The Definition and Computation of a Metric on Plane Curves. The Meaning of a Face on a Geometric Model

Two topics in topology, the comparison of plane curves and faces on geometric models, are discussed. With regard to the first problem, a curve is defined to be a locus of points without any underlying parameterization. A metric on a class of plane curves is defined, a finite computation of this metric is given for the case of piecewise linear curves, and it is shown how to approximate curves that have bounded curvature by piecewise linear curves. In this way a bound on the distance between two curves can be computed. With regard to the second problem, the questions to be discussed are under what circumstances do geometrical faces make sense; how can they be explicity defined; and when are these geometrical faces homeomorphic to the realization of the abstract (topological) face

SurveyMan: Programming and Automatically Debugging Surveys

Surveys can be viewed as programs, complete with logic, control flow, and bugs. Word choice or the order in which questions are asked can unintentionally bias responses. Vague, confusing, or intrusive questions can cause respondents to abandon a survey. Surveys can also have runtime errors: inattentive respondents can taint results. This effect is especially problematic when deploying surveys in uncontrolled settings, such as on the web or via crowdsourcing platforms. Because the results of surveys drive business decisions and inform scientific conclusions, it is crucial to make sure they are correct. We present SurveyMan, a system for designing, deploying, and automatically debugging surveys. Survey authors write their surveys in a lightweight domain-specific language aimed at end users. SurveyMan statically analyzes the survey to provide feedback to survey authors before deployment. It then compiles the survey into JavaScript and deploys it either to the web or a crowdsourcing platform. SurveyMan's dynamic analyses automatically find survey bugs, and control for the quality of responses. We evaluate SurveyMan's algorithms analytically and empirically, demonstrating its effectiveness with case studies of social science surveys conducted via Amazon's Mechanical Turk.Comment: Submitted version; accepted to OOPSLA 201

Prioritized Garbage Collection: Explicit GC Support for Software Caches

Programmers routinely trade space for time to increase performance, often in the form of caching or memoization. In managed languages like Java or JavaScript, however, this space-time tradeoff is complex. Using more space translates into higher garbage collection costs, especially at the limit of available memory. Existing runtime systems provide limited support for space-sensitive algorithms, forcing programmers into difficult and often brittle choices about provisioning. This paper presents prioritized garbage collection, a cooperative programming language and runtime solution to this problem. Prioritized GC provides an interface similar to soft references, called priority references, which identify objects that the collector can reclaim eagerly if necessary. The key difference is an API for defining the policy that governs when priority references are cleared and in what order. Application code specifies a priority value for each reference and a target memory bound. The collector reclaims references, lowest priority first, until the total memory footprint of the cache fits within the bound. We use this API to implement a space-aware least-recently-used (LRU) cache, called a Sache, that is a drop-in replacement for existing caches, such as Google's Guava library. The garbage collector automatically grows and shrinks the Sache in response to available memory and workload with minimal provisioning information from the programmer. Using a Sache, it is almost impossible for an application to experience a memory leak, memory pressure, or an out-of-memory crash caused by software caching.Comment: to appear in OOPSLA 201

Exchange Enhancement of the Electron-Phonon Pair Interaction

The critical temperature of high-$T_c$ superconductors is determined, at least in part, by the electron-phonon coupling. We include the effect of an exchange interaction between the electrons and calculate the renormalization of the bare phonon frequencies and the electron-phonon verticies in a random phase approximation and obtain a strongly enhanced attractive phonon-induced electron-electron interaction. Using Fast Fourier Transform techniques, the weak-coupling selfconsistency equation for the order parameter is solved in the 2D first Brillouin zone for the Emery tight-binding band with different band fillings. The enhancement of $T_c$ arises primarily from the softening of the phonon frequencies rather than the vertex renormalization.Comment: (2 pages, postscript file, hardcopies available from the authors

Evolution of Magnetic and Superconducting Fluctuations with Doping of High-Tc Superconductors (An electronic Raman scattering study)

For YBa_2Cu_3O_{6+\delta} and Bi_2Sr_2CaCu_2O_8 superconductors, electronic Raman scattering from high- and low-energy excitations has been studied in relation to the hole doping level, temperature, and energy of the incident photons. For underdoped superconductors, it is concluded that short range antiferromagnetic (AF) correlations persist with hole doping and doped single holes are incoherent in the AF environment. Above the superconducting (SC) transition temperature T_c the system exhibits a sharp Raman resonance of B_1g symmetry and about 75 meV energy and a pseudogap for electron-hole excitations below 75 meV, a manifestation of a partially coherent state forming from doped incoherent quasi-particles. The occupancy of the coherent state increases with cooling until phase ordering at T_c produces a global SC state.Comment: 5 pages, 4 EPS figures; SNS'97 Proceedings to appear in J. Phys. Chem. Solid