This thesis develops an engineering practice and design methodology to enable us to use CMOS analog VLSI chips to perform more accurate and precise computation. These techniques form the basis of an approach that permits us to build computer graphics and neural network applications using analog VLSI. The nature of the design methodology focuses on defining goals for circuit behavior to be met as part of the design process. To increase the accuracy of analog computation, we develop techniques for creating compensated circuit building blocks, where compensation implies the cancellation of device variations, offsets, and nonlinearities. These compensated building blocks can be used as components in larger and more complex circuits, which can then also be compensated. To this end, we develop techniques for automatically determining appropriate parameters for circuits, using constrained optimization. We also fabricate circuits that implement multi-dimensional gradient estimation for a grad...

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This paper addresses the need identified by Graham Jones for more research related to the connections made by students in the middle years between classical and frequentist orientations to probability. It does so based on two extended lessons with a class of Grade 5/6 students and in-depth interviews with five students from the class. The Model 1 version of the software TinkerPlots was used in both settings to simulate increasingly large samples of random events. The aim was to document the students ’ understanding of probability on a continuum from Experimental to Theoretical, including consideration of the interaction of Manipulatives, the Simulator, and the Law of Large Numbers. A cognitive developmental model was used to assess students ’ understanding and recommendations are made for classroom interventions.

We analyze passivity for a class of discrete-time switched nonlinear systems that switch between two modes- an uncontrolled mode in which the system evolves open loop, and a controlled mode in which a control input is applied to the system. Such a model has recently been used for a network controlled system in the presence of packet drops introduced by a communication channel. For the case when the open loop system is non-passive, classical passivity theory considers the switched system to be non-passive as well. We give a new generalized definition of passivity for such a system and show that if the ratio of the time steps for which the system evolves open loop versus the time steps for which the system evolves closed loop is bounded below a critical ratio, then the nonlinear system is locally passive in this sense. Moreover, we show that this generalized definition is useful since it preserves two important properties of the classical passivity concept- that passivity implies asymptotic stability for zero state detectable systems using feedback and that passivity is preserved in parallel and feedback interconnections. I.

Abstract. Some necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Some generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal properties originating from nonwellfounded properties of the empty set is demonstrated. This lattice provides a substrate with both discrete and continuous properties, from which existence of physical universes can be proved, up to the function of conscious perception. Spacetime emerges as an ordered sequence of mappings of closed 3-D Ponicaré sections of a topological 4-space provided by the lattice, and the function of conscious perception is founded on the same properties. Self-evaluation of a system is possible against indecidability barriers through anticipatory mental imaging occurring in biological brain systems; then our embedding universe should be in principle accessible to knowledge. The possibility of existence of spaces with fuzzy dimension or with adjoined parts with decreasing dimensions is raised, together with