15,107 research outputs found
Lectures on the three--dimensional non--commutative spheres
These are expanded notes for a short course given at the Universidad Nacional
de La Plata. They aim at giving a self-contained account of the results of
Alain Connes and Michel Dubois--Violette.Comment: 17 page
Common Representation of Information Flows for Dynamic Coalitions
We propose a formal foundation for reasoning about access control policies
within a Dynamic Coalition, defining an abstraction over existing access
control models and providing mechanisms for translation of those models into
information-flow domain. The abstracted information-flow domain model, called a
Common Representation, can then be used for defining a way to control the
evolution of Dynamic Coalitions with respect to information flow
Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation
Despite the importance of sparse matrices in numerous fields of science,
software implementations remain difficult to use for non-expert users,
generally requiring the understanding of underlying details of the chosen
sparse matrix storage format. In addition, to achieve good performance, several
formats may need to be used in one program, requiring explicit selection and
conversion between the formats. This can be both tedious and error-prone,
especially for non-expert users. Motivated by these issues, we present a
user-friendly and open-source sparse matrix class for the C++ language, with a
high-level application programming interface deliberately similar to the widely
used MATLAB language. This facilitates prototyping directly in C++ and aids the
conversion of research code into production environments. The class internally
uses two main approaches to achieve efficient execution: (i) a hybrid storage
framework, which automatically and seamlessly switches between three underlying
storage formats (compressed sparse column, Red-Black tree, coordinate list)
depending on which format is best suited and/or available for specific
operations, and (ii) a template-based meta-programming framework to
automatically detect and optimise execution of common expression patterns.
Empirical evaluations on large sparse matrices with various densities of
non-zero elements demonstrate the advantages of the hybrid storage framework
and the expression optimisation mechanism.Comment: extended and revised version of an earlier conference paper
arXiv:1805.0338
Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation
Despite the importance of sparse matrices in numerous fields of science,
software implementations remain difficult to use for non-expert users,
generally requiring the understanding of underlying details of the chosen
sparse matrix storage format. In addition, to achieve good performance, several
formats may need to be used in one program, requiring explicit selection and
conversion between the formats. This can be both tedious and error-prone,
especially for non-expert users. Motivated by these issues, we present a
user-friendly and open-source sparse matrix class for the C++ language, with a
high-level application programming interface deliberately similar to the widely
used MATLAB language. This facilitates prototyping directly in C++ and aids the
conversion of research code into production environments. The class internally
uses two main approaches to achieve efficient execution: (i) a hybrid storage
framework, which automatically and seamlessly switches between three underlying
storage formats (compressed sparse column, Red-Black tree, coordinate list)
depending on which format is best suited and/or available for specific
operations, and (ii) a template-based meta-programming framework to
automatically detect and optimise execution of common expression patterns.
Empirical evaluations on large sparse matrices with various densities of
non-zero elements demonstrate the advantages of the hybrid storage framework
and the expression optimisation mechanism.Comment: extended and revised version of an earlier conference paper
arXiv:1805.0338
A geometrical approach to super W-induced gravities in two dimensions
A geometrical study of supergravity defined on (1|1) complex superspace is
presented. This approach is based on the introduction of generalized
superprojective structures extending the notions of super Riemann geometry to a
kind of super W-Riemann surfaces. On these surfaces a connection is
constructed. The zero curvature condition leads to the super Ward identities of
the underlying supergravity. This is accomplished through the symplectic form
linked to the (super)symplectic manifold of all super gauge connections. The
BRST algebra is also derived from the knowledge of the super W-symmetries which
are the gauge transformations of the vector bundle canonically associated to
the generalized superprojective structures. We obtain the possible consistent
BRST (super)anomalies and their cocycles related by the descent equations.
Finally we apply our considerations to the case of supergravity.Comment: 29 pages, latex, no figures, to appear in Nucl. Phys.
Slices for biparabolics of index one
Let be an algebraic Lie subalgebra of a simple Lie algebra
with index \mathfrak a \leq \rank \mathfrak g. Let denote the algebra of invariant polynomial functions on
. An algebraic slice for is an affine subspace
with and a subspace
of dimension index such that restriction of function induces an
isomorphism of onto the algebra of regular
functions on . Slices have been obtained in a number of cases through
the construction of an adapted pair in which is
ad-semisimple, is a regular element of which is an
eigenvector for of eigenvalue minus one and is an stable complement
to (\ad \mathfrak a)\eta in . The classical case is for
semisimple. Yet rather recently many other cases have been
provided. For example if is of type and is a
"truncated biparabolic" or a centralizer. In some of these cases (particular
when the biparabolic is a Borel subalgebra) it was found that could be
taken to be the restriction of a regular nilpotent element in .
Moreover this calculation suggested how to construct slices outside type
when no adapted pair exists. This article makes a first step in taking these
ideas further. Specifically let be a truncated biparabolic of
index one (and then is of type ). In this case it is shown
that the second member of an adapted pair for is the
restriction of a particularly carefully chosen regular nilpotent element of
.Comment: 31 pages, 7 figure
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