679 research outputs found
Breaking Symmetries
A well-known result by Palamidessi tells us that {\pi}mix (the {\pi}-calculus
with mixed choice) is more expressive than {\pi}sep (its subset with only
separate choice). The proof of this result argues with their different
expressive power concerning leader election in symmetric networks. Later on,
Gorla of- fered an arguably simpler proof that, instead of leader election in
symmetric networks, employed the reducibility of "incestual" processes (mixed
choices that include both enabled senders and receivers for the same channel)
when running two copies in parallel. In both proofs, the role of breaking (ini-
tial) symmetries is more or less apparent. In this paper, we shed more light on
this role by re-proving the above result-based on a proper formalization of
what it means to break symmetries-without referring to another layer of the
distinguishing problem domain of leader election.
Both Palamidessi and Gorla rephrased their results by stating that there is
no uniform and reason- able encoding from {\pi}mix into {\pi}sep . We indicate
how the respective proofs can be adapted and exhibit the consequences of
varying notions of uniformity and reasonableness. In each case, the ability to
break initial symmetries turns out to be essential
Breaking Symmetries in Graph Representation
There are many complex combinatorial problems
which involve searching for an undirected graph
satisfying a certain property. These problems are
often highly challenging because of the large number
of isomorphic representations of a possible solution.
In this paper we introduce novel, effective
and compact, symmetry breaking constraints for
undirected graph search. While incomplete, these
prove highly beneficial in pruning the search for a
graph. We illustrate the application of symmetry
breaking in graph representation to resolve several
open instances in extremal graph theory
Breaking symmetries
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.A well-known result by Palamidessi tells us that πmix (the π-calculus with mixed choice) is more expressive than πsep (its subset with only separate choice). The proof of this result analyses their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of ‘incestual’ processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (initial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result – based on a proper formalization of what it means to break symmetries – without referring to another problem domain like leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from πmix into πsep. We indicate how their proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential. Moreover, by abandoning the uniformity criterion, we show that there indeed is a reasonable encoding. We emphasize its underlying principle, which highlights the difference between breaking symmetries locally instead of globally
Resolving sets for breaking symmetries of graphs
This paper deals with the maximum value of the difference between the
determining number and the metric dimension of a graph as a function of its
order. Our technique requires to use locating-dominating sets, and perform an
independent study on other functions related to these sets. Thus, we obtain
lower and upper bounds on all these functions by means of very diverse tools.
Among them are some adequate constructions of graphs, a variant of a classical
result in graph domination and a polynomial time algorithm that produces both
distinguishing sets and determining sets. Further, we consider specific
families of graphs where the restrictions of these functions can be computed.
To this end, we utilize two well-known objects in graph theory: -dominating
sets and matchings.Comment: 24 pages, 12 figure
Lecture Notes on Topological Crystalline Insulators
We give an introduction to topological crystalline insulators, that is,
gapped ground states of quantum matter that are not adiabatically connected to
an atomic limit without breaking symmetries that include spatial
transformations, like mirror or rotational symmetries. To deduce the
topological properties, we use non-Abelian Wilson loops. We also discuss in
detail higher-order topological insulators with hinge and corner states, and in
particular present interacting bosonic models for the latter class of systems.Comment: Lectures given at the San Sebasti\'an Topological Matter School 2017,
published in "Topological Matter. Springer Series in Solid-State Sciences,
vol 190. Springer, Cham
On the origin of families of quarks and leptons - predictions for four families
The approach unifying all the internal degrees of freedom--proposed by one of
us--is offering a new way of understanding families of quarks and leptons: A
part of the starting Lagrange density in d(=1+13), which includes two kinds of
spin connection fields--the gauge fields of two types of Clifford algebra
objects--transforms the right handed quarks and leptons into the left handed
ones manifesting in d=1+3 the Yukawa couplings of the Standard model. We study
the influence of the way of breaking symmetries on the Yukawa couplings and
estimate properties of the fourth family--the quark masses and the mixing
matrix, investigating the possibility that the fourth family of quarks and
leptons appears at low enough energies to be observable with the new generation
of accelerators.Comment: 31 pages,revte
Goldstone Tensor Modes
In the context of brane solutions of supergravity, we discuss a general
method to introduce collective modes of any spin by exploiting a particular way
of breaking symmetries. The method is applied to the D3, M2 and M5 branes and
we derive explicit expressions for how the zero-modes enter the target space
fields, verify normalisability in the transverse directions and derive the
corresponding field equations on the brane. In particular, the method provides
a clear understanding of scalar, spinor, and rank r tensorial Goldstone modes,
chiral as well as non-chiral, and how they arise from the gravity,
Rarita-Schwinger, and rank r+1 Kalb-Ramond tensor gauge fields, respectively.
Some additional observations concerning the chiral tensor modes on the M5 brane
are discussed.Comment: 21 pp, plain tex. A sign corrected for agreement with convention
- …