Signal propagation and noisy circuits

The information carried by a signal decays when the signal is corrupted by random noise. This occurs when a message is transmitted over a noisy channel, as well as when a noisy component performs computation. We first study this signal decay in the context of communication and obtain a tight bound on the rate at which information decreases as a signal crosses a noisy channel. We then use this information theoretic result to obtain depth lower bounds in the noisy circuit model of computation defined by von Neumann. In this model, each component fails (produces 1 instead of 0 or vice-versa) independently with a fixed probability, and yet the output of the circuit is required to be correct with high probability. Von Neumann showed how to construct circuits in this model that reliably compute a function and are no more than a constant factor deeper than noiseless circuits for the function. We provide a lower bound on the multiplicative increase in circuit depth necessary for reliable computation, and an upper bound on the maximum level of noise at which reliable computation is possible

On the maximum tolerable noise of k-input gates for reliable computation by formulas

We determine the precise threshold of component noise below which formulas composed of odd degree components can reliably compute all Boolean functions

Information Theory and Noisy Computation

We report on two types of results. The first is a study of the rate of decay of information carried by a signal which is being propagated over a noisy channel. The second is a series of lower bounds on the depth, size, and component reliability of noisy logic circuits which are required to compute some function reliably. The arguments used for the circuit results are information-theoretic, and in particular, the signal decay result is essential to the depth lower bound. Our first result can be viewed as a quantified version of the data processing lemma, for the case of Boolean random variables

Executive Attention deficits in aphasia: case studies

Many features of language impairments in people with aphasia (PWA) suggest that they have problems with executive functions that control language use (Hula and McNeil, 2008). An outstanding question is the extent to which the executive functions affected in PWA apply in other cognitive domains (Murray, 2012) or are specific to language (Jefferies and Lambon Ralph, 2006; Hoffman et al., 2013). The Executive Attention model (Engle and Kane, 2004) provides a framework for examining this question. It claims the central executive consists of two interacting components: task maintenance, the ability to use task goals to exert proactive control that reduces interference, and conflict resolution, the ability to resolve conflicts generated by interference during goal-directed processing. It is proposed that task maintenance is a domain-general capacity, and that conflict resolution is at least partially encapsulated, with specialized functions responsible for modality-specific interference. Therefore, PWA with task maintenance deficits should be affected in all cognitive areas, whereas PWA with conflict resolution impairments should be affected only in language functions, where they should show increased interference effects even in contexts of minimal task maintenance demand. Hypotheses were tested in two case studies

Program Compression

The talk focused on a grammar-based technique for identifying redundancy in program code and taking advantage of that redundancy to reduce the memory required to store and execute the program. The idea is to start with a simple context-free grammar that represents all valid basic blocks of any program. We represent a program by the parse trees (i.e. derivations) of its basic blocks using the grammar. We then modify the grammar, by considering sample programs, so that idioms of the language have shorter derivations in the modified grammar. Since each derivation represents a basic block, we can interpret the resulting set of derivations much as we would interpret the original program. We need only expand the grammar rules indicated by the derivation to produce a sequence of original program instructions to execute. The result is a program representation that is approximately 40% of the original program size and is interpretable by a very modest-sized interpreter

Changing Labor Market Opportunities for Women and the Quality of Teachers 1957-1992

School officials and policy makers have grown increasingly concerned about their ability to attract and retain talented teachers. A number of authors have shown that in recent years the brightest students at least those with the highest verbal and math scores on standardized tests are less likely to enter teaching. In addition, it is frequently claimed that the ability of schools to attract these top students has been steadily declining for years. There is, however, surprisingly little evidence measuring the extent to which this popular proposition is true. We have good reason to suspect that the quality of those entering teaching has fallen over time. Teaching has remained a predominately female profession for years; at the same time, the employment opportunities for talented women outside of teaching have soared. In this paper, we combine data from four longitudinal surveys of high school graduates spanning the years 1957-1992 to examine how the propensity for talented women to enter teaching has changed over time. We find that while the quality of the average new female teacher has fallen only slightly over this period, the likelihood that a female from the top of her high school class will eventually enter teaching has fallen dramatically from 1964 to 1992 by our estimation, from almost 20% to under 4%.