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Israel Journal of Mathematics, ISSN 0021-2172, 9/2017, Volume 221, Issue 1, pp. 445 - 469
We study the absorbing invariant set of a dynamical system defined by a map derived from Error Diffusion, a greedy online approximation algorithm that... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | CONVEX DYNAMICS | AFFINE MAPS | PIECEWISE ROTATIONS | SETS | Algorithms | Research | Mathematical research | Error analysis (Mathematics) | Invariants
Journal Article
DISCRETE & COMPUTATIONAL GEOMETRY, ISSN 0179-5376, 03/2017, Volume 57, Issue 2, pp. 357 - 370
We study the invariant measures of a piecewise expanding map in defined by an expanding similitude modulo a lattice. Using the result of Bang (Proc Am Math Soc... 
EXPANDING MAPS | MATHEMATICS | DENSITIES | TILES | Tarski's plank problem | CANONICAL NUMBER-SYSTEMS | AFFINE | Beta expansion | COMPUTER SCIENCE, THEORY & METHODS | Invariant measures | TRANSFORMATIONS | COMPLEX NUMBERS | Combinatorics | Theorems | Computational geometry | Texts | Equivalence | Similarity | Lattices | Invariants
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 2003, Volume 303, Issue 2, pp. 303 - 331
Let T be a finite set of tiles. The group of invariants G( T ) , introduced by Pak (Trans. AMS 352 (2000) 5525), is a group of linear relations between the... 
Tile invariants | Undecidability | Conway group | Height function | Polyomino tilings | polyomino tilings | STATISTICAL-MECHANICS | tile invariants | conway group | height function | COMPUTER SCIENCE, THEORY & METHODS | TILING GROUPS | LATTICE | undecidability | TETROMINOES
Journal Article
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), ISSN 1520-6149, 03/2016, Volume 2016-, pp. 3951 - 3955
We present a novel framework for detection, tracking and recognition of deformable objects undergoing geometric and radiometric transformations. Assuming the... 
Manifolds | Space vehicles | Geometry | Matched manifold detection | Manifold Learning | Dictionaries | Dimensionality Reduction | Radiometry | Extraterrestrial measurements | Principal angles | Tracking | Deformation | Tiles | Transformations | Subspaces | Object recognition | Manifolds (mathematics) | Invariants
Conference Proceeding
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2000, Volume 352, Issue 12, pp. 5525 - 5561
Let \mathbf{T} be a finite set of tiles, and \mathcal{B} a set of regions \Gamma tileable by \mathbf{T}. We introduce a {\em tile counting group}... 
Maps | Mathematical theorems | Tiles | Rectangles | Tessellations | Tiling | Combinatorics | Tableaux | Simply connected regions | Vertices | Tile invariants | Polyomino tilings | Young tableaux | Symmetric group | Conway group | Rim hook bijection | Young diagrams | Rim (ribbon) hooks | MATHEMATICS | polyomino tilings | rim hook bijection | tile invariants | symmetric group | rim (ribbon) hooks
Journal Article
Acta Crystallographica Section A, ISSN 2053-2733, 07/2018, Volume 74, Issue 4, pp. 388 - 398
This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are... 
aperiodic tilings | rotation‐invariant tilings | symmetry order | dense tile orientations | substitution tilings | Symmetry order | Aperiodic tilings | Substitution tilings | Dense tile orientations | Rotation-invariant tilings | rotation-invariant tilings | CRYSTALLOGRAPHY | CHEMISTRY, MULTIDISCIPLINARY | Substitutes | Hulls (structures) | Hulls | Symmetry
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 04/2002, Volume 98, Issue 1, pp. 1 - 16
Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were first introduced by the... 
polyomino tilings | Conway group | tile invariants | height representation | Tile invariants | Polyomino tilings | Height representation | MATHEMATICS | TILING GROUPS | LATTICE
Journal Article
IEEE Transactions on Signal Processing, ISSN 1053-587X, 09/1999, Volume 47, Issue 9, pp. 2579 - 2582
It is commonly known that the dyadic structure of wavelet expansions results in both time- and frequency-translation sensitivity of an input signal. We develop... 
Tiles | Cost function | Time frequency analysis | Particle measurements | Wavelet packets | Libraries | Time measurement | Discrete wavelet transforms | Signal representations | Testing | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Analysis | Decomposition (Mathematics) | Wavelet | Frequency shift | Algorithms | Searching | Representations | Invariants
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 09/2013, Volume 120, Issue 7, pp. 1804 - 1816
In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two bars is NP-complete, except for a few trivial special cases. In a... 
Tiling | Rectangles | NP-completeness | P-completeness | MATHEMATICS | TILE INVARIANTS | PLANE | UNIVERSAL TURING-MACHINES | POLYOMINOES | BRICK PACKING | ALGEBRAIC-THEORY | LATTICE
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 1/2001, Volume 26, Issue 1, pp. 147 - 171
We introduce Dehn invariants as a useful tool in the study of the inflation of quasiperiodic space tilings. Tilings by ``golden tetrahedra'' are considered. We... 
Combinatorics | Computational Mathematics and Numerical Analysis | Mathematics | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Inflation (Finance) | Analysis | Inflation | Tiles | Packages | Eigenvalues | Tools | Projection | Tiling | Invariants
Journal Article
01/2014, Volume 34, Issue 1, 8
A fractal tiling (f-tiling) is a tiling whose boundary is fractal. This article presents two families of rare, infinitely many f-tilings. Each f-tiling is... 
computer graphics | tiling | fractal | Boundary conditions | Fractals | Mathematics | invariant mapping | aesthetic pattern | Equations | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SHAPED PROTOTILES | Usage | Triangle | Mathematical models | Design and construction | Geometric constructions | Dynamical systems | Methods | Tiles | Fractal analysis | Segments | Tiling | Mapping | Boundaries | Invariants | Polygons
Magazine Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 2010, Volume 29, Issue 1, pp. 49 - 62
This paper gives necessary and sufficient conditions for a doubly periodic function p ( ξ ) , ξ ∈ R 2 to be the squared modulus of a lowpass filter for a... 
Scaling functions | Self-affine tiles | Attractive shift-invariant sets | Canonical number systems | Lowpass filters | Markov processes | Two's complement representations | Matrix dilations | MATHEMATICS, APPLIED | Analysis
Journal Article
Journal of Operator Theory, ISSN 0379-4024, 10/2010, Volume 64, Issue 2, pp. 299 - 319
A tiling with infinite rotational symmetry, such as the Conway-Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an étale... 
Equivalence relation | Algebra | Tiles | Homeomorphism | Tessellations | Tiling | Mathematics | Rotation | Dynamical systems | Symmetry | Operator algebras | Tilings | Noncommutative geometry | C-algebras | Substitution tilings | MATHEMATICS | dynamical systems | substitution tilings | noncommutative geometry | operator algebras | INVARIANT | tilings | EQUIVALENCE
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 07/1997, Volume 349, Issue 7, pp. 2813 - 2825
We consider 1-cocycles with values in locally compact, sec\-ond countable abelian groups on discrete, nonsingular, ergodic equivalence relations. If such a... 
Ergodic theory | Equivalence relation | Tiles | Second countable spaces | Mathematical lattices | Coordinate systems | Tessellations | Tiling | Automorphisms | Probabilities | MATHEMATICS | SHIFTS | COHOMOLOGY | K PQ MATHEMATICS | FINITE-TYPE
Journal Article
2009 50th Annual IEEE Symposium on Foundations of Computer Science, ISSN 0272-5428, 10/2009, pp. 95 - 104
We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In... 
Stationary state | Quantum Complexity | Boundary conditions | Physics | Computer science | Quantum computing | Tiles | USA Councils | Tiling Complexity | Quantum mechanics | Constraint theory | Polynomials | Translational Invariance
Conference Proceeding
Proceedings of the 6th Nordic Signal Processing Symposium, 2004. NORSIG 2004, 2004, pp. 117 - 120
Conference Proceeding
by Kirat and Kirat and Lau and Lau
Discrete & Computational Geometry, ISSN 0179-5376, 07/2002, Volume 28, Issue 1, pp. 49 - 73
Let T be a self-affine tile that is generated by an expanding integral matrix A and a digit set D . It is known that many properties of T are invariant under... 
Combinatorics | Computational Mathematics and Numerical Analysis | Mathematics | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | HAAR BASES | R(N) | TILINGS | SETS | Geometry | Mathematical analysis | Computational geometry | Tiles | Integrals | Classification | Digits | Polynomials | Invariants
Journal Article
Proceedings 2003 IEEE International Symposium on Computational Intelligence in Robotics and Automation. Computational Intelligence in Robotics and Automation for the New Millennium (Cat. No.03EX694), 2003, Volume 3, pp. 1427 - 1432 vol.3
It is known that texture can be modeled better using both deterministic and random components. The wavelet transform, which can be computed efficiently, is a... 
Wavelet transforms | Surface waves | Statistical analysis | Tiles | Textile technology | Inspection | Wavelet analysis | Surface texture | Image texture analysis | Spline
Conference Proceeding
Lecture Notes-Monograph Series, ISSN 0749-2170, 1/1997, Volume 31, pp. 351 - 362
The bivariate ranks and quantiles based on the bivariate affine equivariant median are considered. Correspondences between two different plots for bivariate... 
Parallelograms | Statistical median | Tiles | Diagrams | Nonparametric Inference | Sine function | Tessellations | Data lines | Covariance matrices | Contour lines | Vertices
Journal Article
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