52,969 research outputs found
Multitasking Correlation Network for Depth Information Reconstruction
In this paper, we propose a novel multi-tasking network for stereo matching. The proposed network is trained to approximate similarity functions in statistics and linear algebra such as correlation coefficient, distance correlation and cosine similarity. By doing this, the proposed method decreases the amount of time needed to calculate the disparity map by using CNN's ability to calculate multiple pairs of image patches at the same time. We then compare the execution time and overall accuracy between the traditional method using functions and our method. The results show the model's ability to mimic the traditional method's performance while taking considerably less time to perform the task
Classical Structures Based on Unitaries
Starting from the observation that distinct notions of copying have arisen in
different categorical fields (logic and computation, contrasted with quantum
mechanics) this paper addresses the question of when, or whether, they may
coincide. Provided all definitions are strict in the categorical sense, we show
that this can never be the case. However, allowing for the defining axioms to
be taken up to canonical isomorphism, a close connection between the classical
structures of categorical quantum mechanics, and the categorical property of
self-similarity familiar from logical and computational models becomes
apparent.
The required canonical isomorphisms are non-trivial, and mix both typed
(multi-object) and untyped (single-object) tensors and structural isomorphisms;
we give coherence results that justify this approach.
We then give a class of examples where distinct self-similar structures at an
object determine distinct matrix representations of arrows, in the same way as
classical structures determine matrix representations in Hilbert space. We also
give analogues of familiar notions from linear algebra in this setting such as
changes of basis, and diagonalisation.Comment: 24 pages,7 diagram
Interior Product, Lie Derivative and Wilson Line in the Subsector of Open String Field Theory
The open string field theory of Witten (SFT) has a close formal similarity
with Chern-Simons theory in three dimensions. This similarity is due to the
fact that the former theory has concepts corresponding to forms, exterior
derivative, wedge product and integration over the manifold. In this paper, we
introduce the interior product and the Lie derivative in the subsector of
SFT. The interior product in SFT is specified by a two-component "tangent
vector" and lowers the ghost number by one (like the ordinary interior product
maps a -form to -form). The Lie derivative in SFT is defined as the
anti-commutator of the interior product and the BRST operator. The important
property of these two operations is that they respect the algebra.
Deforming the original by using the Lie derivative, we can consider
an infinite copies of the algebra, which we call the manifold. As
an application, we construct the Wilson line on the manifold, which could play
a role in reproducing degenerate fluctuation modes around a multi-brane
solution.Comment: 22 pages, 1 figure. title capitalization change
Affine Lie Algebraic Origin of Constrained KP Hierarchies
We present an affine algebraic construction of the basic
constrained KP hierarchy. This hierarchy is analyzed using two approaches,
namely linear matrix eigenvalue problem on hermitian symmetric space and
constrained KP Lax formulation and we show that these approaches are
equivalent. The model is recognized to be the generalized non-linear
Schr\"{o}dinger (\GNLS) hierarchy and it is used as a building block for a
new class of constrained KP hierarchies. These constrained KP hierarchies are
connected via similarity-B\"{a}cklund transformations and interpolate between
\GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers origin
of the Toda lattice structure behind the latter hierarchy.Comment: 25 pgs, LaTeX, IFT-P/029/94 and UICHEP-TH/93-1
Heterotic string field theory with cyclic L-infinity structure
We construct a complete heterotic string field theory that includes both the
Neveu-Schwarz and Ramond sectors. We give a construction of general string
products, which realizes a cyclic L-infinity structure and thus provides with a
gauge-invariant action in the homotopy algebraic formulation. Through a map of
the string fields, we also give the Wess-Zumino-Witten-like action in the large
Hilbert space, and verify its gauge invariance independently.Comment: 31 pages, 1figure, section for four point amplitudes is inserted; v3
English has been improved; v4 English is improved, Eq(5.16b) is corrected
(published as erratum), Eq (A.19) is adde
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