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Sparse topologies with small spectrum size

R. Elsässer, R. Královič, B. Monien
2003 Theoretical Computer Science  
Sparse graphs with small spectra exhibit excellent structural properties and can act as interconnection topologies.  ...  It is known that load balancing can be performed on such graphs in a small number of steps.  ...  In this paper, we focus our attention on scalable families of sparse graphs (maximal vertex degree O(log n) where n is the number of vertices) with small spectra.  ... 
doi:10.1016/s0304-3975(03)00237-8 fatcat:xejzyuue2bbu5glgbggvox4rm4

Spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities

Marija Mitrović, Bosiljka Tadić
2009 Physical Review E  
For the cyclic graphs we find new results with twice larger stretching exponent of the tail of the distribution, which is virtually independent on the size of cycles.  ...  The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network.  ...  EIGENVALUE SPECTRUM OF GROWING MODULAR NETWORKS The sparse network of size N is defined with an N ϫ N adjacency matrix A with binary entries A ij = ͑1,0͒, representing the presence or the absence of a  ... 
doi:10.1103/physreve.80.026123 pmid:19792216 fatcat:qwfc5mpchvgojhki6mn4i73x4m

Formation of pinwheels of preferred orientation by learning sparse neural representations of natural images

A Moukovski, D.M Gorinevski, M.A Giese, W von Seelen
2002 Neurocomputing  
We conclude the functional topology of the visual cortex that may be tailored to optimize the encoding of natural stimuli with minimal redundancy of the underlying representation.  ...  We devise self-organizing model of the striate cortex that learns orientation maps by sparse coding of natural images.  ...  The map (a) was learned with small sparseness enforcement term in the error functional ( = 0:8). The map (b) emerges for = 1:6.  ... 
doi:10.1016/s0925-2312(02)00421-6 fatcat:fq5wiwak3rdkpf42yy2r7am6jq

Spectra of "real-world" graphs: Beyond the semicircle law

Illés J. Farkas, Imre Derényi, Albert-László Barabási, Tamás Vicsek
2001 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
In particular, scale-free graphs develop a triangle-like spectral density with a power law tail, while small-world graphs have a complex spectral density function consisting of several sharp peaks.  ...  The eigenvalue spectrum of these graphs provides information about their structural properties.  ...  Size dependence of the relative variance of the principal eigenvalue, i.e., ( 1 )/E( 1 ), for sparse uncorrelated random graphs ͑ϩ͒, small-world graphs with p r ϭ0.01 ͑᭹͒, and scale-free graphs ͑᭝͒.  ... 
doi:10.1103/physreve.64.026704 pmid:11497741 fatcat:g4rh4k6ne5h4bh7kkomzujvzue

Bulk Spectrum and K-theory for Infinite-Area Topological Quasicrystal [article]

Terry A. Loring
2018 arXiv   pre-print
After making estimates on the spectrum, we deduce a finite system size, above which the K-theory must coincide with the K-theory of the infinite system.  ...  We compute that the spectrum is either two continuous bands, or that any gaps other than the main gap are small.  ...  However, we shall see that there are edge phenomena associated to apparent small gaps in "the bulk spectrum" of modest-sized systems and we can not easily tell if these gaps will disappear when we look  ... 
arXiv:1811.07494v2 fatcat:eiwi7dxnevfuzgweinfxmwvevy

Emergence of loop structure in scale-free networks and dynamical consequences

Xiaojuan Ma, Liang Huang, Ying-Cheng Lai, Zhigang Zheng
2009 Physical Review E  
As the clustering coefficient is increased, the size of the dominant loop increases, leading to continuous degradation of the network synchronizability.  ...  Our proposition is that, as the network becomes more strongly clustered, topological loop structure can emerge, generating a set of eigenvalues that are close to zero.  ...  Two types of network topologies, namely, small-world ͓1͔ and scale-free ͓2͔, are topics of tremendous recent interest.  ... 
doi:10.1103/physreve.79.056106 pmid:19518520 fatcat:cw3ere4x5bbtjh2ncik66jlvkm

Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks

Zhifang Wang, Anna Scaglione, Robert J Thomas
2010 IEEE Transactions on Smart Grid  
, with scalable network size, and with realistic electrical parameter settings.  ...  The most interesting discoveries include: the power grid is sparsely connected with obvious small-world properties; its nodal degree distribution can be well fitted by a mixture distribution coming from  ...  D'Souza for the thoughtful inputs and suggestions on network topology analysis, and to thank E. Yildiz, R. Pagliari, S. Kirti, and H. Wen for the helpful discussions on the usage of algorithms.  ... 
doi:10.1109/tsg.2010.2044814 fatcat:4qkqgjnpabec5hrohbqtsir3oy

On the Role of Topology in Focus+Context Visualization [chapter]

Ivan Viola, Eduard Gröller
2007 Mathematics and Visualization  
The first type combines topology information represented by simple graphical primitives with other forms of visual representations.  ...  This illustrates various roles of topology in scientific visualization.  ...  Acknowledgments The authors thank Tino Weinkauf and Holger Theissel for providing a polygonal model of the topological information of the flow in Figure 1 .  ... 
doi:10.1007/978-3-540-70823-0_12 fatcat:qajydmsv3vhkzptbd7syx6dgpe

Chimera-like states in structured heterogeneous networks

Bo Li, David Saad
2017 Chaos  
The architecture facilitates the analysis of the system, which separates into a densely-connected coherent group of nodes, perturbed by their sparsely-connected drifting neighbors.  ...  To analyze the role of network topology in giving rise to chimera-like states we study a heterogeneous network model comprising two group of nodes, of high and low degrees of connectivity.  ...  are the oscillators with small coupling strength 24, 26 .  ... 
doi:10.1063/1.4981020 pmid:28456179 fatcat:6vzrv4z5qjfd3av6pywk7yplfi

Using the Entropy of the DFT of the Laplacian Eigenvalues to Assess Networks [chapter]

Danilo R. B. de Araújo, Carmelo J. A. Bastos-Filho, Joaquim F. Martins-Filho
2014 Studies in Computational Intelligence  
These metrics, including the spectral-based ones, can be used to retrieve topological properties from the network.  ...  Thus, one can conclude that our metrics is very sensitive to the topological properties of each model and it can be properly used to classify sparse, dense, small and large networks.  ...  We evaluated the ability of our method to classify networks with different sizes and densities.  ... 
doi:10.1007/978-3-319-05401-8_20 fatcat:d64pzjgle5bsxcwz7rl4ak6dri

Redshift survey with multiple pencil beams at the galactic poles

A. S. Szalay, T. J. Broadhurst, N. Ellman, D. C. Koo, R. S. Ellis
1993 Proceedings of the National Academy of Sciences of the United States of America  
We also discuss the sensitivity of pencil-beam surveys to the topology of large-scale structures and compare them with sparsely sampled wide-angle local surveys.  ...  Our results from cross correlations of multiple pencil beams, containing over 1200 galaxies, indicate that the strong peak in the power spectrum results from structures of large transverse size, in agreement  ...  size of the survey volume.  ... 
doi:10.1073/pnas.90.11.4853 pmid:11607399 pmcid:PMC46612 fatcat:2sj2dll3u5f7nlhgzz366zfhl4

Chiral condensate in the deconfined phase of quenched gauge theories

Robert G. Edwards, Urs M. Heller, Joe Kiskis, Rajamani Narayanan
2000 Physical Review D, Particles and fields  
It suggests the existence of a chiral condensate which we confirm with a direct stochastic estimate.  ...  We compute the low lying spectrum of the overlap Dirac operator in the deconfined phase of finite-temperature quenched gauge theory.  ...  For finite temperature with T > T c , the distribution of instanton sizes increases steeply with instanton size until it is cutoff on the large size end by N T .  ... 
doi:10.1103/physrevd.61.074504 fatcat:eov66kxadfaz7l665p27bd4twq

Critical behavior of theXY-rotor model on regular and small-world networks

Sarah De Nigris, Xavier Leoncini
2013 Physical Review E  
We study the XY-rotors model on small networks whose number of links scales with the system size N_links∼ N^γ, where 1<γ<2.  ...  We first analyze the topology and find that the small world regime appears for rewiring probabilities which scale as p_SW∝1/N^γ.  ...  To check with even larger sizes, we consider in Fig. 1b the magnetization for a small energy density ε = 0.1 and several sizes.  ... 
doi:10.1103/physreve.88.012131 pmid:23944438 fatcat:ptmtmhq45rbrjkw77pfy3rp3iu

Quantifying loss of information in network-based dimensionality reduction techniques

Hector Zenil, Narsis A. Kiani, Jesper Tegnér
2015 Journal of Complex Networks  
To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed.  ...  Then at 20% the original trend resurfaces; the resulting sparse graph is truly small as compared with >60% and comes last, with the smallest information content.  ...  It compares the frequency of small subgraphs with randomized versions of the same network (i.e., networks with the same size and the same degree distribution).  ... 
doi:10.1093/comnet/cnv025 fatcat:loarnheyljgvxdaxww5lvksfpe

Towards Scalable Spectral Clustering via Spectrum-Preserving Sparsification [article]

Yongyu Wang, Zhuo Feng
2018 arXiv   pre-print
In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that enables to build ultra-sparse NN (u-NN) graphs with guaranteed preservation of the original graph spectrums  ...  The proposed method starts from constructing low-stretch spanning trees (LSSTs) from the original graphs, which is followed by iteratively recovering small portions of "spectrally critical" off-tree edges  ...  number of centroids using k-means and random-projection trees; [20] introduced a method for compressing the original NN graph into a sparse bipartite graph by generating a small number of "supernodes  ... 
arXiv:1710.04584v4 fatcat:fdfxehvllbddngkifpwgj5jtda
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