A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is
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
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
for closed-loop identification. ... The authors present two ways of solving this algebraic identification problem. ...
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
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
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  for an introduction to the language of sketches as a method of presentation of theories.) ...doi:10.1007/s00283-016-9672-z fatcat:bzceynfie5e5rgcovdmoktyf7a
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  for an introduction to the language of sketches as a method of presentation of theories.) ...doi:10.1515/9781400888559-018 fatcat:jubza4t2i5ac5jpqjlze772nvy
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). ...
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
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
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
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
., 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. ...
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  , Ghrist  . ...arXiv:2101.07752v3 fatcat:rv42imvhira6lgade6chfa7rpe
., 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