The rapid development of space exploration demands real-time backhaul of massive sensing payload data in space-ground integrated telemetry, tracking, and command (TT&C) networks. However, traditional narrow-band TT&C links suffer from severe congestion during massive data backhaul. Since most TT&C applications are inherently task-oriented and do not require pixel-perfect data reconstruction, we propose a task-oriented joint resource allocation framework based on semantic communications. Specifically, we introduce an adaptive semantic split computing mechanism that extracts and transmits only compact, decision-critical features instead of raw bitstreams, fundamentally mitigating the bandwidth bottleneck. The joint optimization of computation offloading, semantic splitting, and continuous on-board computing allocation is formulated as a stochastic mixed-integer nonlinear programming (MINLP) problem. We propose a decoupled algorithm based on Hierarchical Multi-Agent Proximal Policy Optimization (HMAPPO) to solve it. An outer layer employs multi-agent reinforcement learning (MARL) for distributed discrete decision-making, while an inner layer utilizes a Karush–Kuhn–Tucker (KKT)-based solver for continuous space-based computing allocation. This bi-level architecture overcomes the curse of dimensionality and mathematically guarantees zero-violation of physical capacity constraints. Simulations demonstrate that HMAPPO rapidly converges and sustains a high weighted success rate under heavy traffic congestion, significantly improving system utility compared to state-of-the-art baselines.

A global full-dimensional description of interactions in a molecular van der Waals cluster, including both inter and intramolecular degrees of freedom, may seem to be the necessary starting point for high-accuracy nuclear dynamics calculations. Such calculations are currently able to make predictions for clusters, molecular collisions, and condensed phases accurate enough to be confronted with experiment. However, the all-dimensional treatment becomes prohibitively expensive for clusters with more than 6 atoms due to the "curse of dimensionality". On the other hand, the rigid-monomer approximation allows applications to much larger clusters. We show on the example of H2-CO that if the rigidity is imposed via averaging over monomer vibrations, the predictions from such a reduced-dimensionality model can be about as accurate as those from the full-dimensional one; in fact, here both models predict spectra equally well. Moreover, we show that an approximate version of such an averaged surface, based on the Taylor expansion, which does not require the development of a full-dimensional surface and is affordable for larger molecules, also works very well. In contrast, models based on frozen geometries of monomers work much worse. Spectral and scattering calculations with the vibrationally averaged reduced-dimensionality models will result in insights into soft condensed matter properties, cold and ultracold molecular collisions, and physics of cold interstellar clouds that are currently not possible.

Background: The rapid evolution of omnichannel retailing has reshaped retail supply chains (SCs) by coupling replenishment, fulfillment, and service decisions across multiple demand channels under inventory, lead-time, and capacity constraints. These interdependencies create coordination challenges, particularly when demand shocks interact with limited operational capacity. Methods: To address these challenges, this study develops a centralized Hierarchical Reinforcement Learning (HRL) control framework that makes decision timing explicit: replenishment and allocation are optimized weekly, while fulfillment and lateral inventory rebalancing are controlled daily. Policies are learned using Proximal Policy Optimization (PPO) in an actor–critic architecture, with bounded stochastic policies for constrained action spaces. To mitigate the curse of dimensionality in HRL, we introduce a capacity-aware state–action encoding mechanism that compresses the control interface into structured summary signals. Demand shocks are modeled using two specifications: a mixed profile, where half the products follow a uniform demand process and the rest a Merton-type jump-diffusion process, and a fully shock-driven profile. Results: The framework is evaluated against forecast-driven base-stock and greedy fulfillment heuristics, and a perfect-information oracle, with pairwise differences examined through Wilcoxon signed-rank tests. Conclusions: Overall, the proposed framework improves learning efficiency and scalability, outperforming heuristic baselines while remaining below the oracle bound.

The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number of dimensions, a phenomenon called the curse of dimensionality. The problem is so substantial that one usually employs sampling methods, like Monte Carlo, to avoid integration altogether. Here, we derive and implement a quantum-inspired algorithm to decompose a multidimensional integrand into a product of matrix-valued functions – a spectral tensor train – changing the computational complexity of integration from exponential to polynomial. The algorithm constructs a spectral tensor train representation of the integrand by applying a sequence of quantum gates, where each gate corresponds to an interaction that involves increasingly more degrees of freedom in the action. Because it allows for the systematic elimination of small contributions to the integral through decimation, we call the method integral decimation. The functions in the spectral basis are analytically differentiable and integrable, and in applications to the partition function, integral decimation numerically factorizes an interacting system into a product of non-interacting ones. We illustrate integral decimation by evaluating the absolute free energy and entropy of a chiral XY model as a continuous function of temperature. We also compute the nonequilibrium time-dependent reduced density matrix of a quantum chain with between two and forty levels, each coupled to colored noise. When other methods provide numerical solutions to these models, they quantitatively agree with integral decimation. When conventional methods become intractable, integral decimation can be a powerful alternative.

High-dimensional data clustering poses significant challenges due to the curse of dimensionality, noise, and sparsity. Traditional clustering algorithms often struggle with scalability and accuracy in such contexts. To address these issues, this paper proposes a hybrid clustering model that integrates Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Gaussian Mixture Models (GMM), leveraging the strengths of both approaches using machine learning techniques. DBSCAN efficiently identifies dense regions and eliminates noise, while GMM provides probabilistic soft clustering suitable for overlapping data distributions. By first using DBSCAN for pre-processing and noise reduction, followed by GMM for refined clustering, the hybrid model enhances performance in complex high-dimensional datasets. Dimensionality reduction techniques such as PCA and t-SNE are also incorporated to visualize and improve cluster quality. The proposed method is evaluated on benchmark high-dimensional datasets and compared against standalone clustering algorithms. Results demonstrate improved cluster compactness, separation, and computational efficiency, showcasing the effectiveness of the hybrid approach for high-dimensional data analysis in fields such as bioinformatics, image processing, and text mining.

The ability to enforce a given behaviour on the electromagnetic field intensity distribution is relevant in a wide range of applications, including the particularly challenging case where shaping is required in heterogeneous media. In this respect, with reference to scalar fields, the paper proposes a new effective approach to design the optimal complex excitations feeding an antenna array able to ensure a shaped field intensity distribution within a specified region of interest while keeping under control the field intensity in other areas. To tackle the challenges and the curse of dimensionality of such a problem, the proposed strategy represents the unknown complex field as a combination of elementary (eventually focused) bricks. Then, the corresponding linear superposition coefficients are evaluated by using a semidefinite relaxation framework and by minimizing the nuclear norm of an auxiliary matrix. The approach is tested against 2D inhomogeneous lossless scenarios. Comparisons with respect to previous approaches are also provided.

Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in L-sense

Overcoming the dimensionality curse in decomposition integrals: Polynomial approximations and exact sparse structures

Accurate, global Potential Energy Surfaces (PESs) expressed in sum-of-products (SOP) form are a prerequisite for efficient high-dimensional quantum dynamics simulations using the multi-configuration time-dependent Hartree method. This work introduces a methodology for constructing such surfaces by combining hierarchical sparse grid sampling with a single-layer neural network using sinusoidal activation functions (sinNN). The sparse grid strategy provides a rigorous, unbiased discretization of the configuration space, enabling systematic improvement of the PES fidelity, where accuracy is strictly controlled by the refinement level, while successfully mitigating the curse of dimensionality. The sinNN fitting approach leverages a trigonometric factorization identity to maintain a compact SOP form, offering superior numerical stability compared to "standard" exponential-based networks for the molecular systems investigated. We validate this framework by refitting an analytical PES for nitrous acid (HONO). The flexibility of the sparse grid methodology is demonstrated through a dual-reference strategy, where grids centered on distinct isomers are merged to eliminate topological bias. This optimized sampling yields a global PES that reproduces fundamental vibrational transition energies for both trans- and cis-HONO with spectroscopic precision (<2.5 cm-1) and high data efficiency. Finally, the methodology is applied to fit potential energies computed via the AI-enhanced quantum mechanical method (AIQM2). The resulting AIQM2-based PES for HONO reproduces experimental vibrational frequencies with a root mean square deviation of ∼16 cm-1, a performance comparable to high-level abinitio methods. The robustness of the approach is further confirmed on larger molecules, formic acid (HCOOH) and carbamic acid (H2NCOOH), establishing the combination of sparse grid sampling and sinNN fitting as a powerful, automated tool for generating topologically sound, spectroscopic-quality potential energy surfaces.

Extremely Large-Scale Multiple-Input Multiple-Output (XL-MIMO) is positioned as a transformative technology for sixth-generation (6G) networks, effectively turning base stations into high-resolution sensing and communication hubs. However, the practical deployment of XL-MIMO is hindered by the "curse of dimensionality," specifically the prohibitive overhead associated with Channel State Information (CSI) sensing and feedback, alongside the computational latency of massive antenna arrays. To resolve the conflict between high-resolution sensing requirements and limited bandwidth resources, this paper proposes a novel two-stage beamforming architecture that synergizes physics-aware dimensionality reduction with deep learning. First, by exploiting the inherent sparsity of XL-MIMO channels in the angle-delay domain, we design a Spatial-Frequency Concentration Block (SFCB). This module functions as a hard-attention sensing mechanism, performing efficient source-end dimensionality reduction on raw CSI at the User Equipment (UE) via precise feature extraction and adaptive energy truncation. Second, we develop a highly adaptable Direct Integrated Precoding Network (DIP-I). Departing from the conventional "sense-reconstruct-then-precode" paradigm, DIP-I learns end-to-end mapping to directly regress the optimal precoding matrix at the Base Station (BS). Comprehensive simulations utilizing the COST 2100 and QuaDRiGa hybrid channel models demonstrate that, under a massive 512-antenna configuration, the proposed framework achieves exceptional beamforming gain. Furthermore, it significantly reduces sensing data overhead and inference latency, offering a superior trade-off between spectral efficiency and hardware resource consumption for future 6G sensing-communication integrated systems.

Epidemic risk assessment poses inherent challenges, with traditional approaches often failing to balance health outcomes and economic constraints. This paper presents a data-driven decision support tool that models epidemiological dynamics and optimises vaccination strategies to control disease spread while minimising economic losses. The proposed economic-epidemiological framework comprises three phases: modelling, optimising, and analysing. First, a stochastic SVEI3RD compartmental model with eight state variables captures epidemic dynamics, stratifying infections by severity to enable detailed healthcare cost estimation. Second, an optimal control problem is formulated to derive vaccination strategies that minimise pandemic-related expenditures, encompassing vaccination costs, quarantine subsidies, healthcare expenditures, and economic productivity losses. The resulting high-dimensional stochastic control problem renders classical numerical methods computationally intractable due to the curse of dimensionality. To overcome this challenge, Physics-Informed Neural Networks are employed to calibrate model parameters by embedding the stochastic differential equations into the loss function. For the optimal control problem, a deep neural network architecture comprising feedforward subnetworks at each time step directly approximates the time-varying vaccination rate. The framework is demonstrated using COVID-19 data from Victoria, Australia. The numerical results show that, compared to the no-vaccination strategy, the optimal strategy reduces cumulative hospital-days by 85.3%, deaths by 84.4%, and total costs by 22.3%. These reductions exceed those achieved by the actual government rollout by approximately 4 to 6 percentage points. By employing this framework, policymakers can continuously update strategies to minimise aggregate costs and aid future pandemic preparedness.

Shape constraints in nonparametric regression provide a powerful framework for estimating regression functions under realistic assumptions without tuning parameters. However, most existing methods—except additive models—impose too weak restrictions, often leading to overfitting in high dimensions. Conversely, additive models can be too rigid, failing to capture covariate interactions. This article introduces a novel multivariate shape-constrained regression approach based on total concavity, originally studied by T. Popoviciu. Our method allows interactions while mitigating the curse of dimensionality, with convergence rates that depend only logarithmically on the number of covariates. We characterize and compute the least squares estimator over totally concave functions, derive theoretical guarantees, and demonstrate its practical effectiveness through empirical studies on real-world datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Biological matrix data are essential for computational analysis, providing a structured framework to identify patterns and relationships in biological systems. Many other biological data types, including sequences, networks, and images, can be transformed into matrix representations through feature extraction and encoding. However, their high dimensionality complicates analysis, leading to increased computational complexity and the risk of overfitting, known as the curse of dimensionality. To address these challenges, we developed SIBioX, a matrix-based bioinformatics tool powered by swarm intelligence algorithms. It integrates 54 swarm intelligence methods, 5 conventional feature selection techniques, and 17 machine learning models, enabling comprehensive analysis of biological matrix data. With a user-friendly graphical interface, it supports operations such as feature normalization, selection, classification, clustering, statistical analysis, and data visualization. Additionally, it converts nonmatrix biological data, like gene and protein sequences, into matrix formats for further study. Experimental results demonstrate that SIBioX not only attains high accuracy in feature selection but also effectively reduces dimensionality, thereby streamlining bioinformatics workflows and promoting greater efficiency in biomedical research.

Abstract Hyperspectral change detection has emerged as a vital tool in modern remote sensing applications such as environmental monitoring, urban expansion, and agricultural health. Unlike multispectral systems, hyperspectral imaging captures hundreds of narrow spectral bands, enabling granular material-specific analysis. However, its high dimensionality, spectral variability, and sub-pixel mixing introduce challenges such as data redundancy, noise amplification, and difficulty in isolating meaningful changes. Traditional methods struggle to disentangle mixed pixels or model complex spatial–spectral–temporal relationships, limiting their ability to detect changes. The curse of dimensionality further exacerbates computational inefficiency and sensitivity to environmental noise. Thus, we introduce UnTrNet, an advanced transformer-based approach designed specifically for hyperspectral change detection. UnTrNet begins by applying linear spectral unmixing to each pair of bitemporal images, generating a set of compact abundance maps that highlight the most informative material signatures. These maps are then tokenized and processed through a lightweight transformer encoder, where multi-head self-attention is used to capture fine-grained spectral–spatial patterns and long-range temporal dependencies. This design enables UnTrNet to focus computational resources on the most critical features, improving both efficiency and accuracy. Extensive experiments were conducted on three benchmark datasets: China Farmland, USA, and Urban. UnTrNet performance was evaluated by varying the number of transformer layers and attention heads. Results demonstrate that UnTrNet achieves competitive accuracy on the China Farmland dataset, with the 12-layer configuration achieving the highest accuracy of 98.89%. On the USA dataset, the 12-layer UnTrNet with 16 attention heads outperforms state-of-the-art methods, achieving an accuracy of 97.89%. Additionally, on the Urban dataset, all configurations of UnTrNet achieve over 99% accuracy due to the dataset's well-structured spatial and spectral features.

Quantifying the complex spatial–temporal correlations and generating representative high-dimensional coupled scenario sets are essential for the robust planning and risk assessment of large-scale hybrid energy systems (HESs). Although numerous models have been developed for this purpose, as the number of plants scales up to hundreds, existing approaches suffer from the curse of dimensionality, often resulting in high computational burden, posterior collapse, and distributional oversmoothing. To address this gap, this paper proposes a Spatial-Clustering Conditional Variational Auto-Encoder (SC-CVAE) framework, which employs spatial clustering to decompose the high-dimensional global problem into tractable subproblems and integrates adaptive deep networks to accurately capture high-dimensional spatiotemporal complementarity. Case studies on the Yalong River energy base, featuring massive wind and solar integration, demonstrate that SC-CVAE reduces global spatial correlation error by 56% compared to the Independent Baseline, while achieving a 2.4-fold computational speedup over the monolithic Global Baseline. Crucially, by mitigating posterior collapse to alleviate oversmoothing effects inherent in high-dimensional VAEs, the proposed framework improves the capture rate of high-impact extreme events by 3.4-fold and reduces the Energy Score error by 65%. This high-fidelity reconstruction of tail characteristics provides a more reliable basis for identifying supply-deficit risks in basin-wide HESs. The proposed framework enables scalable and high-fidelity generative modeling, establishing a robust methodology for stochastic optimization and long-term security assessments in the global transition toward decarbonized power systems.

Bayesian nonparametric density estimation procedures are typically based on single-scale priors, such as Dirichlet process mixtures. Alternative multiscale density priors built on decision trees have many well-known advantages, including the ability to characterize abrupt local changes and to provide an estimate with a desired level of resolution. Despite their theoretical appeal, multiscale methods have typically been developed in the literature as univariate. Their multivariate versions are generally costly to implement in applications due to rapidly increasing number of mixture components. We propose a random Bernstein polynomial prior on the unit hypercube of arbitrary dimension with a spike-and-slab shrinkage structure. The prior induces posterior sparsity of the multiscale decision tree, alleviating the curse of dimensionality. We embed the proposed model in the form of a copula link function along with nonparametric marginals in a composite prior over general spaces of densities. We provide conditions for posterior consistency under the weak topology and assess the finite-sample properties in a simulation study. We further illustrate the practical use of the model in an application to forecasting the Value at Risk and Expected Shortfall of a financial portfolio in a scenario where sampling from the non-sparse posterior would be infeasible. Supplemental materials for this article are available online.

The next-generation approach to research in the behavioral sciences is based on intensive collections of data and complex models characterized by many parameters for a limited sample size. This introduces new challenges for traditional latent-variable methods, as they are found to fail or yield unstable solutions when the number of variables is large relative to the sample size. To tackle this issue, we propose a two-stage regularized approach for exploratory structural equation modeling. In the first stage, we introduce a novel (exploratory) approximate factor analysis technique that not only estimates the measurement model but also the factor scores; indeterminacy of the measurement model is addressed by imposing simple structure through regularizing techniques (LASSO penalty and cardinality constraint). The factor scores can then be used to estimate the structural model in the second stage. An extensive simulation shows that the proposed method outperforms other approaches in recovering the underlying simple structure of the measurement model in both low-dimension high-sample-size and high-dimension low-sample-size settings. The use of the method is demonstrated on two empirical datasets. An implementation of the proposed method in the R software is publicly available: https://github.com/trale97/regularizedESEM .

High-dimensional data classification remains challenging for machine learning models due to sparsity and overfitting caused by the ‘curse of dimensionality‘. As the number of features increases, data points become sparse, hindering generalization in classification and leading to higher computational costs and reduced accuracy. To address these issues, we propose an ensemble classifier based on random subspaces implemented in the Spark framework. The proposed framework comprises three key stages. First, the high-dimensional data is normalised through min-max normalisation. Second, the master node partitions the data by using improved deep fuzzy clustering (IDFC). In contrast, the slave node applies support vector machine-modified recursive feature elimination (SVM-MRFE) for efficient feature selection, followed by feature fusion. Finally, we introduced an improved subspace-based ensemble classifier (ISSBEC) that comprises a feature-fusion-based random subspace (FF-RSS), mixed-space enhancement (MSE), and multiple base classifiers. The efficacy of the ISSBEC classifier was evaluated using a set of performance metrics and compared with state-of-the-art methods. Experimental results demonstrate that the proposed approach improves both accuracy and robustness, offering a scalable solution to the limitations of high-dimensional datasets.

The existing research on Android malware detection using graph neural networks (GNNs) has largely focused on architectural improvements, while input node feature representations have received less systematic attention. This study adopts a representation-centric approach to enhance function call graph (FCG)-based malware classification through interpretability-driven feature engineering. We propose a dual-level structural feature framework integrating local topological patterns with global graph-level properties. The initial feature set comprises 13 dimensions: five local degree profile (LDP) features and eight global structural features capturing community structure, execution flow, and connectivity patterns. To mitigate the curse of dimensionality, we apply an interpretability-driven selection using integrated gradients (IG), gradient-weighted class activation mapping (GradCAM), and Shapley additive explanations (SHAP), yielding an optimized seven-dimensional subset. Experiments on the MalNet-Tiny benchmark demonstrate that the proposed approach achieves 94.47 ± 0.25% accuracy with jumping knowledge GraphSAGE (JK-GraphSAGE), improving the LDP-only baseline by 0.32 percentage points while reducing feature dimensionality by 46%. The selected features exhibit consistent importance across four GNN architectures and multiple message-passing layers, demonstrating model-agnostic effectiveness. The results reveal that aggregation mechanisms critically influence feature utility, highlighting the necessity of interpretability-guided design for robust malware detection. This work provides a systematic methodology for feature engineering in graph-based security applications.

Unpaired H&E-to-IHC Stain Translation aims to generate immunohistochemistry (IHC) staining from Hematoxylin and Eosin (H&E) staining. It offers clearer diagnostic insights and potentially expands access to advanced pathology services in resource-limited areas. This task faces two primary challenges: capturing target domain style characteristics and preserving topological features in histological images. Recently, Schrödinger Bridge (SB)-based methods have offered a solution for unpaired image-to-image translation, addressing the mode collapse and artifact issues in CycleGAN-based approaches, as well as the Gaussian prior assumption limitation in diffusion-based methods. While SB-based methods suffer from the curse of dimensionality with high-resolution images, the Unpaired Neural Schrödinger Bridge (UNSB) overcomes this challenge and achieves state-of-the-art (SOTA) performance on natural images. However, UNSB has two key issues in histological images: (1) loss of topological features and (2) IHC staining representation. UNSB focuses only on the optimal path from source to target domains, ignoring local structure paths. Convolutional neural networks (CNNs) do not perfectly preserve critical anatomical structures due to limitations like receptive field size or model capacity. To address these challenges, we introduce the Topology-aware Diffusion Schrödinger Bridge (TDSB), integrating a Topology Guidance (TG) module and Dual-Domain Adaptive Patch-based noise contrastive estimation (DDAP). Experiments on seven translation tasks across three datasets show that our method achieves SOTA performance in unpaired H&E-to-IHC stain translation. Clinical evaluation through pathologists' assessments further validates the effectiveness of our method.