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2012, Annals of mathematics studies, ISBN 9780691154251, Volume no. 183, vi, 289
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This... 
Mumford-Tate groups | Group Theory | Geometry | PBG | Algebraic | PBMW | Mathematics | PBKB | PBKD | Complex Analysis | Hodge theory | Geometry, Algebraic
Book
2017, ISBN 9781551646077, ix, 274 pages
"In this remarkable new book Brian Morris examines the lives, works and philosophy of three key thinkers in the field of modern ecology. Lewis Mumford, René... 
Bookchin, Murray, 1921-2006 | Dubos, René J. 1901-1982 | Ecology | Mumford, Lewis, 1895-1990 | Humanism | Philosophy
Book
Pattern Recognition, ISSN 0031-3203, 06/2015, Volume 48, Issue 6, pp. 2029 - 2042
Image segmentation and image restoration are two important topics in image processing with a number of important applications. In this paper, we propose a new... 
Image segmentation | Piecewise constant Mumford–Shah model | Image restoration | Piecewise constant | Mumford-Shah model | MUMFORD | REGULARIZATION | NOISE REMOVAL | Piecewise constant Mumford-Shah model | IMPULSE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Models | Algorithms | Image processing | Analysis
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 12/2017, Volume 350, pp. 657 - 667
We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford–Shah... 
Image segmentation | Piecewise constant Mumford–Shah functional | Iterative thresholding | Convolution | Fast Fourier transform | Piecewise constant Mumford-Shah functional | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | MUMFORD | SHAH MODEL | PHYSICS, MATHEMATICAL | GRAPHS | Image processing | Methods | Algorithms
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 07/2016, Volume 41, Issue 1, pp. 94 - 138
Journal Article
1971, [1st ed.]. --, ISBN 0151547505, xxiii, 167
Book
Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2020, Volume 224, Issue 7, p. 106306
In this article, we prove that for several classes of graphs, the Castelnuovo-Mumford regularity of symbolic powers of their edge ideals coincide with that of... 
Castelnuovo-Mumford regularity | Edge ideal | Symbolic powers
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 05/2012, Volume 31, Issue 3, pp. 1 - 14
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2018, Volume 511, pp. 471 - 485
We begin the study of the notion of diameter of an ideal I⊂S=k[x1,…,xn], an invariant measuring the distance between the minimal primes of I. We provide large... 
Castelnuovo–Mumford regularity | Gorenstein algebras | Dual graph | Diameter | MATHEMATICS | CONNECTEDNESS | Castelnuovo-Mumford regularity | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2020, Volume 541, pp. 345 - 358
Let G be a unicyclic graph with edge ideal I(G). For any integer s≥1, we denote the s-th symbolic power of I(G) by I(G)(s). It is shown that... 
Castelnuovo–Mumford regularity | Unicyclic graph | Edge ideal | Symbolic power | MATHEMATICS | Castelnuovo-Mumford regularity | BOUNDS | PROJECTIVE DIMENSION | Computer science
Journal Article
Journal of Algebra, ISSN 0021-8693, 08/2019, Volume 532, pp. 311 - 322
Let G be a finite simple graph on the vertex set V(G)={x1,…,xn} and I(G)⊂K[V(G)] its edge ideal, where K[V(G)] is the polynomial ring in x1,…,xn over a field K... 
Castelnuovo–Mumford regularity | Induced matching number | h-Polynomial | Edge ideal | MATHEMATICS | Castelnuovo-Mumford regularity | REGULARITY | Information science | Statistics
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2018, Volume 370, Issue 4, pp. 2299 - 2320
We work over an algebraically closed field of characteristic zero. The purpose of this paper is to characterize a nondegenerate projective variety X with a... 
Ideal sheaf | Castelnuovo | Linear projection | Mumford regularity
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2019, Volume 349, pp. 438 - 451
An extension of the Mumford–Shah model for image segmentation is introduced to segment real-valued functions having values on a complete, connected, 2-manifold... 
Mumford–Shah variational model | Convex non-convex optimization | Mesh segmentation | Non-convex regularization | Mumford-Shah variational model | MATHEMATICS, APPLIED | Image processing | Analysis
Journal Article
Forum Mathematicum, ISSN 0933-7741, 03/2019, Volume 31, Issue 2, pp. 465 - 477
Let Δ be a matroid complex. In this paper, we explicitly compute the regularity of all the symbolic powers of its Stanley–Reisner ideal in terms of... 
Castelnuovo–Mumford regularity | 05E40 | arboricity | Stanley–Reisner ideal | Matroid | circumference | 13D45 | 05E45 | Stanley-Reisner ideal | Castelnuovo-Mumford regularity | MATHEMATICS | MATHEMATICS, APPLIED | Stanley Reisner ideal | COHEN-MACAULAYNESS | Castelnuovo Mumford regularity | MONOMIAL IDEALS | ASYMPTOTIC-BEHAVIOR
Journal Article
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