Searchable Sky Coverage of Astronomical Observations: Footprints and Exposures

Sky coverage is one of the most important pieces of information about astronomical observations. We discuss possible representations, and present algorithms to create and manipulate shapes consisting of generalized spherical polygons with arbitrary complexity and size on the celestial sphere. This shape specification integrates well with our Hierarchical Triangular Mesh indexing toolbox, whose performance and capabilities are enhanced by the advanced features presented here. Our portable implementation of the relevant spherical geometry routines comes with wrapper functions for database queries, which are currently being used within several scientific catalog archives including the Sloan Digital Sky Survey, the Galaxy Evolution Explorer and the Hubble Legacy Archive projects as well as the Footprint Service of the Virtual Observatory.Comment: 11 pages, 7 figures, submitted to PAS

Data-Driven Methods and Applications for Optimization under Uncertainty and Rare-Event Simulation

For most of decisions or system designs in practice, there exist chances of severe hazards or system failures that can be catastrophic. The occurrence of such hazards is usually uncertain, and hence it is important to measure and analyze the associated risks. As a powerful tool for estimating risks, rare-event simulation techniques are used to improve the efficiency of the estimation when the risk occurs with an extremely small probability. Furthermore, one can utilize the risk measurements to achieve better decisions or designs. This can be achieved by modeling the task into a chance constrained optimization problem, which optimizes an objective with a controlled risk level. However, recent problems in practice have become more data-driven and hence brought new challenges to the existing literature in these two domains. In this dissertation, we will discuss challenges and remedies in data-driven problems for rare-event simulation and chance constrained problems. We propose a robust optimization based framework for approaching chance constrained optimization problems under a data-driven setting. We also analyze the impact of tail uncertainty in data-driven rare-event simulation tasks. On the other hand, due to recent breakthroughs in machine learning techniques, the development of intelligent physical systems, e.g. autonomous vehicles, have been actively investigated. Since these systems can cause catastrophes to public safety, the evaluation of their machine learning components and system performance is crucial. This dissertation will cover problems arising in the evaluation of such systems. We propose an importance sampling scheme for estimating rare events defined by machine learning predictors. Lastly, we discuss an application project in evaluating the safety of autonomous vehicle driving algorithms.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163270/1/zhyhuang_1.pd

Control Barrier Function Based Design of Gradient Flows for Constrained Nonlinear Programming

This paper considers the problem of designing a continuous time dynamical system to solve constrained nonlinear optimization problems such that the feasible set is forward invariant and asymptotically stable. The invariance of the feasible set makes the dynamics anytime, when viewed as an algorithm, meaning that it is guaranteed to return a feasible solution regardless of when it is terminated. The system is obtained by augmenting the gradient flow of the objective function with inputs, then designing a feedback controller to keep the state evolution within the feasible set using techniques from the theory of control barrier functions. The equilibria of the system correspond exactly to critical points of the optimization problem. Since the state of the system corresponds to the primal optimizer, and the steady-state input at equilibria corresponds to the dual optimizer, the method can be interpreted as a primal-dual approach. The resulting closed-loop system is locally Lipschitz continuous, so classical solutions to the system exist. We characterize conditions under which local minimizers are Lyapunov stable, drawing connections between various constraint qualification conditions and the stability of the local minimizer. The algorithm is compared to other continuous time methods for optimization

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

A survey of visual preprocessing and shape representation techniques

Many recent theories and methods proposed for visual preprocessing and shape representation are summarized. The survey brings together research from the fields of biology, psychology, computer science, electrical engineering, and most recently, neural networks. It was motivated by the need to preprocess images for a sparse distributed memory (SDM), but the techniques presented may also prove useful for applying other associative memories to visual pattern recognition. The material of this survey is divided into three sections: an overview of biological visual processing; methods of preprocessing (extracting parts of shape, texture, motion, and depth); and shape representation and recognition (form invariance, primitives and structural descriptions, and theories of attention)

Models and algorithms for multi-agent search problems

The problem of searching for objects of interest occurs in important applications ranging from rescue, security, transportation, to medicine. With the increasing use of autonomous vehicles as search platforms, there is a need for fast algorithms that can generate search plans for multiple agents in response to new information. In this dissertation, we develop new techniques for automated generation of search plans for different classes of search problems. First, we study the problem of searching for a stationary object in a discrete search space with multiple agents where each agent can access only a subset of the search space. In these problems, agents can fail to detect an object when inspecting a location. We show that when the probabilities of detection only depend on the locations, this problem can be reformulated as a minimum cost network optimization problem, and develop a fast specialized algorithm for the solution. We prove that our algorithm finds the optimal solution in finite time, and has worst-case computation performance that is faster than general minimum cost flow algorithms. We then generalize it to the case where the probabilities of detection depend on the agents and the locations, and propose a greedy algorithm that is 1/2-approximate. Second, we study the problem of searching for a moving object in a discrete search space with multiple agents where each agent can access only a subset of a discrete search space at any time and agents can fail to detect objects when searching a location at a given time. We provide necessary conditions for an optimal search plan, extending prior results in search theory. For the case where the probabilities of detection depend on the locations and the time periods, we develop a forward-backward iterative algorithm based on coordinate descent techniques to obtain solutions. To avoid local optimum, we derive a convex relaxation of the dynamic search problem and show this can be solved optimally using coordinate descent techniques. The solutions of the relaxed problem are used to provide random starting conditions for the iterative algorithm. We also address the problem where the probabilities of detection depend on the agents as well as the locations and the time periods, and show that a greedy-style algorithm is 1/2-approximate. Third, we study problems when multiple objects of interest being searched are physically scattered among locations on a graph and the agents are subject to motion constraints captured by the graph edges as well as budget constraints. We model such problem as an orienteering problem, when searching with a single agent, or a team orienteering problem, when searching with multiple agents. We develop novel real-time efficient algorithms for both problems. Fourth, we investigate classes of continuous-region multi-agent adaptive search problems as stochastic control problems with imperfect information. We allow the agent measurement errors to be either correlated or independent across agents. The structure of these problems, with objectives related to information entropy, allows for a complete characterization of the optimal strategies and the optimal cost. We derive a lower bound on the performance of the minimum mean-square error estimator, and provide upper bounds on the estimation error for special cases. For agents with independent errors, we show that the optimal sensing strategies can be obtained in terms of the solution of decoupled scalar convex optimization problems, followed by a joint region selection procedure. We further consider search of multiple objects and provide an explicit construction for adaptively determining the sensing actions