Irreversibility in a simple reversible model

This paper studies a parametrized family of familiar generalized baker maps, viewed as simple models of time-reversible evolution. Mapping the unit square onto itself, the maps are partly contracting and partly expanding, but they preserve the global measure of the definition domain. They possess periodic orbits of any period, and all maps of the set have attractors with well defined structure. The explicit construction of the attractors is described and their structure is studied in detail. There is a precise sense in which one can speak about absolute age of a state, regardless of whether the latter is applied to a single point, a set of points, or a distribution function. One can then view the whole trajectory as a set of past, present and future states. This viewpoint is then applied to show that it is impossible to define a priori states with very large "negative age". Such states can be defined only a posteriori. This gives precise sense to irreversibility -- or the "arrow of time" -- in these time-reversible maps, and is suggested as an explanation of the second law of thermodynamics also for some realistic physical systems.Comment: 15 pages, 12 Postscript figure

Functional Genomics Unique to Week 20 Post Wounding in the Deep Cone/Fat Dome of the Duroc/Yorkshire Porcine Model of Fibroproliferative Scarring

Background: Hypertrophic scar was first described over 100 years ago; PubMed has more than 1,000 references on the topic. Nevertheless prevention and treatment remains poor, because 1) there has been no validated animal model; 2) human scar tissue, which is impossible to obtain in a controlled manner, has been the only source for study; 3) tissues typically have been homogenized, mixing cell populations; and 4) gene-by-gene studies are incomplete.Methodology/Principal Findings: We have assembled a system that overcomes these barriers and permits the study of genome-wide gene expression in microanatomical locations, in shallow and deep partial-thickness wounds, and pigmented and non-pigmented skin, using the Duroc( pigmented fibroproliferative)/Yorkshire( non-pigmented non-fibroproliferative) porcine model. We used this system to obtain the differential transcriptome at 1, 2, 3, 12 and 20 weeks post wounding. It is not clear when fibroproliferation begins, but it is fully developed in humans and the Duroc breed at 20 weeks. Therefore we obtained the derivative functional genomics unique to 20 weeks post wounding. We also obtained long-term, forty-six week follow-up with the model.Conclusions/Significance: 1) the scars are still thick at forty-six weeks post wounding further validating the model. 2) the differential transcriptome provides new insights into the fibroproliferative process as several genes thought fundamental to fibroproliferation are absent and others differentially expressed are newly implicated. 3) the findings in the derivative functional genomics support old concepts, which further validates the model, and suggests new avenues for reductionist exploration. in the future, these findings will be searched for directed networks likely involved in cutaneous fibroproliferation. These clues may lead to a better understanding of the systems biology of cutaneous fibroproliferation, and ultimately prevention and treatment of hypertrophic scarring.The National Institute on Disability and Rehabilitation ResearchThe National Institutes of HealthThe Washington State Council of Fire Fighters Burn FoundationThe Northwest Burn FoundationUniv Washington, Dept Surg, Div Plast Surg, Seattle, WA 98195 USAIowa State Univ, Dept Anim Sci, Ames, IA USAUniv Washington, Dept Biostat, Seattle, WA 98195 USAMahidol Univ, Ramathibodi Hosp, Dept Surg, Bangkok 10700, ThailandUniv Washington, Dept Environm & Occupat Hlth Sci, Seattle, WA 98195 USAUniversidade Federal de São Paulo, Div Plast Surg, Dept Surg, São Paulo, BrazilUniversidade Federal de São Paulo, Div Plast Surg, Dept Surg, São Paulo, BrazilThe National Institute on Disability and Rehabilitation Research: H133G050022The National Institutes of Health: 1R21GM074673The National Institutes of Health: 5U54GM062119-09Web of Scienc