Self-Excited Multifractal Dynamics

We introduce the self-excited multifractal (SEMF) model, defined such that the amplitudes of the increments of the process are expressed as exponentials of a long memory of past increments. The principal novel feature of the model lies in the self-excitation mechanism combined with exponential nonlinearity, i.e. the explicit dependence of future values of the process on past ones. The self- excitation captures the microscopic origin of the emergent endogenous self-organization properties, such as the energy cascade in turbulent flows, the triggering of aftershocks by previous earthquakes and the "reflexive" interactions of financial markets. The SEMF process has all the standard stylized facts found in financial time series, which are robust to the specification of the parameters and the shape of the memory kernel: multifractality, heavy tails of the distribution of increments with intermediate asymptotics, zero correlation of the signed increments and long-range correlation of the squared increments, the asymmetry (called "leverage" effect) of the correlation between increments and absolute value of the increments and statistical asymmetry under time reversal

Homogeneous Volatility Bridge Estimators

We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process, and in its close value, for a given time interval. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass and Parkinson estimators.Comment: 25 pages, 9 figure

L’ensemble architectural de Tâq-e Sarrafân à Boukhara

Dans la seconde moitié du XVIe siècle, sous le règne de ‘Abdallâh Khân II (1557-1598), une intense activité de construction donna à Boukhara redevenue, après une grande rupture, capitale, l’aspect qu’elle a conservé jusqu’à notre siècle. Cet héritage fut apprécié à sa juste valeur par ses descendants. Mais le rôle de Boukhara, en tant que capitale de deux khans sheybanides, ‘Obeydallâh (m. 1540) et son fils ‘Abd al-‘Aziz (r. 1540-1550), reste encore incomplètement étudié et compris. Cependant..

Prostaglandin H synthase kinetics in the two-phase aqueous-micellar system

AbstractReaction mixture for PGHS (prostaglandin-H-synthase) is a two-phase system including micellar hydrophobic phase and hydrophilic aqueous phase. Reagents added to the mixture are distributed between phases, thus concentrations of reagents dissolved in phases can differ significantly from their overall contents.Using dynamic light scattering we found that the hydrophobic phase produced by tween-20 consists of micelles, which radius (4–5nm) does not depend on either tween-20 overall content (0.1%–1% v/v) or arachidonic acid (AA) addition (10–1000μM) or PGHS addition (1μM).Tween-20 overall content changing from 0.1% to 2% v/v dramatically affected COX kinetic, but accounting AA distribution between phases allowed us to estimate “true” parameters, independent of the tween-20 overall content and the concentration of another substrate: KMOx equals 9.8μM O2 in the aqueous phase or 0.0074bar in the gaseous phase, KMAA equals 5400μM AA in the phase of tween-20 micelles and 5400/PμM AA in the aqueous phase (P is the distribution ratio for the AA between the aqueous phase and the hydrophobic phase (P≫1000)). This approach allowed to evaluate PS, the distribution ratio for the AA between the hydrophobic phase and the PGHS active center (PS ~310). This coefficient indicates the AA selectivity toward the cyclooxygenase active center