Preface Through many centuries physics has been one of the most fruitful sources of inspiration for mathematics. As a consequence, mathematics has become an economic language providing a few basic principles which allow to explain a large variety of physical phenomena. Many of them are described in terms of partial diierential equations (PDEs). In recent years, however, mathematics also has been stimulated by other novel elds such as image processing. Goals like image segmentation, multiscale image representation, or image restoration cause a lot of challenging mathematical questions. Nevertheless, these problems frequently have been tackled with a pool of heuristical recipes. Since the treatment of digital images requires very much computing power, these methods had to be fairly simple. With the tremendous advances in computer technology in the last decade, it has become possible to apply more sophisticated techniques such as PDE-based methods which have been inspired by physical processes. Among these techniques, parabolic PDEs have found a lot of attention for smoothing and restoration purposes, see e.g. 113]. To restore images these equations frequently arise from gradient descent methods applied to variational problems. Image smoothing by parabolic PDEs is closely related to the scale-space concept where one embeds the original image into a family of subsequently simpler , more global representations of it. This idea plays a fundamental role for extracting semantically important information. The pioneering work of Alvarez, Guichard, Lions and Morel 11] has demonstrated that all scale-spaces fulllling a few fairly natural axioms are governed by parabolic PDEs with the original image as initial condition. Within this framework, two classes can be justiied in a rigorous way as scale-spaces: the linear diiusion equation with constant dif-fusivity and nonlinear so-called morphological PDEs. All these methods satisfy a monotony axiom as smoothing requirement which states that, if one image is brighter than another, then this order is preserved during the entire scale-space evolution. An interesting class of parabolic equations which pursue both scale-space and restoration intentions is given by nonlinear diiusion lters. Methods of this type have been proposed for the rst time by Perona and Malik in 1987 190]. In v vi PREFACE order to smooth the image and to simultaneously enhance semantically important features such as edges, they apply a diiusion process whose diiusivity is steered by local image properties. These lters are diicult to analyse mathematically , as they may act locally like a backward diiusion process. …

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Anisotropic diffusion in image processing

Researchers studying hidden populations–including injection drug users, men who have sex with men, and the homeless–find that standard probability sampling methods are either inapplicable or prohibitively costly because their subjects lack a sampling frame, have privacy concerns, and constitute a small part of the general population. Therefore, researchers generally employ non-probability methods, including location sampling methods such as targeted sampling, and chain-referral methods such as snowball and respondent-driven sampling. Though nonprobability methods succeed in accessing the hidden populations, they have been insufficient for statistical inference. This paper extends the respondent-driven sampling method to show that when biases associated with chain-referral methods are analyzed in sufficient detail, a statistical theory of the sampling process can be constructed, based on which the sampling process can be redesigned to permit the derivation of indicators that are not biased and have known levels of precision. The results are based on a study of 190 injection drug users in a small Connecticut city.

https://www.jstor.org/stable/10.1525/sp.2002.49.1.11

Respondent-Driven Sampling II: Deriving Valid Population Estimates from Chain-Referral Samples of Hidden Populations

The design of efficient storage hierarchies generally involves the repeated running of "typical" program address traces through a simulated storage system while various hierarchy design parameters are adjusted.

This paper describes a new and efficient method of determining, in one pass of an address trace, performance measures for a large class of demand-paged, multilevel storage systems utilizing a variety of mapping schemes and replacement algorithms.

The technique depends on an algorithm classification, called "stack algorithms," examples of which are "least frequently used," "least recently used," "optimal," and "random replacement" algorithms. The techniques yield the exact access frequency to each storage device, which can be used to estimate the overall performance of actual storage hierarchies.

Evaluation techniques for storage hierarchies

The purpose of this article is to integrate previous theory and research addressing interpersonal complementarity, a construct that is central to refined and extended research and clinical applications of interpersonal theory. The article first describes the 1982 Interpersonal Circle, which the author constructed as a comprehensive taxonomy of the domain of two-dimensional interpersonal behavior. The 1982 Circle integrates and expands the content of four major adult interpersonal measures (LaForge & Suczek's Interpersonal Check List, Wiggins's Interpersonal Adjective Scales, Lorr & McNair's Interpersonal Behavior Inventory, and Kiesler et al.'s Impact Message Inventory) to provide a circle taxonomy consisting of 16 segments, 128 subclasses, 2 levels, and 350 bipolar items. Second, the article reviews previous conceptions of interpersonal complementarity and, using the 1982 Circle as a theoretical and operational guide, derives 11 propositions of complementarity as they apply in personality, psychopathology, and psychotherapy.

The 1982 Interpersonal Circle: A taxonomy for complementarity in human transactions

We study learning in a setting where agents receive independent noisy signals about the true value of a variable and then communi cate in a network. They naively update beliefs by repeatedly taking weighted averages of neighbors' opinions. We show that all opinions in a large society converge to the truth if and only if the influence of the most influential agent vanishes as the society grows. We also identify obstructions to this, including prominent groups, and pro vide structural conditions on the network ensuring efficient learn ing. Whether agents converge to the truth is unrelated to how quickly consensus is approached. (JEL D83, D85, Z13)

/pdf/naive-learning-in-social-networks-and-the-wisdom-of-crowds-15d43bhpge.pdf

Naïve Learning in Social Networks and the Wisdom of Crowds

Markov chains are one of the most useful classes of stochastic processes, being • simple, flexible and supported by many elegant theoretical results • valuable for building intuition about random dynamic models • central to quantitative modeling in their own right You will find them in many of the workhorse models of economics and finance. In this lecture we review some of the theory of Markov chains. We will also introduce some of the high quality routines for working with Markov chains available in QuantEcon.jl. Prerequisite knowledge is basic probability and linear algebra.

K. A. Bush

Papers

Finite Markov Chains.