74 research outputs found
Inflationary Magnetogenesis and Anomaly Cancellation in Electrodynamics
Primordial magnetic field generated in the inflationary era can act as a
viable source for present day intergalactic magnetic field of significant
strength. We present a fundamental origin for such primordial generation of
magnetic field, namely through anomaly cancellation of gauge field in
quantum electrodynamics. Addition of this term explicitly breaks conformal
invariance of the theory necessary to generate magnetic field of sufficient
strength. We have analysed at length the power spectrum of the magnetic field
thus generated. We have also found that magnetic power spectrum has significant
scale-dependance giving rise to a non-trivial magnetic spectral index, a key
feature of this model. Interestingly, there exists a large parameter space
where magnetic field of significant strength can be produced.Comment: v2, Revised version, 25 pages, 4 figures and 1 tabl
Higgs inflation from new K\"ahler potential
We introduce a new class of models of Higgs inflation using the
superconformal approach to supergravity by modifying the Khler
geometry. Using such a mechanism, we construct a phenomenological functional
form of a new Khler potential. From this we construct various types
of models which are characterized by a superconformal symmetry breaking
parameter , and depending on the numerical values of we classify
all of the proposed models into three categories. Models with minimal coupling
are identified by branch which are made up of shift
symmetry preserving flat directions. We also propose various other models by
introducing a non-minimal coupling of the inflaton field to gravity described
by branch. We employ all these proposed models to study
the inflationary paradigm by estimating the major cosmological observables and
confront them with recent observational data from WMAP9 along with other
complementary data sets, as well as independently with PLANCK. We also mention
an allowed range of non-minimal couplings and the {\it Yukawa} type of
couplings appearing in the proposed models used for cosmological parameter
estimation.Comment: 13 pages, 6 figures, version to appear in Nuclear Physics
A Generalization of the {\L}o\'s-Tarski Preservation Theorem over Classes of Finite Structures
We investigate a generalization of the {\L}o\'s-Tarski preservation theorem
via the semantic notion of \emph{preservation under substructures modulo
-sized cores}. It was shown earlier that over arbitrary structures, this
semantic notion for first-order logic corresponds to definability by
sentences. In this paper, we identify two properties of
classes of finite structures that ensure the above correspondence. The first is
based on well-quasi-ordering under the embedding relation. The second is a
logic-based combinatorial property that strictly generalizes the first. We show
that starting with classes satisfying any of these properties, the classes
obtained by applying operations like disjoint union, cartesian and tensor
products, or by forming words and trees over the classes, inherit the same
property. As a fallout, we obtain interesting classes of structures over which
an effective version of the {\L}o\'s-Tarski theorem holds.Comment: 28 pages, 1 figur
Balancing Scalability and Uniformity in SAT Witness Generator
Constrained-random simulation is the predominant approach used in the
industry for functional verification of complex digital designs. The
effectiveness of this approach depends on two key factors: the quality of
constraints used to generate test vectors, and the randomness of solutions
generated from a given set of constraints. In this paper, we focus on the
second problem, and present an algorithm that significantly improves the
state-of-the-art of (almost-)uniform generation of solutions of large Boolean
constraints. Our algorithm provides strong theoretical guarantees on the
uniformity of generated solutions and scales to problems involving hundreds of
thousands of variables.Comment: This is a full version of DAC 2014 pape
On synthesizing Skolem functions for first order logic formulae
Skolem functions play a central role in logic, from eliminating quantifiers
in first order logic formulas to providing functional implementations of
relational specifications. While classical results in logic are only interested
in their existence, the question of how to effectively compute them is also
interesting, important and useful for several applications. In the restricted
case of Boolean propositional logic formula, this problem of synthesizing
Boolean Skolem functions has been addressed in depth, with various recent work
focussing on both theoretical and practical aspects of the problem. However,
there are few existing results for the general case, and the focus has been on
heuristical algorithms.
In this article, we undertake an investigation into the computational
hardness of the problem of synthesizing Skolem functions for first order logic
formula. We show that even under reasonable assumptions on the signature of the
formula, it is impossible to compute or synthesize Skolem functions. Then we
determine conditions on theories of first order logic which would render the
problem computable. Finally, we show that several natural theories satisfy
these conditions and hence do admit effective synthesis of Skolem functions
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