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It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.
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The visual analysis of cardiotocographic examinations is a very subjective process. The accurate detection and segmentation of the fetal heart rate (FHR) features and their correlation with the uterine contractions in time allow a better diagnostic and the possibility of anticipation of many problems related to fetal distress. This paper presents a computerized diagnostic aid system based on digital signal processing techniques to detect and segment changes in the FHR and the uterine tone signals automatically. After a pre-processing phase, the FHR baseline detection is calculated. An auxiliary signal called detection line is proposed to support the detection and segmentation processes. Then, the Hilbert transform is used with an adaptive threshold for identifying fiducial points on the fetal and maternal signals. For an antepartum (before labor) database, the positive predictivity value (PPV) is 96.80% for the FHR decelerations, and 96.18% for the FHR accelerations. For an intrapartum (during labor) database, the PPV found was 91.31% for the uterine contractions, 94.01% for the FHR decelerations, and 100% for the FHR accelerations. For the whole set of exams, PPV and SE were both 100% for the identification of FHR DIP II and prolonged decelerations.