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Topology

 Topology (from the Greek t?p??, “place”, and ?????, “study”) is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example, deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation.

Quasi Set Topological Vector Subspaces

By: Florentin Smarandache; W. B. Vasantha Kandasamy

Chapter one is introductory in nature and chapter two uses vector spaces to build quasi set topological vector subspaces. Not only we use vector spaces but we also use S-vector spaces, set vector spaces, semigroup vector spaces and group vector spaces to build set topological vector subspaces. These also give several finite set topological spaces. Such study is carried out in chapters three and four.

To every quasi set topological vector subspace T relative to the set P  F, we have a lattice associated with it we call this lattice as the Representative Quasi Set Topological Vector subspace lattice (RQTV-lattice) of T relative to P. When T is finite we have a nice representation of them. In case T is infinite we have a lattice which is of infinite order. We can in all cases give the atoms of the lattice which is in fact the basic set of T over P. It is pertinent ...

A Research on Spatial Topological Association Rules Mining : Volum...

By: P. Zhang; S. Liu; Z. Sha; J. Chen

Description: School of Remote Sensing and Information Engineering ,Wuhan University , 129 Luoyu Road ,Wuhan ,China ,430079. Spatial association rules mining is a process of acquiring information and knowledge from large databases. Due to the nature of geographic space and the complexity of spatial objects and relations, the classical association rule mining methods are not suitable for the spatial association rule mining. Classical association rule mining treats all inpu...

Monitoring Magnetosheath-magnetosphere Interconnection Topology fr...

By: C. J. Farrugia; P. E. Sandholt

Description: Department of Physics, University of Oslo, Oslo, Norway. A strong southward rotation of the IMF (BZ from 5 to -6 nT in ~ 20 s) on 4 January 1995 caused an abrupt reconfiguration of midday aurorae and plasma convection consisting of the following: (1) the red-line aurora associated with magnetosheath plasma transfer at the low-latitude magnetopause appeared at the same time that (2) the green-line aurora from precipitating energetic plasm...

High Latitude Magnetospheric Topology and Magnetospheric Substorm ...

By: K. G. Orlova; I. L. Ovchinnikov; I. P. Kirpichev; E. E. Antonova; M. V. Stepanova

Description: Skobeltsyn Institute of Nuclear Physics Moscow State University, Moscow, Russia. This study is focused on the problem of the localization of substorm expansion onset. In this context, the high latitude topology of transverse magnetospheric currents has been analyzed. This study has included the radial distribution of plasma pressure near noon, obtained using the THEMIS-B satellite data, the daytime compression of magnetic field lines and the existence o...

Antonova, E. E., Kornilov, I. A., Kornilova, T. A., Kornilov, O. I., and Stepanova, M. V.: Features of auroral breakup obtained using data of ground-based television observations: case study, Ann. Geophys., 27, 1413–1422, 2009a.; Antonova, E. E., Kirpichev, I. P., Stepanova, M. V., Orlova, K. G., and Ovchinnikov, I. L.: Topology of the high latitude magnetosphere during large magnetic storms and the main mechanisms of relativistic electron acceleration, Adv. Space Res., ...

Topological 3D Modeling Using Indoor Mobile Lidar Data : Volume Xl...

By: M. Nakagawa; T. Ohhashi; M. Shiozaki; T. Yamamoto; S. Tanaka

Description: Dept. of Civil Engineering, Shibaura Institute of Technology, Tokyo, Japan. We focus on a region-based point clustering to extract a polygon from a massive point cloud. In the region-based clustering, RANSAC is a suitable approach for estimating surfaces. However, local workspace selection is required to improve a performance in a surface estimation from a massive point cloud. Moreover, the conventional RANSAC is hard to determine whether a point lies ins...

Representation of the Kinematic Topology of Mechanisms for Kinemat...

By: A. Müller

Description: Johannes Kepler University, Altenbergerstr. 69, 4040 Linz, Austria. The kinematic modeling of multi-loop mechanisms requires a systematic representation of the kinematic topology, i.e. the arrangement of links and joints. A linear graph, called the topological graph, is used to this end. Various forms of this graph have been introduced for application in mechanism kinematics and multibody dynamics aiming at matrix formulations of the governing equations...

Angeles, J.: Fundamentals of robotic mechanical systems, 2nd Edn., Springer International Publishing, Swizterland, 2003.; Arabyan, A. and Wu, F.: An improved formulation for constrained mechanical systems, Multibody Syst. Dynam., 2, 49–69, 1998.; Arczewski, K.: Graph theoretical approach – I. determination of kinetic energy for a class of particle systems, J. Franklin Inst., 329, 469–481, 1992a.; Arczewski, K.: Graph theoretical approach – II. determination of generalize...

Topological Complexity of Frictional Interfaces: Friction Networks...

By: H. O. Ghaffari; R. P. Young

Description: Department of Civil Engineering and Lassonde Institute, University of Toronto, Toronto, ON, Canada. Through research conducted in this study, a network approach to the correlation patterns of void spaces in rough fractures (crack type II) was developed. We characterized friction networks with several networks characteristics. The correlation among network properties with the fracture permeability is the result of friction networks. The revealed hubs in t...

Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., and Hwang, D.-U.: Complex networks: Structure and dynamics, Phys. Rep., 424, 175–308, 2006.; Bowden, F. and Tabor, D.: The Friction and Lubrication of Solids, Oxford University Press, New York, 2001.; Abe, S. and Suzuki, N.: Complex-network description of seismicity, Nonlin. Processes Geophys., 13, 145–150, doi:10.5194/npg-13-145-2006, 2006.; Aharoni, H. and Sharon, ...

Geometric and Topological Approaches to Significance Testing in Wa...

By: C. Duffy; R. G. Najjar; J. A. Schulte

Description: Department of Meteorology, Pennsylvania State University, University Park, Pennsylvania, USA. Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, i.e., contiguous regions of significant wavelet power coefficients with respect to some noise model. This geometric significance test was found to produc...

Barber, C. B., Dobkin, D. P., and Huhdanpaa, H.: Quickhull Algorithm for Convex Hulls, ACM T. Math. Software, 22, 469–483, 1996.; Baxandall, P. and Liebeck, H.: Vector Calculus, Dover Publications, Inc., Mineloa, New York, USA, 550 pp., 2008.; Benjamini, Y. and Hochberg, Y.: Controlling the False Discovery Rate: A Practical and Power Approach to Multiple Testing, J. Roy. Stat. Soc., 57, 289–300, 1995.; Benjamini, Y. and Yekutieli, D.: The Control of the False Discovery R...

Plos One : Extracting Labeled Topological Patterns from Samples of...

By: Stefano Boccaletti

Description : An advanced graph theoretical approach is introduced that enables a higher level of functional interpretation of samples of directed networks with identical fixed pairwise different vertex labels that are drawn from a particular population. Compared to the analysis of single networks, their investigation promises to yield more detailed information about the represented system. Often patterns of directed edges in sample element networks are too intractable f...

Algebraic Topology by Michael Hopkins and Akhil Mathew

By: Michael Hopkins; Akhil Mathew

Description: This lecture note explains everything about Algebraic Topology

The Isomorphism and Thermal Properties of the Feldspars

By: Allen, Eugene Thomas, 1864; Iddings, Joseph Paxson, 1857-1920; Day, Arthur Louis, 1869

Pt. I. Thermal study / by Arthur L. Day and E.T. Allen. -- Pt. II. Optical study / by J.P. Iddings ; with an introduction by George F. Becker

The Isomorphism and Thermal Properties of the Feldspars

By: Day, Arthur Louis, 1869-1960; Iddings, Joseph Paxson, 1857-1920; Becker, George Ferdinand, 1847-1919; Allen, Eugene Thomas, 1864-1964

Pt. I. Thermal study / Arthur L. Day and E.T. Allen -- Pt. II. Optical study / J.P. Iddings ; with an introduction by George F. Becker

Chapter VI Topological Entropy I : Definitions

Mathematics document containing theorems and formulas.

Excerpt: In this section we introduce an invariant of topological conjugacy for topological dynamical systems. The original definition, due to Adler, Konheim and McAndrew, applies to continuous maps of compact topological spaces. We shall use first a later definition, due to Bowen and Dinaburg, which applies to uniformly continuous maps of metric spaces, not necessarily compact. It turns out that for our purposes the extra generality of allowing non{compact spaces is mor...

K-theory and Geometric Topology

By: Jonathan Rosenberg

Description: this article, geometric topology will mean the study of the topology of manifolds and manifold-like spaces, of simplicial and CWcomplexes, and of automorphisms of such objects. As such, it is a vast subject, and so it will be impossible to survey everything that might relate this subject to K-theory. I instead hope to hit enough of the interesting areas to give the reader a bit of a feel for the subject, and the desire to go o# and explore more of the literature

Plos Computational Biology : a Topological Paradigm for Hippocampa...

By: Y. Dabaghian

Description : An animal’s ability to navigate through space rests on its ability to create a mental map of its environment. The hippocampus is the brain region centrally responsible for such maps, and it has been assumed to encode geometric information (distances, angles). Given, however, that hippocampal output consists of patterns of spiking across many neurons, and downstream regions must be able to translate those patterns into accurate information about an animal’s ...

Plos Computational Biology : Transmembrane Topology and Signal Pep...

By: Burkhard Rost

Description : Hidden Markov models (HMMs) have been successfully applied to the tasks of transmembrane protein topology prediction and signal peptide prediction. In this paper we expand upon this work by making use of the more powerful class of dynamic Bayesian networks (DBNs). Our model, Philius, is inspired by a previously published HMM, Phobius, and combines a signal peptide submodel with a transmembrane submodel. We introduce a two-stage DBN decoder that combines the...

Topological Entropy Ii: Homogeneous Measures

Mathematics document containing theorems and formulas.

Excerpt: In this section we show how the topological entropy of simple examples may be computed explicitly, and then show that in good situations certain measure{ theoretic entropies may be deduced. A topological Kolmogorov {Sinai type theorem We have seen that if f ng is a sequence of open covers with diam( n) ! 0, then h(T) = limn!1 h(T; n). This is a topological analogue of Theorem 4.10. We now give a topological analogue of Theorem 4.6. Let X denote a compact metric ...

Plos Computational Biology : Energetic Selection of Topology in Fe...

By: J. Dongun Kim

Description : Models of early protein evolution posit the existence of short peptides that bound metals and ions and served as transporters, membranes or catalysts. The Cys-X-X-Cys-X-X-Cys heptapeptide located within bacterial ferredoxins, enclosing an Fe4S4 metal center, is an attractive candidate for such an early peptide. Ferredoxins are ancient proteins and the simple a+b fold is found alone or as a domain in larger proteins throughout all three kingdoms of life. Pre...

Plos One : Voting-based Cancer Module Identification by Combining ...

By: Dongxiao Zhu

Description : Recently, computational approaches integrating copy number aberrations (CNAs) and gene expression (GE) have been extensively studied to identify cancer-related genes and pathways. In this work, we integrate these two data sets with protein-protein interaction (PPI) information to find cancer-related functional modules. To integrate CNA and GE data, we first built a gene-gene relationship network from a set of seed genes by enumerating all types of pairwise ...

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