Nuclear spin-hyperpolarization generated in a flavoprotein under illumination: experimental field-dependence and theoretical level crossing analysis

The solid-state photo-chemically induced dynamic nuclear polarization (photo-CIDNP) effect generates non-equilibrium nuclear spin polarization in frozen electron-transfer proteins upon illumination and radical-pair formation. The effect can be observed in various natural photosynthetic reaction center proteins using magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, and in a flavin-binding light-oxygen-voltage (LOV) domain of the blue-light receptor phototropin. In the latter system, a functionally instrumental cysteine has been mutated to interrupt the natural cysteine-involving photochemistry allowing for an electron transfer from a more distant tryptophan to the excited flavin mononucleotide chromophore. We explored the solid-state photo-CIDNP effect and its mechanisms in phototropin-LOV1-C57S from the green alga Chlamydomonas reinhardtii by using field-cycling solution NMR. We observed the 13C and, to our knowledge, for the first time, 15N photo-CIDNP signals from phototropin-LOV1-C57S. Additionally, the 1H photo-CIDNP signals of residual water in the deuterated buffer of the protein were detected. The relative strengths of the photo-CIDNP effect from the three types of nuclei, 1H, 13C and 15N were measured in dependence of the magnetic field, showing their maximum polarizations at different magnetic fields. Theoretical level crossing analysis demonstrates that anisotropic mechanisms play the dominant role at high magnetic fields.

ALTERNATIVE ANALYSIS OF FINITE-TIME PROBABILITY DISTRIBUTIONS OF RENEWAL THEORY

We introduce a level-crossing analysis of the finite time-t probability distributions of the excess life, age, total life, and related quantities of renewal processes. The technique embeds the renewal process as one cycle of a regenerative process with a barrier at level t, whose limiting probability density function leads directly to the time-t quantities. The new method connects the analysis of renewal processes with the analysis of a large class of stochastic models of Operations Research. Examples are given.

PORTFOLIO SELECTION USING LEVEL CROSSING ANALYSIS

Asset allocation is one of the most important and also challenging issues in finance. In this paper using level crossing analysis we introduce a new approach for portfolio selection. We introduce a portfolio index that is obtained based on minimizing the waiting time to receive known return and risk values. By the waiting time, we mean time that a special level is observed in average. The advantage of this approach is that the investors are able to set their goals based on gaining return and knowing the average waiting time and risk value at the same time. As an example we use our model for forming portfolio of stocks in Tehran Stock Exchange (TSE).

ON THE FLUCTUATIONS OF WATER WAVES GOVERNED BY THE CAMASSA–HOLM AND KdV EQUATIONS IN (1+1)-DIMENSION

In this paper, we are planning to consider the fluctuations of two nonlinear equations which govern the dynamics of water waves named Camassa–Holm and KdV. We consider the total number of positive slopes [Formula: see text] produced when the fluctuations of the wave velocity u(x) of a surface wave of a fluid, for example water, is crossed by the level [Formula: see text] in the Camassa–Holm and KdV equations. Here, we just concentrate on the high Reynolds number limit and do the level crossing analysis where υ → 0. In our desired limit, the dissipative term becomes absent or very weak compared to the nonlinear term which is responsible for increasing the amplitude and creating wave steepening, which results in the appearance of shocks. Thus, our analysis works at the times before the appearance of shocks. Our aim in this paper is to show how the quantity, [Formula: see text], counts the fluctuations of the wave velocity in the surface water wave fluctuations which are governed by the KdV and Camassa–Holm (CH) equations.

LEVEL CROSSING ANALYSIS OF THE MAGNETOHYDRODYNAMIC EQUATION IN (1+1)-DIMENSION

In this paper we investigate the average frequency [Formula: see text] of a certain positive slope which is produced when the velocity and magnetic fields Vy and Bx are crossed by the level [Formula: see text] in the magnetohydrodynamic equation. This level crossing analysis is in the inviscid limit where υ→0 and of course before the appearance of the shocks. The main goal of this paper is to show that this quantity, [Formula: see text], is a good measure for the fluctuations of the velocity and magnetic fields in the magnetohydrodynamic turbulence.