Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes

A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space \eufrak{h} and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over \eufrak{h}. The derivation operator is then used to give sufficient conditions for the existence of smooth Wigner densities for pairs of operators satisfying the canonical commutation relations. For \eufrak{h}=L^2(\mathbb{R}_+), the divergence operator is shown to coincide with the Hudson-Parthasarathy quantum stochastic integral for adapted integrable processes and with the non-causal quantum stochastic integrals defined by Lindsay and Belavkin for integrable processes.Comment: 28 pages, amsart styl

Quicksort with unreliable comparisons: a probabilistic analysis

We provide a probabilistic analysis of the output of Quicksort when comparisons can err.Comment: 29 pages, 3 figure

Performance Comparison of Hyperspectral Target Detection Algorithms in Altitude Varying Scenes

Many different hyperspectral target detection algorithms have been developed and tested under various assumptions, methods, and data sets. This work examines the spectral angle mapper (SAM), adaptive coherence estimator (ACE), and constrained energy maximization (CEM) algorithms. Algorithm performance is examined over multiple images, targets, and backgrounds. Methods to examine algorithm performance are plentiful and several different metrics are used here. Quantitative metrics are used to make direct comparisons between algorithms. Further analysis using visual performance metrics is made to examine interesting trends in the data. Results show an increase in detection algorithm performance as image altitude increases and spatial information decreases. Theories to explain this phenomenon are introduced

Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self electromagnetic force on an extended charged sphere of radius "a" are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, transition forces must be included during these transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solutions to the equation of motion without the transition forces. For the extended charged sphere, the transition forces can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, it is shown that renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.Comment: 13 pages, No figure

Self-forces on extended bodies in electrodynamics

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion. We place essentially no restrictions (other than boundedness) on the shape of the charge, and allow for inhomogeneity, internal currents, elasticity, and spin. Even if the angular momentum remains small, many such systems are found to be affected by large self-interaction effects beyond the standard Lorentz-Dirac force. These are particularly significant if the particle's charge density fails to be much greater than its 3-current density (or vice versa) in the center-of-mass frame. Additional terms also arise in the equations of motion if the dipole moment is too large, and when the `center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly speaking). These conditions are often quite restrictive. General equations of motion were also derived under the assumption that the particle can only interact with the radiative component of its self-field. These are much simpler than the equations derived using the full retarded self-field; as are the conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for publication in Phys. Rev.

A Combinatorial Interpretation of Lommel Polynomials and Their Derivatives

In this paper we present interpretations of Lommel polynomials and their derivatives. A combinatorial interpretation uses matchings in graphs. This gives an interpretation for the derivatives as well. Then Lommel polynomials are considered from the point of view of operator calculus. A step-3 nilpotent Lie algebra and finite-difference operators arise in the analysis

Incorporation of Polarization Into the DIRSIG Synthetic Image Generation Model

The Digital Imaging and Remote Sensing Synthetic Image Generation (DIRSIG) model uses a quantitative first principles approach to generate synthetic hyperspectral imagery. This paper presents the methods used to add modeling of polarization phenomenology. The radiative transfer equations were modified to use Stokes vectors for the radiance values and Mueller matrices for the energy-matter interactions. The use of Stokes vectors enables a full polarimetric characterization of the illumination and sensor reaching radiances. The bi-directional reflectance distribution function (BRDF) module was rewritten and modularized to accommodate a variety of polarized and unpolarized BRDF models. Two new BRDF models based on Torrance- Sparrow and Beard-Maxwell were added to provide polarized BRDF estimations. The sensor polarization characteristics are modeled using Mueller matrix transformations on a per pixel basis. All polarized radiative transfer calculations are performed spectrally to preserve the hyperspectral capabilities of DIRSIG. Integration over sensor bandpasses is handled by the sensor module