On the topological structure of configuration spaces

1993 ◽  
pp. 50-64
Author(s):  
Jürgen Sellen
Keyword(s):  
Topological Structure ◽  
Configuration Spaces

Amplitude Spectra of Fitness Landscapes

1998 ◽  
Vol 01 (01) ◽  
pp. 39-66 ◽  
Author(s):  
Wim Hordijk ◽  
Peter F. Stadler
Keyword(s):  
Fourier Transform ◽  
Topological Structure ◽  
Empirical Studies ◽  
Amplitude Spectrum ◽  
Fitness Landscapes ◽  
Configuration Spaces ◽  
Amplitude Spectra ◽  
Different Types ◽  
Reliable Procedure ◽  
The Fourier Transform

Fitness landscapes can be decomposed into elementary landscapes using a Fourier transform that is determined by the structure of the underlying configuration space. The amplitude spectrum obtained from the Fourier transform contains information about the ruggedness of the landscape. It can be used for classification and comparison purposes. We consider here three very different types of landscapes using both mutation and recombination to define the topological structure of the configuration spaces. A reliable procedure for estimating the amplitude spectra is presented. The method is based on certain correlation functions that are easily obtained from empirical studies of the landscapes.

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.

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 Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Prashanth Raman ◽  
Chi Zhang
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Moduli Space ◽  
Cluster Algebras ◽  
Configuration Spaces ◽  
Minkowski Sum ◽  
Canonical Forms ◽  
Infinite Class ◽  
Special Cases ◽  
Generalized Associahedra

Abstract Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type An and Bn generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite α′, and the configuration space is binary although the u equations take a more general form than those “perfect” ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type An and Bn integrals, which have perfect u equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.

scholarly journals Modifications in the Topological Structure of EEG Functional Connectivity Networks during Listening Tonal and Atonal Concert Music in Musicians and Non-Musicians

2021 ◽  
Vol 11 (2) ◽  
pp. 159
Author(s):  
Almudena González ◽  
Manuel Santapau ◽  
Antoni Gamundí ◽  
Ernesto Pereda ◽  
Julián J. González
Keyword(s):  
Topological Structure ◽  
Phase Synchronization ◽  
Random Network ◽  
Small World ◽  
Surrogate Data ◽  
Musical Structure ◽  
Beta Band ◽  
Tonal Music ◽  
Frequency Bands ◽  
Concert Music

The present work aims to demonstrate the hypothesis that atonal music modifies the topological structure of electroencephalographic (EEG) connectivity networks in relation to tonal music. To this, EEG monopolar records were taken in musicians and non-musicians while listening to tonal, atonal, and pink noise sound excerpts. EEG functional connectivities (FC) among channels assessed by a phase synchronization index previously thresholded using surrogate data test were computed. Sound effects, on the topological structure of graph-based networks assembled with the EEG-FCs at different frequency-bands, were analyzed throughout graph metric and network-based statistic (NBS). Local and global efficiency normalized (vs. random-network) measurements (NLE|NGE) assessing network information exchanges were able to discriminate both music styles irrespective of groups and frequency-bands. During tonal audition, NLE and NGE values in the beta-band network get close to that of a small-world network, while during atonal and even more during noise its structure moved away from small-world. These effects were attributed to the different timbre characteristics (sounds spectral centroid and entropy) and different musical structure. Results from networks topographic maps for strength and NLE of the nodes, and for FC subnets obtained from the NBS, allowed discriminating the musical styles and verifying the different strength, NLE, and FC of musicians compared to non-musicians.

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