Average flow constraints and stabilizability in uncertain production-distribution systems

We consider a multi-inventory system with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first-order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of two requirements: (i) meeting any possible demand at each time (worst case stability) or (ii) achieving a predefined flow in the average (average flow constraints). Necessary and sufficient conditions for the achievement of both goals have been proposed by the authors. In this paper, we face the case in which these conditions are not satisfied. We show that, if we ignore the requirement on worst case stability, we can find a control strategy driving the expected value of the state to zero. On the contrary, if we ignore the average flow constraints, we can find a control strategy that satisfies worst case stability while optimizing any linear cost on the average control. In the latter case, we provide a tight bound for the cost

Cellulite histopathology and related mechanobiology.

Cellulite, sometimes called gynoid lipodystrophy, is much more prevalent in women than in men. There are glaring discrepancies regarding the microanatomical descriptions of this condition in the literature. A lumpy aspect of the dermo-hypodermal interface is often cited, but it appears to represent a gender-linked characteristic of the thighs and buttocks without being a specific sign of cellulite. Incipient cellulite recognized by a discrete padded look or 'orange peel' aspect appears correlated with the presence of a network of focally enlarged fibrosclerotic strands partitioning the hypodermis and serving as a physiological buttress limiting the outpouching of fat lobules on pinching the skin. These connective tissue structures might represent a hormonal-dependent reactive process to sustained mechanical tensions caused by the adipocyte lobules. Full blown cellulite is recognized by a lumpy-bumpy and dimpled skin surface. It likely represents subjugation of the hypertrophic response of the hypodermal connective tissue strands when their resistance is overcome by progressive fat accumulation. In these cases, histological aspects reminiscent of striae distensae are identified within the hypodermal connective tissue strands. The mechanical properties of skin involved by cellulite process are altered, but may tend to resume to normal under treatment. These functional changes influence the mechanobiology of connective tissue cells, in particular the Factor XIIIa-positive dermal dendrocytes