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Recently, there has been a significant increase in interest in cross-modal hashing technology. For hash code learning, most previous supervision methods use label information to create a similarity matrix in a straightforward manner. However, there are still the following challenges: (1) The asymmetric similarity matrix method only considers the similarity of labels, and the discriminant constraint in Hamming space is ignored; (2) there are optimization errors between the cross-modal semantic correlation of the Hamming space and the nonlinearity of the feature space; and (3) the cross-modal hash matrix is in a dynamic state during the optimization process, and the hash code is easily disturbed and there is bit uncertainty. To this end, we propose the Discriminative Latent Semantics-preserving Similarity Embedding Cross-modal Hashing (DLSSECH) method. Specifically, to reduce the quantization error, we introduce a non-asymmetric similarity decomposition based on orthogonal rotation bias. It can decompose the bitwise correlation of the learned hash code to capture more discriminative semantic information and compact hash code. In addition, to capture the cross-modal semantic correlation of nonlinear feature transformation and reduce quantization error, we propose the latent correlation error matrices based on orthogonal rotation decomposition. The model maintains the maximum difference in semantic dependencies between the projected data and its semantic representation. Finally, we use a sparse common hash matrix and non-asymmetric similarity decomposition factors to solve the uncertainty of the dynamic changes of the hash code. The effectiveness of DLSSECH has demonstrated through experiments on four cross-modal retrieval datasets, where it outperformed some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, the open-loop and closed-loop local and remote stochastic nonzero-sum game (LRSNG) problem is investigated. Different from previous works, the stochastic nonzero-sum game problem under consideration is essentially a special class of two-person nonzero-sum game problem, in which the information sets accessed by the two players are inconsistent. More specifically, both the local player and the remote player are involved in the system dynamics, and the information sets obtained by the two players are different, and each player is designed to minimise its own cost function. For the considered LRSNG problem, both the open-loop and closed-loop Nash equilibrium are derived. The contributions of this paper are given as follows. Firstly, the open-loop optimal Nash equilibrium is derived, which is determined in terms of the solution to the forward and backward stochastic difference equations (FBSDEs). Furthermore, by using the orthogonal decomposition method and the completing square method, the feedback representation of the optimal Nash equilibrium is derived for the first time. Finally, the effectiveness of our results is verified by a numerical example. [ABSTRACT FROM AUTHOR]

Hypercomplex numbers, which are multi-dimensional extensions of complex numbers, have been proven beneficial in the development of advanced signal processing algorithms, including multi-dimensional filter design, linear regression and classification. We focus on multicomplex numbers, sets of hypercomplex numbers with commutative products, and introduce a vector representation allowing one to isolate the hyperbolic real and imaginary parts of a multicomplex number. The orthogonal decomposition of a multicomplex number is also discussed, and its connection with Hadamard matrices is highlighted. Finally, a multicomplex polar representation is provided. These properties are used to extend the standard complex baseband signal representation to the multi-dimensional case. It is shown that a set of 2 n Radio Frequency (RF) signals can be represented as the real part of a single multicomplex signal modulated by several frequencies. The signal RFs are related through a Hadamard matrix to the modulating frequencies adopted in the multicomplex baseband representation. Moreover, an orthogonal decomposition is provided for the obtained multicomplex baseband signal as a function of the complex baseband representations of the input RF signals. [ABSTRACT FROM AUTHOR]

The problem of finite-time robust adaptive stabilisation for a class of input saturated time-delay nonlinear systems with unknown parameters is studied in this article. Firstly, by applying the orthogonal decomposition method, a finite-time adaptive stabilisation controller is designed for the system. Then the finite-time robust adaptive stabilisation result for the system with external disturbance is obtained. Finally, a practical system example is presented to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

We generalize certain well known orthogonal decompositions of model spaces and obtain similar decompositions for the wider class of shifted model spaces, allowing us to establish conditions for near invariance of the latter with respect to certain operators which include, as a particular case, the backward shift S*. In doing so, we illustrate the usefulness of obtaining appropriate decompositions and, in connection with this, we prove some results on model spaces which are of independent interest. We show moreover how the invariance properties of the kernel of an operator T, with respect to another operator, follow from certain commutation relations between the two operators involved. [ABSTRACT FROM AUTHOR]

A framework of the topology optimization incorporated with the phase field method considering the interfacial damage for optimizing the fracture resistance of inclusion-matrix composites is presented. The topology optimization was performed to redistribute the inclusion phase in order to reduce its volume while keeping the fracture resistance value of the initial design unchanged. The phase field method uses two scalar phase field variables: one is for the bulk crack and the other is for the interfacial crack. The decomposition of the strain tensor into compression and tension parts was incorporated into this phase field method to improve the mechanical behaviors of the materials. These compression and tension strain parts are orthogonal in the context of the inner product in which the tensor of elastic stiffness behaves as a metric. Moreover, in the simulation process, an investigation of the effects of the interfacial parameters on the numerical results was discussed. Through the obtained results, the method proposed is demonstrated to be accurate and efficient in eliminating spurious effects and singularity points on the behavior curves in the damage process. [ABSTRACT FROM AUTHOR]

Reducing multidimensional relative poverty is one of the important issues in the current global poverty governance field. This article takes 12 ethnic regions in China as the research object and constructs a multidimensional relative poverty measurement system. The calculated multidimensional relative poverty index is decomposed according to provinces, cities, dimensions, and indicators. Then, the Dagum Gini coefficient and convergence analysis are used to analyze spatiotemporal heterogeneity and convergence characteristics. The results show that the multi-dimensional relative poverty situation of various provinces in ethnic minority areas has improved from 2012 to 2021, among which Tibet province is the most serious and Shaanxi is the best. According to the analysis of convergence, it was observed that there is no σ-convergence of multidimensional relative poverty in ethnic areas in general, and there is absolute β-convergence in general and in the southwest and northwest regions, and there is no absolute β-convergence in the northeast region. Based on this, policy recommendations for reducing multidimensional relative poverty are proposed at the end of the article. Compared with previous studies, this article focuses on ethnic regions that are easily overlooked. Starting from the dimensions of economy, social development, and ecological environment, the poverty measurement system has been enriched. [ABSTRACT FROM AUTHOR]

With different shapes and material properties, fish all achieve undulatory swimming gait under the action of internal active muscle stimulation and external fluid forces. Such locomotion can be decomposed into deformation affected by internal and external forces in the body frame and overall translation and rotation solely determined by fluid forces. In order to revisit the undulatory swimming gait, we investigate the hydrodynamic performance of two-dimensional flexible carangiform swimmers with varying stiffnesses and thicknesses, which are driven by the active internal bending moments, and employ the complex orthogonal decomposition and Fourier decomposition methods to quantitatively measure and analyze the proportion of undulation. It is found that standing wave deformation characteristics are prominently observed along fish-like bodies with high stiffness, whereas traveling wave characteristics are more evident in bodies with lower stiffness. The self-propelled fish body demonstrates lateral oscillation and rotation around its center of mass, namely, the heaving and pitching movement, particularly in specimens with high stiffness. The present analysis shows that the heaving and pitching locomotion induced by the fluid significantly increase the traveling wave proportion by modulating the amplitude and phase of the left and right traveling waves viewed in forward frame. We called it fluidic undulation effects (FUE), which is different from the undulation of body deformation. This effect is more pronounced for large stiffnesses and thin airfoils. The standing wave deformation observed with a large stiffness transforms into a traveling wave propulsion pattern, with its traveling wave index even slightly surpassing that of a small-stiffness pattern. Although the efficiency of the standing wave deformation is low, it facilitates a faster forward speed (body lengths per stroke). The positive impact of the FUE on the swimming performance is also confirmed by restricting the recoil motions of the lateral translation and rotation of the body. Furthermore, we observe that there is no undulatory swimming gait that has both the highest energy efficiency and the highest speed. [ABSTRACT FROM AUTHOR]

This paper presents an extended interaction klystron (EIK) operating at 0.22 THz based on a four-sheet-beam orthogonal interconnection structure (OIS). The proposed OIS comprises four vertically positioned trapezoidal line structures, significantly enhancing the coupling efficiency between cavities and achieving optimal interactions with the TM81 mode. This study investigates the dispersion characteristics and field distribution numerically, while the optimal working parameters and output structure were analyzed using the particle-in-cell (PIC) studio. The parameters of each cavity and the selection of five intermediate cavities were finalized by calculating the beam conductance, external quality factor, and stagger-tuning. The EIK generated a continuous 480 W output power with a four-sheet-beam at 17.5 kV and a current density of 200 A/cm2 from an input drive signal of 20 mW. The gain was approximately 43.8 dB. [ABSTRACT FROM AUTHOR]

We consider the massless Dirac operator with the MIT bag boundary conditions on an unbounded three‐dimensional circular cone. For convex cones, we prove that this operator is self‐adjoint defined on four‐component H1$H^1$‐functions satisfying the MIT bag boundary conditions. The proof of this result relies on separation of variables and spectral estimates for one‐dimensional fiber Dirac‐type operators. Furthermore, we provide a numerical evidence for the self‐adjointness on the same domain also for non‐convex cones. Moreover, we prove a Hardy‐type inequality for such a Dirac operator on convex cones, which, in particular, yields stability of self‐adjointness under perturbations by a class of unbounded potentials. Further extensions of our results to Dirac operators with quantum dot boundary conditions are also discussed. [ABSTRACT FROM AUTHOR]

In seismic data processing, data recovery including reconstruction of the missing trace and removal of noise from the recorded data are the key steps in improving the signal-to-noise ratio (SNR). The reconstruction of seismic data and removal of noise becomes a sparse optimization problem that can be solved by using sparse regularization. Sparse regularization is a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed inverses feasible. It deals with ill-posedness by replacing an ill-posed inverse problem with a well-posed problem that has a solution close to the true solution. In the last 2 decades, interest has shifted from linear toward nonlinear regularization methods even for linear inverse problems. In inverse problems, regularizations serve as stabilizing the solution of ill-posed inverse problems and give a solution that adequately fits measurements without producing unjustifiably complex artifacts. In this paper, we present a novel sparse regularization based on a tensor-based dictionary method for inverse problems (seismic data interpolation and denoising). This regularization avoids the vectorization step for sparse representation of seismic data during the reconstruction process. The key step in sparsifying signals is the choice of sparsity-promoting dictionary learning. The learning-based approach can adaptively sparsify datasets but has high computational complexity and involves no prior-constraint pattern information for the dataset. Many existing dictionary learning methods would be computationally infeasible for the high dimensional seismic data processing. These methods also destroy the essential information as well as it reduces the discriminability and expressibility of the signal, since they deal with vectorization. In this paper, the orthogonal tensor dictionary learning that learns a dictionary from the input data by employing orthogonality and separability is proposed as sparse regularization for the inverse problems. The performance of the proposed method was validated in seismic data interpolation and denoising individually as well as simultaneously. Numerical examples of synthetic and real seismic datasets demonstrate the validity of the proposed method. The SNR of the recovered data confirms that the proposed method is the most effective method than K-singular value decomposition and orthogonal dictionary learning methods. [ABSTRACT FROM AUTHOR]

In this article, an optimal robust constraint-following control is proposed for the underactuated vehicle path tracking problem. First, an underactuated dynamic model is established according to Udwadia–Kalaba (UK) equation, and the system uncertainty is decomposed into matching and mismatching portions based on the system geometric characteristics. The mismatching uncertainty is orthogonal to task space; thus, its influence on system stability is eliminated. Second, the diffeomorphism method is used to creatively set inequality and equality constraints into new equality constraints, and a robust control method for front steering vehicles with parameter-tunable is proposed. Third, an optimal design scheme is proposed for the tunable parameters to minimize the comprehensive index of system performance and control cost. Carsim-Simulink co-simulation shows the effectiveness of the proposed optimal robust control. This article creatively solves the problem of optimal robust control for path tracking of multi-constrained underactuated vehicles. [ABSTRACT FROM AUTHOR]

The first part of the Hilbert–Huang transformation is named the empirical mode decomposition (EMD). Which employed to decompose the non-stationary and non-linear time series dataset into a finite set of orthogonal decomposition components. These components have been used in several studies as the new predictor variables to predict the behavior of the response variables. Adaptive LASSO (AdLASSO) regression is a technical penalized regression method used to determine the most relevant predictors on the response variable with achieving the consistency in terms of variable selection and ensuring that they are asymptotically normal. Hence, the main objective of this study is to apply the proposed EMD-AdLASSO method involving two cases of initial weights to identify the decomposed components that exhibit the strongest effects to produce a consistent model and to improve the prediction accuracy. The simulation study and real dataset used the daily exchange rate dataset of three countries against the US dollar are applied. The results showed that the proposed method in the two cases of the initial weight outperformed other existing methods by effectively identifying the decomposition components, with high prediction accuracy. This is primarily observed in the case of using the ridge regression method based on the EMD as the initial weight in the proposed EMD-AdLASSO method. [ABSTRACT FROM AUTHOR]

Non-orthogonal eigenstates are a fundamental feature of non-Hermitian systems and are accompanied by the emergence of nontrivial features. However, the platforms to explore non-Hermitian mode couplings mainly measure near-field effects, and the far-field behaviours remain mostly unexplored. Here, we study how a microcavity with non-Hermitian mode coupling exhibits eigenstate non-orthogonality by investigating the spatial field and the far-field polarization of cavity modes. The non-Hermiticity arises from asymmetric backscattering, which is controlled by integrating two scatterers of different size and location into a microdisk. We observe that the spatial field overlap of two modes increases abruptly to its maximum value, whilst different far-field elliptical polarizations of two modes coalesce when approaching an exceptional point. We demonstrate such features experimentally by measuring the far-field polarization from the fabricated microdisks. Our work reveals the non-orthogonality in the far-field degree of freedom, and the integrability of the microdisks paves a way to integrate more non-Hermitian optical properties into nanophotonic systems. Whispering gallery mode microcavities with asymmetric backscattering provide a platform to characterise non-orthogonal Hermitian features, but the majority of the studies focus on near-field measurements. The authors realize a non-Hermitian platform and characterise its far-field features in terms of polarization via confocal micro-photoluminescence. [ABSTRACT FROM AUTHOR]

Conducting large-scale numerical computations to obtain flow field during the hypersonic vehicle engineering design phase can be excessively costly. Although deep learning algorithms enable rapid flow field prediction with high-precision, they require a significant investment in training samples, contradicting the motivation of reducing the cost of acquiring flow field. The combination of feature extraction algorithms and regression algorithms can also achieve high-precision prediction of flow fields, which is more suitable to tackle three-dimensional flow prediction with a small dataset. In this study, we propose a reduced-order model (ROM) for the three-dimensional hypersonic vehicle flow prediction utilizing proper orthogonal decomposition to extract representative features and Gaussian process regression with improved automatic kernel construction (AKC-GPR) to perform a nonlinear mapping of physical features for prediction. The selection of variables is based on sensitivity analysis and modal assurance criterion. The underlying relationship is unveiled between flow field variables and inflow conditions. The ROM exhibits high predictive accuracy, with mean absolute percentage error (MAPE) of total field less than 3.5%, when varying altitudes and Mach numbers. During angle of attack variations, the ROM only effectively reconstructs flow distribution by interpolation with a MAPE of 7.02%. The excellent small-sample fitting capability of our improved AKC-GPR algorithm is demonstrated by comparing with original AKC-GPRs with a maximum reduction in a MAPE of 35.28%. These promising findings suggest that the proposed ROM can serve as an effective approach for rapid and accurate vehicle flow predicting, enabling its application in engineering design analysis. [ABSTRACT FROM AUTHOR]

In the face of mounting economic constraints, researchers are increasingly turning to data-driven methods for reconstructing unknown global fields from limited data. While traditional compressed sensing (CS) technology addresses this challenge, the least absolute shrinkage and selection operator algorithm within CS encounters difficulties in precisely solving basis coefficients. This challenge is exacerbated by the frequently unknown observation matrix, often necessitating optimization methods for resolution. This study introduces the CS-FNN (CS-Fully Connected Neural Network) method, leveraging neural network technology to refine CS-obtained basis coefficients. This approach proves particularly advantageous in scenarios involving custom observation points. Focused on hydrofoil pressure fields, our comparative analysis with CS-PSO (CS-Particle Swarm Optimization) covers the reconstruction accuracy, the performance in varied unsteady situations, and robustness concerning the number of truncated proper orthogonal decomposition modes, measuring point distribution, and real noise environments. Results demonstrate the superiority of CS-FNN over CS-PSO in predicting global hydrofoil pressure fields, with higher reconstruction accuracy, a more flexible arrangement of measuring points, and a balance between robustness and accuracy that meets the requirements of practical engineering. This innovative method introduces a new and effective approach for recovering high-dimensional data, presenting significant potential for practical engineering applications. [ABSTRACT FROM AUTHOR]

We prove that if G$G$ is a finite irreducible solvable subgroup of an orthogonal group O(V,Q)$O(V,Q)$ with dimV$\dim V$ odd, then G$G$ preserves an orthogonal decomposition of V$V$ into 1‐spaces. In particular G$G$ is monomial. This generalizes a theorem of Rod Gow. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time robust adaptive simultaneous stabilisation for nonlinear time-delay systems, taking into account actuator saturation and unknown parameters. Firstly, by employing adaptive control strategies and finite-time stability theory, a finite-time adaptive simultaneous stabilisation scheme for the nonlinear time-delay systems is developed. Secondly, utilising the orthogonal decomposition method, a finite-time robust adaptive simultaneous stabilisation scheme for nonlinear time-delay systems with external disturbances is proposed. Finally, simulations demonstrate the effectiveness of the provided control scheme. [ABSTRACT FROM AUTHOR]

A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a coarse-scale representation of the elliptic operator, enriched by fine-scale information on the diffusion. Optimal order strong convergence is derived. The LOD technique is combined with a (multilevel) Monte Carlo estimator and the weak error is analyzed. Numerical examples that confirm the theoretical findings are provided, and the computational efficiency of the method is highlighted. [ABSTRACT FROM AUTHOR]

In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and localized trust-region reduced basis method. Localization is obtained based on a Petrov–Galerkin localized orthogonal decomposition method and its recently introduced two-scale reduced basis approximation. We derive efficient localizable a posteriori error estimates for the optimality system, as well as for the two-scale reduced objective functional. While the relaxation of the outer trust-region optimization loop still allows for a rigorous convergence result, the resulting method converges much faster due to larger step sizes in the initial phase of the iterative algorithms. The resulting algorithm is parallelized in order to take advantage of the localization. Numerical experiments are given for a multiscale thermal block benchmark problem. The experiments demonstrate the efficiency of the approach, particularly for large scale problems, where methods based on traditional finite element approximation schemes are prohibitive or fail entirely. [ABSTRACT FROM AUTHOR]

A bionic robotic fish based on compliant structure can excite the natural modes of vibration, thereby mimicking the body waves of real fish to generate thrust and realize undulate propulsion. The fish body wave is a result of the fish body's mechanical characteristics interacting with the surrounding fluid. Thoroughly analyzing the complex modal characteristics in such robotic fish contributes to a better understanding of the locomotion behavior, consequently enhancing the swimming performance. Therefore, the complex orthogonal decomposition (COD) method is used in this article. The traveling index is used to quantitatively describe the difference between the real and imaginary modes of the fish body wave. It is defined as the reciprocal of the condition number between the real and imaginary components. After introducing the BCF (body and/or caudal fin) the fish's body wave curves and the COD method, the structural design and parameter configuration of the tensegrity robotic fish are introduced. The complex modal characteristics of the tensegrity robotic fish and real fish are analyzed. The results show that their traveling indexes are close, with two similar complex mode shapes. Subsequently, the relationship between the traveling index and swimming performance is expressed using indicators reflecting linear correlation (correlation coefficient ( R c ) and p value). Based on this correlation, a preliminary optimization strategy for the traveling index is proposed, with the potential to improve the swimming performance of the robotic fish. [ABSTRACT FROM AUTHOR]

An H $H$‐decomposition of a graph G $G$ is a partition of the edge set of G $G$ into subsets, where each subset induces a copy of the graph H $H$. A k $k$‐orthogonal H $H$‐decomposition of G $G$ is a set of k $k$H $H$‐decompositions of G $G$ such that any two copies of H $H$ in distinct H $H$‐decompositions intersect in at most one edge. When G=Kv $G={K}_{v}$, we call the H $H$‐decomposition an H $H$‐system of order v $v$. In this paper, we consider the case H $H$ is an ℓ $\ell $‐cycle and construct a pair of orthogonal ℓ $\ell $‐cycle systems for all admissible orders when ℓ∈{5,6,7,8,9} $\ell \in \{5,6,7,8,9\}$, except when ℓ=v $\ell =v$. [ABSTRACT FROM AUTHOR]

This paper is concerned with the outlier-resistant observer-based control problem for a class of interval type-2 (IT2) Takagi–Sugeno (T-S) fuzzy systems under adaptive event-triggered protocol (AETP). To improve the efficiency of resource utilization, AETP is mainly through an adjustable threshold parameter to dynamically schedule the data transmission, which occurs in the sensor-to-controller channel. In order to resist the abnormal measurement values, an output saturation composition is constructed in the observer. With the aid of Lyapunov theory, sufficient conditions are obtained to ensure the desired performance. Furthermore, the desired controller is designed for a class of IT2 T-S fuzzy systems. The combination of orthogonal decomposition and linear matrix inequalities is implemented to deal with the nonlinear coupling terms in the gain solving process. Finally, a numerical example is employed to justify the practicality and effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In the field of scientific computation, orthogonal iteration is an essential method for computing the invariant subspace corresponding to the largest r eigenvalues. In this paper, we construct a flow that connects the sequence of matrices generated by the orthogonal iteration. Such a flow is called an orthogonal flow. In addition, we show that the orthogonal iteration forms a time-one mapping of the orthogonal flow. A generalized orthogonal flow is constructed that has the same column space as the orthogonal flow. By using a suitable change of variables, the generalized orthogonal flow can be transformed into the solution of a Riccati differential equation (RDE). Conversely, an RDE can also be transformed into a flow that can be represented by a generalized orthogonal flow. [ABSTRACT FROM AUTHOR]

The vertical structure of subinertial variability is examined using full-depth horizontal velocity and vertical isopycnal displacement observations derived from the Ocean Observatory Initiative (OOI). Vertical profiles on time scales between 100 h and 1 yr or longer are characterized through empirical orthogonal function decomposition and qualitatively compared with theoretical modal predictions for the cases of flat, sloping, and rough bathymetry. OOI observations were obtained from mooring clusters at four deep-ocean sites: Argentine Basin, Southern Ocean, Station Papa, and Irminger Sea. Because no single OOI mooring in these arrays provides temperature, salinity, and horizontal velocity information over the full water column, sensor observations from two or more moorings are combined. Depths greater than ∼150–300 m were sampled by McLane moored profilers; in three of the four cases, two profilers were utilized on the moorings. Because of instrument failures on the deployments examined here, only ∼2 yr of full-ocean-depth observations are available from three of the four sites and some 3+ yr from the other. Results from the OOI "global" sites are contrasted with a parallel analysis of 3.5 yr of observations about the axis of the Gulf Stream where much of the subinertial variability is associated with stream meandering past the moorings. Looking across the observations, no universal vertical structure is found that characterizes the subinertial variability at the five sites examined; regional bathymetry, stratification, baroclinicity, nonlinearity, and the forcing (both local and remote) likely all play a role in shaping the vertical structure of the subinertial variability in individual ocean regions. [ABSTRACT FROM AUTHOR]

In this article, we aim to prove the solvability for the fractional viscoelastic plate vibration model through the Galerkin argument in Sobolev spaces as a compensation for the absence of its mathematical theory, then propose an efficient compact difference-proper orthogonal decomposition (CD-POD) algorithm. Rigorous numerical analyses are conducted to show that the CD-POD algorithm inherits the merits of the compact difference and the proper orthogonal decomposition technique, that is, it is unconditionally stable, possesses the spatial and temporal convergence rates of fourth order and second order, respectively, and reduces greatly the storage and computing cost, and thus may adapts for long time simulation for the plate vibration model. As a bridge for the plate vibration model and the CD-POD algorithm, a compact difference scheme is also proposed and analyzed previously. Numerical experiments, one of which is for resonance case, indicate that the CPU time of the CD-POD algorithm is at least 20 times less than that of the compact difference scheme, for resonance case or for non-resonance case, and thus verifies again that the CD-POD algorithm is a reasonable computation candidate for long time simulation of the viscoelastic plate vibration model. [ABSTRACT FROM AUTHOR]

This study examines the dependence of Arctic stratospheric polar vortex (SPV) variations on the meridional positions of the sea surface temperature (SST) anomalies associated with the first leading mode of North Pacific SST. The principal component 1 (PC1) of the first leading mode is obtained by empirical orthogonal function decomposition. Reanalysis data, numerical experiments, and CMIP5 model outputs all suggest that the PC1 events (positive-minus-negative PC1 events), located relatively northward (i.e., North PC1 events), more easily weaken the Arctic SPV compared to the PC1 events located relatively southward (i.e., South PC1 events). The analysis indicates that the North PC1-related Aleutian low anomaly is located over the northern North Pacific and thus enhances the climatological trough, which strengthens the planetary-scale wave 1 at mid-to-high latitudes and thereby weakens the SPV. The weakened stratospheric circulation further extends into the troposphere and favors negative surface temperature anomalies over Eurasia. By contrast, the South PC1-related Aleutian low anomaly is located relatively southward, and its constructive interference with the climatological trough is less efficient at high latitudes. Thus, the South PC1 events could not induce an evident enhancement of the planetary-scale waves at high latitudes and thereby a weakening of the SPV on average. The Eurasian cooling associated with South PC1 events (positive-minus-negative PC1 events) is also not prominent. The results of this study suggest that the meridional positions of the PC1 events may be useful for predicting the Arctic SPV and Eurasian surface temperature variations. [ABSTRACT FROM AUTHOR]

Classical models for the passive myocardium, such as the Fung and Holzapfel-Ogden models, are known to have high degeneracy as well as numerous mechanical and mathematical limitations, preventing their utility in microstructural experiments and precision medicine. Hence, the upper triangular (QR) decomposition and orthogonal strain attributes were leveraged to develop a new model using published biaxial data on slabs of left myocardium, resulting in a separable strain energy function. This new model, the Criscione-Hussein model, was compared with both the Fung and Holzapfel-Ogden models by quantifying the uncertainty, computational efficiency, and material parameter fidelity for all three models. As a result, the Criscione-Hussein model was found to significantly reduce the uncertainty and computational time (p < 0.05) and enhance the fidelity of the material parameters. Hence, the Criscione-Hussein model enhances the predictability for the passive behavior of the myocardium and may serve a role in creating more accurate computational models that provide better visualizations for the mechanical behavior of the heart and enable the experimental connection between the model and the myocardial microstructure. [ABSTRACT FROM AUTHOR]

Within a flow of a viscous fluid the effects of compression and viscosity are closely coupled with inertia. Discrete mechanics gives a physical sense of these interactions by showing that they exist only in a dynamic vision where the variation of the velocity in time generates the entanglement of the effects of compression and shearing. These two phenomena are described in the form of a Helmholtz–Hodge decomposition by two orthogonal terms within the discrete equation of motion, the first curl-free and the second divergence-free. They can only exchange mechanical energy if the acceleration is nonzero. This entanglement, which occurs at all spatial scales, is a function of longitudinal and transverse celerities. After a presentation of the formal framework, simple examples allow to understand the temporal shifts of direct and induced flows in accordance with the causality principle. [ABSTRACT FROM AUTHOR]

Many stable and convergent numerical methods are not pressure robust for an incompressible flow problem, due to the relaxation of a discrete divergence constraint called poor mass conservation. As a result, the velocity error is polluted by the pressure error, particularly when the fluid viscosity is relatively small and pressure is comparably large. A grad-div stabilization is an efficient remedy in conforming finite element methods. In this paper, an analogue of the grad-div stabilization that the penalization of the jumps of the normal velocities over facets of the triangulation in discontinuous Galerkin (DG) methods is investigated for a coupled Stokes and Darcy problem, it can efficiently improve the accuracy of velocity and mass conservation. Firstly, we present the existence and uniqueness of a solution, unconditional stability and a priori estimates for the DG method. Then, by using the principle of superposition and orthogonal decomposition cleverly, we prove the limiting behavior that the DG method with an analogue of grad-div stabilization for a coupled Stokes and Darcy problem converge to the strongly conservative BDM DG method with a convergence rate of O (λ f − 1 + λ s − 1) , it allows for arbitrarily large stabilization parameters. Finally, some numerical tests are given to validate the optimal convergence rates and their effectiveness. [ABSTRACT FROM AUTHOR]

This paper is concerned with the multiplicative-noise rational expectations (MRE) problem. By resorting to a linear quadratic optimal control (LQOC) problem, the approximate solution to the MRE problem can be obtained. It is worth highlighting that this approximate solution can be highly close to the exact solution by adjusting weighted matrices in the cost function of the LQOC problem. Since the conditional expectation of the state is involved in the cost function, the LQOC problem is an optimization control with an additional measurability restriction, which is very involved. The orthogonal decomposition technique is used to deal with this measurability restriction. The solvability condition and the optimal decision are given by developing generalized Riccati-type equations. Numerical experiments are provided to illustrate the effectiveness of the achieved results. [ABSTRACT FROM AUTHOR]

Regional persistent extreme cold events are meteorological disasters that cause serious harm to people's lives and production; however, they are very difficult to predict. Low-temperature weather systems and their effects have a significant low-frequency oscillation period (10–20 d and 30–60 d). This paper uses deep learning to analyze the extended-range time scale and predict regional persistent extreme cold events. The dominant low-frequency oscillation components of cold events are obtained via wavelet transform and Butterworth filtering. The low-frequency oscillation component is decomposed via empirical orthogonal function decomposition to extract the main spatial mode and time coefficient. A convolutional neural network is used to establish the correlation between large-scale circulations and the time coefficient of the low-frequency oscillation component of the lowest temperature. The proposed deep learning model exhibits good prediction accuracy for regional persistent extreme cold events with low-frequency oscillations. [ABSTRACT FROM AUTHOR]

Microcapsules are widely used in various fields. However, there is no way to predict the mechanical response of microcapsules accurately. To address this problem, the improved Reissner theory and the Tatara theory are employed to establish the mechanical response models of the capsule shell and the capsule core, respectively. Moreover, the capsule core loss, which is always neglected in prior study, is obtained through the mass ratio of the capsule core. Therefore, a universal and effective mechanical response model with microcapsule characteristics is developed. In addition, a set of orthogonal tests are designed based on the mechanical response model to analyze the contributions of the microcapsule components to the mechanical response. The results show that: (1) the proposed microcapsule mechanical response model has prediction errors of less than 30% for various types of microcapsule mechanical response results, and the gray correlation degree of the prediction trend is above 0.6. Compared to traditional models that can only predict trends, with an error rate of 400%, the proposed model has an improvement; (2) the loss of core is inevitable, and the three microcapsules in the study all have a core loss volume of 10–30%; (3) when the strain is large, the mechanical response of overall microcapsules is determined by the size and core of microcapsules. The results provide a theoretical basis for designing the microcapsules. [ABSTRACT FROM AUTHOR]

The interannual variations in salt flux on the 80°E section in the equatorial Indian Ocean were explored based on the ORAS5 data, which was quite consistent with the observational data among the four available reanalysis datasets. The results indicated that the area with significant interannual variations in salt flux coincided with that of significant climatological mean salt flux in general and was mainly located in the upper 150 m layer. Specifically, three important areas were identified in the north-south direction, i.e., (1) the Equatorial Indian Ocean Area (EIOA, 3°S–3°N), where the mean salt flux was eastward with the largest value on the section and associated with the most significant interannual variations mainly modulated by the Wyrtki Jets and the Equatorial Undercurrent; (2) the South Equatorial Indian Ocean Area (SEIOA, 3°S–6°S), where the mean salt flux changed in the vertical direction from strong eastward flux in the upper layer to weak westward flux in the subsurface layer and associated with significant interannual variations in the upper 100 m layer, which was affected by the South Equatorial Countercurrent; and (3) the North Equatorial Indian Ocean Area (NEIOA, 3°N–6°N), where the mean salt flux changed in the north-south direction from strong westward flux to the north of 5°N to weak eastward flux in the south and associated with relatively significant interannual variations, which was mainly influenced by the South Sri Lanka Coastal Current. Two leading interannual variation modes were revealed by the empirical orthogonal function decomposition. The first mode accounted for 39% of the total variance and had four significant spatial antinodes; two of those in-phase antinodes were located at SEIOA and upper 75 m of EIOA, and the other two opposite in-phase antinodes were located at NEIOA and below 75 m of EIOA. The second mode accounted for 17% of the total variance having four antinodes with two dominant out-of-phase antinodes located at the subsurface of EIOA and SEIOA. The temporal components of the two leading modes showed a 1–4 year variation with a main period of 2 years, in which the first mode showed a greater correlation with the Indian Ocean Dipole, while the second mode showed a weak correlation with the Indian Ocean Dipole and the El Niño-Southern Oscillation. Variance analysis showed that the interannual variations in salt flux were mainly determined by the variations in the current, and the spatial distribution was modulated by temporal mean salinity. Composite strong interannual events showed interannual variations in current, and so the salt flux was driven by the interannual anomaly of the wind field and sea surface temperature associated with the Indian Ocean Dipole. [ABSTRACT FROM AUTHOR]

The factors influencing precipitation in western China are quite complex, which increases the difficulty in determining accurate predictors. Hence, this paper models the monthly measured precipitation data from 240 meteorological stations in mainland China and the precipitation data from the European Centre for Medium-Range Weather Forecasts and the National Climate Centre and employs 88 atmospheric circulation indices to develop a precipitation prediction scheme. Specifically, a high-quality grid-point field is created by fusing and revising the precipitation data from multiple sources. This field is combined with the Empirical Orthogonal Function decomposition and the causal information flow. Next, the best predictors are screened through Empirical Orthogonal Function decomposition and causal information flow, and a data-driven precipitation prediction model is established using a Back Propagation Neural Network and a Random Forest algorithm to conduct the 1-month, 3-month, and 6-month precipitation predictions. The results show that: The machine learning-based precipitation prediction model has high accuracy and is generally able to predict the precipitation trend in the western region better. The Random Forest algorithm significantly outperforms the Back Propagation Neural Network algorithm in the prediction of the three starting times, and the prediction ability of both models gradually decreases as the starting time increases. Compared with the 2022 flood season prediction scores of the Institute of Atmospheric Sciences of the Chinese Academy of Sciences, the model improves the prediction of 1-month and 3-month precipitation in the western region and provides a new idea for the short-term climate prediction of precipitation in western China. [ABSTRACT FROM AUTHOR]

In recent years, MIMO high-frequency surface wave radar (MIMO-HFSWR) plays an increasingly important role in sea surveillance because of its wide-area surveillance capabilities. In signal processing, the coherent targets with the same distance and speed can only be distinguished in the angle dimension. However, HF radar's angular resolution is poor because of the restrictions of the aperture, which causes aliasing of targets on the range–angle (RA) spectrum. Traditional super-resolution algorithms, such as MUSIC, are also inapplicable because of the targets' coherence. Therefore, the spatial smoothing algorithm is usually used to realize the decoherence of echo at the cost of array aperture. The loss of array aperture makes the algorithm fail when there are too many targets in the echo. Aiming at this problem, this paper proposes an iterative calculation method (iterative calculation via weight vector orthogonal decomposition, IC-WORD) to estimate the angle of multiple coherent targets. Through the verification of simulation, it is proved that IC-WORD has better performance than the traditional spatial smoothing algorithm. More specifically, IC-WORD can correct spectral peak shift, improve angle measurement accuracy, and still operate stably under the condition of multiple coherent targets. This paper also uses the measured data from one of the most advanced HFSWR stations in China to validate the algorithm, which makes the paper have strong practical significance. [ABSTRACT FROM AUTHOR]

Purpose : To assess how eye axes and multifocal intraocular lens (MIOL) centration may impact the light distortion index (LDI) and ocular scatter index (OSI). Methods: Fifty-eight subjects implanted with the trifocal MIOL Q-Flex M 640PM or Liberty 677MY (Medicontur) were included in this retrospective analysis. The following variables were collected with the Pentacam Wave (Oculus) considering the vertex normal as the coordinates center: chord-mu to the center of the pupil, chord-alpha to the geometrical center of the cornea, and chord-MIOL to the center of the diffractive ring. These measurements were correlated with OSI (HD Analyzer, Visiometrics) and LDI (light distortion analyzer, CEORLab). Results: Chord-MIOL centroid was 0.12 mm at 62°, chord-mu was 0.09 mm at 174°, and chord-alpha was 0.38 mm at 188°. A relationship was found between OSI and LDI, rho = 0.58, p < 0.0005). No relationships were found between chord-mu or chord-alpha and the LDI or OSI, neither for the total magnitude, nor the decomposition in orthogonal components (p > 0.05). The LDI was significantly correlated with the temporal centration of the MIOL versus the vertex normal (rho = 0.32, p = 0.02). Conclusions: As opposed to what has been previously described, the temporal centration of the MIOL was related to a decrease in the LDI. Future studies with extreme values of the included variables are required to establish cut-offs for considering these variables as exclusion criteria in the implantation of a MIOL. [ABSTRACT FROM AUTHOR]

As the penetration rate of distributed generators (DG) in active distribution networks (ADNs) gradually increases, it is necessary to accurately estimate the operating state of the ADNs to ensure their safe and stable operation. However, the high randomness and volatility of distributed generator output and active loads have increased the difficulty of state estimation. To solve this problem, a method is proposed for forecasting-aided state estimation (FASE) in ADNs, which integrates the optimal extreme random forest based on the maximum average energy concentration (MAEC) and variable mode decomposition (VMD) of states. Firstly, a parameter optimization model based on MAEC is constructed to decompose the state variables of the ADNs into a set of intrinsic mode components using VMD. Then, strongly correlated weather and date features in ADNs state prediction are selected using the multivariate rapid maximum information coefficient (RapidMIC) based on Schmidt orthogonal decomposition. Finally, by combining the set of intrinsic mode functions of the ADNs state, calendar rules, and weather features, an ensemble FASE method based on the extreme random tree (ERT) ensemble for the ADNs based on cubature particle filtering (CPF) is developed. An optimization model based on mean absolute error and root mean square error is established to obtain the optimal integration strategy and final estimation results. Simulation verification is performed on the IEEE 118-bus standard distribution system. The results show that the proposed method achieves higher accuracy compared to other estimation methods, with root mean square errors of 1.4902 × 10−4 for voltage magnitude and 4.8915 × 10−3 for phase angle. [ABSTRACT FROM AUTHOR]

To ensure the accuracy and stability of intelligent-vehicle-trajectory tracking, a robust trajectory-tracking control strategy based on generalized Hamilton theory is proposed. Firstly, a dynamic Hamilton dissipative controller (DHDC) and trajectory-tracking Hamilton dissipative controller (TTHDC) were designed based on the established vehicle-dynamics control system and trajectory-tracking control system using the orthogonal decomposition method and control-switching method. Next, the feedback-dissipative Hamilton realizations of the two systems were obtained separately to ensure the convergence of the system. Secondly, based on the dissipative Hamilton system designed by TTHDC, a generalized Hamilton robust controller (GHRC) was designed. Finally, the co-simulation of Carsim and MATLAB/Simulink was used to verify the effectiveness of the three control algorithms. The simulation results show that DHDC and TTHDC can achieve self-stabilizing control of vehicles and enable certain control effects for the trajectory tracking of vehicles. The GHRC solves the problems of low tracking accuracy and poor stability of DHDC and TTHDC. Compared with the sliding mode controller (SMC) and linear quadratic regulator (LQR) controller, the GHRC can reduce the lateral error by 84.44% and the root mean square error (RMSE) by 83.92%, which effectively improves the accuracy and robustness of vehicle-trajectory tracking. [ABSTRACT FROM AUTHOR]

This paper focuses on the linear quadratic optimal control problem for stochastic systems with a special terminal penalty. The specialty lies in that the terminal penalty is a quadratic term over the conditional expectations of the terminal state. The essential difficulty lies in an additional measurability constraint on the input induced by the conditional expectation term, which is shared by the control problems for the stochastic system with delays, rational expectations problems, control problems involving conditional expectation terms, asymmetric information control and so on. A new idea, dynamic programming combined with orthogonal decomposition, is proposed to deal with this problem. The orthogonal decomposition eliminates the additional measurability constraint on the input. The solvability condition and the optimal controller are obtained by developing generalised Riccati equations. Numerical experiment is provided to support the achieved results. [ABSTRACT FROM AUTHOR]

We report a study on granular matter with and without small additions of silicon oil, under low-frequency and large amplitude oscillatory shear strain under constant normal pressure, by running experiments with a rotational rheometer with a cup-and-plate geometry. We analysed the expansion with the Chebyshev polynomials of the orthogonal decomposition of stress–strain Lissajous–Bowditch loops. We found the onset of the strain amplitude for the yielding regime indicated a regime change from filament-like structures of grains to grain rearrangements for the dry granulate and from oscillations to the breaking and regeneration of liquid bridges for wet granulates. We have shown that this viscoelastic dynamics can be characterized by a noise temperature following Sollich et al. (Phys Rev Lett https://doi.org/10.1103/PhysRevLett.78.2020, 1997). The analysis of the first harmonics of the Chebyshev expansion showed that the state of disorder of dry and wet granular matter in pre-yielding and yielding regimes involved ensembles of different inherent states; thus, each of them was governed by a different noise temperature. The higher-order harmonics of the Chebyshev expansion revealed a proportionality between the viscous nonlinearity and the variation in the elastic nonlinearity induced by the deformation, which shows the coupling between the elastic deformation and the viscous flow of mesoscopic-scale structures. [ABSTRACT FROM AUTHOR]

We are concerned with employing model order reduction to efficiently solve parameterized multiscale problems using the localized orthogonal decomposition (LOD) multiscale method. Like many multiscale methods, the LOD follows the idea of separating the problem into localized fine-scale subproblems and an effective coarse-scale system derived from the solutions of the local problems. While the reduced basis (RB) method has already been used to speed up the solution of the fine-scale problems, the resulting coarse system remained untouched, thus limiting the achievable speedup. In this work, we address this issue by applying the RB methodology to a new two-scale formulation of the LOD. By reducing the entire two-scale system, this two-scale RB LOD approach yields reduced order models that are completely independent from the size of the coarse mesh of the multiscale approach, allowing an efficient approximation of the solutions of parameterized multiscale problems even for very large domains. A rigorous and efficient a posteriori estimator bounds the model reduction error, taking into account the approximation error for both the local fine-scale problems and the global coarse-scale system. [ABSTRACT FROM AUTHOR]

In this paper we revisit a two-level discretization based on localized orthogonal decomposition (LOD). It was originally proposed in [P. Henning, A. Målqvist, and D. Peterseim, SIAM J. Numer. Anal., 52 (2014), pp. 1525--1550] to compute ground states of Bose--Einstein condensates by finding discrete minimizers of the Gross--Pitaevskii energy functional. The established convergence rates for the method appeared, however, suboptimal compared to numerical observations and a proof of optimal rates in this setting remained open. In this paper we shall close this gap by proving optimal order error estimates for the L² - and H¹-errors between the exact ground state and discrete minimizers, as well as error estimates for the ground state energy and the ground state eigenvalue. In particular, the achieved convergence rates for the energy and the eigenvalue are of 6th order with respect to the mesh size on which the discrete LOD space is based, without making any additional regularity assumptions. These high rates justify the use of very coarse meshes, which significantly reduces the computational effort for finding accurate approximations of ground states. In addition, we include numerical experiments that confirm the optimality of the new theoretical convergence rates, for both smooth and discontinuous potentials. [ABSTRACT FROM AUTHOR]

The extended phase-consistent dynamic mode decomposition (DMD) method, which reconstructs density fields from density gradient fields in multiple directions, was developed and applied to schlieren images in the low-density wind tunnel tests. Schlieren images were acquired in the Re = 3000, 10,000, and M = 0.15, 0.50 flows around a triangular airfoil, and the density gradient fields were calculated from the calibration of the optical system. The proposed density field reconstruction method adopts the extended phase-consistent DMD principle for the estimation of the DMD modes of the density field. The density field was reconstructed with good accuracy in a numerical simulation for comparison, and the density fluctuation region caused by vortex shedding around a triangular airfoil was visualized by the experimental data. [ABSTRACT FROM AUTHOR]

In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only. Hence, no restrictive assumptions on the coefficient, the domain, or the exact solution are required. In the spirit of localized orthogonal decomposition, the method constructs coarse problem-adapted ansatz spaces by solving auxiliary problems on local subdomains. More precisely, our approach is based on the strategy presented by Maier [SIAM J. Numer. Anal., 59 (2021), pp. 1067--1089]. The unique selling point of the proposed method is an improved localization strategy curing the effect of deteriorating errors with respect to the mesh size when the local subdomains are not large enough. We present a rigorous a priori error analysis and demonstrate the performance of the method in a series of numerical experiments. [ABSTRACT FROM AUTHOR]

We show that the stability conditions on the Kuznetsov component of a Gushel–Mukai threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre functor, up to the action of the universal cover of GL2+(R)$\text{GL}^+_2(\operatorname{\mathbb {R}})$. As application, we construct stability conditions on the Kuznetsov component of special Gushel–Mukai fourfolds. [ABSTRACT FROM AUTHOR]

Orbital angular momentum (OAM) multiplexing is a recently considered solution for enhancing wireless and free-space optical communications channel capacity, whether implemented separately or in combination with existing multiplexing techniques. The theoretically infinite number of paraxially propagating and mutually orthogonal OAM modes is expected to increase the channel capacity. However, the orthogonality for different OAM modes has been shown to decrease for far link range distances, and the paraxiality of the OAM beams is not very good for small radiating sources. Based on the current knowledge, OAM beams are most likely to be used for short-range communications. Many models of the electromagnetic (EM) fields carrying the OAM neglect the fact that the OAM beam sources could be electrically large or introduce other approximations that are appropriate for far-field analysis only. An in-depth analysis of the short-range properties of OAM EM fields is still lacking. To address this problem, we propose the use of the infinitesimal (Hertz) dipole method customized for the analysis of the OAM EM fields. This technique can model the positioning and basic radiation properties of separate antennas or antenna sub-arrays that are the building blocks of OAM arrays exactly and efficiently. Similar modeling can represent the OAM sources for free-space optical communications. We focus here on the uniform circular antenna arrays and provide an in-depth analysis of what can and cannot be expected, in the best case, in their utilization. We assume low losses, which is a common assumption for many methods, except for computationally much more demanding full-wave simulations. The obtained results indicate the need to simultaneously optimize the transmission of all planned OAM modes and allow estimates of the link distances that could provide adequate OAM wave reception in various cases. [ABSTRACT FROM AUTHOR]

The estimation of time-resolved three-dimensional (3D) density fields of an underexpanded jet at the nozzle pressure ratio of 2.42, a so-called "spatiotemporal super-resolution" was conducted using non-time-resolved three-dimensional background-oriented schlieren (3D-BOS) and time-resolved microphone measurements. This approach aims to reconstruct three-dimensional density fields associated with the intermittent and switching behavior of the B mode of a screeching jet from the microphone data by constructing a linear regression model. An azimuthal Fourier decomposition is applied to the 3D-BOS and microphone data, and the proper orthogonal decomposition (POD) is performed for each of their azimuthal Fourier modes. The m = 1 azimuthal Fourier mode is dominant in both cases, and the leading two POD modes in the m = 1 azimuthal mode of the microphone data are associated with the B mode. The linear regression model is constructed from the POD modes of the m = 1 azimuthal 3D-BOS data and the first two microphone POD modes of the m = 1 azimuthal mode of the microphone data. The three-dimensional density fields reconstructed from each POD mode of the m = 1 azimuthal mode of the microphone data have helical structures with opposite rotation directions. The amplitudes of those POD modes change with time, and the azimuthal structure associated with the B mode is determined depending on those amplitudes. The present result showed that intermittency in the flapping to helical structures and their strength can be interpreted by the temporal changes in the strengths of two rotating helical structures with opposite rotation directions. [ABSTRACT FROM AUTHOR]