Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems

We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main idea is to show that for sufficiently small noise intensity and slow time dependence, the vast majority of paths remain in small space-time sets, typically in the neighbourhood of potential wells. The size of these sets often has a power-law dependence on the small parameters, with universal exponents. The overall probability of exceptional paths is exponentially small, with an exponent also showing power-law behaviour. The results cover time spans up to the maximal Kramers time of the system. We apply our method to three phenomena characteristic for bistable systems: stochastic resonance, dynamical hysteresis and bifurcation delay, where it yields precise bounds on transition probabilities, and the distribution of hysteresis areas and first-exit times. We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure

Signs of asphyxia at birth and risk of schizophrenia - Population-based case-control study

BACKGROUND: Previous research has found an association between obstetric complications and schizophrenia, but in many studies the sample size was limited, and no assessment of specific exposures was possible. AIMS: To assess the role of different complications, and in particular to distinguish between disordered foetal development and hypoxia at birth. METHOD: From the Stockholm County In-Patient Register and community registers, we identified 524 cases of schizophrenia and 1043 controls, matched for age, gender, hospital and parish of birth. Data on obstetric complications were obtained from birth records. RESULTS: There was a strong association between signs of asphyxia at birth and schizophrenia (OR 4.4; 95% C11.9-10.3) after adjustment for other obstetric complications, maternal history of psychotic illness and social class. CONCLUSIONS: Signs of asphyxia at birth are associated with an increased risk of schizophrenia in adults

Obstetric complications and risk of schizophrenia - Effect of gender, age at diagnosis and maternal history of psychosis

BACKGROUND: Obstetric complications have been studied frequently as possible risk factors for schizophrenia. AIMS: To test the hypotheses that individual obstetric complications are most strongly associated with an increased risk of schizophrenia in males, in patients with an early age at first diagnosis and in subjects with a maternal history of psychosis. METHOD: Cases of schizophrenia diagnosed between January 1971 and June 1994 were identified in the Stockholm County In-Patient Register. Controls were matched on age, gender, hospital of birth and parish of birth. Obstetric data were recorded blind to case-control status for 524 cases and 1043 controls. RESULTS: This study did not find any large or consistent effect of gender, age at diagnosis or maternal history of psychosis on the risk of schizophrenia associated with individual complications. CONCLUSIONS: Future studies should examine these effects using a much larger sample that includes patients with schizophrenia and control subjects whose genetic risk of schizophrenia has been assessed accurately