722 research outputs found
A transition in the spectrum of the topological sector of theory at strong coupling
We investigate the strong coupling region of the topological sector of the
two-dimensional theory. Using discrete light cone quantization (DLCQ),
we extract the masses of the lowest few excitations and observe level
crossings. To understand this phenomena, we evaluate the expectation value of
the integral of the normal ordered operator and we extract the number
density of constituents in these states. A coherent state variational
calculation confirms that the number density for low-lying states above the
transition coupling is dominantly that of a kink-antikink-kink state. The
Fourier transform of the form factor of the lowest excitation is extracted
which reveals a structure close to a kink-antikink-kink profile. Thus, we
demonstrate that the structure of the lowest excitations becomes that of a
kink-antikink-kink configuration at moderately strong coupling. We extract the
critical coupling for the transition of the lowest state from that of a kink to
a kink-antikink-kink. We interpret the transition as evidence for the onset of
kink condensation which is believed to be the physical mechanism for the
symmetry restoring phase transition in two-dimensional theory.Comment: revtex4, 14 figure
The numerical study of the solution of the model
We present a numerical study of the nonlinear system of equations
of motion. The solution is obtained iteratively, starting from a precise
point-sequence of the appropriate Banach space, for small values of the
coupling constant. The numerical results are in perfect agreement with the main
theoretical results established in a series of previous publications.Comment: arxiv version is already officia
Trees, forests and jungles: a botanical garden for cluster expansions
Combinatoric formulas for cluster expansions have been improved many times
over the years. Here we develop some new combinatoric proofs and extensions of
the tree formulas of Brydges and Kennedy, and test them on a series of
pedagogical examples.Comment: 37 pages, Ecole Polytechnique A-325.099
A rigorous analysis using optimal transport theory for a two-reflector design problem with a point source
We consider the following geometric optics problem: Construct a system of two
reflectors which transforms a spherical wavefront generated by a point source
into a beam of parallel rays. This beam has a prescribed intensity
distribution. We give a rigorous analysis of this problem. The reflectors we
construct are (parts of) the boundaries of convex sets. We prove existence of
solutions for a large class of input data and give a uniqueness result. To the
author's knowledge, this is the first time that a rigorous mathematical
analysis of this problem is given. The approach is based on optimal
transportation theory. It yields a practical algorithm for finding the
reflectors. Namely, the problem is equivalent to a constrained linear
optimization problem.Comment: 5 Figures - pdf files attached to submission, but not shown in
manuscrip
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Point and interval estimation in two-stage adaptive designs with time to event data and biomarker-driven subpopulation selection
In personalized medicine, it is often desired to determine if all patients or only a subset of them benefit from a treatment. We consider estimation in two‐stage adaptive designs that in stage 1 recruit patients from the full population. In stage 2, patient recruitment is restricted to the part of the population, which, based on stage 1 data, benefits from the experimental treatment. Existing estimators, which adjust for using stage 1 data for selecting the part of the population from which stage 2 patients are recruited, as well as for the confirmatory analysis after stage 2, do not consider time to event patient outcomes. In this work, for time to event data, we have derived a new asymptotically unbiased estimator for the log hazard ratio and a new interval estimator with good coverage probabilities and probabilities that the upper bounds are below the true values. The estimators are appropriate for several selection rules that are based on a single or multiple biomarkers, which can be categorical or continuous
The embedding structure and the shift operator of the U(1) lattice current algebra
The structure of block-spin embeddings of the U(1) lattice current algebra is
described. For an odd number of lattice sites, the inner realizations of the
shift automorphism areclassified. We present a particular inner shift operator
which admits a factorization involving quantum dilogarithms analogous to the
results of Faddeev and Volkov.Comment: 14 pages, Plain TeX; typos and a terminological mishap corrected;
version to appear in Lett.Math.Phy
A Novel Approach to Multimedia Ontology Engineering for Automated Reasoning over Audiovisual LOD Datasets
Multimedia reasoning, which is suitable for, among others, multimedia content
analysis and high-level video scene interpretation, relies on the formal and
comprehensive conceptualization of the represented knowledge domain. However,
most multimedia ontologies are not exhaustive in terms of role definitions, and
do not incorporate complex role inclusions and role interdependencies. In fact,
most multimedia ontologies do not have a role box at all, and implement only a
basic subset of the available logical constructors. Consequently, their
application in multimedia reasoning is limited. To address the above issues,
VidOnt, the very first multimedia ontology with SROIQ(D) expressivity and a
DL-safe ruleset has been introduced for next-generation multimedia reasoning.
In contrast to the common practice, the formal grounding has been set in one of
the most expressive description logics, and the ontology validated with
industry-leading reasoners, namely HermiT and FaCT++. This paper also presents
best practices for developing multimedia ontologies, based on my ontology
engineering approach
Fock representations from U(1) holonomy algebras
We revisit the quantization of U(1) holonomy algebras using the abelian C*
algebra based techniques which form the mathematical underpinnings of current
efforts to construct loop quantum gravity. In particular, we clarify the role
of ``smeared loops'' and of Poincare invariance in the construction of Fock
representations of these algebras. This enables us to critically re-examine
early pioneering efforts to construct Fock space representations of linearised
gravity and free Maxwell theory from holonomy algebras through an application
of the (then current) techniques of loop quantum gravity.Comment: Latex file, 30 pages, to appear in Phys Rev
On the support of the Ashtekar-Lewandowski measure
We show that the Ashtekar-Isham extension of the classical configuration
space of Yang-Mills theories (i.e. the moduli space of connections) is
(topologically and measure-theoretically) the projective limit of a family of
finite dimensional spaces associated with arbitrary finite lattices. These
results are then used to prove that the classical configuration space is
contained in a zero measure subset of this extension with respect to the
diffeomorphism invariant Ashtekar-Lewandowski measure.
Much as in scalar field theory, this implies that states in the quantum
theory associated with this measure can be realized as functions on the
``extended" configuration space.Comment: 22 pages, Tex, Preprint CGPG-94/3-
Quantum Gowdy Model: Schrodinger Representation with Unitary Dynamics
The linearly polarized Gowdy model is paradigmatic for studying
technical and conceptual issues in the quest for a quantum theory of gravity
since, after a suitable and almost complete gauge fixing, it becomes an exactly
soluble midisuperspace model. Recently, a new quantization of the model,
possessing desired features such as a unitary implementation of the gauge group
and of the time evolution, has been put forward and proven to be essentially
unique. An appropriate setting for making contact with other approaches to
canonical quantum gravity is provided by the Schr\"odinger representation,
where states are functionals on the configuration space of the theory. Here we
construct this functional description, analyze the time evolution in this
context and show that it is also unitary when restricted to physical states,
i.e. states which are solutions to the remaining constraint of the theory.Comment: 21 pages, version accepted for publication in Physical Review
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