748 research outputs found
Higgs diphoton rate enhancement from supersymmetric physics beyond the MSSM
We show that supersymmetric "new physics" beyond the MSSM can naturally
accommodate a Higgs mass near 126 GeV and enhance the signal rate in the Higgs
to diphoton channel, while the signal rates in all the other Higgs decay
channels coincide with Standard Model expectations, except possibly the Higgs
to Z-photon channel. The "new physics" that corrects the relevant Higgs
couplings can be captured by two supersymmetric effective operators. We provide
a simple example of an underlying model in which these operators are
simultaneously generated. The scale of "new physics" that generates these
operators can be around 5 TeV or larger, and outside the reach of the LHC.Comment: 24 pages, 4 figure
Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases
Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought
of as two, rather different, methods of looking at systems of equations and, in
the case of Cylindrical Algebraic Decomposition, inequalities. However, even
for a mixed system of equalities and inequalities, it is possible to apply
Gr\"obner bases to the (conjoined) equalities before invoking CAD. We see that
this is, quite often but not always, a beneficial preconditioning of the CAD
problem.
It is also possible to precondition the (conjoined) inequalities with respect
to the equalities, and this can also be useful in many cases.Comment: To appear in Proc. CICM 2012, LNCS 736
05391 Abstracts Collection -- Algebraic and Numerical Algorithms and Computer-assisted Proofs
From 25.09.05 to 30.09.05, the Dagstuhl Seminar 05391 ``Algebraic and Numerical Algorithms and Computer-assisted Proofs\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper.
Links to extended abstracts or full papers are provided, if available
A Factorization Algorithm for G-Algebras and Applications
It has been recently discovered by Bell, Heinle and Levandovskyy that a large
class of algebras, including the ubiquitous -algebras, are finite
factorization domains (FFD for short).
Utilizing this result, we contribute an algorithm to find all distinct
factorizations of a given element , where is
any -algebra, with minor assumptions on the underlying field.
Moreover, the property of being an FFD, in combination with the factorization
algorithm, enables us to propose an analogous description of the factorized
Gr\"obner basis algorithm for -algebras. This algorithm is useful for
various applications, e.g. in analysis of solution spaces of systems of linear
partial functional equations with polynomial coefficients, coming from
. Additionally, it is possible to include inequality constraints
for ideals in the input
Fast Reduction of Bivariate Polynomials with Respect to Sufficiently Regular Gröbner Bases
International audienc
Constructing Mutually Unbiased Bases in Dimension Six
The density matrix of a qudit may be reconstructed with optimal efficiency if
the expectation values of a specific set of observables are known. In dimension
six, the required observables only exist if it is possible to identify six
mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard
matrix, we construct all others mutually unbiased to it, using algebraic
computations performed by a computer program. We repeat this calculation many
times, sampling all known complex Hadamard matrices, and we never find more
than two that are mutually unbiased. This result adds considerable support to
the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical
approximations and corrected the number of triples existing for non-affine
families (cf Table 3
05391 Executive Summary -- Numerical and Algebraic Algorithms and Computer-assisted Proofs
The common goal of self-validating methods and computer
algebra methods is to solve mathematical problems with complete rigor
and with the aid of computers. The seminar focused on several aspects
of such methods for computer-assisted proofs
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
Proof-Pattern Recognition and Lemma Discovery in ACL2
We present a novel technique for combining statistical machine learning for
proof-pattern recognition with symbolic methods for lemma discovery. The
resulting tool, ACL2(ml), gathers proof statistics and uses statistical
pattern-recognition to pre-processes data from libraries, and then suggests
auxiliary lemmas in new proofs by analogy with already seen examples. This
paper presents the implementation of ACL2(ml) alongside theoretical
descriptions of the proof-pattern recognition and lemma discovery methods
involved in it
Growth Histories in Bimetric Massive Gravity
We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity
for general homogeneous and isotropic backgrounds. In the de Sitter
approximation, we obtain decoupled sets of massless and massive scalar
gravitational fluctuations. Matter perturbations then evolve like in Einstein
gravity. We perturb the future de Sitter regime by the ratio of matter to dark
energy, producing quasi-de Sitter space. In this more general setting the
massive and massless fluctuations mix. We argue that in the quasi-de Sitter
regime, the growth of structure in bimetric gravity differs from that of
Einstein gravity.Comment: 28 pages + appendix, 11 figure
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