9,506 research outputs found
Trustworthy Refactoring via Decomposition and Schemes: A Complex Case Study
Widely used complex code refactoring tools lack a solid reasoning about the
correctness of the transformations they implement, whilst interest in proven
correct refactoring is ever increasing as only formal verification can provide
true confidence in applying tool-automated refactoring to industrial-scale
code. By using our strategic rewriting based refactoring specification
language, we present the decomposition of a complex transformation into smaller
steps that can be expressed as instances of refactoring schemes, then we
demonstrate the semi-automatic formal verification of the components based on a
theoretical understanding of the semantics of the programming language. The
extensible and verifiable refactoring definitions can be executed in our
interpreter built on top of a static analyser framework.Comment: In Proceedings VPT 2017, arXiv:1708.0688
Two-dimensional quantum Yang-Mills theory with corners
The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds
is well known. We bring this solution into a TQFT-like form and extend it to
include corners. Our formulation is based on an axiomatic system that we hope
is flexible enough to capture actual quantum field theories also in higher
dimensions. We motivate this axiomatic system from a formal
Schroedinger-Feynman quantization procedure. We also discuss the physical
meaning of unitarity, the concept of vacuum, (partial) Wilson loops and
non-orientable surfaces.Comment: 31 pages, 6 figures, LaTeX + AMS; minor corrections, reference
update
Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Pleba\'nski
We present first heavenly equation of Pleba\'nski in a two-component
evolutionary form and obtain Lagrangian and Hamiltonian representations of this
system. We study all point symmetries of the two-component system and, using
the inverse Noether theorem in the Hamiltonian form, obtain all the integrals
of motion corresponding to each variational (Noether) symmetry. We derive two
linearly independent recursion operators for symmetries of this system related
by a discrete symmetry of both the two-component system and its symmetry
condition. Acting by these operators on the first Hamiltonian operator we
obtain second and third Hamiltonian operators. However, we were not able to
find Hamiltonian densities corresponding to the latter two operators.
Therefore, we construct two recursion operators, which are either even or odd,
respectively, under the above-mentioned discrete symmetry. Acting with them on
, we generate another two Hamiltonian operators and and find
the corresponding Hamiltonian densities, thus obtaining second and third
Hamiltonian representations for the first heavenly equation in a two-component
form. Using P. Olver's theory of the functional multi-vectors, we check that
the linear combination of , and with arbitrary constant
coefficients satisfies Jacobi identities. Since their skew symmetry is obvious,
these three operators are compatible Hamiltonian operators and hence we obtain
a tri-Hamiltonian representation of the first heavenly equation. Our
well-founded conjecture applied here is that P. Olver's method works fine for
nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian
structures crucially depends on the validity of this conjecture.Comment: Some text overlap with our paper arXiv:1510.03666 is caused by our
use here of basically the same method for discovering the Hamiltonian and
bi-Hamiltonian structures of the equation, but the equation considered here
and the results are totally different from arXiv:1510.0366
Learning Compositional Visual Concepts with Mutual Consistency
Compositionality of semantic concepts in image synthesis and analysis is
appealing as it can help in decomposing known and generatively recomposing
unknown data. For instance, we may learn concepts of changing illumination,
geometry or albedo of a scene, and try to recombine them to generate physically
meaningful, but unseen data for training and testing. In practice however we
often do not have samples from the joint concept space available: We may have
data on illumination change in one data set and on geometric change in another
one without complete overlap. We pose the following question: How can we learn
two or more concepts jointly from different data sets with mutual consistency
where we do not have samples from the full joint space? We present a novel
answer in this paper based on cyclic consistency over multiple concepts,
represented individually by generative adversarial networks (GANs). Our method,
ConceptGAN, can be understood as a drop in for data augmentation to improve
resilience for real world applications. Qualitative and quantitative
evaluations demonstrate its efficacy in generating semantically meaningful
images, as well as one shot face verification as an example application.Comment: 10 pages, 8 figures, 4 tables, CVPR 201
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