scispace - formally typeset
Search or ask a question
Author

Horst Sachs

Bio: Horst Sachs is an academic researcher. The author has contributed to research in topics: Mathematics & Symmetric graph. The author has an hindex of 3, co-authored 3 publications receiving 3887 citations.

Papers
More filters
Book
01 Jan 1995
TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.
Abstract: Introduction. Basic Concepts of the Spectrum of a Graph. Operations on Graphs and the Resulting Spectra. Relations Between Spectral and Structural Properties of Graphs. The Divisor of a Graph. The Spectrum and the Group of Automorphisms. Characterization of Graphs by Means of Spectra. Spectra Techniques in Graph Theory and Combinatories. Applications in Chemistry an Physics. Some Additional Results. Appendix. Tables of Graph Spectra Biblgraphy. Index of Symbols. Index of Names. Subject Index.

2,119 citations

Book
01 Jan 1980

1,729 citations


Cited by
More filters
Journal ArticleDOI
TL;DR: A method based on the negative binomial distribution, with variance and mean linked by local regression, is proposed and an implementation, DESeq, as an R/Bioconductor package is presented.
Abstract: High-throughput sequencing assays such as RNA-Seq, ChIP-Seq or barcode counting provide quantitative readouts in the form of count data. To infer differential signal in such data correctly and with good statistical power, estimation of data variability throughout the dynamic range and a suitable error model are required. We propose a method based on the negative binomial distribution, with variance and mean linked by local regression and present an implementation, DESeq, as an R/Bioconductor package.

13,356 citations

Journal ArticleDOI
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

9,441 citations

Book
01 Jan 1976
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Abstract: (1977). Graph Theory with Applications. Journal of the Operational Research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.

7,497 citations

Proceedings ArticleDOI
30 Aug 1999
TL;DR: These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period, and can be used to generate and select realistic topologies for simulation purposes.
Abstract: Despite the apparent randomness of the Internet, we discover some surprisingly simple power-laws of the Internet topology. These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period. We show that our power-laws fit the real data very well resulting in correlation coefficients of 96% or higher.Our observations provide a novel perspective of the structure of the Internet. The power-laws describe concisely skewed distributions of graph properties such as the node outdegree. In addition, these power-laws can be used to estimate important parameters such as the average neighborhood size, and facilitate the design and the performance analysis of protocols. Furthermore, we can use them to generate and select realistic topologies for simulation purposes.

5,023 citations

Journal ArticleDOI
TL;DR: A Nyquist criterion is proved that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability, and a method for decentralized information exchange between vehicles is proposed.
Abstract: We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.

4,377 citations