920 research outputs found
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Neurons and symbols: a manifesto
We discuss the purpose of neural-symbolic integration including its principles, mechanisms and applications. We outline a cognitive computational model for neural-symbolic integration, position the model in the broader context of multi-agent systems, machine learning and automated reasoning, and list some of the challenges for the area of
neural-symbolic computation to achieve the promise of effective integration of robust learning and expressive reasoning under uncertainty
Dark Radiation in Anisotropic LARGE Volume Compactifications
Dark radiation is a compelling extension to CDM: current
experimental results hint at , which is
increased to if the recent BICEP2 results are
included. In recent years dark radiation has been considered in the context of
string theory models such as the LARGE Volume Scenario of type IIB string
theory, forging a link between present-day cosmological observations and models
of physics at the Planck scale. In this paper I consider an extension of the
LARGE Volume Scenario in which the bulk volume is stabilised by two moduli
instead of one. Consequently, the lightest modulus no longer corresponds to the
compactification volume but instead to a transverse direction in the bulk
geometry. I focus on scenarios in which sequestering of soft masses is achieved
by localising the Standard Model on D3 branes at a singularity. The fraction of
dark radiation produced in such models vastly exceeds experimental bounds,
ruling out the sequestered LARGE Volume Scenario with two bulk moduli as a
model of the early Universe.Comment: 12 pages, no figures; v3 - expanded discussions, clarified
terminology, corrected error in equation (3.11); version to be published in
JHE
Codensity Lifting of Monads and its Dual
We introduce a method to lift monads on the base category of a fibration to
its total category. This method, which we call codensity lifting, is applicable
to various fibrations which were not supported by its precursor, categorical
TT-lifting. After introducing the codensity lifting, we illustrate some
examples of codensity liftings of monads along the fibrations from the category
of preorders, topological spaces and extended pseudometric spaces to the
category of sets, and also the fibration from the category of binary relations
between measurable spaces. We also introduce the dual method called density
lifting of comonads. We next study the liftings of algebraic operations to the
codensity liftings of monads. We also give a characterisation of the class of
liftings of monads along posetal fibrations with fibred small meets as a limit
of a certain large diagram.Comment: Extended version of the paper presented at CALCO 2015, accepted for
publication in LMC
Reduction and reconstruction of stochastic differential equations via symmetries
An algorithmic method to exploit a general class of infinitesimal symmetries
for reducing stochastic differential equations is presented and a natural
definition of reconstruction, inspired by the classical reconstruction by
quadratures, is proposed. As a side result the well-known solution formula for
linear one-dimensional stochastic differential equations is obtained within
this symmetry approach. The complete procedure is applied to several examples
with both theoretical and applied relevance
Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states
We study relations between --KMS states on Cuntz--Krieger algebras
and the dual of the Perron--Frobenius operator .
Generalising the well--studied purely hyperbolic situation, we obtain under
mild conditions that for an expansive dynamical system there is a one--one
correspondence between --KMS states and eigenmeasures of
for the eigenvalue 1. We then consider
representations of Cuntz--Krieger algebras which are induced by Markov fibred
systems, and show that if the associated incidence matrix is irreducible then
these are --isomorphic to the given Cuntz--Krieger algebra. Finally, we
apply these general results to study multifractal decompositions of limit sets
of essentially free Kleinian groups which may have parabolic elements. We
show that for the Cuntz--Krieger algebra arising from there exists an
analytic family of KMS states induced by the Lyapunov spectrum of the analogue
of the Bowen--Series map associated with . Furthermore, we obtain a formula
for the Hausdorff dimensions of the restrictions of these KMS states to the set
of continuous functions on the limit set of . If has no parabolic
elements, then this formula can be interpreted as the singularity spectrum of
the measure of maximal entropy associated with .Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact
LARGE Volume String Compactifications at Finite Temperature
We present a detailed study of the finite-temperature behaviour of the LARGE
Volume type IIB flux compactifications. We show that certain moduli can
thermalise at high temperatures. Despite that, their contribution to the
finite-temperature effective potential is always negligible and the latter has
a runaway behaviour. We compute the maximal temperature , above which
the internal space decompactifies, as well as the temperature , that is
reached after the decay of the heaviest moduli. The natural constraint
implies a lower bound on the allowed values of the internal
volume . We find that this restriction rules out a significant
range of values corresponding to smaller volumes of the order , which lead to standard GUT theories. Instead, the bound favours
values of the order , which lead to TeV scale
SUSY desirable for solving the hierarchy problem. Moreover, our result favours
low-energy inflationary scenarios with density perturbations generated by a
field, which is not the inflaton. In such a scenario, one could achieve both
inflation and TeV-scale SUSY, although gravity waves would not be observable.
Finally, we pose a two-fold challenge for the solution of the cosmological
moduli problem. First, we show that the heavy moduli decay before they can
begin to dominate the energy density of the Universe. Hence they are not able
to dilute any unwanted relics. And second, we argue that, in order to obtain
thermal inflation in the closed string moduli sector, one needs to go beyond
the present EFT description.Comment: 54 pages + appendix, 5 figures; v2: minor corrections, references and
footnotes added, version published on JCA
Proton Decay, Yukawa Couplings and Underlying Gauge Symmetry in String Theory
In string theory, massless particles often originate from a symmetry breaking
of a large gauge symmetry G to its subgroup H. The absence of dimension-4
proton decay in supersymmetric theories suggests that (\bar{D},L) are different
from \bar{H}(\bar{\bf 5}) in their origins. In this article, we consider a
possibility that they come from different irreducible components in
. Requiring that all the Yukawa coupling constants
of quarks and leptons be generated from the super Yang--Mills interactions of
G, we found in the context of Georgi--Glashow H=SU(5) unification that the
minimal choice of G is E_7 and E_8 is the only alternative. This idea is
systematically implemented in Heterotic String, M theory and F theory,
confirming the absence of dimension 4 proton decay operators. Not only H=SU(5)
but also G constrain operators of effective field theories, providing
non-trivial information.Comment: 73 page
G_4 flux, chiral matter and singularity resolution in F-theory compactifications
We construct a set of chirality inducing G_4-fluxes in global F-theory
compactifications on Calabi-Yau four-folds. Special emphasis is put on models
with gauge group SU(5) x U(1)_X relevant in the context of F-theory GUT model
building, which are described in terms of a U(1)-restricted Tate model. In this
type of constructions, the G_4-flux arises in a manner completely analogous to
the U(1)_X gauge potential. We describe in detail the resolution by blow-up of
the various singularities responsible for the U(1)_X factor and the standard
SU(5) gauge group and match the result with techniques applied in the context
of toric geometry. This provides an explicit identification of the structure of
the resolved fibre over the matter curves and over the enhancement points
relevant for Yukawa couplings. The U(1)_X flux induces a chiral matter
spectrum. We compute the chiral index both of SU(5) charged matter and of SU(5)
singlets charged only under U(1)_X localised on curves which are not contained
in the SU(5) locus. We furthermore discuss global consistency conditions such
as D3-tadpole cancellation, D-term supersymmetry and Freed-Witten quantisation.
The U(1)_X gauge flux is a global extension of a class of split spectral cover
bundles. It constitutes an essential ingredient in the construction of globally
defined F-theory compactifications with chiral matter. We exemplify this in a
three-generation SU(5) x U(1)_X model whose flux satisfies all of the above
global consistency conditions. We also extend our results to chiral fluxes in
models without U(1) restriction.Comment: 53 pages, 2 figures; v2: details on Freed-Witten quantisation
condition included, typos correcte
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