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Geometric Homogeneity And Stabilization
 In Preprints of IFAC Nonlinear Control Systems Design Symposium (NOLCOS'95
, 1995
"... . We present a consistent, geometric notion of homogeneity, for vector fields (differential equations and control systems), functions, differential forms and endomorphisms. The fundamental observation is that homogeneity is an intrinsic, geometric property. Accordingly, a coordinatefree characte ..."
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. We present a consistent, geometric notion of homogeneity, for vector fields (differential equations and control systems), functions, differential forms and endomorphisms. The fundamental observation is that homogeneity is an intrinsic, geometric property. Accordingly, a coordinate
Geometric Homogeneity with Applications to
, 2004
"... This paper studies properties of homogeneous systems in a geometric, coordinatefree setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes i ..."
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This paper studies properties of homogeneous systems in a geometric, coordinatefree setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes
Does the brain prefer geometrical homogeneity?
, 2010
"... Abstract. Some patients with frontotemporal lobar degeneration (FTLD) have shown the development of painting or musical abilities after the onset of the disease. In this report, we present another emergent ability. A female patient with FTLD showing dense atrophy of the bilateral anterior lobes and ..."
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of paper, she showed quite unique geometrical preferences. Her severely degenerated brain combined with her geometrical abilities suggests that the human brain is naturally affected by geometrical homogeneity.
Geometric homogeneity and configuration controllability of nonlinear systems
, 2003
"... Abstract This paper exploits notions of geometric homogeneity to show that (configuration) controllability results for a large class of mechanical systems with drift can be recovered by investigating a class of nonlinear dynamical systems satisfying certain homogeneity conditions. This broad class o ..."
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Cited by 2 (0 self)
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Abstract This paper exploits notions of geometric homogeneity to show that (configuration) controllability results for a large class of mechanical systems with drift can be recovered by investigating a class of nonlinear dynamical systems satisfying certain homogeneity conditions. This broad class
Geometric homogeneity and controllability of nonlinear systems. available electronically http:www.cds.caltech.edu/˜pvela
 Submitted IEEE Conf. Dec. Contr
, 2003
"... Abstract. We followup on a suggestion from Bullo and Lewis [1] concerning the importance of geometric homogeneity for mechanical systems. It is shown that controllability results for a large class of mechanical systems with drift can be recovered by considering a class of nonlinear dynamical systems ..."
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Cited by 1 (1 self)
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Abstract. We followup on a suggestion from Bullo and Lewis [1] concerning the importance of geometric homogeneity for mechanical systems. It is shown that controllability results for a large class of mechanical systems with drift can be recovered by considering a class of nonlinear dynamical
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
 Proceedings of the National Academy of Sciences
, 2005
"... of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace operators ..."
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Cited by 257 (45 self)
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of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace
Homogeneous Designs and Geometric Lattices
 JOURNAL OF COMBINATORIAL THEORY SERIES A
, 1985
"... During the last 20 years, there has been a great deal of research concerning designs with A = 1 admitting 2transitive groups. The following theorems will be proved in this note; they are fairly simple consequences of the classification ’ of all finite simple groups (see, e.g., [6]). THEOREM 1. Let ..."
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Cited by 44 (4 self)
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, or (v) One of two designs having u = 36 and k = 3 ’ [12]. THEOREM 2. Let Y be a finite geometric lattice of rank at least 3 such that Aut 6p is transitive on ordered bases. Then either (i) Y is a truncation of a Boolean lattice or a projective or affine geometry, (ii) 9 is the lattice associated with a
Locally homogeneous geometric manifolds
 Proceedings of the 2010 International Congress of Mathematicians
"... Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally homogeneous spaces later formed the context ..."
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Cited by 11 (1 self)
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Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally homogeneous spaces later formed the context
BASISHOMOGENEOUS GEOMETRIC LATTICES
"... We classify the finite point—and basis—homogeneous geometric lattices having a line of size greater than 2. As a consequence, the finite basishomogeneous geometric lattices are known, up to the knowledge of those having only lines of size 2. 1. ..."
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Cited by 2 (1 self)
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We classify the finite point—and basis—homogeneous geometric lattices having a line of size greater than 2. As a consequence, the finite basishomogeneous geometric lattices are known, up to the knowledge of those having only lines of size 2. 1.
Results 1  10
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