Lag synchronization and scaling of chaotic attractor in coupled system

We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the Ro?ssler system, a Sprott system, and a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.     

Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

Connections on the Total Space of a Holomorphic Lie Algebroid

The main purpose of the paper is the study of the total space of a holomorphic Lie algebroid E. The paper is structured in three parts. In the first section, we briefly introduce basic notions on holomorphic Lie algebroids. The local expressions are written and the complexified holomorphic bundle is introduced. The second section presents two approaches on the study of the geometry of the complex manifold E. The first part contains the study of the tangent bundle \(T_{\mathbb {C}}E=T'E\oplus T''E\) and its link, via the tangent anchor map, with the complexified tangent bundle \(T_{\mathbb {C}}(T'M)=T'(T'M)\oplus T''(T'M)\). A holomorphic Lie algebroid structure is emphasized on \(T'E\). A special study is made for integral curves of a spray on \(T'E\). Theorem 2.8 gives the coefficients of a spray, called canonical, obtained from a complex Lagrangian on \(T'E\). In the second part of section two, we study the holomorphic prolongation \(\mathcal {T}'E\) of the Lie algebroid E. In the third section, we study how a complex Lagrange (Finsler) structure on \(T'M\) induces a Lagrangian structure on E. Three particular cases are analysed by the rank of the anchor map, the dimensions of manifold M, and those of the fibres. We obtain the correspondent on E of the Chern–Lagrange nonlinear connection from \(T'M\).     

Automated chemical resonance generation and structure filtration for kinetic modeling

This work discusses efficient and automated methods for constructing a set of representative resonance structures for arbitrary chemical species, including radicals and biradicals, consisting of the elements H, C, O, N, and S. Determining the representative reactive structures of chemical species is crucial for identification of reactive sites and consequently applying the correct reaction templates to generate the set of important reactions during automated chemical kinetic model generation. We describe a fundamental set of resonance pathway types, accounting for simple resonating structures, as well as global approaches for polycyclic aromatic species. Automatically discovering potential localized structures along with filtration to identify the representative structures was shown to be robust and relatively fast. The algorithms discussed here were recently implemented in the Reaction Mechanism Generator (RMG) software. The final structures proposed by this method were found to be in reasonable agreement with quantum chemical computation results of localized structure contributions to the resonance hybrid.     

Fast‐Track,One‐Step E. coli Detection: A Miniaturized Hydrogel Array Permits Specific Direct PCR and DNA Hybridization while Amplification

A timesaving and convenient method for bacterial detection based on one‐step, one‐tube deoxyribonucleic acid (DNA) hybridization on hydrogel array while target gene amplification is described. The hydrogel array is generated by a fast one‐pot synthesis, where N,N′‐dimethylacrylamide/polyethyleneglycol(PEG₁₉₀₀)‐bisacrylamide mixture polymerizes via radical photoinitiation by visible light within 20 min concomitant with in situ capture probe immobilization. These DNA‐functionalized hydrogel droplets arrayed on a planar glass surface are placed in the polymerase chain reaction (PCR) mixture during the thermal amplification cycles. The bacterial cells can be implemented in a direct PCR reaction, omitting the need for prior template DNA extraction. The resulting fluorescence signal is immediately detectable after the end of the PCR (1 h) following one short washing step by microscopy. Therefore a valid signal can be reached within 1.5 h including 10 min for pipetting and placement of the tubes and chips. The performance of this novel hydrogel DNA array was successfully proven with varying cell numbers down to a limit of 10¹Escherichia coli cells.

     

Thermal behavior of some new triazole derivative complexes

A series of new complexes with mixed ligands of the type [ML(C₃H₃O₂)₂]·nH₂O (((1) M=Mn, n=1; (2) M=Co(II), n=2; (3) M=Ni(II), n=4; (4) M=Cu(II), n=1.5; (5) M=Zn(II), n=0; L=3-amino-1,2,4-triazole and (C₃H₃O₂)=acrylate anion) were synthesized and characterised by chemical analysis and IR data. In all complexes the 3-amino-1,2,4-triazole acts as bridge while the acrylate acts as bidentate ligand except for complex (5) where it is found as unidentate. The thermal behaviour steps were investigated in nitrogen flow. The thermal transformations are complex processes according to TG and DTG curves including dehydration, acrylate ion and 3-amino-1,2,4-triazole degradation respectively. The final products of decomposition are the most stable metal oxides, except for complex (4) that leads to metallic copper.     

A concise total synthesis of largazole, solution structure, and some preliminary structure activity relationships

A total synthesis of largazole that proceeds in 8 steps from commercial materials is reported, along with some structure-activity relationships. A combination of NMR studies and molecular modeling have also provided a preliminary picture of the conformation of largazole.     

Vapour pressure and excess Gibbs energy of binary 1,2-dichloroethane + cyclohexanone,chloroform + cyclopentanone and chloroform + cyclohexanone mixtures at temperatures from 298.15 to 318.15 K

The vapour pressures of the binary systems 1,2-dichloroethane + cyclohexanone, chloroform + cyclopentanone and chloroform + cyclohexanone mixtures were measured at temperatures between 298.15 and 318.15 K. The vapour pressures vs. liquid phase composition data for three isotherms have been used to calculate the activity coefficients of the two components and the excess molar Gibbs energies, G^E, for these mixtures, using Barker's method. Redlich–Kister, Wilson, NRTL and UNIQUAC equations, taking into account the vapour phase imperfection in terms of the 2-nd virial coefficient, have represented the G^E values. No significant difference between G^E values obtained with these equations has been observed. Our data on vapour–liquid equilibria (VLE) and excess properties of the studied systems are examined in terms of the DISQUAC and modified UNIFAC (Dortmund) predictive group contributions models.     

The unusual stability of H-bonded complexes in solvent caused by greater solvation energy of complex compared to those of isolated fragments

Here, the effect of solvent on the stability of non-covalent complexes, was studied. These complexes were from previously published S22, S66, and X40 datasets, which include hydrogen-, halogen- and dispersion-bonded complexes. It was shown that the charge transfer in the complex determines whether the complex is stabilized or destabilized in solvent.