51 research outputs found
Active compensation of aperture discontinuities for WFIRST-AFTA: analytical and numerical comparison of propagation methods and preliminary results with a WFIRST-AFTA-like pupil
The new frontier in the quest for the highest contrast levels in the focal
plane of a coronagraph is now the correction of the large diffractive artifacts
effects introduced at the science camera by apertures of increasing complexity.
The coronagraph for the WFIRST/AFTA mission will be the first of such
instruments in space with a two Deformable Mirrors wavefront control system.
Regardless of the control algorithm for these multi Deformable Mirrors, they
will have to rely on quick and accurate simulation of the propagation effects
introduced by the out-of-pupil surface. In the first part of this paper, we
present the analytical description of the different approximations to simulate
these propagation effects. In Annex A, we prove analytically that, in the
special case of surfaces inducing a converging beam, the Fresnel method yields
high fidelity for simulations of these effects. We provide numerical
simulations showing this effect. In the second part, we use these tools in the
framework of the Active Compensation of Aperture Discontinuities technique
(ACAD) applied to pupil geometries similar to WFIRST-AFTA. We present these
simulations in the context of the optical layout of the High-contrast imager
for Complex Aperture Telescopes, which will test ACAD on a optical bench. The
results of this analysis show that using the ACAD method, an apodized pupil
lyot coronagraph and the performance of our current deformable mirrors, we are
able to obtain, in numerically simulations, a dark hole with an AFTA-like
pupil. Our numerical simulation shows that we can obtain contrast better than
in monochromatic light and better than 3.e-8 with 10% bandwidth
between 5 and 14 lambda/D.Comment: 16 pages, 5 figures, Accepted for publication (Oct. 23, 2015) in
Journal of Astronomical Telescopes, Instruments, and Systems, special
WFIRST-AFTA coronagrap
Polynomial distribution functions on bounded closed intervals
The thesis explores several topics, related to polynomial distribution functions
and their densities on [0,1]M, including polynomial copula functions and their
densities. The contribution of this work can be subdivided into two areas.
- Studying the characterization of the extreme sets of polynomial densities
and copulas, which is possible due to the Choquet theorem.
- Development of statistical methods that utilize the fact that the density
is polynomial (which may or may not be an extreme density).
With regard to the characterization of the extreme sets, we first establish
that in all dimensions the density of an extreme distribution function is an extreme
density. As a consequence, characterizing extreme distribution functions
is equivalent to characterizing extreme densities, which is easier analytically.
We provide the full constructive characterization of the Choquet-extreme polynomial
densities in the univariate case, prove several necessary and sufficient
conditions for the extremality of densities in arbitrary dimension, provide necessary
conditions for extreme polynomial copulas, and prove characterizing
duality relationships for polynomial copulas. We also introduce a special case
of reflexive polynomial copulas.
Most of the statistical methods we consider are restricted to the univariate
case. We explore ways to construct univariate densities by mixing the extreme
ones, propose non-parametric and ML estimators of polynomial densities. We
introduce a new procedure to calibrate the mixing distribution and propose
an extension of the standard method of moments to pinned density moment
matching. As an application of the multivariate polynomial copulas, we introduce
polynomial coupling and explore its application to convolution of coupled
random variables.
The introduction is followed by a summary of the contributions of this thesis
and the sections, dedicated first to the univariate case, then to the general
multivariate case, and then to polynomial copula densities. Each section first
presents the main results, followed by the literature review
The core of games on ordered structures and graphs
In cooperative games, the core is the most popular solution concept, and its
properties are well known. In the classical setting of cooperative games, it is
generally assumed that all coalitions can form, i.e., they are all feasible. In
many situations, this assumption is too strong and one has to deal with some
unfeasible coalitions. Defining a game on a subcollection of the power set of
the set of players has many implications on the mathematical structure of the
core, depending on the precise structure of the subcollection of feasible
coalitions. Many authors have contributed to this topic, and we give a unified
view of these different results
Explainable contextual data driven fusion
Numerous applications require the intelligent combining of disparate sensor data streams to create a more complete and enhanced observation in support of underlying tasks like classification, regression, or decision making. This presentation is focused on two underappreciated and often overlooked parts of information fusion, explainability and context. Due to the rapidly increasing deployment and complexity of machine learning solutions, it is critical that the humans who deploy these algorithms can understand why and how a given algorithm works, as well as be able to determine when an algorithm is suitable for use in a particular instance of the problem. The first half of this paper outlines a new similarity measure for capacities and integrals. This measure is used to compare machine learned fusion solutions and explain what a single fusion solution learned. The second half of the paper is focused on contextual fusion with respect to incomplete (limited knowledge) models and metadata for unmanned aerial vehicles (UAVs). Example UAV metadata includes platform (e.g., GPS, IMU, etc.) and environmental (e.g., weather, solar position, etc.) data. Incomplete models herein are a result of limitations of machine learning related to under-sampling of training data. To address these challenges, a new contextually adaptive online Choquet integral is outlined
Polynomial distribution functions on bounded closed intervals
The thesis explores several topics, related to polynomial distribution functions and their densities on [0,1]M, including polynomial copula functions and their densities. The contribution of this work can be subdivided into two areas. - Studying the characterization of the extreme sets of polynomial densities and copulas, which is possible due to the Choquet theorem. - Development of statistical methods that utilize the fact that the density is polynomial (which may or may not be an extreme density). With regard to the characterization of the extreme sets, we first establish that in all dimensions the density of an extreme distribution function is an extreme density. As a consequence, characterizing extreme distribution functions is equivalent to characterizing extreme densities, which is easier analytically. We provide the full constructive characterization of the Choquet-extreme polynomial densities in the univariate case, prove several necessary and sufficient conditions for the extremality of densities in arbitrary dimension, provide necessary conditions for extreme polynomial copulas, and prove characterizing duality relationships for polynomial copulas. We also introduce a special case of reflexive polynomial copulas. Most of the statistical methods we consider are restricted to the univariate case. We explore ways to construct univariate densities by mixing the extreme ones, propose non-parametric and ML estimators of polynomial densities. We introduce a new procedure to calibrate the mixing distribution and propose an extension of the standard method of moments to pinned density moment matching. As an application of the multivariate polynomial copulas, we introduce polynomial coupling and explore its application to convolution of coupled random variables. The introduction is followed by a summary of the contributions of this thesis and the sections, dedicated first to the univariate case, then to the general multivariate case, and then to polynomial copula densities. Each section first presents the main results, followed by the literature review.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Mathematical Game Theory
These lecture notes attempt a mathematical treatment of game theory akin to
mathematical physics. A game instance is defined as a sequence of states of an
underlying system. This viewpoint unifies classical mathematical models for
2-person and, in particular, combinatorial and zero-sum games as well as models
for investing and betting. n-person games are studied with emphasis on notions
of utilities, potentials and equilibria, which allows to subsume cooperative
games as special cases. The represenation of a game theoretic system in a
Hilbert space furthermore establishes a link to the mathematical model of
quantum mechancis and general interaction systems
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