A Computational Model for Observation in Quantum Mechanics

A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and unexpected behavior of some quantum mechanical systems. As examples, the model is used to simulate three seminal quantum mechanical experiments. The results obtained agree with the predictions of quantum mechanics (and physical measurements), yet the model is perfectly deterministic and maintains a notion of locality.

Computational Structure of Human Language

The central thesis of this report is that human language is NP-complete. That is, the process of comprehending and producing utterances is bounded above by the class NP, and below by NP-hardness. This constructive complexity thesis has two empirical consequences. The first is to predict that a linguistic theory outside NP is unnaturally powerful. The second is to predict that a linguistic theory easier than NP-hard is descriptively inadequate. To prove the lower bound, I show that the following three subproblems of language comprehension are all NP-hard: decide whether a given sound is possible sound of a given language; disambiguate a sequence of words; and compute the antecedents of pronouns. The proofs are based directly on the empirical facts of the language user's knowledge, under an appropriate idealization. Therefore, they are invariant across linguistic theories. (For this reason, no knowledge of linguistic theory is needed to understand the proofs, only knowledge of English.) To illustrate the usefulness of the upper bound, I show that two widely-accepted analyses of the language user's knowledge (of syntactic ellipsis and phonological dependencies) lead to complexity outside of NP (PSPACE-hard and Undecidable, respectively). Next, guided by the complexity proofs, I construct alternate linguisitic analyses that are strictly superior on descriptive grounds, as well as being less complex computationally (in NP). The report also presents a new framework for linguistic theorizing, that resolves important puzzles in generative linguistics, and guides the mathematical investigation of human language.

Reconfigurable Architectures for General-Purpose Computing

General-purpose computing devices allow us to (1) customize computation after fabrication and (2) conserve area by reusing expensive active circuitry for different functions in time. We define RP-space, a restricted domain of the general-purpose architectural space focussed on reconfigurable computing architectures. Two dominant features differentiate reconfigurable from special-purpose architectures and account for most of the area overhead associated with RP devices: (1) instructions which tell the device how to behave, and (2) flexible interconnect which supports task dependent dataflow between operations. We can characterize RP-space by the allocation and structure of these resources and compare the efficiencies of architectural points across broad application characteristics. Conventional FPGAs fall at one extreme end of this space and their efficiency ranges over two orders of magnitude across the space of application characteristics. Understanding RP-space and its consequences allows us to pick the best architecture for a task and to search for more robust design points in the space. Our DPGA, a fine- grained computing device which adds small, on-chip instruction memories to FPGAs is one such design point. For typical logic applications and finite- state machines, a DPGA can implement tasks in one-third the area of a traditional FPGA. TSFPGA, a variant of the DPGA which focuses on heavily time-switched interconnect, achieves circuit densities close to the DPGA, while reducing typical physical mapping times from hours to seconds. Rigid, fabrication-time organization of instruction resources significantly narrows the range of efficiency for conventional architectures. To avoid this performance brittleness, we developed MATRIX, the first architecture to defer the binding of instruction resources until run-time, allowing the application to organize resources according to its needs. Our focus MATRIX design point is based on an array of 8-bit ALU and register-file building blocks interconnected via a byte-wide network. With today's silicon, a single chip MATRIX array can deliver over 10 Gop/s (8-bit ops). On sample image processing tasks, we show that MATRIX yields 10-20x the computational density of conventional processors. Understanding the cost structure of RP-space helps us identify these intermediate architectural points and may provide useful insight more broadly in guiding our continual search for robust and efficient general-purpose computing structures.

Computational Models of Object Recognition in Cortex: A Review

Understanding how biological visual systems perform object recognition is one of the ultimate goals in computational neuroscience. Among the biological models of recognition the main distinctions are between feedforward and feedback and between object-centered and view-centered. From a computational viewpoint the different recognition tasks - for instance categorization and identification - are very similar, representing different trade-offs between specificity and invariance. Thus the different tasks do not strictly require different classes of models. The focus of the review is on feedforward, view-based models that are supported by psychophysical and physiological data.

FastAero – A Precorrected FFT – Fast Multipole Tree Steady and Unsteady Potential Flow Solver

In this paper a precorrected FFT-Fast Multipole Tree (pFFT-FMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and hands-off steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex participle method. Some simple steady state flow solutions are performed to demonstrate the basic capabilities of the solver. Although this paper focuses primarily on steady state solutions, it should be noted that this approach is designed to be a robust and efficient unsteady potential flow simulation tool, useful for rapid computational prototyping.