Pay Equity Legislation in the 109th Congress

The term pay equity originates from the fact that women as a group are paid less than men. In 2003, for example, women with a strong commitment to the work force earned about 76-79 cents for every dollar earned by men. As women’s earnings as a percentage of men’s earnings have narrowed by just 15 percentage points over the past 40-plus years (from about 60% in the 1960s and 1970s to more than 70% since 1990), some members of the public policy community have argued that current anti-discrimination laws should be strengthened and that additional measures should be enacted. Others, in contrast, believe that further government intervention is unnecessary because the gender wage gap will narrow on its own as women’s labor market qualifications continue to more closely resemble those of men

Apollonian structure in the Abelian sandpile

The Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 neighbors. When begun from a large stack of chips, the terminal state of the sandpile has a curious fractal structure which has remained unexplained. Using a characterization of the quadratic growths attainable by integer-superharmonic functions, we prove that the sandpile PDE recently shown to characterize the scaling limit of the sandpile admits certain fractal solutions, giving a precise mathematical perspective on the fractal nature of the sandpile.Comment: 27 Pages, 7 Figure

Parental Liability for the Torts of Their Minor Children: Limits, Logic & Legality

Throughout history, children have had a tendency to cause mischief, damage and often injury to people and the property of others

The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website

Theory of the Circular Diffraction Antenna

The circular diffraction antenna consists of a coaxial wave guide fitted with an infinite‐plane conducting baffle, and open to free space. An equivalent circuit description, appropriate to principal‐mode propagation in the coaxial region, is investigated theoretically. Variational expressions for the circuit parameters are derived, and used for accurate numerical evaluation

A Model of Agenda Influence on Committee Decisions

Within a range of circumstances it appears to be possible to control a group's decision by controlling only the agenda. The boundaries of the range over which the agenda is such an overwhelmingly important parameter are not yet known, and the exact principles upon which the influence rests have not been identified. However, the research results reported below provide a first step in answering these questions. Our approach to this problem originated in both practical and theoretical considerations. As a practical matter, we were involved in an important and complex committee decision. A large flying club in which we held membership was meeting to vote upon the size and composition of the aircraft fleet which would be available to the membership for flying. As members we had preferences about the fleet available to us and an opportunity to shape the agenda. Preliminary discussions and meetings had narrowed the range of possibilities greatly from hundreds of thousands of competing alternatives to a few hundred. Over these remaining possibilities, however, there were conflicting and strongly held opinions. The group was to meet once and decide the issue by majority vote

Apollonian structure in the Abelian sandpile

The Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 neighbors. When begun from a large stack of chips, the terminal state of the sandpile has a curious fractal structure which has remained unexplained. Using a characterization of the quadratic growths attainable by integer-superharmonic functions, we prove that the sandpile PDE recently shown to characterize the scaling limit of the sandpile admits certain fractal solutions, giving a precise mathematical perspective on the fractal nature of the sandpile.National Science Foundation (U.S.) (grants DMS-1004696, DMS-1004595 and DMS- 1243606

On Using the Agenda to Influence Group Decisions: Theory, Experiments, and an Application

Three general claims are made in the paper. First, the agenda or groupings in which alternatives are considered for adoption or elimination is a major parameter in determining what a group will choose. Secondly, the nature of this influence is sufficiently systematic to yield to an analytical model. Finally, it is claimed that this discovery has important practical implications. In support of these claims, the paper offers a theory of the basis of the influence together with an attempt to capture this theory within a mathematical model. The results of an application of the theory to a real situation and the results of several series of experiments are reported