Decomposition Scheme Research Articles

Least-Squares Reverse-Time Migration of Water-Bottom-Related Multiples

Reverse-time migration of multiples can generate imaging results with wider illumination, higher folds, and broader wavenumber spectra than the conventional migration of primaries. However, the results of the migration of multiples retain heavy crosstalks generated by interactions between unrelated multiples, thereby seriously degrading imaging qualities. To eliminate such crosstalks, we propose a least-squares optimized algorithm of multiples. In this method, different-order water-column multiples and water-bottom-related multiples are extracted using multiple decomposition strategies before migration procedures. The proposed method treats the nth-order water-column multiples as virtual sources for Born modeling to produce the predicted (n+1)th-order water-bottom-related multiples. In each iteration, the gradients are calculated by crosscorrelating the forward-propagated nth-order water-column multiples with the backward-propagated seismic residuals between the observed and predicted (n+1)th-order water-bottom-related multiples. The developed approach is referred to as the least-squares reverse-time migration of water-bottom-related multiples (LSRTM-WM). Numerical experiments on a layered model and the Pluto 1.5 model demonstrate that LSRTM-WM can significantly remove crosstalks and considerably improve spatial resolution.

Nature of Beryllium, Magnesium, and Zinc Bonds in Carbene⋯MX2 (M = Be, Mg, Zn; X = H, Br) Dimers Revealed by the IQA, ETS-NOCV and LED Methods.

The nature of beryllium−, magnesium− and zinc−carbene bonds in the cyclopropenylidene⋯MX2 (M = Be, Mg, Zn; X = H, Br) and imidazol-2-ylidene⋯MBr2 dimers is investigated by the joint use of the topological QTAIM-based IQA decomposition scheme, the molecular orbital-based ETS-NOCV charge and energy decomposition method, and the LED energy decomposition approach based on the state-of-the-art DLPNO-CCSD(T) method. All these methods show that the C⋯M bond strengthens according to the following order: Zn < Mg << Be. Electrostatics is proved to be the dominant bond component, whereas the orbital component is far less important. It is shown that QTAIM/IQA underestimates electrostatic contribution for zinc bonds with respect to both ETS-NOCV and LED schemes. The σ carbene→MX2 donation appears to be much more important than the MX2→ carbene back-donation of π symmetry. The substitution of hydrogen atoms by bromine (X in MX2) strengthens the metal−carbene bond in all cases. The physical origin of rotational barriers has been unveiled by the ETS-NOCV approach.

Energetic Origins of Force Constants: Adding a New Dimension to the Hessian Matrix via Interacting Quantum Atoms.

The Interacting Quantum Atoms (IQA) energy decomposition scheme divides the total energy of a molecule into intra- and interatomic contributions. While the former relates to the kinetic and potential energies of electrons inside a unique individual atomic basin, the latter contains the Coulomb and exchange-correlation potentials between electrons from two atomic basins. Considering that the molecular energy is a sum of IQA contributions, the Hessian matrix can also be written as a sum of "IQA Hessian" matrices, whose elements are second derivatives of IQA terms. Herein, we present a mathematical formalism for the IQA decomposition of force constants revealing their energetic origins. The method consists of adding a new dimension to the Hessian matrix, which becomes 3N × 3N × N2, with N being the number of atoms in the molecule and N2 the number of IQA terms. Since there is no analytical method that produces the IQA second derivatives, the three-dimensional IQA Hessian is numerically calculated. When studying molecular vibrations, force constants, providing information about the nature of chemical bond and related to infrared frequencies, can be obtained by Wilson's FG method, which involves detailed manipulations of the Hessian matrix. In this paper, the methodology is reported and validated for a set of 30 molecules and more than 200 force constants and their interactions. Energetic origins of force constants are presented for diatomics and small molecules containing carbon-carbon, oxygen-oxygen, and carbon-oxygen bonds with different bond orders. It is found that bond stability and stiffness can have strikingly different energetic origins.

Error Decomposition of CRA40-Land and ERA5-Land Reanalysis Precipitation Products over the Yongding River Basin in North China

Long-term and high-resolution reanalysis precipitation datasets provide important support for research on climate change, hydrological forecasting, etc. The comprehensive evaluation of the error performances of the newly released ERA5-Land and CRA40-Land reanalysis precipitation datasets over the Yongding River Basin in North China was based on the two error decomposition schemes, namely, decomposition of the total mean square error into systematic and random errors and decomposition of the total precipitation bias into hit bias, missed precipitation, and false precipitation. Then, the error features of the two datasets and precipitation intensity and terrain effects against error features were analyzed in this study. The results indicated the following: (1) Based on the decomposition approach of systematic and random errors, the total error of ERA5-Land is generally greater than that of CRA40-Land. Additionally, the proportion of random errors was higher in summer and over mountainous areas, specifically, the ERA5-Land accounts for more than 75%, while the other was less than 70%; (2) Considering the decomposition method of hit, missed, and false bias, the total precipitation bias of ERA5-Land and CRA40-Land was consistent with the hit bias. The magnitude of missed precipitation and false precipitation was less than the hit bias. (3) When the precipitation intensity is less than 38 mm/d, the random errors of ERA5-Land and CRA40-Land are larger than the systematic error. The relationship between precipitation intensity and hit, missed, and false precipitation is complicated, for the hit bias of ERA5-L is always smaller than that of CRA40-L, and the missed precipitation and false precipitation are larger than those ofCRA40-L when the precipitation is small. The error of ERA5-Land and CRA40-Land was significantly correlated with elevation. A comprehensive understanding of the error features of the two reanalysis precipitation datasets is valuable for error correction and the construction of a multi-source fusion model with gauge-based and satellite-based precipitation datasets.

On multivariate randomized classification trees: [formula omitted]-based sparsity, VC dimension and decomposition methods

Decision trees are widely-used classification and regression models because of their interpretability and good accuracy. Classical methods such as CART are based on greedy approaches but a growing attention has recently been devoted to optimal decision trees. We investigate the nonlinear continuous optimization formulation proposed in Blanquero et al. (2020) for training sparse optimal randomized classification trees. Sparsity is important not only for feature selection but also to improve interpretability. We first consider alternative methods to sparsify such trees based on concave approximations of the l0 “norm”. Promising results are obtained on 24 datasets in comparison with the original l1 and l∞ regularizations. Then, we derive bounds on the VC dimension of multivariate randomized classification trees. Finally, since training is computationally challenging for large datasets, we propose a general node-based decomposition scheme and a practical version of it. Experiments on larger datasets show that the proposed decomposition method is able to significantly reduce the training times without compromising the testing accuracy.

Accelerating logic-based Benders decomposition for railway rescheduling by exploiting similarities in delays

The operation of a railway system is subject to unpredictable delays or disruptions. Operators control the railway system to minimize losses in performance. Real-time rescheduling is the adaptation of a railway schedule to any unforeseen delay or disturbance and recovers an optimal system state. In this work we propose the extension of an existing Benders decomposition scheme used so far for timetabling, to the case of railway rescheduling. We show how to increase its computational speed by a factor 2, by considering libraries of Benders cuts computed for other instances, to be reused in the solution. We show how including extra cuts has to balance a speedup potential, with a general slowdown due to optimization problems of increased sizes. We show that, if delays in an instance of rescheduling are in fact unknown, but come from a known statistical distribution, we can use a similarity measure to identify a-priori the most promising libraries of Benders cuts, which lead to speedups up to 20%.

Nonlocal optimized schwarz methods for time-harmonic electromagnetics

We introduce a new domain decomposition strategy for time harmonic Maxwell’s equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is guaranteed and we present a complete analysis of the matrix form of the method. The method involves transmission matrices responsible for imposing coupling between subdomains. We discuss the choice of such matrices, their construction and the impact of this choice on the convergence of the domain decomposition algorithm. Numerical results and algorithms are provided.

Are We Healthier Together? Two Strategies for Supporting Macronutrient Assessment Skills and How the Crowd Can Help (or Not)

Learning macronutrient assessment skills can support improved health outcomes and overall wellbeing. We conducted two Mechanical Turk studies to investigate how users might benefit from the crowd's input in macronutrient assessment education. We first determined whether the wisdom of the crowd alone would provide users with enough insight to arrive at accurate macronutrient estimates. Next, we tested two methods of teaching macronutrient assessment skills (Comparison and Decomposition) and analyzed their effectiveness. Results from these studies indicate that while the crowd alone may not be sufficient to support this type of education, users may yet benefit from access to community-generated photos and labels while they use either the Comparison or Decomposition strategy.

Interference fringe suppression in tunable diode laser absorption spectroscopy based on CEEMDAN-WTD

Owing to interference fringes in the multireflective gas cell, the detection sensitivity of a system in tunable diode laser absorption spectroscopy (TDLAS) will decrease significantly. In this work, a combined scheme of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and wavelet threshold denoising (WTD) is proposed. Theoretical simulations were performed to validate the effects of the proposed algorithm, which was also verified via a CO2 detection experiment. After CEEMDAN-WTD processing, the noisy intrinsic mode function (IMF), pure IMF, and residual components of the detection signal were identified and reconstructed successfully. Based on analysis of the simulations, CEEMDAN-WTD algorithm improved the signal-to-noise ratio by 1.87 times and decreased the root mean-squared error by 37.6% than the moving average algorithm. For the CO2 detection system, R2 = 0.999 was determined by the calibration experiment. Additionally, based on Allan variance analysis and a long-time experiment, the limit of detection was estimated to be 3.08 ppm for an average time of 148 s and measurement accuracy of 0.65%, respectively. The obtained results sufficiently validate that the CEEMDAN-WTD algorithm can effectively suppress interference fringe noise in TDLAS.

Cascaded Reinforcement Learning Agents for Large Action Spaces in Autonomous Penetration Testing

Organised attacks on a computer system to test existing defences, i.e., penetration testing, have been used extensively to evaluate network security. However, penetration testing is a time-consuming process. Additionally, establishing a strategy that resembles a real cyber-attack typically requires in-depth knowledge of the cybersecurity domain. This paper presents a novel architecture, named deep cascaded reinforcement learning agents, or CRLA, that addresses large discrete action spaces in an autonomous penetration testing simulator, where the number of actions exponentially increases with the complexity of the designed cybersecurity network. Employing an algebraic action decomposition strategy, CRLA is shown to find the optimal attack policy in scenarios with large action spaces faster and more stably than a conventional deep Q-learning agent, which is commonly used as a method for applying artificial intelligence to autonomous penetration testing.

Dynamic scheduling of home care patients to medical providers

Home care provides personalized medical care and social support to patients within their own homes. Our work proposes a dynamic scheduling framework to assist in the assignment of health practitioners (HPs) to patients who arrive stochastically over time and are heterogeneous with respect to their health requirements, service duration, and region of residence. We model the decision of which patients to assign to HPs as a discrete‐time, rolling‐horizon, infinite‐stage Markov decision process. Due to the curse of dimensionality and the combinatorial structure associated with an HP's travel, we propose an approximate dynamic programming (ADP) approach based on a one‐step policy improvement heuristic. Four policies are investigated: The first two prioritize HP fairness by balancing service and travel times, respectively, while the other two are based on fluid approximations of the system. We show that the first fluid model is optimal if the number of patient arrivals is sufficiently large while the second performs better experimentally; both approaches leverage pricing and decomposition strategies. We compare our framework to more commonly implemented policies—constrained versions of the classical vehicle routing problem—in a simulation study using data collected from a Canadian home care provider. We show that, in contrast to these approaches, by accounting for future uncertainty, substantial cost savings can be obtained while a fewer number of referrals are rejected. We also find that well‐performing policies assign patients to HPs operating within a small set of adjacent regions while considering the number of periods that a patient requires care for. Otherwise, HP workload may not be appropriately balanced over the long‐term even if travel time is minimized.

Matroid Stratifications of Hypergraph Varieties, Their Realization Spaces, and Discrete Conditional Independence Models

Abstract We study varieties associated to hypergraphs from the point of view of projective geometry and matroid theory. We describe their decompositions into matroid varieties, which may be reducible and can have arbitrary singularities by the Mnëv–Sturmfels universality theorem. We focus on various families of hypergraph varieties for which we explicitly compute an irredundant irreducible decomposition. Our main findings in this direction are three-fold: (1) we describe minimal matroids of such hypergraphs; (2) we prove that the varieties of these matroids are irreducible and their union is the hypergraph variety; and (3) we show that every such matroid is realizable over real numbers. As corollaries, we give conceptual decompositions of various, previously studied, varieties associated with graphs, hypergraphs, and adjacent minors of generic matrices. In particular, our decomposition strategy gives immediate matroid interpretations of the irreducible components of multiple families of varieties associated to conditional independence models in statistical theory and unravels their symmetric structures which hugely simplifies the computations.

Can guided decomposition help end-users write larger block-based programs? a mobile robot experiment

Block-based programming environments, already popular in computer science education, have been successfully used to make programming accessible to end-users in domains like robotics, mobile apps, and even DevOps. Most studies of these applications have examined small programs that fit within a single screen, yet real-world programs often grow large, and editing these large block-based programs quickly becomes unwieldy. Traditional programming language features, like functions, allow programmers to decompose their programs. Unfortunately, both previous work, and our own findings, suggest that end-users rarely use these features, resulting in large monolithic code blocks that are hard to understand. In this work, we introduce a block-based system that provides users with a hierarchical, domain-specific program structure and requires them to decompose their programs accordingly. Through a user study with 92 users, we compared this approach, which we call guided program decomposition, to a traditional system that supports functions, but does not require decomposition. We found that while almost all users could successfully complete smaller tasks, those who decomposed their programs were significantly more successful as the tasks grew larger. As expected, most users without guided decomposition did not decompose their programs, resulting in poor performance on larger problems. In comparison, users of guided decomposition performed significantly better on the same tasks. Though this study investigated only a limited selection of tasks in one specific domain, it suggests that guided decomposition can benefit end-user programmers. While no single decomposition strategy fits all domains, we believe that similar domain-specific sub-hierarchies could be found for other application areas, increasing the scale of code end-users can create and understand.

Solving the Multisensor Resource Scheduling Problem for Missile Early Warning by a Hybrid Discrete Artificial Bee Colony Algorithm

Aiming at the problem of multisensor resource scheduling in missile early warning operation, a scheduling decomposition strategy for missile early warning tasks under cooperative detection is proposed. Taking the detection benefit factor, target threat factor, and handover factor as the fitness function, we establish a sensor-subtask assignment (SSA) model and propose a hybrid discrete artificial bee colony (HDABC) algorithm to solve the optimal solution of the SSA model. The HDABC algorithm has the following improvements: in the initialization stage, a sensor-subtask-based coding method is designed to reduce the solution dimension, and the heuristic rules are used to obtain excellent populations to improve the convergence speed; in the employed bee and onlooker bee stage, a food source update strategy based on discrete differential mutation (DDM) operation is proposed to improve the searchability of the algorithm, and a sorting-based adaptive probability (SAP) selection method is applied to enhance the global search and local optimization capacities. Simulation experiments were carried out in operation scenarios of different scales. Experimental results showed that the proposed HDABC algorithm can obtain the optimal scheduling schemes and had a better solving performance when solving the SSA model, especially in the medium-scale and large-scale operation scenarios.

Investigations into Gas-Pore Effects on Fatigue Strength with a Peridynamic Approach

Fatigue evaluations are one of the main challenges to applying additively manufactured primary structural elements onto aircraft, especially for the gas-pore effects on fatigue strength. In this work, a bond decomposition strategy (BDS) in peridynamics (PD) is proposed; combined with our previously proposed model for fatigue damage, numerical simulations were performed to study the effect of Gas Pore (GP) on fatigue strength. Compared with the strategies in original paradigm of peridynamics, BDS achieves more elaborate description for bond status, predicts deformation fields around discontinuities with improved accuracy, and makes the spacing of material points become independent of discontinuity geometries. Two initiation modes are found in PD simulations, which exert an obvious impact on the final fatigue lifetimes; furthermore, it is revealed that GP not only leads to lower fatigue strength but also results in dispersity of fatigue strength data, in which dispersity is more severe if the GP size is larger, and the decline of fatigue strength is the most severe if the GP is located at subsurface for the same GP size.

Surface-engineered Ti3C2T x MXene enabling rapid sodium/potassium ion storage

MXene with expanding interlayer and tunable terminations emerge as promising candidates for metal ion storage. Herein, we develop a facile urea decomposition strategy to obtain ultrathin nitrogen-modified Ti3C2T x (N-UT-Ti3C2T x ) with optimized terminations as anode for sodium/potassium ion storage. Experimental results have shown that NH3 molecules produced by urea pyrolysis could introduce two types of nitrogen modifications in Ti3C2, function substitution for –OH (FS) and surface absorption on –O (SA). During subsequent hydrothermal and heating processes, the nitrogen atoms in situ substitute the lattice carbon in Ti3C2 (LS). Further, the effects of these nitrogen modifications in Ti3C2 on diffusion kinetics of Na+ and K+ are investigated by first-principles calculations. The superior Na+ storage performances of the N-UT-Ti3C2T x anode are the main attribute of the nitrogen modification of LS in Ti3C2, while the excellent K+ storage performances come from the synergistic effects of the nitrogen modifications of FS and LS in Ti3C2. This work emphasizes the effectiveness of surface engineering of nitrogen modifications and optimized terminations for improving the electrochemical performances of Ti3C2T x and inspires the design of heteroatom modified MXenes for energy storage.

Infrared and visible image fusion based on contrast enhancement guided filter and infrared feature decomposition

Infrared (IR) and visible (VIS) images represent the features of the scene at different wavelengths, and the features they contain have different properties. Therefore, the traditional weighted fusion strategy is challenging to preserve the different types of feature information. In addition, VIS images are highly susceptible to bad weather, which also seriously affects the quality of fused images in complex environments. To solve the above problems, we propose a feature enhancement fusion method. First, a fusion model called contrast enhancement guided filter (CEGF) is proposed. The new model enables the texture information of VIS images to be presented with the intensity of infrared pixels, which solves the problem of combining different attribute features and removes the influence of harsh lighting conditions. To improve the visibility of texture details under different lighting conditions, a contrast modulation factor is added to the cost function design of the filter to enhance the contrast of visible details. Second, we use a dual-scale decomposition strategy to enhance the infrared feature information of the fusion results. Finally, we apply the method of this paper with ten classical image fusion algorithms in two types of datasets. The visual effect and objective evaluation of the fusion results verify that the proposed method preserves the characteristics of the high contrast of IR images and improves the visibility of infrared scenes for subsequent target identification and detection.

Joint matrix decomposition for deep convolutional neural networks compression

Deep convolutional neural networks (CNNs) with a large number of parameters require intensive computational resources, and thus are hard to be deployed in resource-constrained platforms. Decomposition-based methods, therefore, have been utilized to compress CNNs in recent years. However, since the compression factor and performance are negatively correlated, the state-of-the-art works either suffer from severe performance degradation or have relatively low compression factors. To overcome this problem, we propose to compress CNNs and alleviate performance degradation via joint matrix decomposition, which is different from existing works that compressed layers separately. The idea is inspired by the fact that there are lots of repeated modules in CNNs. By projecting weights with the same structures into the same subspace, networks can be jointly compressed with larger ranks. In particular, three joint matrix decomposition schemes are developed, and the corresponding optimization approaches based on Singular Value Decomposition are proposed. Extensive experiments are conducted across three challenging compact CNNs for different benchmark data sets to demonstrate the superior performance of our proposed algorithms. As a result, our methods can compress the size of ResNet-34 by 22× with slighter accuracy degradation compared with several state-of-the-art methods.

How External Electric Field Modulates the Rotation Energy Profiles of Dipolar Dopants Inside C70: A Theoretical Interpretation with Electrostatic Shielding Effect Incorporated

AbstractEndohedral fullerenes, which can switch between distinct states with different geometries when triggered by external electric fields (EFs), can be used as logical devices at the molecular scale. However, the movement of electrons around fullerenes exerts an electrostatic shielding effect which alleviates the Coulomb force experienced by endohedral dopants, and thus must be properly evaluated for better elucidating the switching mechanism. Here we introduced new components to the energy decomposition scheme based on the block‐localized wavefunction method (i. e., BLW‐ED), to incorporate the shielding effect explicitly. We analyzed the external EF‐driven rotation of enclosed dipolar molecules inside C70 and evaluated the magnitudes of shielding in terms of the gradients of electrostatic potential and energy. In the absence of external EF, intrinsic rotational barriers are dominated by the Pauli exchange repulsion between enclosed molecules and C70. When an external EF was applied, computations showed that only about 18% of external EFs can penetrate into the cage and interact with dipolar molecules. Thus, the shielding effect dramatically reduces the energy contribution originated from the interaction between endohedral dopants and external EFs. BLW‐ED analyses were further performed to inspect the effect of external EFs on the potential energy surfaces associated with the molecular rotation processes. Indeed, the interaction between penetrated EFs and enclosed molecules can still govern the orientational preferences of dipolar molecules and lower the rotational barrier for some dipolar molecules. But for other molecules, both the intrinsic electrostatic interaction and the Pauli repulsion respond to external EFs more sensitively and rule the changes of barrier heights and orientational preferences.

Subdomain solution decomposition method for nonstationary problems

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in time. The traditional construction approach of splitting schemes is based on an additive representation of the problem operator(s) and uses explicit-implicit approximations for individual terms. Recently (Efendiev and Vabishchevich (2021) [22]), a new class of methods of approximate solution of nonstationary problems has been introduced based on decomposition not of operators but of the solution itself. This new approach with subdomain solution selection is used in this paper to construct domain decomposition schemes. The boundary value problem for a second-order parabolic equation in a rectangle with a difference approximation in space is typical. Two and three-level schemes for decomposition of the domain with and without overlapping subdomains are investigated. Our numerical experiments complement the theoretical results.