25,999 research outputs found
On tree decomposability of Henneberg graphs
In this work we describe an algorithm that generates well constrained geometric constraint graphs which are solvable by the tree-decomposition constructive technique. The algorithm is based on Henneberg constructions and would be of help in transforming underconstrained problems into well constrained problems as well as in exploring alternative constructions over a given set of geometric elements.Postprint (published version
On the Minimal Model of Anyons
We present new geometric formulations for the fractional spin particle models
on the minimal phase spaces. New consistent couplings of the anyon to
background fields are constructed. The relationship between our approach and
previously developed anyon models is discussed.Comment: 17 pages, LaTex, no figure
Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings
The aim of this paper is to study the relationship between Hamiltonian
dynamics and constrained variational calculus. We describe both using the
notion of Lagrangian submanifolds of convenient symplectic manifolds and using
the so-called Tulczyjew's triples. The results are also extended to the case of
discrete dynamics and nonholonomic mechanics. Interesting applications to
geometrical integration of Hamiltonian systems are obtained.Comment: 33 page
Parallel Graph Partitioning for Complex Networks
Processing large complex networks like social networks or web graphs has
recently attracted considerable interest. In order to do this in parallel, we
need to partition them into pieces of about equal size. Unfortunately, previous
parallel graph partitioners originally developed for more regular mesh-like
networks do not work well for these networks. This paper addresses this problem
by parallelizing and adapting the label propagation technique originally
developed for graph clustering. By introducing size constraints, label
propagation becomes applicable for both the coarsening and the refinement phase
of multilevel graph partitioning. We obtain very high quality by applying a
highly parallel evolutionary algorithm to the coarsened graph. The resulting
system is both more scalable and achieves higher quality than state-of-the-art
systems like ParMetis or PT-Scotch. For large complex networks the performance
differences are very big. For example, our algorithm can partition a web graph
with 3.3 billion edges in less than sixteen seconds using 512 cores of a high
performance cluster while producing a high quality partition -- none of the
competing systems can handle this graph on our system.Comment: Review article. Parallelization of our previous approach
arXiv:1402.328
6D supergravity without tensor multiplets
We systematically investigate the finite set of possible gauge groups and
matter content for N = 1 supergravity theories in six dimensions with no tensor
multiplets, focusing on nonabelian gauge groups which are a product of SU(N)
factors. We identify a number of models which obey all known low-energy
consistency conditions, but which have no known string theory realization. Many
of these models contain novel matter representations, suggesting possible new
string theory constructions. Many of the most exotic matter structures arise in
models which precisely saturate the gravitational anomaly bound on the number
of hypermultiplets. Such models have a rigid symmetry structure, in the sense
that there are no moduli which leave the full gauge group unbroken.Comment: 31 pages, latex; v2, v3: minor corrections, references adde
Relative Entropy Relaxations for Signomial Optimization
Signomial programs (SPs) are optimization problems specified in terms of
signomials, which are weighted sums of exponentials composed with linear
functionals of a decision variable. SPs are non-convex optimization problems in
general, and families of NP-hard problems can be reduced to SPs. In this paper
we describe a hierarchy of convex relaxations to obtain successively tighter
lower bounds of the optimal value of SPs. This sequence of lower bounds is
computed by solving increasingly larger-sized relative entropy optimization
problems, which are convex programs specified in terms of linear and relative
entropy functions. Our approach relies crucially on the observation that the
relative entropy function -- by virtue of its joint convexity with respect to
both arguments -- provides a convex parametrization of certain sets of globally
nonnegative signomials with efficiently computable nonnegativity certificates
via the arithmetic-geometric-mean inequality. By appealing to representation
theorems from real algebraic geometry, we show that our sequences of lower
bounds converge to the global optima for broad classes of SPs. Finally, we also
demonstrate the effectiveness of our methods via numerical experiments
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