Bernstein Processes Associated with a Markov Process

Abstract. A general description of Bernstein processes, a class of diffusion processes, relevant to the probabilistic counterpart of quantum theory known as Euclidean Quantum Mechanics, is given. It is compatible with finite or infinite dimensional state spaces and singular interactions. Although the rela-tions with statistical physics concepts (Gibbs measure, entropy,...) is stressed here, recent developments requiring Feynman’s quantum mechanical tools (ac-tion functional, path integrals, Noether’s Theorem,...) are also mentioned and suggest new research directions, especially in the geometrical structure of our approach. This is a review of various recent developments regarding the construction and properties of Bernstein processes, a class of diffusions originally introduced for the purpose of Euclidean Quantum Mechanics (EQM), a probabilistic analogue o

Random parallel transport on surfaces of finite type, and relations to homotopy

For general surfaces of finite type, probability measures for parallel transport are con­structed. Relations to the topology of the surface are pointed out. We also discuss possible loop invariants

Dextran- Versus Crystalloid-Based Prime in Cardiac Surgery: A Prospective Randomized Pilot Study

BACKGROUND: The optimum priming fluid for the cardiopulmonary bypass (CPB) circuit is still debated. We compared a new hyperoncotic priming solution containing dextran 40, which has an electrolyte composition that mimics extracellular fluid, with a standard crystalloid-based prime. METHODS: Eighty cardiac surgery patients were included in this double-blind randomized single-centre study. The patients were randomized to either a dextran-based prime or a crystalloid prime containing Ringer acetate and mannitol. The primary endpoint was colloid oncotic pressure (COP) in serum during CPB. Secondary endpoints included fluid balance, bleeding and transfusion requirements, pulmonary function, hemolysis, systemic inflammation, and markers of renal, hepatic, myocardial, and brain injury. Blood samples were collected before, during, and after CPB. RESULTS: COP was higher in the dextran group than in the crystalloid prime group on CPB (18.8±2.9 vs. 16.4±2.9 mmHg, p<0.001) and 10 min after CPB (19.2±2.7 vs. 16.8±2.9 mmHg, p<0.001). Patients in the dextran group required less intravenous fluid during CPB (1090±499 vs. 1437±543 ml; p=0.003) and net fluid balance was less positive 12h after surgery (+1,431±741 vs. +1,901±922 ml; p=0.014). Plasma free hemoglobin was significantly lower in the dextran group 2h after CPB (0.18±0.11 vs 0.41±0.33, p=0.001). There were no significant differences in bleeding, transfusion requirements, organ function, systemic inflammation, or brain and myocardial injury markers between the groups at any time point. CONCLUSIONS: Our results suggest that a hyperoncotic dextran-based priming solution preserves intraoperative COP compared to crystalloid prime. Larger studies with clinically valid endpoints are necessary to evaluate hyperoncotic prime solutions further