Skeleton Decomposition Research Articles

A top-down lashing bridge collaborative design method

ABSTRACT The short detailed design cycle of lashing bridges on container ships needs to ensure that various designs have different requirements at multiple locations on the ship, making the design methodology for complex products challenging. Currently, research on the design methodology of lashing bridges lacks in-depth investigation into detailed design aspects. This work addressed research gaps through a top-down collaborative design approach and analysed the principles of propagating design changes in computer-aided design (CAD), as well as proposed a design methodology consisting of four core steps, namely, skeleton decomposition, feature aggregation, detailed design and product structure (PS) expansion. The effectiveness of this methodology was validated through practical design examples and specific variant design instances of a certain type of container ship. The validation demonstrated that the proposed design methodology, in contrast to traditional three-dimensional design methods, supported design process reuse and significantly improved design efficiency in complex product designs.

Insight into Multiple Intermolecular Coordination of Composite Solid Electrolytes via Cryo-Electron Microscopy for High-Voltage All-Solid-State Lithium Metal Batteries.

Polymer/ceramic-based composite solid electrolytes (CSE) are promising candidates for all-solid-state lithium metal batteries (SLBs), benefiting from the combined mechanical robustness of polymeric electrolytes and the high ionic conductivity of ceramic electrolytes. However, the interfacial instability and poorly understood interphases of CSE hinder their application in high-voltage SLBs. Herein, a simple but effective CSE that stabilizes high-voltage SLBs by forming multiple intermolecular coordination interactions between polyester and ceramic electrolytes is discovered. The multiple coordination between the carbonyl groups in poly(ε-caprolactone) and the fluorosulfonyl groups in anions with Li6.5 La3 Zr1.5 Ta0.5 O12 nanoparticles is directly visualized by cryogenic transmission electron microscopy and further confirmed by theoretical calculation. Importantly, the multiple coordination in CSE not only prevents the continuous decomposition of polymer skeleton by shielding the vulnerable carbonyl sites but also establishes stable inorganic-rich interphases through preferential decomposition of anions. The stable CSE and its inorganic-rich interphases enable Li||Li symmetric cells with an exceptional lifespan of over 4800 h without dendritic shorting at 0.1mA cm-2 . Moreover, the high-voltage SLB with LiNi0.5 Co0.2 Mn0.3 O2 cathode displays excellent cycling stability over 1100 cycles at a 1C charge/discharge rate. This work reveals the underlying mechanism behind the excellent stability of coordinating composite electrolytes and interfaces in high-voltage SLBs.

Modify Self-Attention via Skeleton Decomposition for Effective Point Cloud Transformer

Although considerable progress has been achieved regarding the transformers in recent years, the large number of parameters, quadratic computational complexity, and memory cost conditioned on long sequences make the transformers hard to train and implement, especially in edge computing configurations. In this case, a dizzying number of works have sought to make improvements around computational and memory efficiency upon the original transformer architecture. Nevertheless, many of them restrict the context in the attention to seek a trade-off between cost and performance with prior knowledge of orderly stored data. It is imperative to dig deep into an efficient feature extractor for point clouds due to their irregularity and a large number of points. In this paper, we propose a novel skeleton decomposition-based self-attention (SD-SA) which has no sequence length limit and exhibits favorable scalability in long-sequence models. Due to the numerical low-rank nature of self-attention, we approximate it by the skeleton decomposition method while maintaining its effectiveness. At this point, we have shown that the proposed method works for the proposed approach on point cloud classification, segmentation, and detection tasks on the ModelNet40, ShapeNet, and KITTI datasets, respectively. Our approach significantly improves the efficiency of the point cloud transformer and exceeds other efficient transformers on point cloud tasks in terms of the speed at comparable performance.

Preparation and properties of degradable hydrogels as a temporary plugging agent used for acidizing treatments to enhance oil recovery

Temporary plugging and diverting acidizing treatments have been proved to be a simple and effective method in stimulating the conventional/unconventional reservoirs. Importantly, the key of this technology lies in the temporary plugging agent (TPA). However, the existing particulate TPAs are of poor acid resistance, poor degradability and involved in complex removal process. Aiming at solving those problems, a novel degradable hydrogel ZDDA was prepared through aqueous radical polymerization in this study. The synthetic conditions of ZDDA were preferentially optimized by orthogonal experiment. The chemical composition, thermal stability and morphology were characterized. The degradable behavior of ZDDA in different media was investigated to understand its degradable mechanism. The results showed that the degradation rate of ZDDA is less than 6% in 2 h in 20% HCl solution. Besides, ZDDA can be completely degraded in solution of 3–20% HCl, 2–10% NaCl, 0.5–2.5% CaCl2, and water, respectively. The scanning electron microscopy (SEM) experiments demonstrated that the degradation process of ZDDA could be described as swelling from the initial water absorption to final degradation into linear polymers. Meanwhile, the degradation mechanism of ZDDA is accompanied by shifting the surface erosion mechanism to the decomposition of the molecular skeleton. Furthermore, the core displacement experiments revealed that the bearing capacity of ZDDA can reach 7.8 MPa. The plugging rate is more than 84%, and the core permeability recovery is more than 97%. Overall, ZDDA has proved to be a promising TPA in acidizing treatments.

Graphon convergence of random cographs

AbstractWe study the behavior of random labeled and unlabeled cographs with n vertices as n tends to infinity. We show that both models admit a novel random graphon W1/2 as distributional limit. Our main tool is an enhanced skeleton decomposition of the random Pólya tree with n leaves and no internal vertices having only one child. As a byproduct, we obtain limits describing the asymptotic shape of this model of random trees.

A decorated tree approach to random permutations in substitution-closed classes

We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a criticality constraint. It also enables us to reprove and strengthen permuton limits for these classes in a new way, that uses a semi-local version of Aldous' skeleton decomposition for size-constrained Galton--Watson trees.

Ozone as a Pretreatment Method for Antibiotic Contaminated Wastewater and Sludge

ABSTRACTThe capability of ozone to reduce the hazardous impact of environmentally persistent antibiotic tiamulin in term of toxicity reduction and enhancement of biodegradability was investigated. Different ozone doses were applied but ozonation was not effective enough to increase the biodegradability of tiamulin in the aqueous phase. The opposite effect was observed in anaerobic digestion experiments, where ozonation as a pretreatment step of antibiotic-contaminated sludge detoxify tiamulin and improves biogas production for 75%. As confirmed by 1H NMR and HPLC-HRMS analyses, the tiamulin molecule completely reacts with ozone at low ozone/COD molar ratio of 0.03, primarily attacking the vinyl double bond with further oxidation of sulfur and nitrogen atom, and gradual decomposition of tiamulin skeleton.

The skeleton of the UIPT, seen from infinity

We prove that geodesic rays in the Uniform Infinite Planar Triangulation (UIPT) coalesce in a strong sense using the skeleton decomposition of random triangulations discovered by Krikun. This implies the existence of a unique horofunction measuring distances from infinity in the UIPT. We then use this horofunction to define the skeleton "seen from infinity" of the UIPT and relate it to a simple Galton--Watson tree conditioned to survive, giving a new and particularly simple construction of the UIPT. Scaling limits of perimeters and volumes of horohulls within this new decomposition are also derived, as well as a new proof of the $2$-point function formula for random triangulations in the scaling limit due to Ambj{\o}rn and Watabiki.

Skeleton Decomposition and Law of Large Numbers for Supercritical Superprocesses

The goal of this paper has two-folds. First, we establish skeleton and spine decompositions for superprocesses whose underlying processes are general symmetric Hunt processes. Second, we use these decompositions to obtain weak and strong law of large numbers for supercritical superprocesses where the spatial motion is a symmetric Hunt process on a locally compact metric space $E$ and the branching mechanism takes the form $$\psi_{\beta}(x,\lambda)=-\beta(x)\lambda+\alpha(x)\lambda^{2}+\int_{(0,{\infty})}(e^{-\lambda y}-1+\lambda y)\pi(x,dy)$$ with $\beta\in\mathcal{B}_{b}(E)$, $\alpha\in \mathcal{B}^{+}_{b}(E)$ and $\pi$ being a kernel from $E$ to $(0,{\infty})$ satisfying $\sup_{x\in E}\int_{(0,{\infty})} (y\wedge y^{2}) \pi(x,dy)<{\infty}$. The limit theorems are established under the assumption that an associated Schr\"{o}dinger operator has a spectral gap. Our results cover many interesting examples of superprocesses, including super Ornstein-Uhlenbeck process and super stable-like process. The strong law of large numbers for supercritical superprocesses are obtained under the assumption that the strong law of large numbers for an associated supercritical branching Markov process holds along a discrete sequence of times, extending an earlier result of Eckhoff, Kyprianou and Winkel [Ann. Probab.,43(5), 2594--2659, 2015] for superdiffusions to a large class of superprocesses. The key for such a result is due to the skeleton decomposition of superprocess, which represents a superprocess as an immigration process along a supercritical branching Markov process.

Volumes in the Uniform Infinite Planar Triangulation: From Skeletons to Generating Functions

We develop a method to compute the generating function of the number of vertices inside certain regions of the Uniform Infinite Planar Triangulation (UIPT). The computations are mostly combinatorial in flavour and the main tool is the decomposition of the UIPT into layers, called the skeleton decomposition, introduced by Krikun [20]. In particular, we get explicit formulas for the generating functions of the number of vertices inside hulls (or completed metric balls) centred around the root, and the number of vertices inside geodesic slices of these hulls. We also recover known results about the scaling limit of the volume of hulls previously obtained by Curien and Le Gall by studying the peeling process of the UIPT in [17].

Shape Descriptors for Porous Media Analysis Using Computed Tomography Images

In this study, we propose a new framework for 3D porous media shape characterization using quantitative data driven shape descriptors. The main conceptual innovations are the introduction of shape descriptors based on geometrical parameters of the shape and empirical mode decomposition (EMD) of the shape skeleton. The EMD yields a decomposition with intrinsic mode functions based on local properties of the skeleton. Efficient methods for computing the defined descriptors from a network of balls representation of the pore space are provided. A multivariate analysis is carried out to describe the relationships between the shape descriptors and justify their use in the context of shape analysis. The proposed descriptors are also used to group together objects by their similarity and perform optimal approximation of the porous media by primitives set. Properties on the approximation are given and discussed. The proposed framework is illustrated with computed tomography images of real soil sample. The results have demonstrated the performance of our methodology for shape characterization, optimal shape decomposition and comparison.

Similarity matrix framework for data from union of subspaces

This paper presents a framework for finding similarity matrices for the segmentation of data W = [ w 1 ⋯ w N ] ⊂ R D drawn from a union U = ⋃ i = 1 M S i of independent subspaces { S i } i = 1 M of dimensions { d i } i = 1 M . It is shown that any factorization of W = B P , where columns of B form a basis for data W and they also come from U , can be used to produce a similarity matrix Ξ W . In other words, Ξ W ( i , j ) ≠ 0 , when the columns w i and w j of W come from the same subspace, and Ξ W ( i , j ) = 0 , when the columns w i and w j of W come from different subspaces. Furthermore, Ξ W = Q d m a x , where d m a x = max ⁡ { d i } i = 1 M and Q ∈ R N × N with Q ( i , j ) = | P T P ( i , j ) | . It is shown that a similarity matrix obtained from the reduced row echelon form of W is a special case of the theory. It is also proven that the Shape Interaction Matrix defined as V V T , where W = U Σ V T is the skinny singular value decomposition of W , is not necessarily a similarity matrix. But, taking powers of its absolute value always generates a similarity matrix. An interesting finding of this research is that a similarity matrix can be obtained using a skeleton decomposition of W . First, a square sub-matrix A ∈ R r × r of W with the same rank r as W is found. Then, the matrix R corresponding to the rows of W that contain A is constructed. Finally, a power of the matrix P T P where P = A − 1 R provides a similarity matrix Ξ W . Since most of the data matrices are low-rank in many subspace segmentation problems, this is computationally efficient compared to other constructions of similarity matrices.

Fabrication of PdOx loaded highly mesoporous WO3/TiO2 hybrid nanofibers by stepwise pore-generation for enhanced photocatalytic performance

Highly mesoporous WO3/TiO2 nanofibers were fabricated through the combination of an advanced electrospinning strategy in the presence of porogenic agent and the subsequent heat treatment. It was found that the introduced porogenic agent of diisopropyl azodiformate (DIAD) within the precursor solution plays a crucial role on the formation of highly mesoporous WO3/TiO2 nanofibers, enabling their mesopores tunable. The obtained mesoporous nanofibers from the stepwise decomposition of DIAD and polymer skeleton possess more homogeneous and smaller pore sizes in their morphology and thus a higher surface area than that obtained without porogenic agent. The highest surface area can reach 92.3m2g−1, which is ca. 5 times larger than that of the pure TiO2 nanofibers obtained without DIAD addition. These highly mesoporous WO3/TiO2 nanofibers were further modified by PdOx nanoparticles via photodeposition. The as-fabricated mesoporous PdOx/WO3/TiO2 hybrid nanofibers exhibit excellent photocatalytic activity and significant stability towards acetaldehyde decomposition compared to the conventional nanofibers under visible light and UV–vis light irradiation. The present work suggests a facile preparation of PdOx loaded mesoporous WO3/TiO2 nanofibers, which may provide new solution to prepare the inorganic nanofibers with highly mesoporous structure.

Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles

On etudie un mouvement brownien branchant $Z$ dans $\mathbb{R}^{d}$ qui se deplace parmi des obstacles qui sont disperses par rapport a une mesure aleatoire de Poisson d’une intensite declinant radialement. Les obstacles sont des boules de rayon constant, et lorsqu’une particule rencontre un tel obstacle, tout le mouvement s’arrete. En considerant une distribution generale pour le nombre de descendants, on calcule le taux de decroissance de la probabilite que toutes les particules de $Z$ evitent les pieges, asymptotiquement en temps. Cela se revele etre un probleme riche qui motive la preuve d’un resultat plus general concernant la vitesse du mouvement brownien branchant conditionne a survivre. Dans le cas sur-critique on fournit une decomposition appropriee pour le processus de Galton–Watson sous-jacent, et on montre que les particules ne contribuent pas au taux de decroissance asymptotique.

Скелетные разложения линейных операторов в теории нерегулярных систем с частными производными

Скелетные разложения линейных операторов в теории нерегулярных систем с частными производными

Solution of Irregular Systems of Partial Differential Equations Using Skeleton Decomposition of Linear Operators

Solution of Irregular Systems of Partial Differential Equations Using Skeleton Decomposition of Linear Operators

Survival of branching Brownian motion in a uniform trap field

We study a branching Brownian motion Z evolving in Rd, where a uniform field of Poissonian traps are present. We consider a general offspring distribution for Z and find the asymptotic decay rate of the annealed survival probability, conditioned on non-extinction. The method of proof is to use a skeleton decomposition for the Galton–Watson process underlying Z and to show that the particles of finite line of descent do not contribute to the survival asymptotics. This work is a follow-up to Öz and Çağlar (2013) and solves the problem considered therein completely.

Spines, skeletons and the strong law of large numbers for superdiffusions

Consider a supercritical superdiffusion $(X_{t})_{t\ge0}$ on a domain $D\subseteq\mathbb{R}^{d}$ with branching mechanism \[(x,z)\mapsto-\beta(x)z+\alpha(x)z^{2}+\int_{(0,\infty)}(e^{-zy}-1+zy)\Pi(x,dy).\] The skeleton decomposition provides a pathwise description of the process in terms of immigration along a branching particle diffusion. We use this decomposition to derive the strong law of large numbers (SLLN) for a wide class of superdiffusions from the corresponding result for branching particle diffusions. That is, we show that for suitable test functions $f$ and starting measures $\mu$, \[\frac{\langle f,X_{t}\rangle}{P_{\mu}[\langle f,X_{t}\rangle]}\to W_{\infty}\qquad P_{\mu}\mbox{-}\mathrm{almost} \mathrm{surely} \mathrm{as} t\to\infty,\] where $W_{\infty}$ is a finite, non-deterministic random variable characterized as a martingale limit. Our method is based on skeleton and spine techniques and offers structural insights into the driving force behind the SLLN for superdiffusions. The result covers many of the key examples of interest and, in particular, proves a conjecture by Fleischmann and Swart [Stochastic Process. Appl. 106 (2003) 141–165] for the super-Wright–Fisher diffusion.

Hollow silica-copper-carbon anodes using copper metal-organic frameworks as skeletons.

Hollow silica-copper-carbon (H-SCC) nanocomposites are first synthesized using copper metal-organic frameworks as skeletons to form Cu-MOF@SiO(2) and then subjected to heat treatment. In the composites, the hollow structure and the void space from the collapse of the MOF skeleton can accommodate the huge volume change, buffer the mechanical stress caused by lithium ion insertion/extraction and maintain the structural integrity of the electrode and a long cycling stability. The ultrafine copper with a uniform size of around 5 nm and carbon with homogeneous distribution from the decomposition of the MOF skeleton can not only enhance the electrical conductivity of the composite and preserve the structural and interfacial stabilization, but also suppress the aggregation of silica nanoparticles and cushion the volume change. In consequence, the resulting material as an anode for lithium-ion batteries (LIBs) delivers a reversible capacity of 495 mA h g(-1) after 400 cycles at a current density of 500 mA g(-1). The synthetic method presented in this paper provides a facile and low-cost strategy for the large-scale production of hollow silica/copper/carbon nanocomposites as an anode in LIBs.

Nanostructured gadolinium-doped ceria microsphere synthesis from ion exchange resin: Multi-scale in-situ studies of solid solution formation

In the current nano-sized material revolution, the main limitations to a large-scale deployment of nanomaterials involve health concerns related to nano-dissemination via air. Developing new chemical routes benefiting from nano-size advantages while avoiding their hazards could overcome these limitations. Addressing this need, a chemical route leading to soft nano-particle agglomerates, i.e., macroscopic precursors presenting the ability to be decomposed into nano-sized materials, was developed and applied to Ce0.8Gd0.2O2−δ. Using cerium/gadolinium-loaded ion exchange resin, the Ce0.8Gd0.2O2−δ solid solution formation as a function of temperature was studied in-situ through X-ray diffraction, X-ray absorption spectroscopy and Raman spectroscopy. Temperatures corresponding to the organic skeleton decomposition and to the mixed oxide crystallization were identified. An optimal heat treatment, leading to nanostructured soft agglomerates, was established. Microsphere processing capabilities were evaluated and particle size distribution measurements were recorded. A very low fracture strength was calculated, and a nanometric particle size distribution (170nm) was determined.