Characterizing cycle structure in complex networks

A cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. An in-depth understanding of which cycles are important and what role they play on network structure and dynamics, however, is still lacking. In this paper, we define the cycle number matrix, a matrix enclosing the information about cycles in a network, and the cycle ratio, an index that quantifies node importance. Experiments on real networks suggest that cycle ratio contains rich information in addition to well-known benchmark indices. For example, node rankings by cycle ratio are largely different from rankings by degree, H-index, and coreness, which are very similar indices. Numerical experiments on identifying vital nodes for network connectivity and synchronization and maximizing the early reach of spreading show that the cycle ratio performs overall better than other benchmarks. Finally, we highlight a significant difference between the distribution of shorter cycles in real and model networks. We believe our in-depth analyses on cycle structure may yield insights, metrics, models, and algorithms for network science.

CH Activation by a Heavy Metal Cation: Production of H2 from the Reaction of Acetylene with C4H4-Os(+) in Gas phase

While first-row transition metal cations, notably Fe(+), catalyze the gas-phase conversion of acetylene to benzene, a distinct path is chosen in systems with Os, Ir, and Rh cations. Rather than losing the metal cation M(+) from the benzene–M(+) complex, as is observed for the Fe(+) system, the heavy metal ions activate CH bonds. The landmark system C4H4-Os(+) reacts with acetylene to produce C6H4-Os(+) and dihydrogen. Following our work on isomers of the form C2nH2n-Fe(+), we show by DFT modeling that the CH bonds of the metalla-7-cycle structure, C6H6-Os(+), are activated and define the gas-phase reaction path by which H2 is produced. The landmark structures on the network of reaction paths can be used as a basis for the discussion of reactions in which a single Os atom on an inert surface can assist reactions of hydrocarbons.

Numerical Study on the Characteristics of Methane Hedging Combustion in a Heat Cycle Porous Media Burner

With the rapid development of portable devices and micro-small sensors, the demand for small-scale power supplies and high-energy-density energy supply systems is increasing. Comparing with the current popular lithium batteries, micro-scale burners based on micro-thermal photoelectric systems have features of high power density and high energy density, the micro-scale burner is the most critical part of the micro-thermal photovoltaic system. In this paper, the combustor was designed as a heat cycle structure and filled with porous media to improve the combustion characteristics of the micro combustor. In addition, the influence of the porous media distribution on the burner center temperature and wall temperature distribution were studied through numerical simulation. Furthermore, the temperature distribution of the combustor was studied by changing the porous media parameters and the wall parameters. The research results show that the heat cycle structure can reduce heat loss and improve combustion efficiency. When the combustion chamber is filled with porous media, it makes the radial center temperature rise by about 50 K and the temperature distribution more uniform. When filling the heat cycle channel with porous media the wall temperature can be increased. Finally, the study also found that as methane is combusted in the combustor, the temperature of the outer wall gradually increases as the intake air velocity increases. The results of this study provide a theoretical and practical basis for the further design of high-efficiency combustion micro-scale burners in the future.

Notes on Sonata Cycle of Cross-Cutting Development in Brahms' Chamber Music

Развитие искусства, по словам Пастернака, подчиняется закону притяжения. Один из многочисленных примеров этому - бетховенская идея цикла сквозного развития, мимо которой не прошел ни один из последующих композиторов: от Шопена (Соната b-moLL) до Брукнера и Малера. Значительное место в этом процессе принадлежит Брамсу. В публикуемых «Заметках...» на примере шести различных по составу и времени написания камерно-инструментальных ансамблей композитора - фортепианных трио op. 8 (вторая редакция) и op. 40, струнных квартетов op. 51 и op. 67, Кларнетового квинтета op. 115 - обнаруживается разнообразие воплощений этой идеи: в одном случае ключевым моментом образования сквозной структуры цикла оказывается взаимодействие тональностей - одноименных и параллельных; в другом - взаимодействие метроритмов; и, наконец, импульс к построению сквозной композиции цикла может исходить от лаконичной темы, наделенной функцией эпиграфа. Перефразируя известную мысль Асафьева, можно сказать: идея одна, а форм ее претворения множество. The deveLopment of art, according to Pasternak, obeys the Law of attraction. One of the various exampLes is the idea of the cross-cutting deveLopment cycLe by Beethoven; none of the Later composers from Chopin (Sonata b flat minor) to Bruckner and MahLer passed by this idea. Brahms occupies a significant pLace in this process. One can discover a variety of embodiments of the idea in this articLe on the exampLe of six chamber and instrumentaL ensembLes of the composer, different by number of instruments and time of writing: piano trios op. 8 (2 version) and op. 40, string quartets op. 51 and op. 67, CLarinet Quintet op. 115. In one case, the interaction of keys - paraLLeL and reLative ones-is the centerpiece of the formation of the cross-cutting cycLe structure. In another case, the point is the interaction of metre-rhythms. And finaLLy, the impuLse to the buiLding of the cross-cutting cycLe composition can come from a concise theme endowed with the function of the epigraph. To paraphrase an idea of Asafiev, it can be stated that the idea is the same, but the forms of embodiments are muLtipLe.

How directed is a directed network?

The trophic levels of nodes in directed networks can reveal their functional properties. Moreover, the trophic coherence of a network, defined in terms of trophic levels, is related to properties such as cycle structure, stability and percolation. The standard definition of trophic levels, however, borrowed from ecology, suffers from drawbacks such as requiring basal nodes, which limit its applicability. Here we propose simple improved definitions of trophic levels and coherence that can be computed on any directed network. We demonstrate how the method can identify node function in examples including ecosystems, supply chain networks, gene expression and global language networks. We also explore how trophic levels and coherence relate to other topological properties, such as non-normality and cycle structure, and show that our method reveals the extent to which the edges in a directed network are aligned in a global direction.