Noise Folding in Completely Perturbed Compressed Sensing

This paper first presents a new generally perturbed compressed sensing (CS) model y=(A+E)(x+u)+e, which incorporated a general nonzero perturbation E into sensing matrix A and a noise u into signal x simultaneously based on the standard CS model y=Ax+e and is called noise folding in completely perturbed CS model. Our construction mainly will whiten the new proposed CS model and explore in restricted isometry property (RIP) and coherence of the new CS model under some conditions. Finally, we use OMP to give a numerical simulation which shows that our model is feasible although the recovered value of signal is not exact compared with original signal because of measurement noise e, signal noise u, and perturbation E involved

Triaqua­bis{μ-N-[N-(4-meth­oxy-2-oxidobenzyl­idene)glyc­yl]glycinato(3−)}cadmium(II)dicopper(II) dihydrate

In the title compound, [CdCu2(C12H11N2O5)2(H2O)3]·2H2O, the CuII atoms are in a square plane of N2O2 atoms contributed by the tetra­dentate Schiff base trianion. The CuII atoms are coordinated by one phenolate O atom, one imine N atom, one amido N atom and one carboxyl­ate O atom. The CdII atom is connected via the carboxyl­ate groups, forming a heterotrinuclear CuII–CdII–CuII system. The CdII atom is seven-coordinate in a penta­gonal-bipyramidal geometry with four O atoms from two carboxyl­ate groups and three aqua ligands. The heterotrinuclear mol­ecules are linked to the uncoordinated water mol­ecules by O—H⋯O hydrogen bonds into a three-dimensional framework

Hexaaqua­magnesium(II) bis­{[N-(4-meth­oxy-2-oxidobenzyl­idene)glycyl­glycinato(3−)]cuprate(II)} hexa­hydrate

In the title complex, [Mg(H2O)6][Cu(C12H11N2O5)]2·6H2O, the CuII atoms lie at the center of the square plane of triple negatively charged O,N,N′,O′-tetra­dentate Schiff base ligands, which are coordinated by one phenolate O atom, one imine N atom, one deprotonated amide N atom and one carboxyl­ate O atom. The MgII center, which sits on an inversion center, is coordinated by six aqua ligands and exhibits a slightly distorted octa­hedral conformation. The asymmetric unit consists of an [N-(4-meth­oxy-2-oxidobenzyl­idene)glycyl­glycinato]cuprate(II) anion, one half of an [Mg(H2O)6]2+ cation and three free water mol­ecules. The cations and anions form columns by O—H⋯O hydrogen bonds

Hexaaqua­cobalt(II) bis­{[N-(4-meth­oxy-2-oxidobenzyl­idene)glycylglycinato]nickel(II)} hexa­hydrate

In the title compound, [Co(H2O)6][Ni(C12H11N2O5)]2·6H2O, the NiII atom has a nearly square-planar coordination with two N and two O atoms of the N-(4-meth­oxy-2-oxidobenzyl­idene)glycylglycinate Schiff base ligand (L 3−). The CoII atom sits on an inversion center and is coordinated to six aqua ligands in a slightly distorted octa­hedral geometry. The [Co(H2O)6]2+ cations and [NiL]− anions form columns along the a axis by O—H⋯O hydrogen bonds. Additional hydrogen bonds between the uncoordinated and coordinated water molecules help to consolidate the crystal packing

AEDNet: Adaptive Edge-Deleting Network For Subgraph Matching

Subgraph matching is to find all subgraphs in a data graph that are isomorphic to an existing query graph. Subgraph matching is an NP-hard problem, yet has found its applications in many areas. Many learning-based methods have been proposed for graph matching, whereas few have been designed for subgraph matching. The subgraph matching problem is generally more challenging, mainly due to the different sizes between the two graphs, resulting in considerable large space of solutions. Also the extra edges existing in the data graph connecting to the matched nodes may lead to two matched nodes of two graphs having different adjacency structures and often being identified as distinct objects. Due to the extra edges, the existing learning based methods often fail to generate sufficiently similar node-level embeddings for matched nodes. This study proposes a novel Adaptive Edge-Deleting Network (AEDNet) for subgraph matching. The proposed method is trained in an end-to-end fashion. In AEDNet, a novel sample-wise adaptive edge-deleting mechanism removes extra edges to ensure consistency of adjacency structure of matched nodes, while a unidirectional cross-propagation mechanism ensures consistency of features of matched nodes. We applied the proposed method on six datasets with graph sizes varying from 20 to 2300. Our evaluations on six open datasets demonstrate that the proposed AEDNet outperforms six state-of-the-arts and is much faster than the exact methods on large graphs

A Supramolecular Strategy to Assemble Multifunctional Viral Nanoparticles

Using a one-pot approach driven by the supramolecular interaction between β-cyclodextrin and adamantyl moieties, multifunctional viral nanoparticles can be facilely formulated for biomedical applications

Dimethyl 2,2′-[ethane-1,2-diylbis(sulfanedi­yl)]dibenzoate

The title compound, C18H18O4S2, was synthesized by the reaction of 1,2-dibromo­ethane with methyl thio­salicylate. The complete molecule is generated by crystallographic twofold symmetry: two methyl benzoate units are linked by an –S–(CH2)2–S– bridging chain with a gauche S—CH2—CH2—S torsion angle [72.88 (16)°]. The two aromatic rings form a dihedral angle of 79.99 (6)°. In the crystal, adjacent mol­ecules are linked into a three-dimensional network by non-classical C—H⋯O hydrogen bonds

Sub-GMN: The Neural Subgraph Matching Network Model

As one of the most fundamental tasks in graph theory, subgraph matching is a crucial task in many fields, ranging from information retrieval, computer vision, biology, chemistry and natural language processing. Yet subgraph matching problem remains to be an NP-complete problem. This study proposes an end-to-end learning-based approximate method for subgraph matching task, called subgraph matching network (Sub-GMN). The proposed Sub-GMN firstly uses graph representation learning to map nodes to node-level embedding. It then combines metric learning and attention mechanisms to model the relationship between matched nodes in the data graph and query graph. To test the performance of the proposed method, we applied our method on two databases. We used two existing methods, GNN and FGNN as baseline for comparison. Our experiment shows that, on dataset 1, on average the accuracy of Sub-GMN are 12.21\% and 3.2\% higher than that of GNN and FGNN respectively. On average running time Sub-GMN runs 20-40 times faster than FGNN. In addition, the average F1-score of Sub-GMN on all experiments with dataset 2 reached 0.95, which demonstrates that Sub-GMN outputs more correct node-to-node matches. Comparing with the previous GNNs-based methods for subgraph matching task, our proposed Sub-GMN allows varying query and data graphes in the test/application stage, while most previous GNNs-based methods can only find a matched subgraph in the data graph during the test/application for the same query graph used in the training stage. Another advantage of our proposed Sub-GMN is that it can output a list of node-to-node matches, while most existing end-to-end GNNs based methods cannot provide the matched node pairs

1,1′-(p-Phenyl­enedimethyl­idene)diimidazol-3-ium bis­{2-[(2-carb­oxy­phen­yl)disulfan­yl]benzoate} dihydrate

The title salt, C14H16N4 2+·2C14H9O4S2 −·2H2O, was obtained by the co-crystalization of 2,2′-dithio­dibenzoic acid with 1,4-bis­(imidazol-1-ylmeth­yl)benzene. It consists of 2-[(2-carb­oxy­phen­yl)disulfan­yl]benzoate anions, centrosymmetric 1,1′-(p-phenyl­enedimethyl­idene)diimidazol-3-ium cations and water mol­ecules. O—H⋯O, O—H⋯S and N—H⋯O hydrogen-bonding inter­actions among the components lead to the formation of a three-dimensional network