Dimensional Space Research Articles

Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time–frequency domain with the STFT, which describes the local characteristic of the signal from the time–frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Multi-armed bandit algorithm for sequential experiments of molecular properties with dynamic feature selection.

Sequential optimization is one of the promising approaches in identifying the optimal candidate(s) (molecules, reactants, drugs, etc.) with desired properties (reaction yield, selectivity, efficacy, etc.) from a large set of potential candidates, while minimizing the number of experiments required. However, the high dimensionality of the feature space (e.g., molecular descriptors) makes it often difficult to utilize the relevant features during the process of updating the set of candidates to be examined. In this article, we developed a new sequential optimization algorithm for molecular problems based on reinforcement learning, multi-armed linear bandit framework, and online, dynamic feature selections in which relevant molecular descriptors are updated along with the experiments. We also designed a stopping condition aimed to guarantee the reliability of the chosen candidate from the dataset pool. The developed algorithm was examined by comparing with Bayesian optimization (BO), using two synthetic datasets and two real datasets in which one dataset includes hydration free energy of molecules and another one includes a free energy difference between enantiomer products in chemical reaction. We found that the dynamic feature selection in representing the desired properties along the experiments provides a better performance (e.g., time required to find the best candidate and stop the experiment) as the overall trend and that our multi-armed linear bandit approach with a dynamic feature selection scheme outperforms the standard BO with fixed feature variables. The comparison of our algorithm to BO with dynamic feature selection is also addressed.

Deal.t: an implementation of multivariate analysis suitable T-splines within the deal.ii framework

AbstractWe present a numerical framework for solving partial differential equations within an isogeometric context using T-splines in two and three space dimensions. Within this paper, we explain the data structures used for the implementation of ( with T-splines) and main differences when using in contrast to . The authors present numerical experiments with error-based refinement (2D) and a priori refinement (3D) for scalar-valued problems. A full tutorial is given in the appendix. Since the new framework is based on , T-splines may be applied to various different PDEs.

Physics-informed neural network simulation of thermal cavity flow

Physics-informed neural networks (PINNs) are an emerging technology that can be used both in place of and in conjunction with conventional simulation methods. In this paper, we used PINNs to perform a forward simulation without leveraging known data. Our simulation was of a 2D natural convection-driven cavity using the vorticity-stream function formulation of the Navier-Stokes equations. We used both 2D simulations across the x and z domains at constant Rayleigh (Ra) numbers and 3D simulations across the x, z and Ra domains. The 3D simulation was tested for a PINN’s ability to learn solutions in a higher-dimensional space than standard simulations. The results were validated against published solutions at Ra values of 103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document}, 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{4}$$\\end{document}, 105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{5}$$\\end{document}, and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{6}$$\\end{document}. Both the 2D simulations and 3D simulations successfully matched the expected results. For the 2D cases, more training iterations were needed for the model to converge at higher Ra values (105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^5$$\\end{document} and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^6$$\\end{document}) than at lower Ra (103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document} and 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}) indicating increased nonlinear fluid-thermal coupling. The 3D case was also able to converge but, but it required more training than any of the 2D cases due to the curse of dimensionality. These results showed the validity of standard simulations via PINNs and the feasibility of higher-order parameter space solutions that are not possible using conventional methods. They also showcased the additional computational demand associated with increasing the dimensionality of the learned parameter space.

Valuation of a financial claim contingent on the outcome of a quantum measurement

We consider a rational agent who at time 0 enters into a financial contract for which the payout is determined by a quantum measurement at some time T > 0. The state of the quantum system is given in the Heisenberg representation by a known density matrix p^ . How much will the agent be willing to pay at time 0 to enter into such a contract? In the case of a finite dimensional Hilbert space H , each such claim is represented by an observable X^T where the eigenvalues of X^T determine the amount paid if the corresponding outcome is obtained in the measurement. We prove, under reasonable axioms, that there exists a pricing state q^ which is equivalent to the physical state p^ such that the pricing function Π0T takes the linear form Π0T(X^T)=P0Ttr(q^X^T) for any claim X^T , where P0T is the one-period discount factor. By ‘equivalent’ we mean that p^ and q^ share the same null space: that is, for any |ξ⟩∈H one has p^|ξ⟩=0 if and only if q^|ξ⟩=0 . We introduce a class of optimization problems and solve for the optimal contract payout structure for a claim based on a given measurement. Then we consider the implications of the Kochen–Specker theorem in this setting and we look at the problem of forming portfolios of such contracts. Finally, we consider multi-period contracts.

Social media and political contention - challenges and opportunities for comparative research

ABSTRACT In this special issue, the authors theoretically, methodologically, and empirically address challenges and opportunities associated with comparative social media analysis in political contention. Actors from civil society, media, and institutional politics use social media to coordinate, mobilise, and communicate, turning public online communication into an arena of conflict that offers researchers valuable windows of observation. In this introduction to the special issue, we systematise comparative perspectives on social media and political contention. We outline the traditional comparative dimensions of space, time, platform, and case; and suggest an approach for comparison within dimensions that are less dependent on the rapidly changing social media environment and more attuned to the interconnection between social media and political contention.

Deep Learning-Based Multi-Fidelity Surrogate Modeling for High Dimensional Reliability Prediction

Abstract Multi-fidelity surrogate modeling offers a cost-effective approach to reduce extensive evaluations of expensive physics-based simulations for reliability predictions. However, considering spatial uncertainties in multi-fidelity surrogate modeling remains extremely challenging due to the curse of dimensionality. To address this challenge, this paper introduces a deep learning-based multi-fidelity surrogate modeling approach that fuses multi-fidelity datasets for high-dimensional reliability analysis of complex structures. It first involves a heterogeneous dimension transformation approach to bridge the gap in terms of input format between the low-fidelity and high-fidelity domains. Then, an explainable deep convolutional dimension-reduction network is proposed to effectively reduce the dimensionality of the structural reliability problems. To obtain a meaningful low dimensional space, a new knowledge reasoning-based loss regularization mechanism is integrated with the covariance matrix adaptation evolution strategy to encourage an unbiased linear pattern in the latent space for reliability predictions. Then, the high-fidelity data can be utilized for bias modeling using Gaussian process regression. Finally, Monte Carlo simulation is employed for the propagation of high-dimensional spatial uncertainties. Two structural examples are utilized to validate the effectiveness of the proposed method.

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

We consider the magnetic nonlinear inhomogeneous Schrödinger equationi∂tu−(−i∇+α|x|2(−x2,x1))2u=±|x|−ϱ|u|p−1u,(t,x)∈R×R2, where α∈R∖Z,ϱ>0,p>1. We establish a dichotomy between global existence and scattering versus finite-time blow-up for energy solutions below the ground state threshold in the inter-critical regime. The scattering result is obtained by employing the novel approach developed by Dodson and Murphy (A new proof of scattering below the ground state for the 3D radial focusing cubic NLS, Proc. Am. Math. Soc. (2017)). We employ Tao's scattering criteria and Morawetz estimates as the foundation of this method. The novelty of our approach lies in two aspects: firstly, we explore the case of nonzero ϱα, and secondly, we consider general energy initial data that need not be radially symmetric. The specific instance of α=0, known as INLS, has garnered significant attention in recent years. Additionally, X. Gao and C. Xu recently investigated the case of ϱ=0 in the homogeneous regime, establishing scattering theory for spherically symmetric data in their work (Scattering theory for NLS with inverse-square potential in 2D, J. Math. Anal. Appl. (2020)). In the radial framework, the aforementioned problem can be translated to the INLS with an inverse square potential, which has been extensively studied in higher-dimensional spaces. The Hardy inequality ‖|x|−1f‖L2(RN)≤2N−2‖∇f‖L2(RN), which establishes the norm equivalence ‖f‖H1≃‖f‖H1+‖|x|−1f‖L2, does not hold in two space dimensions. Consequently, it remains unclear how to handle the NLS with an inverse square potential in the H1 framework for two-dimensional space. This article stands out as the first one to address the NLS with Aharonov-Bohm magnetic potential within the inhomogeneous regime, specifically when ϱ≠0.

Interpretable multi-graph convolution network integrating spatial-temporal attention and dynamic combination for wind power forecasting

Graph neural networks (GNN) can effectively improve wind power forecasting accuracy due to its ability to capture spatial correlations between wind farms. However, conventional GNN-based forecasting models constructing the graphs from only one specific perspective fail to characterize the spatial correlation patterns comprehensively and accurately. Furthermore, their black-box structure leads to deficient interpretability of the forecasting results, which hampers the quantification of forecasts uncertainty and reduces the credibility of applying these forecasting models in practice. To address the above problems, an interpretable ultra-short-term wind power forecasting method is proposed based on multi-graph convolution network integrating spatial–temporal attention and dynamic graph combination. Four undirected weight graphs are constructed to form a multi-graph scheme by considering various geographical and statistical aspects, and then graph convolution network (GCN) and temporal convolution network (TCN) are used to enhance the forecasting performance by leveraging information in both space and time dimensions. Meanwhile, it consists of temporal attention that deeply mines the temporal dependence information and spatial attention that interprets influence of wind farms on the forecasts. Additionally, to boost the adaptability and generalization capability of the proposed method, an improved reinforcement learning is elaborately designed to combine the results of different graphs by dynamically optimizing their weights to obtain the final forecasts. Experiment results suggest that the proposed method exhibits superior forecasting accuracy and reasonable interpretability compared with other benchmark methods.

Distributionally robust chance-constrained kernel-based support vector machine

Support vector machine (SVM) is a powerful model for supervised learning. This article addresses the nonlinear binary classification problem using kernel-based SVM with uncertainty involved in the input data specified by the first- and second-order moments. To achieve a robust classifier with small probabilities of misclassification, we investigate a distributionally robust chance-constrained kernel-based SVM model. Since the moment information in the original problem becomes unclear/unavailable in the feature space via kernel transformation, we develop a data-driven approach utilizing empirical moments to provide a second-order cone programming (SOCP) reformulation for efficient computation. To speed up the required computations for solving large-size problems in higher dimensional space and/or with more sampling points involved in estimating empirical moments, we further design an alternating direction multipliers-based algorithm for fast computations. Extensive computational results support the effectiveness and efficiency of the proposed model and solution method. Results on public benchmark datasets without any moment information indicate that the proposed approach still works and, surprisingly, outperforms some commonly used state-of-the-art kernel-based SVM models.

Improving safety criteria for transporting hazardous goods by road through optimizing the geometric parameters of their stowage

The object of research is the process of cargo transportation by road. The problem of efficient loading and securing of hazardous goods in box containers during their transportation by road is considered. The basic principles of the voxel-based interpretation of the model of loading box containers on road transport are presented, and a general principle for calculating the fractal dimension of such three-dimensional objects has been developed. The calculation is based on the procedure of reducing the dimensionality of space by cutting the object into separate layers and determining the fractal dimensionality of two-dimensional slices. The proposed principle could be used to estimate the fractal dimension of three-dimensional objects in practical tasks in any industry. A method for simplified calculation of fractal characteristics of three-dimensional bill of lading models of cargo stowage has been devised. The method is based on the assessment of the quality of blocking of the constituent elements of the spatial system in three coordinate directions by the fractal dimension of two-dimensional images of their frames. The method provides opportunities for calculating the quantitative characteristics of the quality of cargo stowage from the standpoint of its transportation safety. A method for fractal stowing of goods in box containers on a truck platform has been proposed. This method of fractal stowage provides for the absence of slippage and displacement of boxes in the package and makes it impossible for them to overturn in extreme situations. The use of the fractal stowage method allows for an efficient and low-cost technology of securing the cargo as it involves only a circular bandage of the top layer of the loaded package of boxes and its fastening to the vehicle platform at four points

GAN-Generated Face Detection Based on Multiple Attention Mechanism and Relational Embedding

The rapid development of the Generative Adversarial Network (GAN) makes generated face images more and more visually indistinguishable, and the detection performance of previous methods will degrade seriously when the testing samples are out-of-sample datasets or have been post-processed. To address the above problems, we propose a new relational embedding network based on “what to observe” and “where to attend” from a relational perspective for the task of generated face detection. In addition, we designed two attention modules to effectively utilize global and local features. Specifically, the dual-self attention module selectively enhances the representation of local features through both image space and channel dimensions. The cross-correlation attention module computes similarity between images to capture the global information of the output in the image. We conducted extensive experiments to validate our method, and the proposed algorithm can effectively extract the correlations between features and achieve satisfactory generalization and robustness in generating face detection. In addition, we also explored the design of the model structure and the inspection performance on more categories of generated images (not limited to faces). The results show that RENet also has good detection performance on datasets other than faces.

Determining the time before or after a galaxy merger event

Aims. This work aims to reproduce the time before or after a merger event of merging galaxies from the IllustrisTNG cosmological simulation using machine learning. Methods. Images of merging galaxies were created in the u, g, r, and i bands from IllustrisTNG. The merger times were determined using the time difference between the last simulation snapshot where the merging galaxies were tracked as two galaxies and the first snapshot where the merging galaxies were tracked as a single galaxy. This time was then further refined using simple gravity simulations. These data were then used to train a residual network (ResNet50), a Swin Transformer (Swin), a convolutional neural network (CNN), and an autoencoder (using a single latent neuron) to reproduce the merger time. The full latent space of the autoencoder was also studied to see if it reproduces the merger time better than the other methods. This was done by reducing the latent space dimensions using Isomap, linear discriminant analysis (LDA), neighbourhood components analysis, sparse random projection, truncated singular value decomposition, and uniform manifold approximation and projection. Results. The CNN is the best of all the neural networks. The performance of the autoencoder was close to the CNN, with Swin close behind the autoencoder. ResNet50 performed the worst. The LDA dimensionality reduction performed the best of the six methods used. The exploration of the full latent space produced worse results than the single latent neuron of the autoencoder. For the test data set, we found a median error of 190 Myr, comparable to the time separation between snapshots in IllustrisTNG. Galaxies more than ≈625 Myr before a merger have poorly recovered merger times, as well as galaxies more than ≈125 Myr after a merger event.

Nonlinear Reduced Order Modelling for Korteweg-de Vries Equation

Efficient computational techniques that maintain the accuracy and invariant preservation property of the Korteweg-de Vries (KdV) equations have been studied by a wide range of researchers. In this paper, we introduce a reduced order model technique utilizing kernel principle component analysis (KPCA), a nonlinear version of the classical principle component analysis, in a non-intrusive way. The KPCA is applied to the data matrix, which is formed by the discrete solution vectors of KdV equation. In order to obtain the discrete solutions, the finite differences are used for spatial discretization, and linearly implicit Kahan's method for the temporal one. The back-mapping from the reduced dimensional space, is handled by a non-iterative formula based on the idea of multidimensional scaling (MDS) method. Through KPCA, we illustrate that the reduced order approximations conserve the invariants, i.e., Hamiltonian, momentum and mass structure of the KdV equation. The accuracy of reduced solutions, conservation of invariants, and computational speed enhancements facilitated by classical (linear) PCA and KPCA are exemplified through one-dimensional KdV equation.

Black hole firewalls and quantum mechanics *

Firewalls in black holes are easiest to understand by imposing time reversal invariance, together with a unitary evolution law. The best approach seems to be to split up the time span of a black hole into short periods, during which no firewalls can be detected by any observer. Then, gluing together subsequent time periods, firewalls seem to appear, but they can always be transformed away. At all times we need a Hilbert space of a finite dimension, as long as particles far separated from the black hole are ignored. Our conclusion contradicts other findings, as these assume that information that entered into a black hole, cannot re-emerge. But re-emergence of that information is exactly what our version of firewalls is supposed to ensure. Indeed, the firewall transformation removes the problems caused by entanglement between very early and very late in- and out-particles, in a far from trivial way.

Scattering for quantum Zakharov system in two space dimensions

In this paper, we study long time behavior of solution to the quantum Zakharov system in two dimensions. We construct a small global solution to the quantum Zakharov system which scatters to a given free solution by using space-time resonance method developed by Gustafson-Nakanishi-Tsai [Commun. Contemp. Math. 11 (2009), pp. 657–707] and Germain-Masmoudi-Shatah [Int. Math. Res. Not. IMRN 3 (2009), 414–432; J. Math. Pures Appl. (9) 97 (2012), pp. 505–543] etc.

A priori error estimates of Runge-Kutta discontinuous Galerkin schemes to smooth solutions of fractional conservation laws

Abstract. We give a priori error estimates of second order in time fully explicit Runge-Kutta discontinuous Galerkin schemes using upwind fluxes to smooth solutions of scalar fractional conservation laws in one space dimension. Under the time step restrictions τ ≤ ch for piecewise linear and τ .h4/3 for higher order finite elements, we prove a convergence rate for the energy norm k · kL∞t L2x + | · |L2tHxλ/2 that is optimal for solutions and flux functions that are smooth enough. Our proof relies on a novel upwind projection of the exact solution.

Carleman estimates for third order operators of KdV and non KdV-type and applications

AbstractIn this paper we study a class of variable coefficient third order partial differential operators on $${\mathbb {R}}^{n+1}$$ R n + 1 , containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of $${\mathbb {R}}^{n+1}$$ R n + 1 . A discussion of possible applications in the context of dispersive equations is provided.

A new framework for higher loop Witten diagrams

The differential representation is a novel formalism for studying boundary correlators in (d + 1)-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of operator-valued integrals. We use the differential representation to compute three-point bubble and triangle Witten diagrams with external states of conformal dimension ∆ = d. We compare the former to a position space computation.

Orthognathic surgery improves compromised natural head position and pharyngeal airway in patients with Skeletal Class II or III malocclusion.

Natural head position (NHP), pharyngeal airway and maxillofacial growth pattern are correlated. The author's previous studies proved that following surgical correction of Skeletal Class II malocclusion, the over-extended NHP returned upright, and the pharyngeal airway space (PAS) dimension expanded. The present study compares the post-operative change in NHP and PAS after orthognathic surgery in Skeletal Class II and III malocclusion patients. Patients receiving orthognathic procedures to correct Skeletal Class II or III malocclusions were reviewed in this retrospective study. Pre-operative and 6-week post-operative cone-beam computed tomography datasets were collected. Variables representing the craniofacial pattern, the NHP and the PAS were measured three-dimensionally. Post-operative variables were compared with their pre-operative counterparts using either repeat-measure 2-way analysis of variance or Wilcoxon matched-pairs signed rank test. Thirty cases of Skeletal Class II malocclusion and 13 cases of Skeletal Class III malocclusion were collected. Preoperatively, the inter-group differences were significant in craniofacial pattern (68.14 ± 3.552 degree vs. 79.63 ± 2.497 degree, p < .0001) and the NHP (68.77 ± 11.02 degree vs. 82.83 ± 7.738 degree, p = .0002) while not significant in PAS; after surgery, the intergroup differences in craniofacial pattern and the NHP between groups decreased, and the PAS increased in both groups. Orthognathic surgery may improve compromised NHP and increase PAS in Skeletal Class II and III malocclusion patients.