Decomposition Of Ring Research Articles

Deciphering Deoxynybomycin Biosynthesis Reveals Fe(II)/α-Ketoglutarate-Dependent Dioxygenase-Catalyzed Oxazoline Ring Formation and Decomposition.

The antibacterial agents deoxynybomycin (DNM) and nybomycin (NM) have a unique tetracyclic structure featuring an angularly fused 4-oxazoline ring. Here, we report the identification of key enzymes responsible for forming the 4-oxazoline ring in Embleya hyalina NBRC 13850 by comparative bioinformatics analysis of the biosynthetic gene clusters encoding structurally similar natural products DNM, deoxynyboquinone (DNQ), and diazaquinomycins (DAQs). The N-methyltransferase DnmS plays a crucial role in catalyzing the N-dimethylation of a tricyclic precursor prenybomycin to generate NM D; subsequently, the Fe(II)/α-ketoglutarate-dependent dioxygenase (Fe/αKGD) DnmT catalyzes the formation of a 4-oxazoline ring from NM D to produce DNM; finally, a second Fe/αKGD DnmU catalyzes the C-12 hydroxylation of DNM to yield NM. Strikingly, DnmT is shown to display unexpected functions to also catalyze the decomposition of the 4-oxazoline ring and the N-demethylation, thereby converting DNM back to prenybomycin, to putatively serve as a manner to control the intracellular yield of DNM. Structure modeling, site-directed mutagenesis, and quantum mechanics calculations provide mechanistic insights into the DnmT-catalyzed reactions. This work expands our understanding of the functional diversity of Fe/αKGDs in natural product biosynthesis.

Nonparametric tensor ring decomposition with scalable amortized inference

Multi-dimensional data are common in many applications, such as videos and multi-variate time series. While tensor decomposition (TD) provides promising tools for analyzing such data, there still remains several limitations. First, traditional TDs assume multi-linear structures of the latent embeddings, which greatly limits their expressive power. Second, TDs cannot be straightforwardly applied to datasets with massive samples. To address these issues, we propose a nonparametric TD with amortized inference networks. Specifically, we establish a non-linear extension of tensor ring decomposition, using neural networks, to model complex latent structures. To jointly model the cross-sample correlations and physical structures, a matrix Gaussian process (GP) prior is imposed over the core tensors. From learning perspective, we develop a VAE-like amortized inference network to infer the posterior of core tensors corresponding to new tensor data, which enables TDs to be applied to large datasets. Our model can be also viewed as a kind of decomposition of VAE, which can additionally capture hidden tensor structure and enhance the expressiveness power. Finally, we derive an evidence lower bound such that a scalable optimization algorithm is developed. The advantages of our method have been evaluated extensively by data imputation on the Healing MNIST dataset and four multi-variate time series data.

Effect of Lithium Salts on the Properties of Cassava Starch Solid Biopolymer Electrolytes.

This study evaluates the effect of lithium salts on the structural, electrochemical, and thermal properties of cassava starch solid biopolymer electrolytes (SBPEs). Films of SBPEs were synthesized using plasticizing agents and lithium salts (LiCl, Li2SO4, and CF3LiSO3) via thermochemical method. The SBPEs with lithium salts exhibited characteristic FTIR bands starch, with slight variations in the vibration oxygen-related functional groups compared to salt-free biopolymer spectra. The RCOH/COC index (short-range crystallinity) was higher in the films synthesized without lithium salt and the lowest value was established in the films synthesized with Li2SO4. Thermal degradation involved dehydration between 40 to 110 °C and molecular decomposition between 245 to 335 °C. Degradation temperatures were close when synthesized with salts but differed in films without lithium salt. DSC revealed two endothermic processes: one around 65 °C linked to crystalline structure changes and the second at approximately 271 °C associated with glucose ring decomposition. The electrochemical behavior of the SBPEs varied with the salts used, resulting in differences in the potential and current of peaks from the redox processes and its conductivity, presenting the lowest value (8.42 × 10-5 S cm-1) in the SBPE films without salt and highest value (9.54 × 10-3 S cm-1) in the films with Li2SO4. It was concluded that the type of lithium salt used in SBPEs synthesis affected their properties. SBPEs with lithium triflate showed higher molecular ordering, thermal stability, and lower redox potentials in electrochemical processes.

Weighted Group Sparse Regularized Tensor Decomposition for Hyperspectral Image Denoising

Hyperspectral imaging (HSI) has been used in a wide range of applications in recent years. But in the process of image acquisition, hyperspectral images are subject to various types of noise interference. Noise reduction algorithms can be used to enhance the quality of images and make it easier to detect and analyze features of interest. To realize better image recovery, we propose a weighted group sparsity-regularized low-rank tensor ring decomposition (LRTRDGS) method for hyperspectral image recovery. Tensor ring decomposition can be utilized by this approach to investigate self-similarity and global spectral correlation. Furthermore, weighted group sparsity regularization can be employed to depict the sparsity structure of the group along the spectral dimension of the spatial difference image. Moreover, we solve the proposed model using a symmetric alternating direction method multiplier with the addition of a proximity term. The experimental data verify the effectiveness of our proposed method.

Hyperspectral image reconstruction based on low-rank coefficient tensor and global prior

ABSTRACT Compressive sensing (CS) has been employed to compress and store hyperspectral images (HSI) to transfer extensive data efficiently, and obtaining high-quality reconstructed images is crucial for subsequent applications. Model-based methods usually capture the priors of HSI, including sparsity, global and nonlocal low-rankness, nonlocal self-similarity and global correlation. However, it is challenging to reasonably integrate different regularizations in a united framework and exploit various priors mentioned to reconstruct high-quality images. In this paper, a tensor optimization model based on the low-rank coefficient tensor and global prior (LRCTGP) is proposed for HSI reconstruction. Complementary regularization terms are integrated into a united framework and effectively promote the reconstruction results. First, we apply the mode- tensor-matrix product to decompose the original HSI rather than employing the regularization to capture the spectral low-rankness and simultaneously constrain the original and feature HSI. Then, tensor ring decomposition is employed to constrain the coefficient tensor with fewer bands, which is more efficient in the low-rank approximation and has smaller calculation costs than applying it to the original HSI. Moreover, integrating BM3D as a regularizer is more efficient than other patch-based models. Finally, considering the smoothness and global correlation, spatial-spectral total variation (SSTV) is applied to compensate for the shortcomings after decomposing the original and feature HSI, which complements the overall structure and details of reconstructed images and improves the reconstruction quality. Alternating direction method of multipliers (ADMM) is used to optimize the proposed model. Experimental results of the LRCTGP model on different HSI datasets are better than existing state-of-the-art approaches, which proves the superiority.

TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization

TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization

SDPN: A Slight Dual-Path Network With Local-Global Attention Guided for Medical Image Segmentation.

Accurate identification of lesions is a key step in surgical planning. However, this task mainly exists two challenges: 1) Due to the complex anatomical shapes of different lesions, most segmentation methods only achieve outstanding performance for a specific structure, rather than other lesions with location differences. 2) The huge number of parameters limits existing transformer-based segmentation models. To overcome these problems, we propose a novel slight dual-path network (SDPN) to segment variable location lesions or organs with significant differences accurately. First, we design a dual-path module to integrate local with global features without obvious memory consumption. Second, a novel Multi-spectrum attention module is proposed to pay further attention to detailed information, which can automatically adapt to the variable segmentation target. Then, the compression module based on tensor ring decomposition is designed to compress convolutional and transformer structures. In the experiment, four datasets, including three benchmark datasets and a clinical dataset, are used to evaluate SDPN. Results of the experiments show that SDPN performs better than other start-of-the-art methods for brain tumor, liver tumor, endometrial tumor and cardiac segmentation. To ensure the generalizability, we train the network on Kvasir-SEG and test on CVC-ClinicDB which collected from a different institution. The quantitative analysis shows that the clinical evaluation results are consistent with the experts. Therefore, this model may be a potential candidate for the segmentation of lesions and organs segmentation with variable locations in clinical applications.

Spatiotemporal traffic data imputation by synergizing low tensor ring rank and nonlocal subspace regularization

AbstractSpatiotemporal traffic data usually suffers from missing entries in the data acquisition and transmission process. Existing imputation methods only consider the global/local structure of spatiotemporal traffic data, resulting in insufficient estimation performance. Fortunately, it is found that traffic data admits the nonlocal self‐similarity (NSS) prior. This paper incorporates the global and nonlocal low‐rank priors of traffic data and proposes a tensor completion model for spatiotemporal traffic data imputation. To be specific, the proposed method uses tensor ring (TR) decomposition with an enhanced representation capability to characterize the global low‐TR‐rank prior of traffic data, e.g. the correlation of sensor and time modes of the tensor (i.e. traffic data). An implicit plug‐and‐play (PnP)‐based regularization is further utilized to exploit the NSS prior, which depicts the nonlocal similar traffic data patterns. Furthermore, the proximal alternating minimization algorithm under the PnP framework is derived to solve this model. The experiment results on various datasets and missing scenarios show the superiority of the proposed model.

Incomplete Multiview Clustering via Low-Rank Tensor Ring Completion

Since real-world multiview data frequently contains numerous samples that are not observed from some viewpoints, the incomplete multiview clustering (IMC) issue has received a great deal of attention recently. However, most existing IMC methods choose to zero-fill the missing instances, which leads to the failure to exploit information hidden in the missing instances, and high-order interactions between various views. To tackle these problems, we proposed an effective IMC method using low-rank tensor ring completion, which was demonstrated to be powerful in exploiting high-order correlation. Specifically, we first stack the incomplete similarity graphs of all views into a 3rd-order incomplete tensor and then restore it via the tensor ring decomposition. Next, using an adaptive weighting technique, we apply multiview spectral clustering to all entire graphs in order to balance the contributions of different viewpoints and identify the consensus representation for grouping. Finally, we employ the alternating direction method of multipliers (ADMM) to optimize the suggested model. Numerous experimental findings on numerous different datasets show that the suggested approach is superior to other cutting-edge approaches.

Product decompositions of moment-angle manifolds and B-rigidity

AbstractA simple polytope P is called B-rigid if its combinatorial type is determined by the cohomology ring of the moment-angle manifold $\mathcal {Z}_P$ over P. We show that any tensor product decomposition of this cohomology ring is geometrically realized by a product decomposition of the moment-angle manifold up to equivariant diffeomorphism. As an application, we find that B-rigid polytopes are closed under products, generalizing some recent results in the toric topology literature. Algebraically, our proof establishes that the Koszul homology of a Gorenstein Stanley–Reisner ring admits a nontrivial tensor product decomposition if and only if the underlying simplicial complex decomposes as a join of full subcomplexes.

TR-ReFloc: A TR-based Framework for Recovering Missed RSS for WiFi indoor positioning in the offline and online phase

The research on WiFi-based fingerprint positioning has become an important topic in the field of indoor positioning due to its low-cost deployment and widespread applications. However, received signal strength (RSS) from access points (APs) may be missed due to factors such as Green WiFi or AP malfunctions. Traditional approach often set the missed RSS to a predetermined default value, which may not be accurate. We propose a fingerprint recovery framework based on tensor-ring nuclear norm minimization (TRNNM) algorithm which uses the correlation of RSS to recover missed fingerprints in both offline and online phases, called TR-ReFloc. In the offline phase, the radio map in tensor form is recovered by tensor ring (TR) decomposition. In the online phase, depending on different user requirements, there are two stages to generate the positioning results. First, rapid results are generated in coarse positioning stage. Next, high-precision results generated in fine positioning stage by recovering the missed fingerprints using the correlation of test points (TPs) are closed to the current TP. Experiments demonstrate that the proposed framework is robust for recovering missed RSS and can maintain localization accuracy within 2 m even in cases of high missing rate, demonstrating significant improvement over traditional methods.

Decomposition of quandle rings of dihedral quandles

Decomposition of quandle rings of dihedral quandles

Synthesis of internally carbon-sourced carbon nanofiber forming Ni-graphitic carbon nitride

The present study synthesizes carbon nanofibers (CNF) over a graphitic carbon nitride (g-C3N4) substrate without requiring an external carbon-source. In this novel route of the synthesis, g-C3N4 acts as the substrate as well as the internal source of carbon. Ni nanoparticles (NPs) dispersed in g-C3N4 catalyze the decomposition of triazine rings and N heterocycles in the material to form a web of CNF over g-C3N4. Tested for its catalytic activity towards the reduction of aqueous nitrobenzene (NB) using the hydrazine monohydrate reducing agent, Ni-CNF/g-C3N4 shows an approximately 95% conversion of NB. The high catalytic activity of the material is ascribed to the combined effects of g-C3N4, Ni NPs, and CNF. The present study has clearly established an efficient, easy, and inexpensive route for synthesizing CNF-based 3D nanostructures that are useful in many engineering applications including energy and environment.

Retracted: The Effect of Air on the Oxidation Decomposition of Cationic Exchange Resins in a Ternary Li2CO3−Na2CO3−K2CO3 Molten‐Salt System

AbstractThe molten‐salt oxidation method (MSO) can be applied for disposal of spent cationic exchange resins (CERs) after the treatment of nuclear industry wastewater. In this work, the oxidation decomposition of resins in carbonate molten salt in N2 and air atmospheres was investigated. The SEM morphology and FTIR spectrograms indicated that the addition of air obviously prompted the oxidation decomposition of the benzene ring, S−O bond and S−C bond in residues and the decomposition efficiency of resins reached 98.69 % at 800 °C. The XPS analysis showed the conversion of sulfur species in residues. The peroxide and superoxide ions in carbonate molten salt prompted the decomposition of thiophene sulfur and resulted in the formation of sulfate. The retention rate of sulfur in spent salt was 84.36 % at 800 °C. This work provided more theoretical guidance for the treatment of resins and technical support for the sustainable development of nuclear industry.

Application of Tensor Decomposition to Reduce the Complexity of Neural Min-Sum Channel Decoding Algorithm

Channel neural decoding is very promising as it outperforms the traditional channel decoding algorithms. Unfortunately, it still faces the disadvantage of high computational complexity and storage complexity compared with the traditional decoding algorithms. In this paper, we propose that low rank decomposition techniques based on tensor train decomposition and tensor ring decomposition can be utilized in neural offset min-sum (NOMS) and neural scale min-sim (NSMS) decoding algorithms. The experiment results show that the proposed two algorithms achieve near state-of-the-art performance with low complexity.

The Complexity of Decomposability of Computable Rings

This article studies the complexity of decomposability of rings from the perspective of computability. Based on the equivalence between the decomposition of rings and that of the identity of rings, we propose four kinds of rings, namely, weakly decomposable rings, decomposable rings, weakly block decomposable rings, and block decomposable rings. Let R be the index set of computable rings. We study the complexity of subclasses of computable rings, showing that the index set of computable weakly decomposable rings is m-complete Σ10 within R and that the index set of computable decomposable (resp., weakly block decomposable, block decomposable) rings is m-complete Σ20 within R.

Investigation of Methylcyclopentadiene Reactivity: Abstraction Reactions and Methylcyclopentadienyl Radical Unimolecular Decomposition.

Understanding the reactivities of methylcyclopentadiene and the methylcyclopentadienyl radical is important in order to improve our comprehension of the chemical kinetics leading to the formation, decomposition, and growth of the first aromatic ring, as it has been shown that five-membered-ring species are important intermediates in the reaction kinetics of aromatic species. In this work, the rate constants of some key H-abstraction reactions from methylcyclopentadiene to produce the methylcyclopentadienyl radical and the formation of fulvene and benzene from the latter are theoretically determined. Rate constants are evaluated using the ab initio transition state theory-based master equation approach, determining structures and Hessians of all stationary points at the ωB97X-D/aug-cc-pVTZ level, energies at the CCSD(T) level extrapolated to the complete basis set limit, RRKM rate constants using conventional and variational transition state theory, and phenomenological rate constants through the solution of the one-dimensional master equation. Variational corrections are determined in both internal and Cartesian coordinates, and it is found that the choice of the coordinate system can impact the accuracy of the calculated rate constants by up to a factor of 4 for H-abstraction reactions and 2 for the unimolecular decomposition of the methylcyclopentadienyl radical. The calculated rate constants are in good agreement with the available literature data. Prompt dissociation of methylcyclopentadienyl radicals accessed following H-abstraction from methylcyclopentadiene was also investigated, and the corresponding rate constants were determined; the results show that prompt dissociation plays a key role under combustion conditions. Finally, lumping of theoretically derived rate constants to account for methylcyclopentadiene ⇄ methylcyclopentadienyl tautomerism allowed the derivation of a simplified set of rate constants suitable to be inserted into kinetic mechanisms.

Tensor Ring decomposition for context-aware recommendation

As a powerful tool for processing high-dimensional data, tensor decomposition has been widely used in context-aware recommendation. Most of the current tensor decomposition-based recommendation models use CP decomposition or Tucker decomposition. In practical recommendation applications, fewer parameters limit the performance of CP decomposition, and the high-order tensor kernel makes the computational complexity of Tucker decomposition exponential. In order to improve the performance of recommendation while maintaining high computational efficiency, we propose a bias Tensor Ring decomposition framework for context-aware recommendation, which employs Tensor Ring decomposition to extract user-item-context latent factors. Comparing to current tensor decomposition-based recommendation models, our framework achieves a better balance between recommendation performance and computational complexity by Tensor Ring decomposition. This is a highly scalable recommendation framework that can easily further integrate additional information such as social trust and implicit feedback, thus used for more complex recommendation tasks. To the best of our knowledge, this work is the first to formulate context-aware recommendation as Tensor Ring decomposition process. Our in-depth analyses confirm that Tensor Ring decomposition has certain advantages over CP decomposition and Tucker decomposition. Multiple experiments on three real datasets also show that the proposed framework helps to improve the recommendation performance.

Hyperspectral Anomaly Detection Based on Tensor Ring Decomposition With Factors TV Regularization

Anomaly detection in the hyperspectral image (HSI) has gradually become a hot topic in remote sensing. Recently, some tensor-based methods have been proposed to improve detection performance by exploiting the characteristic of HSI data existing in the inherent multi-dimensional. However, the existing tensor-based methods may only partially use the prior properties in both spatial and spectral dimensions. In this paper, we proposed a novel tensor ring (TR) decomposition with factors TV regularization model for hyperspectral anomaly detection. First, raw HSI data is decomposed into background and anomaly tensors. The tensor ring decomposition is adopted to exploit the low-rank property of the background existing in both spatial and spectral dimensions. Then, the total variation (TV) regularization is designed on the three dimensions of the background tensor to explore the piecewise smoothness of the background existing in both spatial and spectral dimensions. Further, this TV regularization is transferred to each factor tensor by exploiting the relationship between the background tensor and each factor tensor. Next, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> norm regularization is designed on the anomaly tensor to exploit the group sparsity of anomaly pixels. Finally, the alternating direction method of multipliers (ADMM) scheme is adopted to update the involved variables. Experimental results validated on several real hyperspectral datasets demonstrate the effectiveness of the proposed algorithm.

Matrix representations of endomorphism rings for torsion-free abelian groups

Non-isomorphic direct decompositions of torsion-free abelian groups are reflected in their endomorphism ring decompositions which admit matrix representations. The set of possible direct decompositions of a special kind matrix rings into direct sums of one-sided indecomposable ideals is described. This leads to the combinatorial constructions of isomorphisms between non-commutative differently decomposable ring structures.