scholarly journals The topological structure of maximal lattice free convex bodies: The general case

1998 ◽  
Vol 80 (1) ◽  
pp. 1-15 ◽  
Author(s):  
I. Bárány ◽  
H. E. Scarf ◽  
D. Shallcross
Keyword(s):  
Topological Structure ◽  
Convex Bodies ◽  
Maximal Lattice

Uncovering Atherosclerotic Risk Disease Gene Based on Expression and Network Topological Structure*

2010 ◽  
Vol 37 (8) ◽  
pp. 916-922
Author(s):  
Hong WANG ◽  
Xiao-Li QU ◽  
Yan ZHAO ◽  
Jing ZHANG ◽  
Li-Na CHEN
Keyword(s):  
Topological Structure ◽  
Disease Gene

Brief Survey of Biological Network Alignment and a Variant with Incorporation of Functional Annotations

2018 ◽  
Vol 14 (1) ◽  
pp. 4-10
Author(s):  
Fang Jing ◽  
Shao-Wu Zhang ◽  
Shihua Zhang
Keyword(s):  
Gene Ontology ◽  
Topological Structure ◽  
Metabolic Networks ◽  
Biological Network ◽  
Genomic Sequence ◽  
Network Alignment ◽  
Future Directions ◽  
Functional Annotations ◽  
Protein Protein Interaction ◽  
Ppi Networks

Background:Biological network alignment has been widely studied in the context of protein-protein interaction (PPI) networks, metabolic networks and others in bioinformatics. The topological structure of networks and genomic sequence are generally used by existing methods for achieving this task.Objective and Method:Here we briefly survey the methods generally used for this task and introduce a variant with incorporation of functional annotations based on similarity in Gene Ontology (GO). Making full use of GO information is beneficial to provide insights into precise biological network alignment.Results and Conclusion:We analyze the effect of incorporation of GO information to network alignment. Finally, we make a brief summary and discuss future directions about this topic.

Excess entropy of the systems of molecules differing in size and shape

1983 ◽  
Vol 48 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Equation Of State ◽  
Hard Spheres ◽  
Excess Entropy ◽  
Convex Bodies ◽  
Pure Substance ◽  
Liquid Equilibrium ◽  
Simple Rules ◽  
Different Shapes ◽  
The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

Information on evolutionary age in redundancy of complex network

2019 ◽  
Vol 33 (27) ◽  
pp. 1950331
Author(s):  
Shiguo Deng ◽  
Henggang Ren ◽  
Tongfeng Weng ◽  
Changgui Gu ◽  
Huijie Yang
Keyword(s):  
Principal Component Analysis ◽  
Complex Networks ◽  
Metabolic Network ◽  
Complex Network ◽  
Cellular Networks ◽  
Topological Structure ◽  
Quantitative Measure ◽  
Principal Component ◽  
Evolutionary Information ◽  
Local Patterns

Evolutionary processes of many complex networks in reality are dominated by duplication and divergence. This mechanism leads to redundant structures, i.e. some nodes share most of their neighbors and some local patterns are similar, called redundancy of network. An interesting reverse problem is to discover evolutionary information from the present topological structure. We propose a quantitative measure of redundancy of network from the perspective of principal component analysis. The redundancy of a community in the empirical human metabolic network is negatively and closely related with its evolutionary age, which is consistent with that for the communities in the modeling protein–protein network. This behavior can be used to find the evolutionary difference stored in cellular networks.

scholarly journals Topological Structure of Vortex Solution in Jackiw–Pi Model

2007 ◽  
Vol 48 (1) ◽  
pp. 143-146 ◽  
Author(s):  
Li Xi-Guo ◽  
Liu Zi-Yu ◽  
Li Yong-Qing ◽  
Gao Yuan ◽  
Guo Yan-Rui ◽  
...  
Keyword(s):  
Topological Structure ◽  
Vortex Solution

scholarly journals Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

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