Filters








33,638 Hits in 3.3 sec

AN ALGEBRAIC TOPOLOGICAL METHOD FOR FEATURE IDENTIFICATION

ERIK CARLSSON, GUNNAR CARLSSON, VIN DE SILVA
2006 International journal of computational geometry and applications  
This article surveys recent work of Carlsson and collaborators on applications of computational algebraic topology to problems of feature detection and shape recognition in high-dimensional data.  ...  The primary mathematical tool considered is a homology theory for point-cloud data sets-persistent homology-and a novel representation of this algebraic characterizationbarcodes.  ...  Algebraic topology for data Algebraic topology offers a mature set of tools for counting and collating holes and other topological features in spaces and maps between them.  ... 
doi:10.1142/s021819590600204x fatcat:l32fdktzqjcxxa7alwc55exnhe

Deep-Learning-Assisted Topology Identification and Sensor Placement for Active Distribution Network

Juhua Hong, Linyao Zhang, Yufei Yan, Zeqi Wang, Pengzhe Ren, Qiuye Sun
2021 Mathematical Problems in Engineering  
In response to the demand for identification of distribution network topology with a high percentage of renewable energy penetration, a distribution network topology analysis method based on decision trees  ...  Finally, the IEEE-33 bus system with a high proportion of renewable energy is used to verify that the method proposed has a good effect in the identification of the distribution network topology.  ...  Topology Identification Method Based on Machine Learning 3.1. Feature Attribute Selection.  ... 
doi:10.1155/2021/8942733 fatcat:rs4qgeribbcv3n2ze4fmnqx7pu

Page 6842 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
for closed-loop identification.  ...  The authors present two ways of solving this algebraic identification problem.  ... 

Algebraic Connectivity Control in Distributed Networks by Using Multiple Communication Channels

Karlo Griparić
2021 Sensors  
In this paper, a trust-based consensus algorithm for algebraic connectivity estimation has been implemented.  ...  The proposed algebraic connectivity control strategy has been evaluated in simulations and in a real multi-robot system using two channels with different properties and initial topologies.  ...  For instance, the adjacency matrix elements index for the agent with identification number 3 is equal to 2. For this reason, an identification vector M has been introduced.  ... 
doi:10.3390/s21155014 fatcat:5amnvsi5jzeavbnw6i6v5vyuva

The Topological Field Theory of Data: a program towards a novel strategy for data mining through data language

M Rasetti, E Merelli
2015 Journal of Physics, Conference Series  
This paper aims to challenge the current thinking in IT for the Big Data question, proposing -almost verbatim, with no formulas -a program aiming to construct an innovative methodology to perform data  ...  analytics in a way that returns an automaton as a recognizer of the data language: a Field Theory of Data.  ...  Acknowledgments The financial support is acknowledged of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme (FP7) for Research of the European Commission, under  ... 
doi:10.1088/1742-6596/626/1/012005 fatcat:s2vajsknsfewjbyatl2yxvm6lq

Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

Jean-Pierre Marquis
2016 The Mathematical intelligencer  
I first try to clarify the basic components of the abstract method as it developed in the first quarter of the 20th century. I then submit an explication of the notion of levels of abstraction.  ...  Frege, for one, certainly believed that axioms had to have this epistemic feature 5 . This desiderata is clearly not an ingredient of the abstract method.  ...  (See [1] for an introduction to the language of sketches as a method of presentation of theories.)  ... 
doi:10.1007/s00283-016-9672-z fatcat:bzceynfie5e5rgcovdmoktyf7a

Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics [chapter]

Jean-Pierre Marquis, Mircea Pitici
2018 The Best Writing on Mathematics 2017  
I first try to clarify the basic components of the abstract method as it developed in the first quarter of the 20th century. I then submit an explication of the notion of levels of abstraction.  ...  Frege, for one, certainly believed that axioms had to have this epistemic feature 5 . This desiderata is clearly not an ingredient of the abstract method.  ...  (See [1] for an introduction to the language of sketches as a method of presentation of theories.)  ... 
doi:10.1515/9781400888559-018 fatcat:jubza4t2i5ac5jpqjlze772nvy

Page 1341 of Automation and Remote Control Vol. 55, Issue 9 [page]

1994 Automation and Remote Control  
The constructive technique of Sec. 3 enables an obvious extension to cover a certain class of nonlinear differential systems, retaining simultaneously the algebraic topological structure of the mapping  ...  Taking into account that A(-) € C"*"(T) and B(-) € C"*™(T), one could use the Fejér theorem [8, p. 415] for convergence in the topology of sup-norm (if the form of the series (10) is changed).  ... 

Session Introduction

Graciela Gonzalez, Chitta Baral, Jeff Kiefer, Suengchan Kim, Jieping Ye
2015 Pacific Symposium on Biocomputing  
The annotation system aims to provide an accurate description of the locations where the genes are active.  ...  The authors take advantage of their previous tool and methods, BioBin, ATHENA, and Grammatical Evolution Neural Networks (GENN) in the current study based on prior knowledge resources.  ...  However, existing methods for feature selection are less effective when there are strong empirical correlations among the features.  ... 
dblp:conf/psb/GonzalezBKKY15 fatcat:7gng6zhalrechc2ghw3wjylkdu

A relation betweenZ3-graded symmetry and shape invariant supersymmetric systems

V K Oikonomou
2014 Journal of Physics A: Mathematical and Theoretical  
Particularly, we demonstrate that each shape invariant supersymmetric system can constitute a Z_3-graded topological symmetric algebra.  ...  In view of the fact that the shape invariance condition is somewhat an additional algebraic condition, with no origin to some concrete algebraic structure, our results might be useful towards this line  ...  symmetry, we shall relate the Z 3 system with an SO(2, 1) Lie algebra.  ... 
doi:10.1088/1751-8113/47/43/435304 fatcat:6h7mmje42vcq5b65pfawbwgz2m

Electromagnetic Problems Modeling Using Algebraic Topological Method

Vikram Reddy Anapana, Venkata Kowshik Sivva, Pranav Sai, Venkatesh Gongolu, Lanka Mithin Chakravarthy
2021 American Journal of Electromagnetics and Applications  
The measured results show a good agreement between the analytical and the algebraic topological methods.  ...  The algebraic topological method is a direct discrete and computationally ambitious technique that uses only physically measurable scalar quantities.  ...  Algebraic Topological Parameters Simplex The dimension of a spatial object k is its most basic feature.  ... 
doi:10.11648/j.ajea.20210902.11 fatcat:7e4tt5s4avgkbdcw5aafph2tae

Image analysis method for overcoming source distortion using algebraic invariant methods

Boris Kovalerchuk, Richard Chase, Sylvia S. Shen, Paul E. Lewis
2005 Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XI  
Deriving a method that is invariant to disproportional scaling that is based on an algebraic invariant method is a new approach to solving this problem and represents a new mathematical language for the  ...  In addition to geometric shapes and topological data, features and images can also be compared algebraically.  ...  We may have another feature and can build an abstract algebraic system, b=<B 1 ,B 2 ,R 1 ,R 2 ,R 3 ,R 4 > for this feature.  ... 
doi:10.1117/12.602955 fatcat:snenh4qmfrfrdjy6ggb2gptf6i

Page 1108 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
., an upper bound on the Haus- dorff dimension) which may render this identification unlikely. Nevertheless, we find certain qualitative features which would be expected of a c > 1 theory.  ...  In this work the authors perform the contraction of the SL(N,R) algebra in the case N — oo, which can be taken as a for- mulation of topological W,, gravity.  ... 

Characterizing and Measuring the Similarity of Neural Networks with Persistent Homology [article]

David Pérez-Fernández and Asier Gutiérrez-Fandiño and Jordi Armengol-Estapé and Marta Villegas
2021 arXiv   pre-print
We then describe a PH-based representation proposed for characterizing and measuring similarity of neural networks.  ...  This approach based on Topological Data Analysis is a step towards better understanding neural networks and serves as a useful similarity measure.  ...  For a deeper introduction to algebraic topology and computational topology, we refer to Edelsbrunner and Harer [15] , Ghrist [17] .  ... 
arXiv:2101.07752v3 fatcat:rv42imvhira6lgade6chfa7rpe

B. L. Clarkson, P. J. Holmes, and A. Kistner (eds.), Stochastic Problems in Dynamics (Pitman, 1977), 566 pp., £12

R. J. Henery
1979 Proceedings of the Edinburgh Mathematical Society  
., An Introduction to Abstract Algebra (Blackie, 1978) , ix+166 pp., £4-95 (paper covers) .  ...  Topological groups. A novel feature of the book is the early introduction of proximities and uniformities.  ... 
doi:10.1017/s0013091500027899 fatcat:hdpcbhimx5acliqhpwvq44iq4i
« Previous Showing results 1 — 15 out of 33,638 results