23,050 research outputs found
Image Description Using a Multiplier-Less Operator
Cataloged from PDF version of article.A fast algorithm for image classification based on a computationally efficient operator forming a semigroup on real numbers is developed. The new operator does not require any multiplications. The co-difference matrix based on the new operator is defined and an image descriptor using the co-difference matrix is developed. In the proposed method, the multiplication operation of the well-known covariance method is replaced by the new operator. The proposed method is experimentally compared with the regular covariance matrix method. The proposed descriptor performs as well as the the regular covariance method without performing any multiplications. Texture recognition and licence plate identification examples are presented
Programmable remapper for image processing
A video-rate coordinate remapper includes a memory for storing a plurality of transformations on look-up tables for remapping input images from one coordinate system to another. Such transformations are operator selectable. The remapper includes a collective processor by which certain input pixels of an input image are transformed to a portion of the output image in a many-to-one relationship. The remapper includes an interpolative processor by which the remaining input pixels of the input image are transformed to another portion of the output image in a one-to-many relationship. The invention includes certain specific transforms for creating output images useful for certain defects of visually impaired people. The invention also includes means for shifting input pixels and means for scrolling the output matrix
Factoring in a Dissipative Quantum Computer
We describe an array of quantum gates implementing Shor's algorithm for prime
factorization in a quantum computer. The array includes a circuit for modular
exponentiation with several subcomponents (such as controlled multipliers,
adders, etc) which are described in terms of elementary Toffoli gates. We
present a simple analysis of the impact of losses and decoherence on the
performance of this quantum factoring circuit. For that purpose, we simulate a
quantum computer which is running the program to factor N = 15 while
interacting with a dissipative environment. As a consequence of this
interaction randomly selected qubits may spontaneously decay. Using the results
of our numerical simulations we analyze the efficiency of some simple error
correction techniques.Comment: plain tex, 18 pages, 8 postscript figure
New Multiplier Sequences via Discriminant Amoebae
In their classic 1914 paper, Polya and Schur introduced and characterized two
types of linear operators acting diagonally on the monomial basis of R[x],
sending real-rooted polynomials (resp. polynomials with all nonzero roots of
the same sign) to real-rooted polynomials. Motivated by fundamental properties
of amoebae and discriminants discovered by Gelfand, Kapranov, and Zelevinsky,
we introduce two new natural classes of polynomials and describe diagonal
operators preserving these new classes. A pleasant circumstance in our
description is that these classes have a simple explicit description, one of
them coinciding with the class of log-concave sequences.Comment: 11 pages, 6 figures. Submitted for publicatio
Weighted model spaces and Schmidt subspaces of Hankel operators
For a bounded Hankel matrix , we describe the structure of the
Schmidt subspaces of , namely the eigenspaces of
corresponding to non zero eigenvalues. We prove that these subspaces are in
correspondence with weighted model spaces in the Hardy space on the unit
circle. Here we use the term "weighted model space" to describe the range of an
isometric multiplier acting on a model space. Further, we obtain similar
results for Hankel operators acting in the Hardy space on the real line.
Finally, we give a streamlined proof of the Adamyan-Arov-Krein theorem using
the language of weighted model spaces.Comment: Final version, to appear in Journal of the London Mathematical
Societ
Boundary conformal fields and Tomita--Takesaki theory
Motivated by formal similarities between the continuum limit of the Ising
model and the Unruh effect, this paper connects the notion of an Ishibashi
state in boundary conformal field theory with the Tomita--Takesaki theory for
operator algebras. A geometrical approach to the definition of Ishibashi states
is presented, and it is shownthat, when normalisable the Ishibashi states are
cyclic separating states, justifying the operator state correspondence. When
the states are not normalisable Tomita--Takesaki theory offers an alternative
approach based on left Hilbert algebras, opening the way to extensions of our
construction and the state-operator correspondence.Comment: plain Te
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