Central Limit Theory for Multivalued Mappings

This paper presents new fundamental results concerning central limit behavior of sequences of random closed sets, modeled as a multivalued mapping of an underlying asymptotically normal sequence of random variables. The main theorem generalizes the classical result for differentiable functions in a mathematically satisfying way by combining recent developments in convergence theory for random closed sets and recent work in pseudo-differentiability of multifunctions. Potential applications to the asymptotic analysis of solution sets for stochastic and ordinary parametric programs with incomplete information are indicated in the examples. This paper reports research that was partly performed in the Adaptation and Optimization Project of the System and Decision Sciences Program

Central Limit Theory for Lipschitz Mappings

Central limit theorems are derived for mappings that are Lipschitzian at a given point. This theory results from a new perspective on first-order behavior -- the upper pseudo-derivative, the graph of which is the contingent cone to the graph of the mapping at a given point. We adopt the general setting of the convergence in distribution of measures induced by mappings that may be multi-valued on sets of measure zero. By requiring the upper pseudo-derivative to be single-valued a.s., we obtain a central limit theorem under distinctively weaker conditions than classical Frechet differentiability

Asymptotic Distributions for Solutions in Stochastic Optimization and Generalized M-Estimation

New techniques of local sensitivity analysis in nonsmooth optimization are applied to the problem of determining the asymptotic distribution (generally non-normal) for solutions in stochastic optimization, and generalized M-estimation -- a reformulation of the traditional maximum likelihood problem that allows the introduction of hard constraints

Generalized Delta Theorems for Multivalued Mappings and Measurable Selections

The classical delta theorem can be generalized in a mathematically satisfying way to a broad class of multivalued and/or nonsmooth mappings, by examining the convergence in distribution of the sequence of difference quotients from the perspectives of recent developments in convergence theory for random closed sets and new descriptions of first-order behavior of multivalued mappings. Such a theory opens the way to applications of asymptotic techniques in many areas of mathematical optimization where randomness and uncertainty play a role. Of special importance is the asymptotic convergence of measurable selections of multifunctions when the limit multifunction is single-valued almost surely

Asymptotic Theory for Solutions in Generalized M-Estimation and Stochastic Programming

New techniques of local sensitivity analysis in nonsmooth optimization are applied to the problem of studying the asymptotic behavior (generally non-normal) for solutions in stochastic optimization, and generalized M-estimation -- a reformulation of the traditional maximum-likelihood problem that allows the introduction of hard constraints

Epi-Consistency of Convex Stochastic Programs

This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data. Very few additional assumptions are required because of the special properties of convexity and empirical measures; nevertheless the results are broadly applicable to many situations arising in stochastic programming

The Oxidation State of Iron in Silicate Minerals from the Matrices of CO Carbonaceous Chondrites

No abstract available

A Standard Input Format for Computer Codes Which Solve Stochastic Programs with Recourse and a Library of Utilities to Simplify its Use

We explain our suggestions for standardizing input formats for computer codes which solve stochastic programs with recourse. The main reason to set some conventions is to allow programs implementing different methods of solution to be used interchangeably. The general philosophy behind our design is a) to remain fairly faithful to the de facto standard for the statement of LP problems established by IBM for use with MPSX and subsequently adopted by the authors of MINOS, b) to provide sufficient flexibility so that a variety of problems may be expressed in the standard format, c) to allow problems originally formulated as deterministic LP to be converted to stochastic problems with a minimum of effort, d) to permit new options to be added as the need arises, and e) to provide some routines to facilitate the task of reading files specified in the standard format

Leadership, coordinated behaviour, and information use in a social primate.

A substantial body of work has addressed why animals live in groups. However, few studies have described how group-living vertebrates are able to coordinate their actions and make collective decisions crucial if individuals are to maximise the benefits and minimise the costs of grouping. In this thesis, I apply observational, experimental, and theoretical methods to address this paucity of knowledge, using a social primate - chacma baboons (Papio ursinus) - as a model system. Specifically, I investigate three concepts upon which group-living is reliant: information use, coordinated behaviour and leadership. I address each of these concepts in turn. First in the case of information use, I show that the foraging decisions of individual baboons meet the predictions of 'producer- scrounger games' - evolutionary models developed to predict when a social forager should find its own food patch, or join the discovery of a group-mate. I also use a simple theoretical model to show that social information can allow less well-informed members of large groups to reach a correct decision with the same probability as more well-informed members of small groups. Second, in the case of coordinated behaviour, I show that individual state and the environment (both social and ecological conditions) can influence levels of behavioural synchrony in baboons. Moreover, behavioural synchrony in baboon groups was seen to positively influence the behaviour of another species: rock kestrels (Falco rupicolus) derived foraging opportunities by associating with baboons as they travel-forage together in desert vegetation 'flushing' kestrel prey items. Finally, I examined leadership behaviour. I used an experimental design that allowed me to test between two alternate decision-making modes: despotism (i.e. leadership) and democracy (i.e. a majority rule, voting). Baboon group foraging decisions were consistently led by the individual who acquired the most benefits from those decisions, namely the dominant male. Subordinate group members followed the leader despite considerable costs, and follower behaviour was mediated by social ties to the leader

Use of strain-annealing to evolve the grain boundary character distribution in polycrystalline copper

We have used a two-step (low and high temperature) strain-annealing process to evolve the grain boundary character distribution (GBCD) in fully recrystallized oxygen-free electronic (OFE) Cu bar that was forged and rolled. Orientation imaging microscopy has been used to characterize the GBCD after each step in the processing. The fraction of special grain boundaries was {similar_to}70% in the starting recrystallized material. Three different processing conditions were employed: high, moderate, and low temperature. The high-temperature process resulted in a reduction in the fraction of special GBs while both the lower temperature processes resulted in an increase in special fraction up to 85%. Further, the lower temperature processes resulted in average deviation angles from exact misorientation, for special boundaries, that were significantly smaller than observed from the high temperature process. Results indicate the importance of the low temperature part of the two-step strain-annealing process in preparing the microstructure for the higher temperature anneal and commensurate increase in the special fraction