Generalized nonlinear Schrödinger equations describing the Second Harmonic Generation of femtosecond pulse, containing a few cycles, and their integrals of motion.

An interaction of laser pulse, containing a few cycles, with substance is a modern problem, attracting attention of many researches. The frequency conversion is a key problem for a generation of such pulses in various ranges of frequencies. Adequate description of such pulse interaction with a medium is based on a slowly evolving wave approximation (SEWA), which has been proposed earlier for a description of propagation of the laser pulse, containing a few cycles, in a medium with cubic nonlinear response. Despite widely applicability of the frequency conversion for various nonlinear optics problems solutions, SEWA has not been applied and developed for a theoretical investigation of the frequency doubling process until present time. In this study the set of generalized nonlinear Schrödinger equations describing a second harmonic generation of the super-short femtosecond pulse is derived. The equations set contains terms, describing the pulses self-steepening, and the second order dispersion (SOD) of the pulse, a diffraction of the beam as well as mixed derivatives. We propose the transform of the equations set to a type, which does not contain both the mixed derivatives and time derivatives of the nonlinear terms. This transform allows us to derive the integrals of motion of the problem: energy, spectral invariants and Hamiltonian. We show the existence of two specific frequencies (singularities in the Fourier space) inherent to the problem. They may cause an appearance of non-physical absolute instability of the problem solution if the spectral invariants are not taken into account. Moreover, we claim that the energy preservation at the laser pulses propagation may not occur if these invariants do not preserve. Developed conservation laws, in particular, have to be used for developing of the conservative finite-difference schemes, preserving the conservation laws difference analogues, and for developing of adequate theory of the modulation instability of the laser pulses, containing a few cycles.

Efficiency of tabu-search-based conformational search algorithms.

Efficient conformational search or sampling approaches play an integral role in molecular modeling, leading to a strong demand for even faster and more reliable conformer search algorithms. This article compares the efficiency of a molecular dynamics method, a simulated annealing method, and the basin hopping (BH) approach (which are widely used in this field) with a previously suggested tabu-search-based approach called gradient only tabu search (GOTS). The study emphasizes the success of the GOTS procedure and, more importantly, shows that an approach which combines BH and GOTS outperforms the single methods in efficiency and speed. We also show that ring structures built by a hydrogen bond are useful as starting points for conformational search investigations of peptides and organic ligands with biological activities, especially in structures that contain multiple rings.

Chronic alcoholism in rats induces a compensatory response, preserving brain thiamine diphosphate, but the brain 2-oxo acid dehydrogenases are inactivated despite unchanged coenzyme levels.

Thiamine-dependent changes in alcoholic brain were studied using a rat model. Brain thiamine and its mono- and diphosphates were not reduced after 20 weeks of alcohol exposure. However, alcoholism increased both synaptosomal thiamine uptake and thiamine diphosphate synthesis in brain, pointing to mechanisms preserving thiamine diphosphate in the alcoholic brain. In spite of the unchanged level of the coenzyme thiamine diphosphate, activities of the mitochondrial 2-oxoglutarate and pyruvate dehydrogenase complexes decreased in alcoholic brain. The inactivation of pyruvate dehydrogenase complex was caused by its increased phosphorylation. The inactivation of 2-oxoglutarate dehydrogenase complex (OGDHC) correlated with a decrease in free thiols resulting from an elevation of reactive oxygen species. Abstinence from alcohol following exposure to alcohol reactivated OGDHC along with restoration of the free thiol content. However, restoration of enzyme activity occurred before normalization of reactive oxygen species levels. Hence, the redox status of cellular thiols mediates the action of oxidative stress on OGDHC in alcoholic brain. As a result, upon chronic alcohol consumption, physiological mechanisms to counteract the thiamine deficiency and silence pyruvate dehydrogenase are activated in rat brain, whereas OGDHC is inactivated due to impaired antioxidant ability.

Tabu search based strategies for conformational search.

This paper presents an application of the new nonlinear global optimization routine gradient only tabu search (GOTS) to conformational search problems. It is based on the tabu search strategy which tries to determine the global minimum of a function by the steepest descent-modest ascent strategy. The refinement of ranking procedure of the original GOTS method and the exploitation of simulated annealing elements are described, and the modifications of the GOTS algorithm necessary to adopt it to conformation searches are explained. The utility of the GOTS for conformational search problems is tested using various examples.

New Tabu Search based global optimization methods outline of algorithms and study of efficiency.

The study presents two new nonlinear global optimization routines; the Gradient Only Tabu Search (GOTS) and the Tabu Search with Powell's Algorithm (TSPA). They are based on the Tabu-Search strategy, which tries to determine the global minimum of a function by the steepest descent-mildest ascent strategy. The new algorithms are explained and their efficiency is compared with other approaches by determining the global minima of various well-known test functions with varying dimensionality. These tests show that for most tests the GOTS possesses a much faster convergence than global optimizer taken from the literature. The efficiency of the TSPA compares to the efficiency of genetic algorithms.

Gradient tabu search.

This paper presents a modification of the tabu search called gradient tabu search (GTS). It uses analytical gradients for a fast minimization to the next local minimum and analytical diagonal elements of the Hessian to escape local minima. For an efficient blocking of already visited areas tabu regions and tabu directions are introduced into the tabu list (TL). Trials with various well-known test functions indicate that the GTS is a very promising approach to determine local and global minima of differentiable functions. Possible application areas could be optimization routines for force field parameters or conformational searches for large molecules.