Operator ordering and Classical soliton path in Two-dimensional N=2 supersymmetry with Kahler potential

We investigate a 2-dimensional N=2 supersymmetric model which consists of n chiral superfields with Kahler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super Poincare algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of soliton is a straight line in the complex plane of superpotential W and triangular mass inequality holds. And a half of supersymmetry is broken by the presence of soliton.Comment: 13 pages, typos correcte

The horizon problem for prevalent surfaces

We investigate the box dimensions of the horizon of a fractal surface defined by a function $f \in C[0,1]^2$. In particular we show that a prevalent surface satisfies the `horizon property', namely that the box dimension of the horizon is one less than that of the surface. Since a prevalent surface has box dimension 3, this does not give us any information about the horizon of surfaces of dimension strictly less than 3. To examine this situation we introduce spaces of functions with surfaces of upper box dimension at most \alpha, for \alpha $\in$ [2,3). In this setting the behaviour of the horizon is more subtle. We construct a prevalent subset of these spaces where the lower box dimension of the horizon lies between the dimension of the surface minus one and 2. We show that in the sense of prevalence these bounds are as tight as possible if the spaces are defined purely in terms of dimension. However, if we work in Lipschitz spaces, the horizon property does indeed hold for prevalent functions. Along the way, we obtain a range of properties of box dimensions of sums of functions

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-

On the use of non-canonical quantum statistics

We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more understanding on the standard Boltzmann-Gibbs statistics and on the recently developed Tsallis statistics. We conclude on a discussion of the role of entropy and the maximum entropy principle in thermodynamics.Comment: 29 pages, uses iopart.cls, major revisions of text for better readability, added a discussion about essentially microcanonical ensemble

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Density of states of a two-dimensional electron gas in a non-quantizing magnetic field

We study local density of electron states of a two-dimentional conductor with a smooth disorder potential in a non-quantizing magnetic field, which does not cause the standart de Haas-van Alphen oscillations. It is found, that despite the influence of such ``classical'' magnetic field on the average electron density of states (DOS) is negligibly small, it does produce a significant effect on the DOS correlations. The corresponding correlation function exhibits oscillations with the characteristic period of cyclotron quantum $\hbar\omega_c$.Comment: 7 pages, including 3 figure

Fluorescence molecular tomography: Principles and potential for pharmaceutical research

Fluorescence microscopic imaging is widely used in biomedical research to study molecular and cellular processes in cell culture or tissue samples. This is motivated by the high inherent sensitivity of fluorescence techniques, the spatial resolution that compares favorably with cellular dimensions, the stability of the fluorescent labels used and the sophisticated labeling strategies that have been developed for selectively labeling target molecules. More recently, two and three-dimensional optical imaging methods have also been applied to monitor biological processes in intact biological organisms such as animals or even humans. These whole body optical imaging approaches have to cope with the fact that biological tissue is a highly scattering and absorbing medium. As a consequence, light propagation in tissue is well described by a diffusion approximation and accurate reconstruction of spatial information is demanding. While in vivo optical imaging is a highly sensitive method, the signal is strongly surface weighted, i.e., the signal detected from the same light source will become weaker the deeper it is embedded in tissue, and strongly depends on the optical properties of the surrounding tissue. Derivation of quantitative information, therefore, requires tomographic techniques such as fluorescence molecular tomography (FMT), which maps the three-dimensional distribution of a fluorescent probe or protein concentration. The combination of FMT with a structural imaging method such as X-ray computed tomography (CT) or Magnetic Resonance Imaging (MRI) will allow mapping molecular information on a high definition anatomical reference and enable the use of prior information on tissue’s optical properties to enhance both resolution and sensitivity. Today many of the fluorescent assays originally developed for studies in cellular systems have been successfully translated for experimental studies in animals. The opportunity of monitoring molecular processes non-invasively in the intact organism is highly attractive from a diagnostic point of view but even more so for the drug developer, who can use the techniques for proof-of-mechanism and proof-of-efficacy studies. This review shall elucidate the current status and potential of fluorescence tomography including recent advances in multimodality imaging approaches for preclinical and clinical drug development

Pseudospectral Model Predictive Control under Partially Learned Dynamics

Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of model knowledge can be overcome with machine learning techniques, utilizing measurements to build a dynamical model from the data. This paper aims to take the middle ground between these two approaches by introducing a semi-parametric representation of the underlying system dynamics. Our goal is to leverage the considerable information contained in a traditional physics based model and combine it with a data-driven, non-parametric regression technique known as a Gaussian Process. Integrating this semi-parametric model with model predictive pseudospectral control, we demonstrate this technique on both a cart pole and quadrotor simulation with unmodeled damping and parametric error. In order to manage parametric uncertainty, we introduce an algorithm that utilizes Sparse Spectrum Gaussian Processes (SSGP) for online learning after each rollout. We implement this online learning technique on a cart pole and quadrator, then demonstrate the use of online learning and obstacle avoidance for the dubin vehicle dynamics.Comment: Accepted but withdrawn from AIAA Scitech 201