We introduce a new notion of tame geometry for structures admitting an abstract notion of balls. The notion is named b-minimality and is based on definable families of points and balls. We develop a dimension theory and prove a cell decomposition theorem for b-minimal structures. We show that b-minimality applies to the theory of Henselian valued fields of characteristic zero, generalizing work by Denef–Pas [25, 26]. Structures which are o-minimal, v-minimal, or p-minimal and which satisfy some slight extra conditions are (...) also b-minimal, but b-minimality leaves more room for nontrivial expansions. The b-minimal setting is intended to be a natural framework for the construction of Euler characteristics and motivic or p-adic integrals. The b-minimal cell decomposition is a generalization of concepts of Cohen [11], Denef [15], and the link between cell decomposition and integration was first made by Denef [13]. (shrink)

Employers of all types, including group practices, health maintenance organizations, and university and other hospital practices, commonly include noncompetition clauses in physician employment contracts. The clauses only apply in the event physicians leave their employers, and typically only limit activities in relatively narrow geographic areas. Consequently, physicians often agree to the clauses without much thought or analysis. This is a mistake, as the clauses may have broad adverse ramifications for both physicians and patients.This article identifies the standard components of noncompetition (...) clauses, addresses the ethical and practical concerns they raise, and reviews recent court decisions on point. The article concludes that despite public policy concerns, courts can and often do enforce the clauses. The purpose of the article, therefore, is to increase physicians’ awareness of the potential impact of these clauses, and to encourage physicians to carefully consider whether to accept contracts that contain them, or at the very least to negotiate for the least restrictive terms possible. (shrink)

Back injuries have a bad reputation. The workman looks upon them with apprehension, the insurance company with doubt, the medical examiner with suspicion, the lawyer with uncertainty. The medical examiner is faced with the difficulty of estimating the true value of the subjective symptoms in the comparative absence of physical signs. His suspicion is born of the frequent disparity between these two. This prophetic statement made almost 100 years ago highlights an ongoing problem - how people who are incapacitated by (...) painful conditions such as chronic low back pain can be evaluated consistently and equitably for purposes of disability compensation. We confronted this vexing problem when we participated in writing the chapter devoted to impairment associated with pain of the American Medical Association s Guides to the Evaluation of Permanent Impairment, 5th edition AMA Guides 5th Our purposes in this essay are to clarify several important conceptual issues associated with the assessment of pain among disability applicants, and to articulate reasons why pain should be considered in impairment and disability ratings. (shrink)

Denef and Loeser defined a map from the Grothendieck ring of sets definable in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling to apply any cohomological invariant to these sets. We generalize this to perfect, pseudo algebraically closed fields with pro-cyclic Galois group. In addition, we define some maps between different Grothendieck rings of definable sets which provide additional information, not contained in the associated motive. In particular we infer that the map of Denef-Loeser is not injective.

Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers and Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under integration. In this paper, we will present a natural refinement of their definition that allows for stability results to hold within the wider class of [Formula: see text]-minimal structures. One of the main technical improvements is that we remove the requirement of definable Skolem functions from the proofs. As (...) a result, we obtain stability in particular for all intermediate structures between the semi-algebraic and the sub-analytic languages. (shrink)

In this article, we study the commutativity between the pull-back and the push-forward functors on constructible functions in Cluckers–Loeser motivic integration.