autoAx: An Automatic Design Space Exploration and Circuit Building Methodology utilizing Libraries of Approximate Components

Approximate computing is an emerging paradigm for developing highly energy-efficient computing systems such as various accelerators. In the literature, many libraries of elementary approximate circuits have already been proposed to simplify the design process of approximate accelerators. Because these libraries contain from tens to thousands of approximate implementations for a single arithmetic operation it is intractable to find an optimal combination of approximate circuits in the library even for an application consisting of a few operations. An open problem is "how to effectively combine circuits from these libraries to construct complex approximate accelerators". This paper proposes a novel methodology for searching, selecting and combining the most suitable approximate circuits from a set of available libraries to generate an approximate accelerator for a given application. To enable fast design space generation and exploration, the methodology utilizes machine learning techniques to create computational models estimating the overall quality of processing and hardware cost without performing full synthesis at the accelerator level. Using the methodology, we construct hundreds of approximate accelerators (for a Sobel edge detector) showing different but relevant tradeoffs between the quality of processing and hardware cost and identify a corresponding Pareto-frontier. Furthermore, when searching for approximate implementations of a generic Gaussian filter consisting of 17 arithmetic operations, the proposed approach allows us to identify approximately $10^3$ highly important implementations from $10^{23}$ possible solutions in a few hours, while the exhaustive search would take four months on a high-end processor.Comment: Accepted for publication at the Design Automation Conference 2019 (DAC'19), Las Vegas, Nevada, US

Diachronic construction grammar: A state of the art

This paper will offer a state-of-the-art survey of work in historical linguistics (mainly, but not exclusively, on English) that can be brought under the heading of “diachronic construction grammar”. As a new development in diachronic linguistics, this discipline name subsumes two big strands of research. One of these I will simply call the “construction grammar” strand. It consists of work by people who have come to diachronic construction grammar from synchronic construction grammar. The other major strand has its origin in grammaticalization theory and encompasses the research efforts of those working within grammaticalization theory who have relatively recently come to recognize that the most central theoretical concept of construction grammar is a highly relevant and useful one in the description of and theorizing about grammaticalization changes and who have now even started to use the term “constructionalization” in lieu of “grammaticalization”, distinguishing between “grammatical constructionalization” and “lexical constructionalization”. The main difference between both strands is that while the grammaticalization strand is concerned with the question of how languages acquire constructions, first and foremost lexically-specified ones, this is not necessarily the case in the construction grammar strand. Three sub-strands of the latter will be distinguished. A first sub-strand consists of work by Goldbergian construction grammarians who consider particular argument structure constructions from a historical perspective. Another thread of research is work on “constructional attrition”. The third area of investigation appeals to language contact and borrowing to explain the presence of a construction in the constructicon of a language. Returning to the grammaticalization strand of diachronic construction grammar the paper will also address the question of what the conditions are for work on grammaticalization to be considered part of diachronic construction grammar.postprin

Legal Sets

In this Article, I propose that the practices of legal reasoning and analysis are helpfully understood as being primarily concerned not with rules or propositions, but with sets. This Article develops a formal model of the role of sets in the practices of legal actors in a common-law system defined by a recursive relationship between cases and rules. In doing so, it demonstrates how conceiving of legal doctrines as a universe of discourse comprising (sometimes nested or overlapping) sets of cases can clarify the logical structure that governs marginal cases and help organize the available options for resolving such cases according to their form. While many legal professionals may intuitively navigate this set-theoretic structure, the formal model of that structure has important implications for legal theory. In particular, it (1) generates a useful account of the relationships among rules, standards, and principles; (2) provides a novel set of tools for understanding the nature of precedent; and (3) illuminates an extra-linguistic dimension to the problem of judicial discretion. On the last point, I argue that discretion is not merely a product of the imperfect relationship between abstractions and reality, or between natural language and the world, but that it is instead an emergent property of the structure of legal practice: a structure composed of sets “all the way down.

Nuisance as a Modern Mode of Land Use Control

Recognizing the inflexibility inherent in present zoning mechanisms, this comment analyzes the concept of nuisance as an additional, more versatile means of land use control. In an exhaustive categorization and evaluation of Washington cases and those from other jurisdictions, the author sets forth the principles of nuisance law and the factors affecting court decisions on nuisance. Both private and public actionable nuisances are discussed, along with available remedies, within a concise analytical framework

Anatomy of quantum chaotic eigenstates

The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.Comment: Corrected typos, added a few references and updated some result

Understanding the Black-White Test Score Gap in the First Two Years of School

In previous research, a substantial gap in test scores between White and Black students persists, even after controlling for a wide range of observable characteristics. Using a newly available data set (Early Childhood Longitudinal Study), we demonstrate that in stark contrast to earlier studies, the Black-White test score gap among incoming kindergartners disappears when we control for a small number of covariates. Over the first two years of school, however, Blacks lose substantial ground relative to other races. There is suggestive evidence that differences in school quality may be an important part of the explanation. None of the other hypotheses we test to explain why Blacks are losing ground receive any empirical backing. The difference between our findings and previous research is consistent with real gains made by recent cohorts of Blacks, although other explanations are also possible.