Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization

Segmentation of three-dimensional (3D) complicated structures is of great importance for many real applications. In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model. Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations. Instead, the minimum cut on a special designed graph need to be computed. The method is tested on data with complicated structures. It is rather stable with respect to initial value and the algorithm is nearly parameter free. Experiments show that it can solve large problems much faster than traditional approaches.     

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.     

团复形是无圈的平面图是可伸缩图

许宝刚猜想:若图G的团复形是无圈的,则G为可伸缩图．本文证明了该猜想对平面图成立,即:若G是团复形为无圈的平面图,则G为可伸缩图．     

On the Characterization of Maximal Planar Graphs with a Given Signed Cycle Domination Number

Let G =(V, E) be a simple graph. A function f : E → {+1,-1} is called a signed cycle domination function(SCDF) of G if ∑_(e∈E(C))f(e) ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ'_(sc)(G) = min{∑_(e∈E)f(e)| f is an SCDF of G}. This paper will characterize all maximal planar graphs G with order n ≥ 6 and γ'_(sc)(G) = n.     

1,2,4-triazolium-cation-based energetic salts

3,4,5-Triamino-1,2,4-triazole (guanazine, 1) can be readily methylated with methyl iodide yielding methylguanazinium iodide (2). Salts containing the novel methylguanazinium cation with energetic anions were synthesised by metathesis reactions with silver azide (3), silver nitrate (4), silver perchlorate (5), sodium 5,5'-azotetrazolate (6), silver 5-nitrotetrazolate (7) and silver dinitramide (8), yielding a new family of heterocycle-based salts, which were fully characterised by analytical (mass spectrometry and elemental analysis) and spectroscopic methods (IR, Raman and NMR). In addition, the molecular structures of all compounds were confirmed by X-ray analysis, revealing extensive hydrogen-bonding in the solid state and densities between 1.399 (3) and 1.669 g cm(-3) (5). The hydrogen-bonded ring motifs are discussed in the formalism of graph-set analysis for hydrogen-bond patterns and compared to each other. Preliminary sensitivity testing of the crystalline compounds indicate surprisingly low sensitivities to both friction and impact, the highest friction and shock sensitivity being found for the perchlorate (5, 220 N) and the dinitramide (8, 20 J) salts, respectively. In addition, DSC analysis was used to assess the thermal stabilities of the compounds: 3-6 melt above 200 degrees C with concomitant decomposition, whereas 7 and 8 have clearly defined melting points at 162 and 129 degrees C, respectively, and with decomposition occurring about 30 degrees C above the melting point. Lastly all compounds have positive calculated heats of formation between 336 (4) and 4070 kJ kg(-1) (6) and calculated detonation velocities in the range between 8330 (7) and 8922 m s(-1) (6) making them of interest as new highly energetic materials with low sensitivity.     

The de novo design of median molecules within a property range of interest

Summary In this paper an application is presented of the median molecule workflow to the de novo design of novel molecular entities with a property profile of interest. Median molecules are structures that are optimised to be similar to a set of existing molecules of interest as an approach for lead exploration and hopping. An overview of this workflow is provided together with an example of an instance using the similarity to camphor and menthol as objectives. The methodology of the experiments is defined and the workflow is applied to designing novel molecules for two physical property datasets: mean molecular polarisability and aqueous solubility. This paper concludes with a discussion of the characteristics of this method.     

Extracting the mechanisms and kinetic models of complex reactions from atomistic simulation data

Determining reaction mechanisms and kinetic models, which can be used for chemical reaction engineering and design, from atomistic simulation is highly challenging. In this study, we develop a novel methodology to solve this problem. Our approach has three components: (1) a procedure for precisely identifying chemical species and elementary reactions and statistically calculating the reaction rate constants; (2) a reduction method to simplify the complex reaction network into a skeletal network which can be used directly for kinetic modeling; and (3) a deterministic method for validating the derived full and skeletal kinetic models. The methodology is demonstrated by analyzing simulation data of hydrogen combustion. The full reaction network comprises 69 species and 256 reactions, which is reduced into a skeletal network of 9 species and 30 reactions. The kinetic models of both the full and skeletal networks represent the simulation data well. In addition, the essential elementary reactions and their rate constants agree favorably with those obtained experimentally. © 2019 Wiley Periodicals, Inc.