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Miech on 'generational forgetting' about drug-use dangers

Impacts of H-1B visas: Lower prices and higher production - or lower wages and higher profits?

MTF data show 10% of 19-20 year-olds report bouts of drinking 10-plus alcoholic beverages

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Call for papers: Conference on computational social science, April 2017, U-M

Sioban Harlow honored with 2017 Sarah Goddard Power Award for commitment to women's health

Post-doc fellowship in computational social science for summer or fall 2017, U-Penn

ICPSR Summer Program scholarships to support training in statistics, quantitative methods, research design, and data analysis

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Next Brown Bag

Mon, Feb 13, 2017, noon:
Daniel Almirall, "Getting SMART about adaptive interventions"

Qualitative Theory of Compartmental Systems With Lags

Archived Abstract of Former PSC Researcher

Jacquez, J.A., and Carl P. Simon. 2002. "Qualitative Theory of Compartmental Systems With Lags." Mathematical Biosciences, 180(specialissue): 329-362.

Dynamic models of many processes in the biological and physical sciences give systems of ordinary differential equations called compartmental systems. Often, these systems include time lags; in this context, continuous probability density functions (pdfs) of lags are far more important than discrete lags. There is a relatively complete theory of compartmental systems without lags, both linear and non-linear [SIAM Rev. 35 (1993) 43]. The authors extend their previous work on compartmental systems without lags to show that, for discrete lags and for a very large class of pdfs of continuous lags, compartmental systems with lags are equivalent to larger compartmental systems without lags. Consequently, the properties of compartmental systems with lags are the same as those of compartmental systems without lags. For a very large class of compartmental systems with time lags, one can show that the time lags themselves can be generated by compartmental systems without lags. Thus, such systems can be partitioned into a main system, which is the original system without the lags, plus compartmental subsystems without lags that generate the lags. The latter may be linear or non-linear and may be. inserted into main systems that are linear or non-linear. The state variables of the compartmental lag subsystems are hidden variables in the formulation with explicit lags. (C) 2002 Elsevier Science Inc. All rights reserved.

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