Phantom maps and chromatic phantom maps

In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or nothing behaviour is preserved when X is replaced with V smash X for V finite. In the second part, we introduce chromatic phantom maps. A map is n-phantom if it is null when restricted to finite spectra of type at least n. We define divisibility and finite type conditions which are suitable for studying n-phantom maps. We show that the duality functor W_{n-1} defined by Mahowald and Rezk is the analog of Brown-Comenetz duality for chromatic phantom maps, and give conditions under which the natural map Y --> W_{n-1}^2 Y is an isomorphism.Comment: 18 page

Quillen model structures for relative homological algebra

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is encompassed by Quillen's homotopical algebra. The goal of this paper is to show that more general forms of homological algebra also fit into Quillen's framework. Specifically, a projective class on a complete and cocomplete abelian category A is exactly the information needed to do homological algebra in A. The main result is that, under weak hypotheses, the category of chain complexes of objects of A has a model category structure that reflects the homological algebra of the projective class in the sense that it encodes the Ext groups and more general derived functors. Examples include the "pure derived category" of a ring R, and derived categories capturing relative situations, including the projective class for Hochschild homology and cohomology. We characterize the model structures that are cofibrantly generated, and show that this fails for many interesting examples. Finally, we explain how the category of simplicial objects in a possibly non-abelian category can be equipped with a model category structure reflecting a given projective class, and give examples that include equivariant homotopy theory and bounded below derived categories.Comment: 29 pages. v4: Published in Math. Proc. Cambridge Philos. Soc. v5: Minor corrections to published version appear on last pag

Postnikov extensions of ring spectra

We give a functorial construction of k-invariants for ring spectra and use these to classify extensions in the Postnikov tower of a ring spectrum.Comment: This is the version published by Algebraic & Geometric Topology on 1 November 200

Obstruction Theory in Model Categories

Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obstruction theory with respect to all fibrations. Up to weak equivalence, retract, and cobase change, they are the cofibrations with weakly contractible target. Equivalently, they are the retracts of principal cofibrations. Without properness, the same classification holds for cofibrations with cofibrant source. Our results dualize to give a classification of fibrations that have an obstruction theory.Comment: 17 pages. v3 includes improved introduction and several other minor improvement

A curious example of two model categories and some associated differential graded algebras

The paper gives a new proof that the model categories of stable modules for the rings Z/(p^2) and (Z/p)[\epsilon]/(\epsilon^2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with non-isomorphic K-theories

Indicators of Woman Abuse Based on a Chart Review at a Family Practice Center

Objective: To identify demographic and health indicators of domestic violence. Design: Anonymous questionnaire survey of patients regarding violence and a chart review regarding symptoms and diagnoses. Setting: Community-based family practice residency training center in a midwestern city. Participants: Women 18 years of age or older visiting the center over a 2-month period in 1990. Of 476 eligible participants, 394 (82.7%) consented to complete the survey. Measures: A detailed, standardized measure of violence was used. Physical and psychological problems were given codes from the International Classification of Diseases, Ninth Revision (ICD-9). Results: Younger women and those separated or divorced from their partners were more likely to have been victims. Never-married women also had substantially high rates of victimization. Depression was the strongest indicator of victimization, even when controlling for demographic factors. Back pain, ulcers, headaches, and anxiety were not strong indicators of abuse. A classification analysis showed that a combination of all variables could predict lifetime injury only about half the time and violence in the past year only about 20% of the time. Conclusions: Since neither demographic nor health factors could accurately predict who had been victimized, all women need to be asked about abuse. Physicians should also keep in mind that divorced and unmarried women are often affected by abuse, either immediately or by its long term aftereffects.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/89971/1/Saunders-Hamberger-Hovey-1993-Indicators of woman abuse based on a chart review at a family practice center AFM-AMA.pd

Duality and Pro-Spectra

Cofiltered diagrams of spectra, also called pro-spectra, have arisen in diverse areas, and to date have been treated in an ad hoc manner. The purpose of this paper is to systematically develop a homotopy theory of pro-spectra and to study its relation to the usual homotopy theory of spectra, as a foundation for future applications. The surprising result we find is that our homotopy theory of pro-spectra is Quillen equivalent to the opposite of the homotopy theory of spectra. This provides a convenient duality theory for all spectra, extending the classical notion of Spanier-Whitehead duality which works well only for finite spectra. Roughly speaking, the new duality functor takes a spectrum to the cofiltered diagram of the Spanier-Whitehead duals of its finite subcomplexes. In the other direction, the duality functor takes a cofiltered diagram of spectra to the filtered colimit of the Spanier-Whitehead duals of the spectra in the diagram. We prove the equivalence of homotopy theories by showing that both are equivalent to the category of ind-spectra (filtered diagrams of spectra). To construct our new homotopy theories, we prove a general existence theorem for colocalization model structures generalizing known results for cofibrantly generated model categories.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-34.abs.htm

Association study between autistic-like traits and polymorphisms in the autism candidate regions RELN, CNTNAP2, SHANK3, and CDH9/10

The Swedish Research CouncilThe Swedish Council for Working Life and Social ResearchThe Petrus and Augusta Hedlund FoundationÅke Wiberg foundationÅhlens FoundationWilhelm and Martina Lundgren FoundationThe Sahlgrenska AcademyPublishe

Lactation and neonatal nutrition: defining and refining the critical questions.

This paper resulted from a conference entitled "Lactation and Milk: Defining and refining the critical questions" held at the University of Colorado School of Medicine from January 18-20, 2012. The mission of the conference was to identify unresolved questions and set future goals for research into human milk composition, mammary development and lactation. We first outline the unanswered questions regarding the composition of human milk (Section I) and the mechanisms by which milk components affect neonatal development, growth and health and recommend models for future research. Emerging questions about how milk components affect cognitive development and behavioral phenotype of the offspring are presented in Section II. In Section III we outline the important unanswered questions about regulation of mammary gland development, the heritability of defects, the effects of maternal nutrition, disease, metabolic status, and therapeutic drugs upon the subsequent lactation. Questions surrounding breastfeeding practice are also highlighted. In Section IV we describe the specific nutritional challenges faced by three different populations, namely preterm infants, infants born to obese mothers who may or may not have gestational diabetes, and infants born to undernourished mothers. The recognition that multidisciplinary training is critical to advancing the field led us to formulate specific training recommendations in Section V. Our recommendations for research emphasis are summarized in Section VI. In sum, we present a roadmap for multidisciplinary research into all aspects of human lactation, milk and its role in infant nutrition for the next decade and beyond