Working memory, or the ability to maintain and manipulate information such that it can be used to guide behavior, is known to be severely capacity limited, in most circumstances, to about 3-4 objects. Both infants and adults have the ability to surpass these limits by encoding to-be-remembered items in groups or collections, exploiting statistical regularities or conceptual information to devise more efficient coding schema. Despite progress made toward understanding continuities in working memory, little is known about how changes over development interact with the ability to employ maximally efficient mnemonic data structures. Paper 1 demonstrates that although adults can encode at most three mutually exclusive collections that accrue sequentially over time, they can circumvent this limit when items overlap in features (e.g. red and blue circles and triangles) and statistical regularities are introduced among collections defined by a single visual feature (e.g. most red items are triangular and not circular). Adults' performance suggests they are able to encode items from intersecting collections hierarchically and exploit statistical regularities among collections to reconstruct the numerosities of up to six collections in parallel, exemplifying how efficient coding can radically enhance working memory. Paper 2 demonstrates that young preschoolers can also represent three mutually exclusive collections that accrue in an intermixed fashion over time. Results show that the ability to surpass this capacity limit by hierarchically reorganizing collections and exploiting statistical regularities among them develops between the ages of three and seven. These results are discussed in the context of executive function development. Paper 3 provides evidence that computations of average size and orientation rely on qualitatively different processes with distinct developmental trajectories. Experiment 1 demonstrates that while the presence of additional identical elements in an array detrimentally impacts 6-month-olds' representations of element size, it improves the precision with which infants represent orientation. Experiment 2 demonstrates that performance is not affected when infants' attention is cued to a single item within arrays. These results are discussed in the context of the development of controlled attention. / Psychology

published_or_final_version / Mathematics / Master / Master of Philosophy

Experiments have demonstrated that DNA molecules can compute like a machine to solve mathematical problems, which is significant because of their parallel computation ability. However, due to the nature of biochemical reactions, DNA computation suffers from errors, which are its main limitation. The abstract and kinetic Tile Assembly Models are now commonly used to simulate real DNA computing experiments, and to look for new methods to advance the accuracy of DNA-based computation. One means of controlling errors is through proofreading tile sets. Several such tile sets have been proposed in the literature, such as Chen and Goel’s snaked proofreading tile sets, the 2-way and 3-way overlay tile sets of Reif et al., and Rothemund and Cook’s n-way overlay tile sets. In the first part of this thesis, we analyze the performance of the Rothemund-Cook n-way overlay tile sets. We prove that the n-way overlay tile set contains n^2+3n+4 rule tiles. Simulation results show that these tile sets clearly perform better than tile sets without any error-control mechanism, and the performance improves as n increases. It is also proved that the error rates in assemblies formed by the 1-way and 2-way tile sets are O(epsilon^2), where epsilon is the error rate in assemblies without any error correction. In the second part of this thesis, we focus on a different error mechanism, namely,errors caused by imperfect or malformed tiles. We propose a model of malformed tiles, and consider the performance of various proofreading tile sets in the presence of malformed tiles. Our simulation results show that the Reif et al. 3-way overlay tile sets are able to best deal with malformed tiles. During the simulations, we observed that snaked proofreading tile sets always have trouble completing whole patterns when malformed tiles are present. We instead propose two modified snaked proofreading constructions, and verify through both simulations and analysis that the two modified constructions have much better performances. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2009-08-25 11:10:39.142

No description available.

No description available.

We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Bargaining theory seeks to answer the question of how to divide a jointly generated surplus between multiple agents. John Nash proposed the Nash Bargaining Solution to answer this question for the special case of two agents. Kleinberg and Tardos extended this idea to network games, and introduced a model they call the Bargaining Game. They search for surplus divisions with a notion of fairness, defined as balanced solutions, that follow the Nash Bargaining Solution for all contracting agents. Unfortunately, many networks exist where no balanced solution can be found, which we call unstable. In this thesis, we explore methods of changing unstable network structures to find fair bargaining solutions. We define the concept of Blocking Sets, introduced by Biro, Kern and Paulusma, and use them to create stability. We show that by removing a blocking set from an unstable network, we can find a balanced bargaining division in polynomial time. This motivates the search for minimal blocking sets. Unfortunately this problem is NP-hard, and hence no known efficient algorithm exists for solving it. To overcome this hardness, we consider the problem when restricted to special graph classes. We introduce a O(1)-factor approximation algorithm for the problem on planar graphs with unit edge weights. We then provide an algorithm to solve the problem optimally in graphs of bounded treewidth, which generalize trees.

Thesis (MEng)--University of South Australia, 1997

Thesis (M.S.)--Brigham Young University. Dept. of Computer Science, 2007. / Includes bibliographical references (p. 49-50).

Thesis (Ph. D.)--Ohio University, June, 2001. / Title from PDF t.p.