A fully conservative parallel numerical algorithm with adaptive spatial grid for solving nonlinear diffusion equations in image processing

In this paper we present simple yet efficient parallel program implementation of grid-difference method for solving nonlinear parabolic equations, which satisfies both fully conservative property and second order of approximation on non-uniform spatial grid according to geometrical sanity of a task. The proposed algorithm was tested on Perona–Malik method for image noise ltering task based on differential equations. Also in this work we propose generalization of the Perona–Malik equation, which is a one of diffusion in complex-valued region type. This corresponds to the conversion to such types of nonlinear equations like Leontovich–Fock equation with a dependent on the gradient field according to the nonlinear law coefficient of diffraction. This is a special case of generalization of the Perona–Malik equation to the multicomponent case. This approach makes noise removal process more flexible by increasing its capabilities, which allows achieving better results for the task of image denoising

Imitation of optical coherence tomography images by wave Monte Carlo-based approach implemented with the Leontovich–Fock equation

We present a computational modeling approach for imitation of the time-domain optical coherence tomography (OCT) images of biotissues. The developed modeling technique is based on the implementation of the Leontovich–Fock equation into the wave Monte Carlo (MC) method. We discuss the benefits of the developed computational model in comparison to the conventional MC method based on the modeling of OCT images of a nevus. The developed model takes into account diffraction on bulk-absorbing microstructures and allows consideration of the influence of the amplitude–phase profile of the wave beam on the quality of the OCT images. The selection of optical parameters of modeling medium, used for simulation of optical radiation propagation in biotissues, is based on the results obtained experimentally by OCT. The developed computational model can be used for imitation of the light waves propagation both in time-domain and spectral-domain OCT approaches

Statistical parameters of femtosecond laser pulse post-filament propagation on a 65 m air path with localized optical turbulence

High-power femtosecond laser radiation propagates nonlinearly in air, exhibiting pulse self-focusing and strong multiphoton medium ionization, which leads to the spatial fragmentation of laser pulses into highly localized light channels commonly called filaments. Filaments are characterized by high optical intensity and reduced (even zero) angular spreading and can contain laser plasma or be plasmaless (postfilaments). The presence of optical turbulence on the propagation path dramatically changes pulse filamentation dynamics and in some cases causes pulse fragmentation enhancement and collapse arrest. For the first time, to the best of our knowledge, we experimentally and theoretically investigate the transverse profile of Ti:sapphire femtosecond laser radiation nonlinearly propagating a 65mair path to the region of postfilament evolution after passing through an artificial localized air turbulence. We show that when a turbulence layer is placed before the filamentation region, the average number of high-intensity local fluence maxima (“hot points”) in the beam profile and their sizes grow as the turbulence strength increases, and then saturates at some levels. On the contrary, the deposition of a turbulence screen within the filamentation region has almost no effect on either the number or the average diameter of postfilaments

Light distribution in fat cell layers at physiological temperatures

Abstract Adipose tissue (AT) optical properties for physiological temperatures and in vivo conditions are still insufficiently studied. The AT is composed mainly of packed cells close to spherical shape. It is a possible reason that AT demonstrates a very complicated spatial structure of reflected or transmitted light. It was shown with a cellular tissue phantom, is split into a fan of narrow tracks, originating from the insertion point and representing filament-like light distribution. The development of suitable approaches for describing light propagation in a AT is urgently needed. A mathematical model of the propagation of light through the layers of fat cells is proposed. It has been shown that the sharp local focusing of optical radiation (light localized near the shadow surface of the cells) and its cleavage by coupling whispering gallery modes depends on the optical thickness of the cell layer. The optical coherence tomography numerical simulation and experimental studies results demonstrate the importance of sharp local focusing in AT for understanding its optical properties for physiological conditions and at AT heating

Ribosomal position and contacts of mRNA in eukaryotic translation initiation complexes

The position of mRNA on 40S ribosomal subunits in eukaryotic initiation complexes was determined by UV crosslinking using mRNAs containing uniquely positioned 4-thiouridines. Crosslinking of mRNA positions +11 to ribosomal protein (rp) rpS2(S5p) and rpS3(S3p), and +9–+11 and +8–+9 to h18 and h34 of 18S rRNA, respectively, indicated that mRNA enters the mRNA-binding channel through the same layers of rRNA and proteins as in prokaryotes. Upstream of the P-site, the proximity of positions −3/−4 to rpS5(S7p) and h23b, −6/−7 to rpS14(S11p), and −8–−11 to the 3′-terminus of 18S rRNA (mRNA/rRNA elements forming the bacterial Shine–Dalgarno duplex) also resembles elements of the bacterial mRNA path. In addition to these striking parallels, differences between mRNA paths included the proximity in eukaryotic initiation complexes of positions +7/+8 to the central region of h28, +4/+5 to rpS15(S19p), and −6 and −7/−10 to eukaryote-specific rpS26 and rpS28, respectively. Moreover, we previously determined that eukaryotic initiation factor2α (eIF2α) contacts position −3, and now report that eIF3 interacts with positions −8–−17, forming an extension of the mRNA-binding channel that likely contributes to unique aspects of eukaryotic initiation