2,380 research outputs found
A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
Recent perturbative studies show that in 4d non-commutative spaces, the
trivial (classically stable) vacuum of gauge theories becomes unstable at the
quantum level, unless one introduces sufficiently many fermionic degrees of
freedom. This is due to a negative IR-singular term in the one-loop effective
potential, which appears as a result of the UV/IR mixing. We study such a
system non-perturbatively in the case of pure U(1) gauge theory in four
dimensions, where two directions are non-commutative. Monte Carlo simulations
are performed after mapping the regularized theory onto a U(N) lattice gauge
theory in d=2. At intermediate coupling strength, we find a phase in which open
Wilson lines acquire non-zero vacuum expectation values, which implies the
spontaneous breakdown of translational invariance. In this phase, various
physical quantities obey clear scaling behaviors in the continuum limit with a
fixed non-commutativity parameter , which provides evidence for a
possible continuum theory. The extent of the dynamically generated space in the
non-commutative directions becomes finite in the above limit, and its
dependence on is evaluated explicitly. We also study the dispersion
relation. In the weak coupling symmetric phase, it involves a negative
IR-singular term, which is responsible for the observed phase transition. In
the broken phase, it reveals the existence of the Nambu-Goldstone mode
associated with the spontaneous symmetry breaking.Comment: 29 pages, 23 figures, references adde
Permutations of Massive Vacua
We discuss the permutation group G of massive vacua of four-dimensional gauge
theories with N=1 supersymmetry that arises upon tracing loops in the space of
couplings. We concentrate on superconformal N=4 and N=2 theories with N=1
supersymmetry preserving mass deformations. The permutation group G of massive
vacua is the Galois group of characteristic polynomials for the vacuum
expectation values of chiral observables. We provide various techniques to
effectively compute characteristic polynomials in given theories, and we deduce
the existence of varying symmetry breaking patterns of the duality group
depending on the gauge algebra and matter content of the theory. Our examples
give rise to interesting field extensions of spaces of modular forms.Comment: 44 pages, 1 figur
Another look at the Regression Discontinuity Design
The attractiveness of the Regression Discontinuity Design (RDD) rests on its similarity to an experimental design. On the other hand, it is of limited applicability since rarely assignment to the treatment is based on known pre-program measures. Besides, it only allows to identify the mean impact on a very specific sub-population. Here we show that the RDD generalizes to the instances in which eligibility is established on a pre-program measure and eligible individuals are allowed to self-select into the program. This set-up is also convenient to test the validity of conventional non-experimental estimators of the mean impact.program evaluation, second control group, specification tests
Crisp and fuzzy motif and arrangement symmetries in composite geometric figures
AbstractThe notions of motif and arrangement symmetries within composite geometric figures are defined. The relationships between these types of symmetry and the symmetry of the whole figure are clarified by making use of the crystallographic concepts of site symmetry and direction symmetry. From this, it has been deduced that a figure with arbitrary symmetry can be assembled from motifs of likewise arbitrary symmetries. If a motif with symmetry GM is placed on a site having the site symmetry GS ⊆ GM, its contribution to the figure symmetry G is only a subgroup G*MO of its direction symmetry GMO where GS = G*MO ⊆ GMO ⊆ GM. Supernumerary symmetry elements of the motif give rise to intermediate or latent symmetries of the figure. A consequent decomposition of a geometric figure into its constituent points reveals that a large part of the O(n) symmetry of every single point is lost when assembling these points to build up the figure. All “lost” symmetries can, however, be detected as intermediate symmetries of this figure. They can be displayed as fuzzy symmetry landscapes and symmetry profiles for a given figure showing all crisp and intermediate symmetries of interest
Another look at the regression discontinuity design
The attractiveness of the Regression Discontinuity Design (RDD) in its sharp formulation rests on close similarities with a formal experimental design. On the other hand, it is of limited applicability since rarely individuals are assigned to the treatment group on the basis of a pre-program measure observable to the analyst. Besides, it only allows to identify the mean impact of the program for a very specific sub-population of individuals. In this paper we show that the sharp RDD straightforwardly generalizes to the instances in which the eligibility for the program is established with respect to an observable pre-program measure with eligible individuals self-selecting into the treatment group according to an unknown process. This set-up also turns out very convenient to define a specification test on conventional non-experimental estimators of the program effect needed to identify the mean impact away from the threshold for eligibility. Data requirements are made explicit.
Measures induced by units
The half-open real unit interval (0,1] is closed under the ordinary
multiplication and its residuum. The corresponding infinite-valued
propositional logic has as its equivalent algebraic semantics the equational
class of cancellative hoops. Fixing a strong unit in a cancellative hoop
-equivalently, in the enveloping lattice-ordered abelian group- amounts to
fixing a gauge scale for falsity. In this paper we show that any strong unit in
a finitely presented cancellative hoop H induces naturally (i.e., in a
representation-independent way) an automorphism-invariant positive normalized
linear functional on H. Since H is representable as a uniformly dense set of
continuous functions on its maximal spectrum, such functionals -in this context
usually called states- amount to automorphism-invariant finite Borel measures
on the spectrum. Different choices for the unit may be algebraically unrelated
(e.g., they may lie in different orbits under the automorphism group of H), but
our second main result shows that the corresponding measures are always
absolutely continuous w.r.t. each other, and provides an explicit expression
for the reciprocal density.Comment: 24 pages, 1 figure. Revised version according to the referee's
suggestions. Examples added, proof of Lemma 2.6 simplified, Section 7
expanded. To appear in the Journal of Symbolic Logi
Recognition of partially occluded threat objects using the annealed Hopefield network
Recognition of partially occluded objects has been an important issue to airport security because occlusion causes significant problems in identifying and locating objects during baggage inspection. The neural network approach is suitable for the problems in the sense that the inherent parallelism of neural networks pursues many hypotheses in parallel resulting in high computation rates. Moreover, they provide a greater degree of robustness or fault tolerance than conventional computers. The annealed Hopfield network which is derived from the mean field annealing (MFA) has been developed to find global solutions of a nonlinear system. In the study, it has been proven that the system temperature of MFA is equivalent to the gain of the sigmoid function of a Hopfield network. In our early work, we developed the hybrid Hopfield network (HHN) for fast and reliable matching. However, HHN doesn't guarantee global solutions and yields false matching under heavily occluded conditions because HHN is dependent on initial states by its nature. In this paper, we present the annealed Hopfield network (AHN) for occluded object matching problems. In AHN, the mean field theory is applied to the hybird Hopfield network in order to improve computational complexity of the annealed Hopfield network and provide reliable matching under heavily occluded conditions. AHN is slower than HHN. However, AHN provides near global solutions without initial restrictions and provides less false matching than HHN. In conclusion, a new algorithm based upon a neural network approach was developed to demonstrate the feasibility of the automated inspection of threat objects from x-ray images. The robustness of the algorithm is proved by identifying occluded target objects with large tolerance of their features
- …