A new median-based formula for the Black-Scholes-Merton Theory

The Black-Scholes-Merton (BSM) theory for price variation has been well established in mathematical financial engineering. However, it has been recognized that long-term outcomes in practice may divert from the Black-Scholes formula, which is the expected value of the stochastic process of price changes. While the expected value is expected for the long-run average of infinite realizations of the same stochastic process, it may give an erroneous picture of nearly every realization when the probability distribution is skewed, as is the case for prices. Here we propose a new formula of the BSM theory, which is based on the median of the stochastic process. This formula makes a more realistic prediction for the long-term outcomes than the current Black-Scholes formula

DSIF contributes to transcriptional activation by DNA-binding activators by preventing pausing during transcription elongation

The transcription elongation factor 5,6-dichloro-1-β-d-ribofuranosylbenzimidazole (DRB) sensitivity-inducing factor (DSIF) regulates RNA polymerase II (RNAPII) processivity by promoting, in concert with negative elongation factor (NELF), promoter-proximal pausing of RNAPII. DSIF is also reportedly involved in transcriptional activation. However, the role of DSIF in transcriptional activation by DNA-binding activators is unclear. Here we show that DSIF acts cooperatively with a DNA-binding activator, Gal4-VP16, to promote transcriptional activation. In the absence of DSIF, Gal4-VP16-activated transcription resulted in frequent pausing of RNAPII during elongation in vitro. The presence of DSIF reduced pausing, thereby supporting Gal4-VP16-mediated activation. We found that DSIF exerts its positive effects within a short time-frame from initiation to elongation, and that NELF does not affect the positive regulatory function of DSIF. Knockdown of the gene encoding the large subunit of DSIF, human Spt5 (hSpt5), in HeLa cells reduced Gal4-VP16-mediated activation of a reporter gene, but had no effect on expression in the absence of activator. Together, these results provide evidence that higher-level transcription has a stronger requirement for DSIF, and that DSIF contributes to efficient transcriptional activation by preventing RNAPII pausing during transcription elongation

Spin Wave Instability of Itinerant Ferromagnet

We show variationally that instability of the ferromagnetic state in the Hubbard model is largely controlled by softening of a long-wavelength spin-wave excitation, except in the over-doped strong-coupling region where the individual-particle excitation becomes unstable first. A similar conclusion is drawn also for the double exchange ferromagnet. Generally the spin-wave instability may be regarded as a precursor of the metal-insulator transition.Comment: 11 pages, 8 figure

Physical Phenomenology of Phyllotaxis

We propose an evolutionary mechanism of phyllotaxis, regular arrangement of leaves on a plant stem. It is shown that the phyllotactic pattern with the Fibonacci sequence has a selective advantage, for it involves the least number of phyllotactic transitions during plant growth