Decomposition Theory Research Articles

ISMGCC: Finding Gas Structures in Molecular Interstellar Medium Using Gaussian Decomposition and Graph Theory

Molecular line emissions are commonly used to trace the distribution and properties of molecular Interstellar Medium. However, the emissions are heavily blended on the Galactic disk toward the inner Galaxy because of the relatively large line widths and the velocity overlaps of spiral arms. Structure identification methods based on voxel connectivity in Position-Position-Velocity (PPV) data cubes often produce unrealistically large structures, which is the “over-linking” problem. Therefore, identifying molecular cloud structures in these directions is not trivial. We propose a new method based on Gaussian decomposition and graph theory to solve the over-linking problem, named InterStellar Medium Gaussian Component Clustering (ISMGCC). Using the Milky Way Imaging Scroll Painting (MWISP) 13CO(1–0) data in the range of 13.°5 ≤ l ≤ 14.°5, ∣b∣ ≤ 0.°5, and −100 ≤ V lsr ≤ +200 km s−1, our method identified three hundred molecular gas structures with at least 16 pixels. These structures contain 92% of the total flux in the raw data cube and show single-peaked line profiles on more than 93% of their pixels. The ISMGCC method could distinguish gas structures in crowded regions and retain most of the flux without global data clipping or assumptions on the structure geometry, meanwhile, allowing multiple Gaussian components for complicated line profiles.

Dynamic Behaviors of Composite-Laminated Concentrically Stiffened Rectangular Plates by Substructure Modal Synthesis

Existing numerical analysis methods often incur high computational costs when directly solving multi-degree-of-freedom systems due to computer capacity limitations. To address this issue, this paper took the composite laminated concentrically stiffened rectangular plate as the research object. The modal synthesis method was employed to reduce the degrees of freedom of the model, enabling the solution of complex dynamic characteristics. In the research process, the domain decomposition theory was used to divide the research object into plate and rib substructures. Based on the spectral Chebyshev method, the substructure dynamic model of the composite laminated rectangular plate was constructed. Subsequently, the function expressions of the complex load excitation on each substructure were derived, and the fixed modal synthesis method was introduced to construct the spectral Chebyshev reduced model of the substructures. According to the artificial spring theory equivalent, the interface force, and the whole reduction model of the composite laminated concentrically stiffened rectangular plate were obtained by assembling the substructure models. The time–domain and frequency–domain dynamic behaviors of composite laminated concentrically stiffened rectangular plates are yielded by solving the whole reduced model. The novelty of this work lies in combining the spectral Chebyshev method with the modal synthesis method. The established reduced model no longer depended on mesh quality and required fewer matrix dimensions and computation time compared to the whole model, while still achieving sufficiently accurate results. Additionally, based on the reduced model, an effective parametric study scheme was proposed to analyze the impact of dimensions and material properties of rib substructures on the dynamic behaviors of the composite laminated concentrically stiffened rectangular plate. These findings can be used to guide the optimal design of laminated concentrically stiffened rectangular plates in engineering practice.

Non-radiating sources in elastodynamics and their applications in the exterior cloaking

In this work, we develop a mathematical framework on constructed general non-radiating sources of elastic waves governed by the Navier equation via the approach of Helmholtz decomposition and potential theory in elastodynamics. Our study offers a rather comprehensive analysis. We first provide a rigorous justification of the general non-radiating sources. Based on the complete destructive interference of external elastic fields generated by specific radiating sources, a general non-radiating elastic source is derived and shown to possess a hidden interior wave field. For an incident wave, targets remain invisible within non-radiating source regions, and the geometry and boundary conditions of obstacles can be very general, which holds significant practical implications. Moreover, we introduce an effective novel method for designing such generalized non-radiating sources. To avoid the complex structure, we propose to use radiating source overlay construction on specific nodes at the boundary of non-radiating regions construction and derive sharp error estimates to evaluate the cloaking performance. The proposed scheme is capable of nearly cloaking arbitrary obstacles with a high accuracy. Numerical verifications validate the precision of our analytical findings.

Multi-functional periodically heterogeneous structures for energy harvesting and vibration attenuation-effects of piezoelectricity and shunting circuits

Abstract We explore a kind of metamaterial plate structures intended for simultaneous energy harvesting and vibration control. These structures are designed using a periodically perforated piezoelectric plate (the matrix) with elastic inclusions situated in the holes and serving for the resonators. The design options comprise two- and three-phase configurations related to the mechanical connection between the matrix and inclusions. By introducing a singularity—the focal spot created as a defect in the perfectly periodic structure and using the theory of super-cell, an enhanced piezoelectric energy harvester is obtained. It is observed that such a meta-structure serves as a dual-purpose system: efficiently capturing vibrational energy at a focal spot while maintaining the overall vibration attenuation throughout the structure. The band gap analysis based on the Bloch’s wave decomposition theory shows that by concentrating energy and halting vibration propagation, approximately 10 times energy harvesting enhancement and a remarkable 100 dB reduction in vibrations are achieved simultaneously. Besides the passive response of these meta-structures, we consider its extension by an external electric circuit (EC). Such modified configurations enable to exploit ‘actively’ the piezoelectric plate property to transmit the mechanical response between two, or more distant locations. Due to nonlocal interactions introduced by means the controllable EC, we consider optimization of the EC impedance to reduce the vibrations at a selected location of the whole structure without any external energy supply. The computational study discovers perspectives and benefits of designing such active self-powered meta-structures.

Basilica: New canonical decomposition in matching theory

AbstractIn matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are limited because they are only applicable to particular classes of graphs, such as bipartite graphs, or they are too sparse to provide sufficient information. To overcome these limitations, we introduce a new canonical decomposition that is applicable to all graphs and provides much finer information. This decomposition also provides the answer to the longstanding absence of a canonical decomposition that is nontrivially applicable to general graphs with perfect matchings. We focus on the notion of factor‐components as the fundamental building blocks of a graph; through the factor‐components, our new canonical decomposition states how a graph is organized and how it contains all the maximum matchings. The main results that constitute our new theory are the following: (i) a canonical partial order over the set of factor‐components, which describes how a graph is constructed from its factor‐components; (ii) a generalization of the Kotzig–Lovász decomposition, which shows the inner structure of each factor‐component in the context of the entire graph; and (iii) a canonically described interrelationship between (i) and (ii), which integrates these two results into a unified theory of a canonical decomposition. These results are obtained in a self‐contained way, and our proof of the generalized Kotzig–Lovász decomposition contains a shortened and self‐contained proof of the classical counterpart.

Research advance in effects of solar radiation on litter decomposition in terrestrial ecosystems.

Litter decomposition significantly influences the carbon (C) dynamics of terrestrial ecosystems. Solar radiation is not only essential for photosynthetic C fixation and primary productivity, but also can directly or indirectly promote litter decomposition through photodegradation. Recently, photodegradation has been identified as a key factor driving litter decomposition and potentially impacts terrestrial C cycle. To enrich and develop the theory of litter decomposition, we summarized the mechanisms and main driving factors of photodegradation, and compared the responses of photodegradation to environment and climate changes at different scales. Photodegradation primarily includes photomineralization, photoinhibition, and photofaciliation, each affecting litter decomposition differently under various environmental conditions. Photodegradation is closely related to factors such as solar radiation, litter traits, temperature, moisture, microorganisms, and vegetation cover. The interactions among these factors complicate the patterns of photodegradation. Finally, we identified the main issues in litter photodegradation research and prospected future research directions. We emphasized the needs for in-depth exploration of photodegradation pathways and intrinsic mechanisms, quantification of its interactive effects with environmental factors, and optimization of traditional carbon turnover models.

Boundary points guided 3D object detection for point clouds

3D object detection in LiDAR point clouds is crucial for computer vision tasks such as autonomous driving. The two-stage approach with point cloud completion achieves remarkable performance by generating semantic surface points for foreground objects or learning bird’s eye view shape heat map labels. However, these methods require additional completion datasets, leading to substantial computation and memory demands. In this context, we propose a Boundary Points Guided 3D (BPG3D) object detection method that complements point cloud boundary information without the need for additional data. Specifically, we generate Region of Interest (RoI) boundary points to aggregate the neighbor voxel information at the RoI boundary during the refinement stage to complement the missing boundary information. Meanwhile, we design a Dual Feature Selection (DFS) module to adaptively fuse RoI grid point features and RoI boundary point features for bounding box refinement with negligible computational cost. Additionally, inspired by tensor decomposition theory, we use low-rank tensors to reconstruct high-rank tensors in the point cloud feature encoder to enhance contextual semantic information. The proposed method achieves 65.81% mAP on KITTI Test Set, obtaining a good trade-off between accuracy and efficiency.

Partial information decomposition for continuous variables based on shared exclusions: Analytical formulation and estimation.

Describing statistical dependencies is foundational to empirical scientific research. For uncovering intricate and possibly nonlinear dependencies between a single target variable and several source variables within a system, a principled and versatile framework can be found in the theory of partial information decomposition (PID). Nevertheless, the majority of existing PID measures are restricted to categorical variables, while many systems of interest in science are continuous. In this paper, we present a novel analytic formulation for continuous redundancy-a generalization of mutual information-drawing inspiration from the concept of shared exclusions in probability space as in the discrete PID definition of I_{∩}^{sx}. Furthermore, we introduce a nearest-neighbor-based estimator for continuous PID and showcase its effectiveness by applying it to a simulated energy management system provided by the Honda Research Institute Europe GmbH. This work bridges the gap between the measure-theoretically postulated existence proofs for a continuous I_{∩}^{sx} and its practical application to real-world scientific problems.

Shape prediction in continuous roll forming of sheet metal based on rigid rolls

The continuous roll forming based on rigid rolls (CRFRR) is an innovative process for rapid fabrication of doubly curved surfaces of sheet metal. The curved parts with different shapes and sizes can be obtained by adjusting the generatrix radius of the two rigid rolls or controlling the rolling reduction. In this paper, the principle of CRFRR is introduced and the process that a 3D surface of sheet metal with positive or negative Gaussian curvature is formed using two rigid rolls is analyzed based on the distribution of exit velocity. The exit velocity of material after the sheet metal passes through the roll gap is decomposed into two portions: a linearly distributed velocity and a very small additional velocity. On the basis of exit velocity decomposition and shallow shell theory, an analytical method for predicting the shape of formed surface in CRFRR process is proposed for the first time. The primary part of curvature of the formed 3D surface in longitudinal direction is determined by the linear portion of exit velocity and that in transverse direction is determined by the generatrix radius of the two rigid rolls. The curvature change in the final shape of 3D surface is induced by the additional portion of exit velocity and it is solved from equilibrium equation of shallow shell. The final curvature of the formed surface is acquired through superimposing the primary curvature and the curvature change. Numerical simulations and forming experiments have been carried out on convex and saddle-shaped parts, and the results confirm the validity and accuracy of presented method.

Null Phase Assumption-Based Technique for Constructing the Target Model of Seismic Irregularity on High-Speed Railways

High-speed railways are “lifeline projects” that shoulder the heavy responsibility of transporting relief supplies and medical forces for the first time after earthquakes. To ensure the train’s safety after earthquakes, it is of great urgency to ascertain a post-earthquake speed threshold. To that end, a target model for seismic irregularity emerges as a key parameter. In this paper, a null phase assumption-based technique for the mutual conversion between evolutionary power spectral density and non-stationary signal was proposed. Taking a high-speed railway track-bridge system as the research object, the target model of seismic irregularities was constructed based on the proposed technique. The rationality of the target model of seismic irregularities was verified, and the construction parameter settings were discussed. Moreover, a simplified frequency-domain fitting method for the target model of seismic irregularities was proposed based on the spectral decomposition theory. According to the research findings, the null phase assumption-based technique is capable of performing interconversion between seismic irregularity and its evolutionary power spectral density with satisfactory accuracy. It is recommended to set the minimum number of seismic irregularities, spatial sampling interval, hop size, and length of window function as 50, 0.25[Formula: see text]m, 1, and 40 to 100, respectively.

Dynamic characteristics of the tip leakage vortex in an oil–gas multiphase pump based on vorticity decomposition theory

AbstractThe paper combines experimental and numerical simulation methods to investigate the tip leakage vortex (TLV) in an oil–gas multiphase pump. The study aims to understand the evolution and dynamic characteristics of the TLV. The vorticity decomposition theory is used to analyze the spatial–temporal evolution, transient behavior, and rigid vorticity of the TLV. The findings reveal that the TLV is formed near the pressure surface when the tip clearance jet passes through the shear layer. In one impeller rotation period, transient fluctuations of the TLV are attributed to pressure differences and velocity changes across the tip clearance, and the TLV undergoes two split–dissipation–recurrence processes within one impeller rotation cycle. The presence of the gas phase enhances the scale and strength of the TLV while prolonging its existence in the flow channel. Analysis based on the rigid vorticity transport equation shows that the growth of the TLV and collapse are primarily governed by the rigid vortex generation term. The Coriolis force term contributes to stabilizing the TLV, while the rigid vorticity stretching term affects its shape. Furthermore, the gas phase significantly increases the value of the Rigid vorticity Curl of pseudo‐Lamb vector Term (RCT), which plays a crucial role in the prolonged existence of the TLV under gas–liquid two‐phase conditions. From an inlet gas void fraction of 0%–20%, the RCT value increases by 4.8 × 106/s2, the entropy production value increases by 75.55%, and the hydraulic efficiency decreases by 16.29%.

Attractors coexistence and representation research of Lotka–Volterra recurrent neural networks by matrix analysis theory

Attractor neural network models have been extensively studied in maintaining brain working memory state, spatial representation, and other brain processing mechanisms. The coexistence of multiple attractors in nonlinear neural network is particularly worth studying. The attractor is a stable state in the dynamic system, and all adjacent states will eventually be pulled to the attractor over time. Attractors can be regarded as the expression of data in low-dimensional state space, and different kinds of attractors can be used to process different information. The coexistence of multiple attractors means that a neural network can store multiple patterns, that is to say different memory mechanisms appear at the same time. Investigating the coexistence and competition of attractors within Lotka–Volterra(LV) recurrent neural networks presents a pivotal avenue for understanding the dynamical underpinnings of complex systems, particularly in the realm of computational neuroscience and ecological modeling. This paper studies the coexistence of different types of attractors in asymmetric Lotka–Volterra recurrent neural networks. Through the weight matrix block and matrix decomposition theory, we obtain the explicit expressions of continuous attractors and discrete attractors. Since neurons have multiple grouping methods, each weight matrix block satisfying certain conditions corresponds to different attractors. Different from traditional symmetric networks, the eigenvalues of the asymmetric weight matrices may be complex, which may correspond to ring attractors. Our research shows that attractors can coexist under certain conditions, depending on the weight matrix and external input. Moreover, through simulation experiments, we show that external input will cause the competition of attractors. Finally, we provide several simulations of attractor coexistence to illustrate our theory.

Analytical solution for horizontal vibration of partially embedded pipe pile group in layered saturated soil

AbstractBased on Biot's dynamic wave theory and Novak's plane strain model (PSM), an analytical model for the horizontal vibration of a partially embedded pipe pile group (PEPPG) in layered saturated soil (LSS) that considers the soil‐plugging effect was established: First, the frequency‐domain analytical expressions of the saturated surrounding soil (SSS) and soil plug were obtained by introducing operator decomposition theory and the variable separation method. Second, the analytical solution of the horizontal impedance of a partially embedded pipe pile in the LSS is derived using the coupled condition of the pile–soil interface and transfer matrix method. Finally, an analytical solution for the horizontal impedance of PEPPG in LSS was derived by introducing the horizontal dynamic interaction factor of piles and the superposition method. The derived solution is then reduced and compared with existing theoretical solutions to verify its rationality. In addition, further parametric analysis was conducted to investigate the influences of pile spacing, embedment ratio, properties of layered SSS, and soil‐plugging on the horizontal vibration characteristics (HVCs) of PEPPG.

Optimization of handoff for joint uplink base station association and power control with max‐min fairness in NOMA small‐cell networks

SummaryThe handoff rate and load balancing are two important issues that have a great impact on the spectrum and energy efficiency in the small‐cell networks (SCN). This paper investigates the handoff optimization in SCN with power‐domain non‐orthogonal multiple access (NOMA) that uses successive interference cancelation (SIC), considering the fairness among base stations (BSs). We study the joint base station association and power control problem by considering the motion of mobile users (MUs) and load balancing in the SCNs. Under the maximum allowable transmit power and minimum average‐rate constraints, two optimization problems are formulated using the number of associated MUs, the number of handoffs, and the transmit power of all MUs. The total power consumption minimization and the system‐wide and handoff utility maximization problems are combined into a single‐stage optimization problem through the weighted‐sum method. We solve the formulated problem using a game theory‐based algorithm and primal decomposition theory. The simulation results show that our proposed algorithm can significantly reduce the frequent handoffs and bring a fair power‐controlled BS association in SCN.

Hyers–Ulam stability of integral equations with infinite delay

Integral equations with infinite delay are considered as functional equations in a Banach space. Two types of Hyers–Ulam stability criteria are established. First, it is shown that a linear autonomous equation is Hyers–Ulam stable if and only if it has no characteristic value with zero real part. Second, it is proved that the Hyers–Ulam stability of a linear autonomous equation is preserved under sufficiently small nonlinear perturbations. The proofs are based on a recently developed decomposition theory of linear integral equations with infinite delay.

Magnetic resonance image reconstruction based on image decomposition constrained by total variation and tight frame.

Magnetic resonance imaging (MRI) is a commonly used tool in clinical medicine, but it suffers from the disadvantage of slow imaging speed. To address this, we propose a novel MRI reconstruction algorithm based on image decomposition to realize accurate image reconstruction with undersampled k-space data. In our algorithm, the MR images to be recovered are split into cartoon and texture components utilizing image decomposition theory. Different sparse transform constraints are applied to each component based on their morphological structure characteristics. The total variation transform constraint is used for the smooth cartoon component, while the L0 norm constraint of tight frame redundant transform is used for the oscillatory texture component. Finally, an alternating iterative minimization approach is adopted to complete the reconstruction. Numerous numerical experiments are conducted on several MR images and the results consistently show that, compared with the existing classical compressed sensing algorithm, our algorithm significantly improves the peak signal-to-noise ratio of the reconstructed images and preserves more image details. Our algorithm harnesses the sparse characteristics of different image components to reconstruct MR images accurately with highly undersampled data. It can greatly accelerate MRI speed and be extended to other imaging reconstruction fields.

Dynamic response of bored piles with gradient defects during low strain integrity test

With the proposal of the gradient ring-soil pile model, the possibility of utilizing the low strain integrity test for identifying gradient defects of the bored piles embedded in unsaturated soil is confirmed. The gradient ring-soil pile model realizes the simulation of soil-pile interaction at the soil-pile interfaces with arbitrary shapes in the horizontal projection. Compared to existing theoretical answers, this paper extends the low strain test theory to the identification of gradient defects. With the adoption of the Laplace transform, differential operator decomposition theory, variable separation method, and impedance function transfer method, a semi-analytical solution is derived. Taking advantage of the semi-analytical solution, a parametric study is conducted to analyze the variation of the defect shapes on the test signal of the bored pile. Based on the findings, a series of methods for identifying gradient defects in engineering applications are summarized. The main findings can be summarized as follows: 1. The soil filled in the gradient necking defects would significantly decrease the magnitudes of reflected signals at these defects, making them more challenging to be identified; 2. If simply modeling the gradient defects as sudden defects, the severity of defects can be underestimated, resulting in the overestimation of pile capacity; 3. The shape of the gradient defect, as well as the length of the gradient defect, has a significant influence on the reflected signal.

Influence of spatial variability of soil shear-wave velocity considering intralayer correlation on seismic response of engineering site

Shear-wave velocity uncertainty significantly impacts seismic response analysis at engineering sites. Previous studies focused on the correlations of shear-wave velocities within soil layers. However, the influence of the vertical spatial variability of shear-wave velocity within individual soil layers was not considered. This study selected a typical Site Class II engineering site to investigate this influence based on the equivalent linear seismic response analysis method of layered soil deposits. Existing field test data on shear-wave velocity were used to discretize the shear-wave velocity within soil layers into a one-dimensional (1D) random field through covariance matrix decomposition and local average process theory. Monte Carlo simulations generated random shear-wave velocity profiles with different vertical correlation distances. Three artificial records with different earthquake return periods were used as input motions at the engineering bedrock for the 1D free-field model. Considering soil shear-wave velocity uncertainty, the peak shear strain increased by 19–27% with the input ground motion amplitude. Moreover, the site peak shear strain variability increased by 25–34% with the vertical correlation distance. The proposed 1D random field model effectively simulated the interlayer correlation and spatial variability of shear-wave velocity within soil layers, demonstrating its significance in seismic response analysis.

On incentivizing resource allocation and task offloading for cooperative edge computing

Cooperative edge computing serves as an effective solution to provide reliable and elastic edge computing services through pooling geographically proximate edge resources and efficiently allocating them to users. The incentive mechanism is critical for realizing cooperative edge computing. In this paper, we propose a virtual machine (VM) or container based resource allocation scheme and two market-based mechanisms to stimulate collaboration among edge servers (ESs). Our first mechanism is a novel two-stage double auction based approach where edge resources are allocated to services/VMs at the first stage and then distributed among ESs at the second stage via a two-sided multi-unit auction. To make it more practical, we use markups to set the ask and bid prices for the participants in the market. Moreover, with the concept of virtual sellers and virtual buyers, we cast the multi-unit auction as single-unit one so that the auction becomes tractable. We further propose a price-based decentralized mechanism in case there is no central authority. With an appropriately constructed objective function, we formulate the resource allocation task as a network utility maximization (NUM) problem and leverage the dual-based decomposition theory for a distributed solution. We theoretically prove that both mechanisms guarantee properties such as budget balance and individual rationality for all ESs. Numerical studies with real-world dataset are presented to demonstrate the superior performance of our mechanisms over baselines.

Universal slope-based J-integral methods for characterization of the mode I, mode II and mixed mode I/II fracture behaviour of adhesively bonded interfaces

Universal slope-based J-integral methods have been developed for the determination of the energy release rate for adhesively bonded joints under mode I, mode II and mixed-mode (I/II) loading conditions. The individual J components corresponding to the mode I and mode II loading were separated based on the J-integral decomposition theory. The proposed methods use the slopes of the substrates at various locations to characterize the energy release rate and thus avoid the measurement of crack lengths, which are especially suitable for characterizing the tough interfaces associated with large fracture process zones ahead of crack tips. Under linear elastic deformation, the slope-based J equations were found to be equivalent to classical G equations based on linear elastic fracture mechanics (LEFM). Both experimental and numerical testing of adhesively bonded joints were undertaken to validate the slope-based J equations. The universal slope-based J-integral methods provide a reliable alternative to the measurement of G for adhesive joints or laminated composites undergoing nonlinear or inelastic deformations where conventional LEFM is not valid. It is shown that LEFM, even when coupled with an effective crack length approach, can be inaccurate when damage occurs in a test specimen away from the fracture process zone, as was seen here in mode II. Slope-based J equations can avoid these inaccuracies with a careful selection of contour paths. Slope based methods are therefore strong candidates for selection in future test standards for mode II fracture characterisation of structural adhesive joints.