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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.

 
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Plos Biology : Topology and Robustness in the Drosophila Segment P...

By: Arthur Lander

Description : A complex hierarchy of genetic interactions converts a single-celled Drosophila melanogaster egg into a multicellular embryo with 14 segments. Previously, von Dassow et al. reported that a mathematical model of the genetic interactions that defined the polarity of segments (the segment polarity network) was robust (von Dassow et al. 2000). As quantitative information about the system was unavailable, parameters were sampled randomly. A surprisingly large fr...

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Plos Biology : Atypical Membrane Topology and Heteromeric Function...

By: Pamela Bjorkman

Description : Drosophila olfactory sensory neurons (OSNs) each express two odorant receptors (ORs) : a divergent member of the OR family and the highly conserved, broadly expressed receptor OR83b. OR83b is essential for olfaction in vivo and enhances OR function in vitro, but the molecular mechanism by which it acts is unknown. Here we demonstrate that OR83b heterodimerizes with conventional ORs early in the endomembrane system in OSNs, couples these complexes to the con...

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Plos Computational Biology : Functional Modules, Structural Topolo...

By: Osbaldo Resendis-antonio

Description : Modular organization in biological networks has been suggested as a natural mechanism by which a cell coordinates its metabolic strategies for evolving and responding to environmental perturbations. To understand how this occurs, there is a need for developing computational schemes that contribute to integration of genomic-scale information and assist investigators in formulating biological hypotheses in a quantitative and systematic fashion. In this work, ...

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Plos Biology : Topological Reorganization of Odor Representations ...

By: Mike Shipley

Description : Odors are initially represented in the olfactory bulb (OB) by patterns of sensory input across the array of glomeruli. Although activated glomeruli are often widely distributed, glomeruli responding to stimuli sharing molecular features tend to be loosely clustered and thus establish a fractured chemotopic map. Neuronal circuits in the OB transform glomerular patterns of sensory input into spatiotemporal patterns of output activity and thereby extract infor...

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Plos One : Topological and Functional Properties of the Small Gtpa...

By: Elad Katz

Description : Small GTP binding proteins of the Ras superfamily (Ras, Rho, Rab, Arf, and Ran) regulate key cellular processes such as signal transduction, cell proliferation, cell motility, and vesicle transport. A great deal of experimental evidence supports the existence of signaling cascades and feedback loops within and among the small GTPase subfamilies suggesting that these proteins function in a coordinated and cooperative manner. The interplay occurs largely thro...

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Plos One : Persistent Topology and Metastable State in Conformatio...

By: Emanuele Paci

Description : The large amount of molecular dynamics simulation data produced by modern computational models brings big opportunities and challenges to researchers. Clustering algorithms play an important role in understanding biomolecular kinetics from the simulation data, especially under the Markov state model framework. However, the ruggedness of the free energy landscape in a biomolecular system makes common clustering algorithms very sensitive to perturbations of t...

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Electromagnetic Theory and Computation a Topological Approach

By: Paul W. Gross; P. Robert Kotiuga
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Los Alamos Science No. 29, 2005: Complex Networks : The Challenge ...

By: Zoltan Toroczkai

Description: Improving predictive capability is an implicit goal in the major missions of Los Alamos National Laboratory: simulating performance of weapons in the stockpile, quantifying uncertainties in those simulations, and developing strategies to mitigate global threats. Success in achieving this goal depends on closely coordinating theory, experiment, and computer simulation.

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Plos Computational Biology : Metabolic Network Topology Reveals Tr...

By: Aleksej Zelezniak
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Plos One : Transmembrane Protein Alignment and Fold Recognition Ba...

By: Gajendra P.S. Raghava

Description : We compared our method with HHalign, a leading alignment tool using a non-redundant testing dataset including 72 aTMPs and 30 bTMPs. Our method achieved 10% and 9% better accuracies than HHalign in aTMPs and bTMPs, respectively. The raw score generated by TMFR is negatively correlated with the structure similarity between the target and the template, which indicates its effectiveness for fold recognition. The result demonstrates TMFR provides an effective T...

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Plos One : Network Topology Reveals Key Cardiovascular Disease Gen...

By: Franca Fraternali

Description : The structure of protein-protein interaction (PPI) networks has already been successfully used as a source of new biological information. Even though cardiovascular diseases (CVDs) are a major global cause of death, many CVD genes still await discovery. We explore ways to utilize the structure of the human PPI network to find important genes for CVDs that should be targeted by drugs. The hope is to use the properties of such important genes to predict new o...

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Sps 2013 Topology Model

By: Microsoft Corporation
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Algebraic Topology Class Notes 2

By: Denis Sjerve; Benjamin Young

Description: This book covers the following topics: The Mayer-Vietoris Sequence in Homology, CW Complexes, Cellular Homology,Cohomology ring, Homology with Coefficient, Lefschetz Fixed Point theorem, Cohomology, Axioms for Unreduced Cohomology, Eilenberg-Steenrod axioms, Construction of a Cohomology theory, Proof of the UCT in Cohomology, Properties of Ext(A;G).

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Cohomology,connections, Curvature and Characteristic Classes ; Alg...

By: David Mond

Description: This note explains the following topics: Cohomology, The Mayer Vietoris Sequence, Compactly Supported Cohomology and Poincare Duality, The Kunneth Formula for deRham Cohomology, Leray-Hirsch Theorem, Morse Theory, The complex projective space.

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Lecture Notes in Algebraic Topology III

By: James F. Davis; Paul Kirk

Description: This note covers the following topics: Chain Complexes, Homology, and Cohomology, Homological algebra, Products, Fiber Bundles, Homology with Local Coefficient, Fibrations, Cofibrations and Homotopy Groups, Obstruction Theory and Eilenberg-MacLane Spaces, Bordism, Spectra, and Generalized Homology and Spectral Sequences.

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Elliptic Curves and Algebraic Topology 1

By: Matthew Ando

Description: This note covers the following topics: Geometric reformulation, The Adams-Novikov spectral sequence, Elliptic cohomology, What is TMF, Geometric and Physical Aspect.

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Spatial Data Storage and Topology in the Redesigned Maf/Tiger System

By: David Galdi

Statistical Reference Document

Excerpt: The Census Bureau has a long history of innovation in data collection and processing techniques. The Geography Division of the Census Bureau has pioneered efforts in the field of automated cartography, including development of the Address Coding Guide in the 1960?s, the GBF/DIME files in the 1970?s, and the Topologically Integrated Geographic Encoding and Referencing (TIGER) system in the 1980?s (Marx 1986).

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Stability of Map Topology and Robustness of Map Geometry

By: Alan Saalfeld

Statistical Reference Document

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Polygonization and Topological Editing at the Bureau of the Census

By: Alan Saalfeld

Statistical Reference Document

Introduction: The TOPOLY program evolved from an earlier planar sweep program and still retains some of its characteristics. A planar sweep program labels each unique polygon in a graph by visiting each node in the order it would be visited by a line sweeping across the graph (Nievergelt and Preparata, 1982). When 8t 8 node, the algorithm will measure that any few polygon labels placed upon the graph are consistent with existing labels previously applied. The planar swee...

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Stability of Map Topology and Robustness of Map Geometry

By: Alan Saalfeld

Statistical Reference Document

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