2,245 research outputs found
Approximations from Anywhere and General Rough Sets
Not all approximations arise from information systems. The problem of fitting
approximations, subjected to some rules (and related data), to information
systems in a rough scheme of things is known as the \emph{inverse problem}. The
inverse problem is more general than the duality (or abstract representation)
problems and was introduced by the present author in her earlier papers. From
the practical perspective, a few (as opposed to one) theoretical frameworks may
be suitable for formulating the problem itself. \emph{Granular operator spaces}
have been recently introduced and investigated by the present author in her
recent work in the context of antichain based and dialectical semantics for
general rough sets. The nature of the inverse problem is examined from
number-theoretic and combinatorial perspectives in a higher order variant of
granular operator spaces and some necessary conditions are proved. The results
and the novel approach would be useful in a number of unsupervised and semi
supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings,
Springe
A walk in the noncommutative garden
This text is written for the volume of the school/conference "Noncommutative
Geometry 2005" held at IPM Tehran. It gives a survey of methods and results in
noncommutative geometry, based on a discussion of significant examples of
noncommutative spaces in geometry, number theory, and physics. The paper also
contains an outline (the ``Tehran program'') of ongoing joint work with Consani
on the noncommutative geometry of the adeles class space and its relation to
number theoretic questions.Comment: 106 pages, LaTeX, 23 figure
Flux moduli stabilisation, Supergravity algebras and no-go theorems
We perform a complete classification of the flux-induced 12d algebras
compatible with the set of N=1 type II orientifold models that are T-duality
invariant, and allowed by the symmetries of the T^6/(Z_2 x Z_2) isotropic
orbifold. The classification is performed in a type IIB frame, where only H_3
and Q fluxes are present. We then study no-go theorems, formulated in a type
IIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By deriving
a dictionary between the sources of potential energy for the three moduli (S, T
and U) in types IIA and IIB, we are able to combine algebra results and no-go
theorems. The outcome is a systematic procedure for identifying
phenomenologically viable models where Mkw/dS vacua may exist. We present a
complete table of the allowed algebras and the viability of their resulting
scalar potential, and we point at the models which stand any chance of
producing a fully stable vacuum.Comment: Version published in JHE
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