5,086 research outputs found
Increasing symmetry breaking by preserving target symmetries and eliminating eliminated symmetries in constraint satisfaction.
在約束滿足問題中,破壞指數量級數量的所有對稱通常過於昂貴。在實踐中,我們通常只有效地破壞對稱的一個子集。我們稱之為目標對稱。在靜態對稱破壞中,我們的目標是發佈一套約束去破壞這些目標對稱,以達到減少解集以及搜索空間的效果。一個問題中的所有對稱之間是互相交織的。一個旨在特定對稱的破壞對稱約束几乎總會產生副作用,而不僅僅破壞了預期的對稱。破壞相同目標對稱的不同約束可以有不同的副作用。傳統智慧告訴我們應該選擇一個破壞更多對稱從而有更多副作用的破壞對稱約束。雖然這樣的說法在許多方面上都是有效的,我們應該更加注意副作用發生的地方。給與一個約束滿足問題,一個對稱被一個約束保留當且僅當該對稱仍然是新的約束滿足問題的對稱。這個新的約束滿足問題是有原問題加上該約束組成的。我們給出定律和例子,以表明發佈儘量保留目標對稱以及限制它的副作用發生在非目標對稱上的破壞約束是有利的。這些好處來自于被破壞的對稱數目以及一個對稱被破壞(或消除)的程度,并導致一個較小的解集和搜索空間。但是,對稱不一定會被保留。我們顯示,旨在一個已經被消除的目標對稱的破壞對稱約束仍然可以被發佈。我們建議根據問題的約束以及其他破壞對稱約束來選擇破壞對稱約束,以繼續消除更多的對稱。我們進行了廣泛的實驗來確認我們的建議的可行性與效率。Breaking the exponential number of all symmetries of a constraint satisfaction problem is often too costly. In practice, we often aim at breaking a subset of the symmetries efficiently, which we call target symmetries. In static sym-metry breaking, the goal is to post a set of constraints to break these target symmetries in order to reduce the solution set and thus also the search space. Symmetries of a problem are all intertwined. A symmetry breaking constraint intended for a particular symmetry almost always breaks more than just the intended symmetry as a side-effect. Different constraints for breaking the same target symmetry can have different side-effects. Conventional wisdom suggests that we should select a symmetry breaking constraint that has more side-effects by breaking more symmetries. While this wisdom is valid in many ways, we should be careful where the side-effects take place.A symmetry σ of a CSP P =(V, D, C) is preserved by a set of symmetry breaking constraints C{U+02E2}{U+1D47} i σ is a symmetry of P¹ =(V, D, CU C{U+02E2}{U+1D47}). We give theorems and examples to demonstrate that it is beneficial to post symmetry breaking constraints that preserve the target symmetries and restrict the side-effects to only non-target symmetries as much as possible. The benefits are in terms of the number of symmetries broken and the extent to which a symmetry is broken (or eliminated), resulting in a smaller solution set and search space. However, symmetry preservation may not always hold. We illustrate that symmetry breaking constraints, which aim at a target symmetry that is already eliminated, can still be posted. To continue eliminating more symmetries, we suggest to select symmetry breaking constraints based on problem constraints and other symmetry breaking constraints. Extensive experiments are also conducted to confirm the feasibility and efficiency of our proposal empirically.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Li, Jingying.Thesis (M.Phil.)--Chinese University of Hong Kong, 2012.Includes bibliographical references (leaves 101-112).Abstracts also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Constraint Satisfaction Problems --- p.1Chapter 1.2 --- Motivation and Goals --- p.3Chapter 1.3 --- Outline of Thesis --- p.5Chapter 2 --- Background --- p.8Chapter 2.1 --- Constraint Satisfaction Problems --- p.8Chapter 2.1.1 --- Backtracking Search --- p.9Chapter 2.1.2 --- Consistency Techniques --- p.12Chapter 2.1.3 --- Local Consistencies with Backtracking Search --- p.15Chapter 2.2 --- Symmetry Breaking in CSPs --- p.16Chapter 2.2.1 --- Symmetry Classes --- p.18Chapter 2.2.2 --- Breaking Symmetries --- p.22Chapter 2.2.3 --- Variable and Value Symmetries --- p.23Chapter 2.2.4 --- Symmetry Breaking Constraints --- p.26Chapter 3 --- Effects of Symmetry Breaking Constraints --- p.29Chapter 3.1 --- Removing Symmetric Search Space --- p.29Chapter 3.1.1 --- Properties --- p.30Chapter 3.1.2 --- Canonical Variable Orderings --- p.31Chapter 3.1.3 --- Regenerating All Solutions --- p.33Chapter 3.1.4 --- Remaining Solution Set Sizes --- p.36Chapter 3.2 --- Constraint Interactions in Propagation --- p.43Chapter 4 --- Choices of Symmetry Breaking Constraints --- p.45Chapter 4.1 --- Side-Effects --- p.45Chapter 4.2 --- Symmetry Preservation --- p.50Chapter 4.2.1 --- De nition and Properties --- p.50Chapter 4.2.2 --- Solution Reduction --- p.54Chapter 4.2.3 --- Preservation Examples --- p.55Chapter 4.2.4 --- Preserving Order --- p.64Chapter 4.3 --- Eliminating Eliminated Symmetries --- p.65Chapter 4.3.1 --- Further Elimination --- p.65Chapter 4.3.2 --- Aggressive Elimination --- p.71Chapter 4.4 --- Interactions with Problem Constraints --- p.72Chapter 4.4.1 --- Further Simplification --- p.72Chapter 4.4.2 --- Increasing Constraint Propagation --- p.73Chapter 5 --- Experiments --- p.75Chapter 5.1 --- Symmetry Preservation --- p.75Chapter 5.1.1 --- Diagonal Latin Square Problem --- p.76Chapter 5.1.2 --- NN-Queen Problem --- p.77Chapter 5.1.3 --- Error Correcting Code - Lee Distance (ECCLD) --- p.78Chapter 5.2 --- Eliminating Eliminated Symmetries --- p.80Chapter 5.2.1 --- Equidistance Frequency Permutation Array Problem --- p.80Chapter 5.2.2 --- Cover Array Problem --- p.82Chapter 5.2.3 --- Sports League Scheduling Problem --- p.83Chapter 6 --- Related Work --- p.86Chapter 6.1 --- Symmetry Breaking Approaches --- p.86Chapter 6.2 --- Reducing Overhead and Increasing Propagation --- p.90Chapter 6.3 --- Selecting and Generating Choices --- p.91Chapter 6.3.1 --- Reducing Conflict with Search Heuristic --- p.92Chapter 6.3.2 --- Choosing the Subset of Symmetries --- p.93Chapter 6.4 --- Detecting Symmetries --- p.93Chapter 7 --- Conclusion and Remarks --- p.95Chapter 7.1 --- Conclusion --- p.95Chapter 7.2 --- Discussions --- p.97Chapter 7.3 --- Future Work --- p.99Bibliography --- p.10
The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition
The spectrum of the bosonic sector of the D=11 supermembrane with central
charges is shown to be discrete and with finite multiplicities, hence
containing a mass gap. The result extends to the exact theory our previous
proof of the similar property for the SU(N) regularised model and strongly
suggest discreteness of the spectrum for the complete Hamiltonian of the
supermembrane with central charges. This theory is a quantum equivalent to a
symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the
space-like sector is a Riemann surface of positive genus. In this context, it
is argued how the theory in 4D exhibits confinement in the N=1 supermembrane
with central charges phase and how the theory enters in the quark-gluon plasma
phase through the spontaneous breaking of the centre. This phase is interpreted
in terms of the compactified supermembrane without central charges.Comment: 33 pages, Latex. In this new version, several changes have been made
and various typos were correcte
Lattice supersymmetry, superfields and renormalization
We study Euclidean lattice formulations of non-gauge supersymmetric models
with up to four supercharges in various dimensions. We formulate the conditions
under which the interacting lattice theory can exactly preserve one or more
nilpotent anticommuting supersymmetries. We introduce a superfield formalism,
which allows the enumeration of all possible lattice supersymmetry invariants.
We use it to discuss the formulation of Q-exact lattice actions and their
renormalization in a general manner. In some examples, one exact supersymmetry
guarantees finiteness of the continuum limit of the lattice theory. As a
consequence, we show that the desired quantum continuum limit is obtained
without fine tuning for these models. Finally, we discuss the implications and
possible further applications of our results to the study of gauge and
non-gauge models.Comment: 44 pages, 1 figur
Classical skyrmions in SU(N)/SO(N) cosets
We construct the skyrmion solutions appearing in the coset spaces SU(N)/SO(N)
for N > 2 and compute their classical mass. For N = 3, the third homotopy group
pi_3(SU(3)/SO(3)) = Z_4 implies the existence of two distinct solutions: the
skyrmion of winding number two has spherical symmetry and is found to be the
lightest non-trivial field configuration; the skyrmion and antiskyrmion of
winding number plus and minus one are slightly heavier and of toroidal shape.
For N >= 4, there is only one skyrmion since the third homotopy group is Z_2.
It is found to have spherical symmetry and is significantly lighter than the N
= 3 solutions.Comment: 14 pages, 3 figures; v2: discussion improve
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
The New Flavor of Higgsed Gauge Mediation
Recent LHC bounds on squark masses combined with naturalness and flavor
considerations motivate non-trivial sfermion mass spectra in the supersymmetric
Standard Model. These can arise if supersymmetry breaking is communicated to
the visible sector via new extended gauge symmetries. Such extended symmetries
must be spontaneously broken, or confined, complicating the calculation of soft
masses. We develop a new formalism for calculating perturbative gauge-mediated
two-loop soft masses for gauge groups with arbitrary patterns of spontaneous
symmetry breaking, simplifying the framework of "Higgsed gauge mediation." The
resulting expressions can be applied to Abelian and non-Abelian gauge groups,
opening new avenues for supersymmetric model building. We present a number of
examples using our method, ranging from grand unified threshold corrections in
standard gauge mediation to soft masses in gauge extensions of the Higgs sector
that can raise the Higgs mass through non-decoupling D-terms. We also outline a
new mediation mechanism called "flavor mediation", where supersymmetry breaking
is communicated via a gauged subgroup of Standard Model flavor symmetries.
Flavor mediation can automatically generate suppressed masses for
third-generation squarks and implies a nearly exact U(2) symmetry in the first
two generations, yielding a "natural SUSY" spectrum without imposing ad hoc
global symmetries or giving preferential treatment to particular generations.Comment: 13 pages, 3 figures; v2: typos corrected, references adde
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