A Survey of Information Entropy Metrics for Complex Networks

Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts.     

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

氮杂环卡宾-钯配合物催化Buchwald-Hartwig偶联反应最新研究进展*

钯催化的Buchwald-Hartwig偶联反应是用于构建C-N键非常直接有效的方法。氮杂环卡宾-钯配合物具有性能稳定、催化活性高等优点,是Buchwald-Hartwig偶联反应的高效催化剂。对这一领域近3年的研究进展作简要介绍。     

Reactions of a Silylyne Complex with Aldehydes: Formation of W−Si−O−C Four-Membered Metallacycles and Their Metathesis-Like Fragmentation

A tungsten silylyne complex having a W≡Si triple bond reacted with two molecules of aldehydes at room temperature to give W−Si−O−C four-membered metallacycles by [2+2] cycloaddition and subsequent formyl hydrogen transfer from one aldehyde molecule to another. Upon heating to 70 °C, the four-membered metallacycles underwent metathesis-like fragmentation cleanly to afford carbyne complexes and “silanoic esters,” in a manner similar to that of metallacyclobutadiene, an intermediate of alkyne metathesis reactions, and dimerization of the latter products gave 1,3-cyclodisiloxanes. The “silanoic ester” was also trapped by pivalaldehyde to give a [2+2] cycloaddition product in high yield.     

Rare-earth metal derivatives supported by aminophenoxy ligand: Synthesis,characterization and catalytic performance in lactide polymerization

A library of rare-earth metal derivatives supported by an aminophenoxy ligand was prepared and their catalytic performance in lactide polymerization was investigated. It was found that the synthetic strategy had a profound effect on the formation of aminophenoxy rare-earth metal complexes. Amine elimination between Ln[N(SiMe₃)₂]₃(μ-Cl)Li(THF)₃ (Ln = Yb, Y) and 1 equiv. of the aminophenol [HONH] ([HONH] = ο-OCH₃-C₆H₄NHCH₂(3,5-^tBu₂-C₆H₂-2-OH)) in toluene gave the unexpected heterobimetallic bis(aminophenoxy) rare-earth metal complexes [ON]₂LnLi(THF)₂ (Ln = Yb ( 1 ), Y ( 2 )). When the reactions were carried out in THF and TMEDA, amine elimination produced the aminophenoxy rare-earth metal amide complexes {[ON]LnN(SiMe₃)₂}₂ (Ln = Yb ( 5 ), Y ( 6 )) in ca 85% isolated yields. Complexes 5 and 6 could also be obtained from salt metathesis reaction of {[ON]LnCl(THF)}₂ (Ln = Yb ( 3 ), Y ( 4 )) with NaN(SiMe₃)₂ in a 1:2 molar ratio. In addition, treatment of complexes 3 and 4 with NaOAr (Ar = &bond;C₆H₄-4-^tBu) and (SiMe₃)₂NC(NPrⁱ)₂Na in 1:4 and 1:2 molar ratios provided the corresponding aminophenoxy rare-earth metal derivatives {[ON](μ-OAr)Ln(μ-OAr)Na(THF)₂}₂ (Ln = Yb ( 7 ), Y ( 8 )) and {[ON]Ln[(ⁱPrN)₂CN(SiMe₃)₂]}₂ (Ln = Yb ( 9 ), Y ( 10 )), respectively. These complexes were fully characterized, and their molecular structures were determined using single-crystal X-ray diffraction. Polymerization experiments showed that complexes 1 , 2 , 5 , 6 , 9 and 10 were highly active for the ring-opening polymerization of l -lactide in toluene, and complex 1 promoted l -lactide polymerization in a controlled fashion. The polymerization of rac-lactide initiated by the neutral aminophenoxy rare-earth metal complexes 5 , 6 , 9 and 10 in THF afforded heterotactic polymers.     

Ultrasound-assisted nanoscaled supramolecular coordination polymer as an efficient recyclable catalyst for photocatalytic degradation of dye pollutants

An ultrasound-assisted nanoscaled supramolecular coordination polymer (nanosized 1′ ) has been synthesized using a self-assembly reaction of K₃[Cu (CN)₄] and hexamethylenetetramine in the presence of Me₃SnCl under ambient conditions. Nanosized 1′ was examined using elemental analysis, Fourier transform–infrared, transmission electron microscopy, scanning electron microscopy and X-ray powder diffractions. It was structurally compared with the single crystal supramolecular coordination polymer ^∞₃[Cu₆(CN)₇(C₆H₁₂N₄)₂(OH₃)]; SCP 1. The photocatalytic activities of nanosized 1′ and SCP 1 toward different hazardous organic dyes were determined under ambient, UV-light irradiation and ultrasonic conditions. SCP 1 and nanosized 1′ as heterogeneous nanoparticles catalysts exhibited high catalytic activity for degradation of Congo Red, Methyl Violet 2B and Methylene Blue dyes. The effects of operational parameters on catalytic degradation process, identification of the degradation products and recycling of the catalyst were also investigated. SCP 1 and nanosized 1′ are recyclable heterogeneous catalysts and can be reused with efficient activities. The mechanism of degradation using different scavenger techniques iss proposed and discussed. The catalytic oxidation process is mainly caused by ^•OH radicals.     

Copper quinolate: A simple and efficient catalytic complex for coupling reactions

We describe an effective and novel method to prepare N-aryl imidazoles via the copper quinolate-catalyzed N-arylation of aryl halides and imidazoles. A wide range of products were obtained in moderate to excellent yields under the optimal reaction conditions. Applying standard conditions, the model reaction could be performed on a gram scale. This method also presents a new avenue to the “click” reaction of terminal alkynes, benzyl bromide, and sodium azide and to the construction of C–C bonds by homocoupling of phenylboronic acid or phenylacetylene derivatives with the aid of copper quinolate.     

Synthesis of nonplanar bipyridyls bridged by disilane and disiloxane and their phosphorescent copper complexes

Disilane- and disiloxane-bridged bipyridyls ( DSBPy and DSOBPy ) were prepared and their optical properties were investigated in comparison with those of previously reported monosilane- and monogermane-bridged counterparts. The UV–visible absorption and photoluminescence bands of DSBPy and DSOBPy were blue-shifted as a result of elongation of the bridging units from monosilane and monogermane to disilane and disiloxane, likely due to the enhanced twisting of the bipyridyl units. Phosphorescent complexes DSBPy–Cu and DSOBPy–Cu were prepared by the interaction of DSBPy and DSOBPy with Cu₂I₂(PPh₃)₂. X-ray diffraction studies of their single-crystal structures revealed polymeric structures composed of repeat units of DSBPy or DSOBPy and [Cu^II(PPh₃)]₂. Organic light-emitting diodes with the ITO/PEDOT:PSS/ DSBPy–Cu or DSOBPy–Cu :PCTSQ/TAZ/Al structure were fabricated to examine the applications of the complexes as electroluminescent materials. The devices emitted yellow light with emission maxima at approximately 600 nm, and maximal luminance reached 120 and 190 cd m⁻² for devices based on DSBPy–Cu and DSOBPy–Cu , respectively. The performance of the DSOBPy–Cu -based device was improved by using TAZ as the dopant of the emissive layer, and luminance was increased to 390 cd m⁻².     

Salicylaldimine-bridged dinuclear cyclopalladated complexes: Synthesis,characterization and BSA binding studies

Salicylaldimine-bridged dinuclear cyclopalladated complexes were synthesized by the reactions of cyclopalladated chloro dimers [Pd{(4-R)C₆H₃CH=N-C₆H₃–2,6-i-Pr₂}(μ-Cl)]₂ (R = H; OMe) with salen-based bridging ligands. The complexes were characterized by FTIR, NMR spectroscopy, elemental analysis and X-ray crystallography. The binding interaction of cyclopalladated complexes to bovine serum albumin (BSA) was investigated by UV–vis, fluorescence and synchronous fluorescence spectroscopy. The experimental results showed that these Pd (II) complexes could bind to BSA with high affinity and quench its intrinsic fluorescence by a static or combined process. Also the interaction of Pd complexes with BSA affected the conformation of the tryptophan and tyrosine residues.