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 KBcKBc 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 $KBc$ 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 $p$-form to $(p-1)$-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 $KBc$ algebra. Deforming the original $(K,B,c)$ by using the Lie derivative, we can consider an infinite copies of the $KBc$ algebra, which we call the $KBc$ 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 $sl (n+1)$ 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