Computers & Mathematics with Applications, ISSN 0898-1221, 03/2018, Volume 75, Issue 5, p. 1648

The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences....

Studies | Applications of mathematics | Euclidean geometry | Numerical analysis | Approximation | Applied mathematics | Computation | Mathematical analysis | Approximations | Homology | Smoothness | Continuity (mathematics)

Studies | Applications of mathematics | Euclidean geometry | Numerical analysis | Approximation | Applied mathematics | Computation | Mathematical analysis | Approximations | Homology | Smoothness | Continuity (mathematics)

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2015

Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative...

Computer Science | Mathematics

Computer Science | Mathematics

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 2016

Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological...

Computer Science | Mathematics

Computer Science | Mathematics

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 03/2018, Volume 54, Issue 3, pp. 1 - 4

Solving eddy current problems formulated by using a magnetic scalar potential in the insulator requires a topological pre-processing to find the so-called...

Software algorithms | magnetic scalar potential | Magnetic domains | first de Rham cohomology group | Conductors | Generators | Cohomology | Joining processes | Eddy currents | Standards | cuts | eddy currents | PHYSICS, APPLIED | EDDY-CURRENT PROBLEMS | FORMULATION | ENGINEERING, ELECTRICAL & ELECTRONIC | MULTIPLY CONNECTED REGIONS | CONSTRUCTION | BOUNDARY | MAGNETIC SCALAR POTENTIALS | Computational electromagnetics | Algorithms

Software algorithms | magnetic scalar potential | Magnetic domains | first de Rham cohomology group | Conductors | Generators | Cohomology | Joining processes | Eddy currents | Standards | cuts | eddy currents | PHYSICS, APPLIED | EDDY-CURRENT PROBLEMS | FORMULATION | ENGINEERING, ELECTRICAL & ELECTRONIC | MULTIPLY CONNECTED REGIONS | CONSTRUCTION | BOUNDARY | MAGNETIC SCALAR POTENTIALS | Computational electromagnetics | Algorithms

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2013, Volume 253, pp. 530 - 542

The problem of computing cohomology generators of a cell complex is gaining more and more interest in various branches of science ranging from computational...

Computational fluid dynamics | Computation | Focusing | Biology | Generators | Computational efficiency | Computer aided design | Eddy current testing

Computational fluid dynamics | Computation | Focusing | Biology | Generators | Computational efficiency | Computer aided design | Eddy current testing

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 10/2016, Volume 52, Issue 10, pp. 1 - 6

Efficient boundary integral formulations based on stream functions for solving eddy current problems in thin conductors, which are modeled by the orientable...

stream function | homology | relative cohomology generators | Integral equations | Color | Conductors | Generators | Software | Boundary integral (BI) formulation | Eddy currents | Surface treatment | eddy currents | PHYSICS, APPLIED | COHOMOLOGY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Analysis | Eddy currents (Electric) | Electric generators

stream function | homology | relative cohomology generators | Integral equations | Color | Conductors | Generators | Software | Boundary integral (BI) formulation | Eddy currents | Surface treatment | eddy currents | PHYSICS, APPLIED | COHOMOLOGY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Analysis | Eddy currents (Electric) | Electric generators

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 02/2014, Volume 50, Issue 2, pp. 577 - 580

Computing the first cohomology group generators received great attention in computational electromagnetics as a theoretically sound and safe method to produce...

Electric potential | Conductors | magneto-quasi-statics | Generators | Vectors | Complexity theory | Standards | Equations | Cohomology basis selection | (co)homology | minimal cohomology basis | thick cuts | magnetic scalar potential | first cohomology group lazy generators | PHYSICS, APPLIED | (co) homology | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Finite element method | Usage | Electric generators | Innovations | Graph theory | Eddy currents (Electric)

Electric potential | Conductors | magneto-quasi-statics | Generators | Vectors | Complexity theory | Standards | Equations | Cohomology basis selection | (co)homology | minimal cohomology basis | thick cuts | magnetic scalar potential | first cohomology group lazy generators | PHYSICS, APPLIED | (co) homology | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Finite element method | Usage | Electric generators | Innovations | Graph theory | Eddy currents (Electric)

Journal Article

IEEE Transactions on Image Processing, ISSN 1057-7149, 10/2014, Volume 23, Issue 10, pp. 4486 - 4495

A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The...

Image analysis | Three-dimensional displays | Materials | Skeleton | Topology | Indexes | Face | topological image analysis | homology | iterative thinning | skeletonization | topology preservation | ALGORITHM | STENOSES | COLON | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MODELS | ROBUST | SIMPLE POINTS | SKELETONS | CENTERLINE | Data Compression - methods | Reproducibility of Results | Algorithms | Humans | Image Interpretation, Computer-Assisted - methods | Sensitivity and Specificity | Imaging, Three-Dimensional - methods | Image Enhancement - methods | Pattern Recognition, Automated - methods | Usage | Image processing | Visualization (Computers) | Innovations | Diagnostic imaging | Approximation theory | Computer-aided design | Mathematical optimization | Methods | Thinning | Tables | Pattern recognition | Transaction processing | Representations | Preserving | Computer Science - Computer Vision and Pattern Recognition

Image analysis | Three-dimensional displays | Materials | Skeleton | Topology | Indexes | Face | topological image analysis | homology | iterative thinning | skeletonization | topology preservation | ALGORITHM | STENOSES | COLON | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MODELS | ROBUST | SIMPLE POINTS | SKELETONS | CENTERLINE | Data Compression - methods | Reproducibility of Results | Algorithms | Humans | Image Interpretation, Computer-Assisted - methods | Sensitivity and Specificity | Imaging, Three-Dimensional - methods | Image Enhancement - methods | Pattern Recognition, Automated - methods | Usage | Image processing | Visualization (Computers) | Innovations | Diagnostic imaging | Approximation theory | Computer-aided design | Mathematical optimization | Methods | Thinning | Tables | Pattern recognition | Transaction processing | Representations | Preserving | Computer Science - Computer Vision and Pattern Recognition

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 03/2016, Volume 52, Issue 3, pp. 1 - 4

We introduce a novel technique to solve eddy current problems in non-manifold thin conductors by a boundary integral method based on a stream function. The...

Manifolds | Integral methods | Three-dimensional displays | thin shields | Surgery | non-manifold geometry | Conductors | Generators | Current density | Eddy currents | topological surgery | eddy currents | PHYSICS, APPLIED | integral methods | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric conductors | Usage | Research | Integral equations | Eddy currents (Electric) | Computation | Boundary integral method | Continuity

Manifolds | Integral methods | Three-dimensional displays | thin shields | Surgery | non-manifold geometry | Conductors | Generators | Current density | Eddy currents | topological surgery | eddy currents | PHYSICS, APPLIED | integral methods | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric conductors | Usage | Research | Integral equations | Eddy currents (Electric) | Computation | Boundary integral method | Continuity

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 06/2017, Volume 53, Issue 6, pp. 1 - 4

When solving eddy-current problems containing topologically non-trivial conductors with formulations using the magnetic scalar potential in the insulators,...

Software algorithms | Heating | magnetic scalar potential | Conductors | Insulators | Generators | computer aided software engineering | Cohomology | Eddy currents | mathematical software | Standards | cuts | eddy currents | PHYSICS, APPLIED | ENGINEERING, ELECTRICAL & ELECTRONIC | Integrated circuits | Research | Eddy currents (Electric) | Semiconductor chips | Formulations | Algorithms | Downloading | Topology | Mesh generation | Eddy current testing

Software algorithms | Heating | magnetic scalar potential | Conductors | Insulators | Generators | computer aided software engineering | Cohomology | Eddy currents | mathematical software | Standards | cuts | eddy currents | PHYSICS, APPLIED | ENGINEERING, ELECTRICAL & ELECTRONIC | Integrated circuits | Research | Eddy currents (Electric) | Semiconductor chips | Formulations | Algorithms | Downloading | Topology | Mesh generation | Eddy current testing

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 01/2019, Volume 55, Issue 6, p. 1

There are two ways of solving eddy current problems with an edge element [Formula Omitted]-conforming formulation in the case of non-simply-connected...

Formulations | Conductors | Homology | Eddy currents

Formulations | Conductors | Homology | Eddy currents

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 01/2017, Volume 78, pp. 91 - 114

Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological...

Intrinsic dimension | Persistent homology | Topological data analysis | Topological machine learning | Statistical topology | Computer science | Algorithms | Information management | Statistics | Analysis | Machine learning

Intrinsic dimension | Persistent homology | Topological data analysis | Topological machine learning | Statistical topology | Computer science | Algorithms | Information management | Statistics | Analysis | Machine learning

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 06/2019, Volume 55, Issue 6, pp. 1 - 4

There are two ways of solving eddy current problems with an edge element h -conforming...

scalar potential | Magnetic domains | Conductivity | Conductors | Insulators | Generators | Mathematics | Cohomology | fake conductivity | Eddy currents | finite elements | cuts | PHYSICS, APPLIED | ENGINEERING, ELECTRICAL & ELECTRONIC

scalar potential | Magnetic domains | Conductivity | Conductors | Insulators | Generators | Mathematics | Cohomology | fake conductivity | Eddy currents | finite elements | cuts | PHYSICS, APPLIED | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 03/2015, Volume 51, Issue 3, pp. 1 - 4

We present a technique to efficiently compute optimal cuts required to solve 3-D eddy current problems by magnetic scalar potential formulations. By optimal...

Magnetostatics | Conductors | Minimization | Generators | Complexity theory | Eddy currents | Standards | eddy currents | maximum circulation network flow problem | thin and thick cuts | Terms-(Co)homology | MULTIPLY CONNECTED REGIONS | PHYSICS, APPLIED | MESHES | (Co)homology | EDDY-CURRENT PROBLEMS | COHOMOLOGY COMPUTATION | FORMULATION | MAGNETIC SCALAR POTENTIALS | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Usage | Program generators | Code generators | Graph theory | Research | Eddy currents (Electric) | Conduction | Scalars | Boundaries | Circulation | Combinatorial analysis | Optimization | Three dimensional

Magnetostatics | Conductors | Minimization | Generators | Complexity theory | Eddy currents | Standards | eddy currents | maximum circulation network flow problem | thin and thick cuts | Terms-(Co)homology | MULTIPLY CONNECTED REGIONS | PHYSICS, APPLIED | MESHES | (Co)homology | EDDY-CURRENT PROBLEMS | COHOMOLOGY COMPUTATION | FORMULATION | MAGNETIC SCALAR POTENTIALS | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Usage | Program generators | Code generators | Graph theory | Research | Eddy currents (Electric) | Conduction | Scalars | Boundaries | Circulation | Combinatorial analysis | Optimization | Three dimensional

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 11/2016, Volume 334, pp. 60 - 81

Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative...

Inverse analysis | Phase separation mechanisms | Computational topology | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | COREDUCTION HOMOLOGY | ALGORITHM | SPINODAL DECOMPOSITION | PHYSICS, MATHEMATICAL | FREE-ENERGY | NONUNIFORM SYSTEM

Inverse analysis | Phase separation mechanisms | Computational topology | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | COREDUCTION HOMOLOGY | ALGORITHM | SPINODAL DECOMPOSITION | PHYSICS, MATHEMATICAL | FREE-ENERGY | NONUNIFORM SYSTEM

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2018, Volume 75, Issue 5, pp. 1648 - 1666

The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences....

Rigorous approximation of functions | Rigorous arithmetic | Constructive version of simplex approximation theorem | Persistent homology | Rigorous computations | MATHEMATICS, APPLIED | COREDUCTION HOMOLOGY | STABILITY | ALGORITHM | Algebraic Topology | Mathematics

Rigorous approximation of functions | Rigorous arithmetic | Constructive version of simplex approximation theorem | Persistent homology | Rigorous computations | MATHEMATICS, APPLIED | COREDUCTION HOMOLOGY | STABILITY | ALGORITHM | Algebraic Topology | Mathematics

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 01/2010, Volume 48, Issue 4, pp. 1601 - 1601

Two algorithms based upon a tree-cotree decomposition, called in this paper spanning tree technique (STT) and generalized spanning tree technique (GSTT), have...

Concretes | Trees | Algorithms | Numerical analysis | Computational electromagnetics | Homology | Decomposition | Failure

Concretes | Trees | Algorithms | Numerical analysis | Computational electromagnetics | Homology | Decomposition | Failure

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2010, Volume 48, Issue 4, pp. 1601 - 1624

Two algorithms based upon a tree-cotree decomposition, called in this paper spanning tree technique (STT) and generalized spanning tree technique (GSTT), have...

Integers | Linear systems | Algorithms | Fasteners | Cubes | Scalars | Computational electromagnetics | Counterexamples | Magnetic fields | Algebraic topology | Tree-cotree decomposition | Cohomology theory | Homology and cohomology generators | Homology theory | Belted tree | Computational topology | Homology-cohomology duality | Scalar potential in multiply connected regions | cohomology theory | algebraic topology | FIELDS | MATHEMATICS, APPLIED | MESHES | SPACES | ALGORITHM | homology theory | homology-cohomology duality | homology and cohomology generators | CUTS | MULTIPLY CONNECTED REGIONS | belted tree | EDGE ELEMENTS | FORMULATIONS | computational topology | tree-cotree decomposition | COMPUTATION | MAGNETIC SCALAR POTENTIALS | scalar potential in multiply connected regions | Studies | Theoretical mathematics | Mathematical analysis | Applied mathematics | Electromagnetics

Integers | Linear systems | Algorithms | Fasteners | Cubes | Scalars | Computational electromagnetics | Counterexamples | Magnetic fields | Algebraic topology | Tree-cotree decomposition | Cohomology theory | Homology and cohomology generators | Homology theory | Belted tree | Computational topology | Homology-cohomology duality | Scalar potential in multiply connected regions | cohomology theory | algebraic topology | FIELDS | MATHEMATICS, APPLIED | MESHES | SPACES | ALGORITHM | homology theory | homology-cohomology duality | homology and cohomology generators | CUTS | MULTIPLY CONNECTED REGIONS | belted tree | EDGE ELEMENTS | FORMULATIONS | computational topology | tree-cotree decomposition | COMPUTATION | MAGNETIC SCALAR POTENTIALS | scalar potential in multiply connected regions | Studies | Theoretical mathematics | Mathematical analysis | Applied mathematics | Electromagnetics

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2013, Volume 35, Issue 5, pp. B1034 - B1054

Topology is a natural mathematical tool for quantifying complex structures. In many applications, such as, for example, in the context of phase-field models in...

Pattern characterization | Homology | Nodal domain | Nonuniform rectangular grid | Topological information | nodal domain | MATHEMATICS, APPLIED | homology | pattern characterization | COMPLEXES | VALIDATION | topological information | COMPUTATIONS | NONUNIFORM SYSTEM | nonuniform rectangular grid | COREDUCTION HOMOLOGY ALGORITHM | PERSISTENT HOMOLOGY | DOMAINS | FREE ENERGY | Construction | Subdivisions | Algorithms | Approximation | Computation | Mathematical analysis | Mathematical models | Topology

Pattern characterization | Homology | Nodal domain | Nonuniform rectangular grid | Topological information | nodal domain | MATHEMATICS, APPLIED | homology | pattern characterization | COMPLEXES | VALIDATION | topological information | COMPUTATIONS | NONUNIFORM SYSTEM | nonuniform rectangular grid | COREDUCTION HOMOLOGY ALGORITHM | PERSISTENT HOMOLOGY | DOMAINS | FREE ENERGY | Construction | Subdivisions | Algorithms | Approximation | Computation | Mathematical analysis | Mathematical models | Topology

Journal Article

Neuroinformatics, ISSN 1539-2791, 01/2018

Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described...

Algebraic Topology | Computer Science | Mathematics | Bioinformatics

Algebraic Topology | Computer Science | Mathematics | Bioinformatics

Journal Article

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