Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

On Typical Compact Convex Sets in Hilbert Spaces

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

On Uniformly Convex and Uniformly Kadec-Klee Renomings

We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for Lp(X) spaces and C(K) spaces for K scattered compact space.

Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

On the Set of Locally Convex Topologies Compatible with a Given Topology on a Vector Space: Cardinality Aspects

For a topological vector space (X, τ ), we consider the family LCT (X, τ ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ . We prove that for an infinite-dimensional reflexive Banach space (X, τ ), the cardinality of LCT (X, τ ) is at least c.

Automated Feedback for 'Fill in the Gap' Programming Exercises

Timely feedback is a vital component in the learning process. It is especially important for beginner students in Information Technology since many have not yet formed an effective internal model of a computer that they can use to construct viable knowledge. Research has shown that learning efficiency is increased if immediate feedback is provided for students. Automatic analysis of student programs has the potential to provide immediate feedback for students and to assist teaching staff in the marking process. This paper describes a “fill in the gap” programming analysis framework which tests students’ solutions and gives feedback on their correctness, detects logic errors and provides hints on how to fix these errors. Currently, the framework is being used with the Environment for Learning to Programming (ELP) system at Queensland University of Technology (QUT); however, the framework can be integrated into any existing online learning environment or programming Integrated Development Environment (IDE)

Losing their marbles : syntax-free programming for assessing problem-solving skills

Novice programmers have difficulty developing an algorithmic solution while simultaneously obeying the syntactic constraints of the target programming language. To see how students fare in algorithmic problem solving when not burdened by syntax, we conducted an experiment in which a large class of beginning programmers were required to write a solution to a computational problem in structured English, as if instructing a child, without reference to program code at all. The students produced an unexpectedly wide range of correct, and attempted, solutions, some of which had not occurred to their teachers. We also found that many common programming errors were evident in the natural language algorithms, including failure to ensure loop termination, hardwiring of solutions, failure to properly initialise the computation, and use of unnecessary temporary variables, suggesting that these mistakes are caused by inexperience at thinking algorithmically, rather than difficulties in expressing solutions as program code.

Further evidence of a relationship between explaining, tracing and writing skills in introductory programming

This paper reports on a replication of earlier studies into a possible hierarchy of programming skills. In this study, the students from whom data was collected were at a university that had not provided data for earlier studies. Also, the students were taught the programming language Python, which had not been used in earlier studies. Thus this study serves as a test of whether the findings in the earlier studies were specific to certain institutions, student cohorts, and programming languages. Also, we used a non–parametric approach to the analysis, rather than the linear approach of earlier studies. Our results are consistent with the earlier studies. We found that students who cannot trace code usually cannot explain code, and also that students who tend to perform reasonably well at code writing tasks have also usually acquired the ability to both trace code and explain code.

Seeing is understanding : the effect of visualisation in understanding programming concepts

How and why visualisations support learning was the subject of this qualitative instrumental collective case study. Five computer programming languages (PHP, Visual Basic, Alice, GameMaker, and RoboLab) supporting differing degrees of visualisation were used as cases to explore the effectiveness of software visualisation to develop fundamental computer programming concepts (sequence, iteration, selection, and modularity). Cognitive theories of visual and auditory processing, cognitive load, and mental models provided a framework in which student cognitive development was tracked and measured by thirty-one 15-17 year old students drawn from a Queensland metropolitan secondary private girls’ school, as active participants in the research. Seventeen findings in three sections increase our understanding of the effects of visualisation on the learning process. The study extended the use of mental model theory to track the learning process, and demonstrated application of student research based metacognitive analysis on individual and peer cognitive development as a means to support research and as an approach to teaching. The findings also forward an explanation for failures in previous software visualisation studies, in particular the study has demonstrated that for the cases examined, where complex concepts are being developed, the mixing of auditory (or text) and visual elements can result in excessive cognitive load and impede learning. This finding provides a framework for selecting the most appropriate instructional programming language based on the cognitive complexity of the concepts under study.