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Infinite horizon value functions in the Wasserstein spaces
Hynd, Ryan,Kim, Hwa Kil Elsevier 2015 Journal of differential equations Vol.258 No.6
<P><B>Abstract</B></P> <P>We perform a systematic study of optimization problems in the Wasserstein spaces that are analogs of infinite horizon, deterministic control problems. We derive necessary conditions on action minimizing paths and present a sufficient condition for their existence. We also verify that the corresponding generalized value functions are a type of viscosity solution of a time independent, Hamilton–Jacobi equation in the space of probability measures. Finally, we prove a special case of a conjecture involving the subdifferential of generalized value functions and their relation to action minimizing paths.</P>
Fleece Phenotype Influences Susceptibility to Cortisol-induced Follicle Shutdown in Merino Sheep
Ansari-Renani, H.R.,Hynd, P.I.,Aghajanzadeh, A. Asian Australasian Association of Animal Productio 2007 Animal Bioscience Vol.20 No.11
This experiment was conducted to determine the extent to which susceptibility to cortisol-induced follicle shutdown is influenced by fleece phentotype. Twenty Finewool (10 sheep low fibre diameter, low coefficient of fibre diameter-LL and 10 low fibre diameter, high coefficient of variation of fibre diameter-LH) and twenty Strongwool (10 low fibre diameter, low coefficient of variation of fibre diameter-HL and 10 high fibre diameter and high coefficient of variation of fibre diameter-HH) sheep of 9 months of age were individually penned in an animal house and were injected intramuscularly with an aqueous suspension of hydrocortisone acetate at a rate of 1.42 mg/kg body weight for a period of two weeks. Fibre diameter was measured from clipped tattooed patch wool samples. Follicle activity was measured by histological changes in skin biopsies taken weekly. Blood samples were collected at two-week intervals and plasma cortisol measured. Increased plasma cortisol concentration significantly (p<0.05) reduced clean wool production and mean fibre diameter dropped to its lowest level four weeks after commencement and two weeks after the cessation of cortisol injection. Elevation of plasma cortisol concentration significantly (p<0.0001) increased the percentage of inactive follicles two weeks after injection started. High fibre diameter groups (Strongwool sheep; i.e. HL+HH) had significantly (p<0.0001) higher percentage of follicle shutdown than low fibre diameter groups (Finewool sheep; i.e. LL+LH). Average percentage of shutdown follicles for Finewool (LL+LH) and Strongwool (HL+HH) Merino sheep was $9.8{\pm}0.9$ and $13.5{\pm}0.9$ respectively. Shutdown of primary follicles was more pronounced in Finewool than Strongwool sheep. There was no significant effect of coefficient of variation of fibre diameter on propensity to follicle shutdown induced by exogenous cortisol. It is concluded that elevation in plasma cortisol concentration is inhibitory to the normal activity of follicles in Strongwool sheep but that variation in fibre diameter has little or no effect.