that reconstructs the initial tensor with precision within a predetermined tolerance, using only subtensors of limited dimension and a series of matrix transformations. An initial Python implementation has been created for the 3D tensor scenario where 3D tensors are decomposed to be represented using vectors and matrices alone. We illustrate the behavior of the final Recursive Linear Tensor Expansion in Natural basis algorithm in processing random data sets, experimental data sets from diverse sources with both real and complex tensors, and data sets representing both time-independent and time-dependent anharmonic vibrational wave functions of water. Finally, the systematic accuracy control is illustrated for density fitting two-electron repulsion integrals and tested for the second-order correlation energy of molecular nitrogen and benzene.

Tensor decomposition is an efficient and accurate method for reconstructing 5D seismic data with irregular missing traces, using tensor rank-reduction techniques to estimate the data’s low-rank structure. Nevertheless, the reconstruction performance is limited for regularly sampled data that satisfy the low-rank assumption, particularly under the condition of strong spatial aliasing. The Radon transform constrained tensor CANDECOM\PARAFAC decomposition (RCPD) combines sparse Radon transform with low-rank estimation, which can reconstruct regularly missing traces to some extent. However, the reconstruction accuracy can be improved with further anti-aliasing mechanism considerations. As the RCPD method can obtain slope-related Radon coefficients during the low-rank estimation, we propose to use the extracted low-frequency slope information to further constrain the RCPD algorithm of aliased data reconstruction. Synthetic data experiments confirm that the proposed anti-aliasing RCPD method can effectively reconstruct the seismic data with regularly missing traces to improve the lateral continuity with high accuracy. Field data applications further demonstrate the feasibility of the proposed method in providing high-quality regular and dense data for subsequent seismic inversion and imaging.

ABSTRACTNeuromodulation of subcortical network hubs by pharmacologic, electrical, or ultrasonic stimulation is a promising therapeutic strategy for patients with disorders of consciousness (DoC). However, optimal subcortical targets for therapeutic stimulation are not well established. Here, we leveraged 7 Tesla resting‐state functional MRI (rs‐fMRI) data from 168 healthy subjects from the Human Connectome Project to map the subcortical connectivity of six canonical cortical networks that modulate higher‐order cognition and function: the default mode, executive control, salience, dorsal attention, visual, and somatomotor networks. Based on spatiotemporally overlapped networks generated by the Nadam‐Accelerated SCAlable and Robust (NASCAR) tensor decomposition method, our goal was to identify subcortical hubs that are functionally connected to multiple cortical networks. We found that the ventral tegmental area (VTA) in the midbrain and the central lateral and parafascicular nuclei of the thalamus—regions that have historically been targeted by neuromodulatory therapies to restore consciousness—are subcortical hubs widely connected to multiple cortical networks. Further, we identified a subcortical hub in the pontomesencephalic tegmentum that overlapped with multiple reticular and extrareticular arousal nuclei and that encompassed a well‐established “hot spot” for coma‐causing brainstem lesions. Multiple hubs within the brainstem arousal nuclei and thalamic intralaminar nuclei were functionally connected to both the default mode and salience networks, emphasizing the importance of these cortical networks in integrative subcortico‐cortical signaling. Additional subcortical connectivity hubs were observed within the caudate head, putamen, amygdala, hippocampus, and bed nucleus of the stria terminalis, regions classically associated with modulation of cognition, behavior, and sensorimotor function. Collectively, these results suggest that multiple subcortical hubs in the brainstem tegmentum, thalamus, basal ganglia, and medial temporal lobe modulate cortical function in the human brain. Our findings strengthen the evidence for targeting subcortical hubs in the VTA, thalamic intralaminar nuclei, and pontomesencephalic tegmentum to restore consciousness in patients with DoC. We release the subcortical connectivity maps to support ongoing efforts at therapeutic neuromodulation of consciousness.

Abstract Turbulent momentum transport critically influences tropical cyclone (TC) structure and intensity, but its multiscale characteristics remain poorly understood. Using two large eddy simulations, we investigate the Reynolds stress tensor and subfilter‐scale momentum flux tensor during rapid intensification and mature stages of an idealized TC. We find that both tensor type exhibit similar spatial patterns. The mean horizontal momentum fluxes have comparable or greater magnitudes than vertical fluxes, highlighting their essential contribution to angular momentum redistribution. The horizontal components of diffusive tendencies contribute at magnitudes comparable to the vertical components. Alignment analysis using tensor decomposition demonstrates that strain‐rotation interactions dominate turbulent stress transporting in the boundary layer, highlighting limitations in the classical Boussinesq hypothesis. These results highlight the need for turbulence closures that incorporate rotational effects.

Abstract Multivariate time series may be subject to partial structural changes over certain frequency band, for instance, in neuroscience. We study the change point detection problem with high-dimensional time series, within the framework of frequency domain. The overarching goal is to locate all change points and delineate which series are activated by the change, over which frequencies. In practice, the number of activated series per change and frequency could span from a few to full participation. We solve the problem by first computing a CUSUM tensor based on spectra estimated from blocks of the time series. A frequency-specific projection approach is applied for dimension reduction. The projection direction is estimated by a proposed tensor decomposition algorithm that adjusts to the sparsity level of changes. Finally, the projected CUSUM vectors across frequencies are aggregated for change point detection. We provide theoretical guarantees on the number of estimated change points and the convergence rate of their locations. We derive error bounds for the estimated projection direction for identifying the frequency-specific series activated in a change. We provide data-driven rules for the choice of parameters. The efficacy of the proposed method is illustrated by simulation, and applications in stock returns and seizure detection.

ABSTRACT Acoustic emission (AE) is elastic waves generated spontaneously from the creation of micro‐cracks. AE waveforms share significant similarities with microseismic signals and serve as an effective tool for improving the understanding of fracture processes during hydraulic fracturing. AE events typically have small magnitude with low amplitude. To detect weak AE events, it is always necessary to set a larger gain control, but this increases the risk of large amplitude waveform being clipped beyond the saturation level of the A/D converter. Amplitude‐clipped AE events are usually considered unusable and must be excluded from the estimation of source properties such as focal mechanisms. We introduce an extension of compressed sensing methods to reconstruct the clipped waveform and further use them to perform the moment tensor inversions and decomposition. This method assumes that the AE events are band‐limited and the clipped segment of the waveform shares the same frequency content as the unclipped segment. Compared to conventional techniques, the proposed method can effectively reconstruct the clipped waveforms with clipping level less than 0.7, ensuring reliable moment tensor inversions and decomposition. The reconstruction method reduces the risk of confounding reasoning or misinterpretation caused by waveform distortion and provides a more reliable basis for the physical interpretation of AE properties.

Type 2 diabetes (T2D) and its associated complications develop heterogeneously over decades, but few studies span the progression from prediabetes to clinical events. We investigated whether long-term metabolic trajectories beginning in prediabetes delineate subgroups with differential complication risk. Clinical data from 1,732 Diabetes Prevention Program/Outcomes Study participants (follow-up 19 years) were analyzed across 12 phenotypes. Tensor decomposition was used to capture longitudinal patterns, and Gaussian mixture modeling was used to define longitudinal clusters. Cluster-specific complications were quantified with Cox and logistic regression. Four clusters emerged. Clusters 1 and 2 (73% of participants) maintained stable glycemia, blood pressure, and lipids. Although 49% and 71%, respectively, developed T2D, cumulative micro- and macrovascular events remained low. Cluster 3 (12%) showed the steepest rise in insulin resistance and hyperglycemia, with 92% of the subgroup progressing to T2D and a markedly higher rate of retinopathy (odds ratio [OR] 8.8, 95% CI 3.9-20.1) and neuropathy (OR 3.4, 95% CI 2.1-5.5). Cluster 4 (15%) presented with baseline microalbuminuria often prior to the development of T2D (73%). It was distinguished by progressive estimated glomerular filtration rate decline and a doubling of cardiovascular events (hazard ratio 2.0, 95% CI 1.4-3.0), despite serum lipids comparable with other groups. Two-thirds of individuals with prediabetes follow metabolically resilient trajectories, whereas distinct insulin-resistant or renal-dysfunction trajectories precede micro- or macrovascular complications, respectively. The optimal window for macrovascular complication prevention in individuals with prediabetes microalbuminuria may precede progression to T2D.

Tensor analysis of animal behavior by matricization and feature selection.