16,053 research outputs found
Systematic approach to nonlinear filtering associated with aggregation operators. Part 2. Frechet MIMO-filters
Median filtering has been widely used in scalar-valued image processing as an edge preserving operation. The basic idea is that the pixel value is replaced by the median of the pixels contained in a window around it. In this work, this idea is extended onto vector-valued images. It is based on the fact that the median is also the value that minimizes the sum of distances between all grey-level pixels in the window. The Frechet median of a discrete set of vector-valued pixels in a metric space with a metric is the point minimizing the sum of metric distances to the all sample pixels. In this paper, we extend the notion of the Frechet median to the general Frechet median, which minimizes the Frechet cost function (FCF) in the form of aggregation function of metric distances, instead of the ordinary sum. Moreover, we propose use an aggregation distance instead of classical metric distance. We use generalized Frechet median for constructing new nonlinear Frechet MIMO-filters for multispectral image processing. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No 17-07-00886, No 17-29-03369 and by Ural State Forest University Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"
A Comparative Study of Coq and HOL
This paper illustrates the differences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to support some of the arguments discussed in this paper. The mechanisms for specifying definitions and for theorem proving are discussed separately, building in parallel two pictures of the different approaches of mechanisation given by these systems
The exceptional holonomy groups and calibrated geometry
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8
dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat.
This is a survey paper on exceptional holonomy, in two parts.
Part I introduces the exceptional holonomy groups, and explains constructions
for compact 7- and 8-manifolds with holonomy G2 and Spin(7). The simplest such
constructions work by using techniques from complex geometry and Calabi-Yau
analysis to resolve the singularities of a torus orbifold T^7/G or T^8/G, for G
a finite group preserving a flat G2 or Spin(7)-structure on T^7 or T^8. There
are also more complicated constructions which begin with a Calabi-Yau manifold
or orbifold.
Part II discusses the calibrated submanifolds of G2 and Spin(7)-manifolds:
associative 3-folds and coassociative 4-folds for G2, and Cayley 4-folds for
Spin(7). We explain the general theory, following Harvey and Lawson, and the
known examples. Finally we describe the deformation theory of compact
calibrated submanifolds, following McLean.Comment: 32 pages. Lectures given at a conference in Gokova, Turkey, May 200
Constructing compact manifolds with exceptional holonomy
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8
dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat.
This is a survey paper on constructions for compact 7- and 8-manifolds with
holonomy G2 and Spin(7).
The simplest such constructions work by using techniques from complex
geometry and Calabi-Yau analysis to resolve the singularities of a torus
orbifold T^7/G or T^8/G, for G a finite group preserving a flat G2 or
Spin(7)-structure on T^7 or T^8. There are also more complicated constructions
which begin with a Calabi-Yau manifold or orbifold.
All the material in this paper is covered in much more detail in the author's
book, "Compact manifolds with special holonomy", Oxford University Press, 2000.Comment: 17 pages. Lecture for Clay Institute School on Geometry and String
Theory, Cambridge, March 200
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Smart premise selection is essential when using automated reasoning as a tool
for large-theory formal proof development. A good method for premise selection
in complex mathematical libraries is the application of machine learning to
large corpora of proofs. This work develops learning-based premise selection in
two ways. First, a newly available minimal dependency analysis of existing
high-level formal mathematical proofs is used to build a large knowledge base
of proof dependencies, providing precise data for ATP-based re-verification and
for training premise selection algorithms. Second, a new machine learning
algorithm for premise selection based on kernel methods is proposed and
implemented. To evaluate the impact of both techniques, a benchmark consisting
of 2078 large-theory mathematical problems is constructed,extending the older
MPTP Challenge benchmark. The combined effect of the techniques results in a
50% improvement on the benchmark over the Vampire/SInE state-of-the-art system
for automated reasoning in large theories.Comment: 26 page
On Spectral Triples in Quantum Gravity II
A semifinite spectral triple for an algebra canonically associated to
canonical quantum gravity is constructed. The algebra is generated by based
loops in a triangulation and its barycentric subdivisions. The underlying space
can be seen as a gauge fixing of the unconstrained state space of Loop Quantum
Gravity. This paper is the second of two papers on the subject.Comment: 43 pages, 1 figur
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