arXiv subjects

Oleg Kupervasser

Publications and source records attributed to Oleg Kupervasser.

At least 37 records · Page 2Linked to original sources

arXiv2012

Continual Model of Medium III: Calculation of analytical gradients of parameters of surface meshes on the molecular surfaces over atomic coordinates

The problem of finding of analytical gradients (derivatives over atoms coordinates) of solvation energies can be decomposed on two subtasks: at the first stage we search for parameters of the superficial devices (three coordinates, three components of normal vector and square) and their derivatives; at the second stage we differentiate energy and we express it through derivative of the matrixes featuring a problem. But these derivatives of matrix elements can be expressed through derivatives of parameters of surface meshes of SES (solvent excluded surface) or SAS (solvent accessible surface). The purpose of the given paper is finding of these analytical gradients of the parameters of the surface meshes.

physics.chem-ph↗

arXiv2012

Continual Model of Medium II: Universal adaptive algorithm for triangulation of smooth molecular surface

In the given paper the algorithm describing original and universal principles of a triangulation of a smooth molecular surface: solvent excluding solvent (SES), received by primary and secondary rolling, and solvent accessible surface (SAS) is presented. These surfaces are a boundary between molecule and solvent. Originality of the given paper consists in creation of the universal and adaptive algorithm of a triangulation. Universality of algorithm of a triangulation consists that it is suitable for not only for a surface, received by rolling and consisting of fragments of torus and sphere, but for any smooth surface, including any level surface. Adaptability of this algorithm consists in facts that the mesh size of a triangulation can vary depending on its location; reflecting even small, but smooth features of a surface; preventing "jump" to close, but not neighbor sites of the surface, excepting "cut off" of narrow necks and channels. It is reached by either decreasing triangulation lattice step to value smaller than two principal radiuses of curvature of the molecular surface or decreasing triangulation lattice step close to the active centre - closed, but not neighbor sites of the surface. The received triangulated surface can be used for the demonstration purposes in molecular editors (the algorithm is applicable for a triangulation of any smooth surface, for example, level surfaces) together with for calculation of solvation energy and its gradients for continual models of solvent.

physics.chem-ph↗

arXiv2012

Continual Model of Medium IV: Calculation of analytical gradients for solvation energy over atomic coordinates

In the given paper we describe methods finding analytical gradients (derivatives) of solvation energy over atomic coordinates. It is made both for not polar energy and for the polar energy found by methods PCM, COSMO and SGB. These gradients are searched with use of analytical gradients of parameters (coordinates, normal vectors and squares) the surface meshes. The surface meshes are located on both the optimal smooth molecular surfaces: solvent excluded surface (SES) and surface solvent accessible surface (SAS) received from SES. These surfaces are found by methods of primary and secondary rolling according to the algorithm described in the previous papers of the series.

physics.chem-ph↗

arXiv2012

The Mysterious Optimality of Naive Bayes: Estimation of the Probability in the System of "Classifiers"

Bayes Classifiers are widely used currently for recognition, identification and knowledge discovery. The fields of application are, for example, image processing, medicine, chemistry (QSAR). But by mysterious way the Naive Bayes Classifier usually gives a very nice and good presentation of a recognition. It can not be improved considerably by more complex models of Bayes Classifier. We demonstrate here a very nice and simple proof of the Naive Bayes Classifier optimality, that can explain this interesting fact.The derivation in the current paper is based on arXiv:cs/0202020v1

cs.CV↗

arXiv2012

Recovering Epipolar Geometry from Images of Smooth Surfaces

We present four methods for recovering the epipolar geometry from images of smooth surfaces. In the existing methods for recovering epipolar geometry corresponding feature points are used that cannot be found in such images. The first method is based on finding corresponding characteristic points created by illumination (ICPM - illumination characteristic points' method (PM)). The second method is based on correspondent tangency points created by tangents from epipoles to outline of smooth bodies (OTPM - outline tangent PM). These two methods are exact and give correct results for real images, because positions of the corresponding illumination characteristic points and corresponding outline are known with small errors. But the second method is limited either to special type of scenes or to restricted camera motion. We also consider two more methods which are termed CCPM (curve characteristic PM) and CTPM (curve tangent PM), for searching epipolar geometry for images of smooth bodies based on a set of level curves with constant illumination intensity. The CCPM method is based on searching correspondent points on isophoto curves with the help of correlation of curvatures between these lines. The CTPM method is based on property of the tangential to isophoto curve epipolar line to map into the tangential to correspondent isophoto curves epipolar line. The standard method (SM) based on knowledge of pairs of the almost exact correspondent points. The methods have been implemented and tested by SM on pairs of real images. Unfortunately, the last two methods give us only a finite subset of solutions including "good" solution. Exception is "epipoles in infinity". The main reason is inaccuracy of assumption of constant brightness for smooth bodies. But outline and illumination characteristic points are not influenced by this inaccuracy. So, the first pair of methods gives exact results.

cs.CV↗

arXiv2012

The Universal Arrow of Time I: Classical mechanics

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker's map.

physics.gen-ph↗

arXiv2012

Flame Front Propagation and Finger Competition and Formation of a Single Saffman-Taylor Finger without Surface Tension - PhD Thesis

Problems of interface growth have received much attention recently Such are, for example, the duffusion limited aggregation (DLA), random sequential adsorption (RSA), Laplacian growth or flame front propagation. We will mainly pay attention in this Thesis to the numerical and analytical investigation of the last two problems. In addition to the fact that flame front propagation is an interesting physical problem we feel that we can also explain experimental results on the basis of theoretical investigations. There exists possibility to use methods found for the flame front propagation, in different fields where similar problems appear such as the important model of Laplacian growth .

nlin.PS↗

arXiv2012

Vision-Based Navigation I: A navigation filter for fusing DTM/correspondence updates

An algorithm for pose and motion estimation using corresponding features in images and a digital terrain map is proposed. Using a Digital Terrain (or Digital Elevation) Map (DTM/DEM) as a global reference enables recovering the absolute position and orientation of the camera. In order to do this, the DTM is used to formulate a constraint between corresponding features in two consecutive frames. The utilization of data is shown to improve the robustness and accuracy of the inertial navigation algorithm. Extended Kalman filter was used to combine results of inertial navigation algorithm and proposed vision-based navigation algorithm. The feasibility of this algorithms is established through numerical simulations.

cs.CV↗

arXiv2012

Enlarged Surface Meshes and Normalization Conditions for Columns and Rows of Matrices in the COSMO Method

Earlier, normalization conditions for the columns of the PCM (Polarized Continuum Model) were determined and a method of enlarged surface meshes was developed. We developed similar methods for the COSMO (COnductor like Screening MOdel). These methods make it possible to introduce larger surface meshes without loss of accuracy and perform fast calculations of the solvation energy and the Born radii in the SGB (Surface Generalized Born) method. In addition, the corrections proposed in this work provide a significant enhancement in the accuracy of numerical calculations.

physics.chem-ph↗

arXiv2011

Continuous dielectric permittivity II: An Iterative Method for Calculating the Polar Component of the Molecular Solvation Gibbs Energy Under a Smooth Change in the Dielectric Permittivity of a Solution

An iterative method for calculating the polar component of the solvation Gibbs energy under a smooth change in dielectric permittivity, both between a substrate and a solvent and in a solvent is formulated on the basis of a previously developed model. The method is developed in the approximation of the local relationship D = \eps (r) E between the displacement vectors D and the electric field intensity E.

physics.chem-ph↗

arXiv2011

Flame front propagation III: Random Noise and Pole-Dynamics in Unstable Front Propagation (new version)

The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with random initial conditions and perturbations. We argue that the effect of random noise is immense and that it can never be neglected in sufficiently large systems. We present simulations that lead to scaling laws for the velocity and acceleration of the front as a function of the system size and the level of noise, and analytic arguments that explain these results in terms of the noisy pole dynamics.terms of the dynamics of singularities in the complex plane, yielding detailed understanding of the physics of the eigenfunctions and eigenvalues.

nlin.PS↗

arXiv2011

Flame front propagation II: Random Noise and Pole-Dynamics in Unstable Front Propagation

The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales is studied. The analytic tool of pole expansion in the complex plane is emloyed to address the interaction of the unstable growth process with random initial conditions and perturbations. We argue that the effect of random noise is immense and that it can never be neglected in sufficiently large systems. We present simulations that lead to scaling laws for the velocity and acceleration of the front as a function of the system size and the level of noise, and analytic arguments that explain these results in terms of the noisy pole dynamics.

adap-org↗

arXiv2011

Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane

We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space dependent coefficient. Accordingly it involves complicated eigenfunctions. We show that the analysis can be performed to required detail using a finite order dynamical system in terms of the dynamics of singularities in the complex plane, yielding detailed understanding of the physics of the eigenfunctions and eigenvalues.

nlin.PS↗

arXiv2011

Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition

The roughening of expanding flame fronts by the accretion of cusp-like singularities is a fascinating example of the interplay between instability, noise and nonlinear dynamics that is reminiscent of self-fractalization in Laplacian growth patterns. The nonlinear integro-differential equation that describes the dynamics of expanding flame fronts is amenable to analytic investigations using pole decomposition. This powerful technique allows the development of a satisfactory understanding of the qualitative and some quantitative aspects of the complex geometry that develops in expanding flame fronts.

nlin.PS↗

arXiv2011

Flame front propagation VI: Dynamics and Wrinkling of Radially Propagating Fronts Inferred from Scaling Laws in Channel Geometries

Flame Propagation is used as a prototypical example of expanding fronts that wrinkle without limit in radial geometries but reach a simple shape in channel geometry. We show that the relevant scaling laws that govern the radial growth can be inferred once the simpler channel geometry is understood in detail. In radial geometries (in contrast to channel geometries) the effect of external noise is crucial in accelerating and wrinkling the fronts. Nevertheless, once the interrelations between system size, velocity of propagation and noise level are understood in channel geometry, the scaling laws for radial growth follow.

nlin.PS↗

arXiv2011

Vision-Based Navigation III: Pose and Motion from Omnidirectional Optical Flow and a Digital Terrain Map

An algorithm for pose and motion estimation using corresponding features in omnidirectional images and a digital terrain map is proposed. In previous paper, such algorithm for regular camera was considered. Using a Digital Terrain (or Digital Elevation) Map (DTM/DEM) as a global reference enables recovering the absolute position and orientation of the camera. In order to do this, the DTM is used to formulate a constraint between corresponding features in two consecutive frames. In this paper, these constraints are extended to handle non-central projection, as is the case with many omnidirectional systems. The utilization of omnidirectional data is shown to improve the robustness and accuracy of the navigation algorithm. The feasibility of this algorithm is established through lab experimentation with two kinds of omnidirectional acquisition systems. The first one is polydioptric cameras while the second is catadioptric camera.

cs.CV↗

arXiv2011

Vision-Based Navigation II: Error Analysis for a Navigation Algorithm based on Optical-Flow and a Digital Terrain Map

The paper deals with the error analysis of a navigation algorithm that uses as input a sequence of images acquired by a moving camera and a Digital Terrain Map (DTM) of the region been imaged by the camera during the motion. The main sources of error are more or less straightforward to identify: camera resolution, structure of the observed terrain and DTM accuracy, field of view and camera trajectory. After characterizing and modeling these error sources in the framework of the CDTM algorithm, a closed form expression for their effect on the pose and motion errors of the camera can be found. The analytic expression provides a priori measurements for the accuracy in terms of the parameters mentioned above.

cs.CV↗

arXiv2011

Continuous dielectric permittivity I: Specific features of the dielectric continuum solvation model with a position-dependent permittivity function

We consider a modified formulation for the recently developed new approach in the continuum solvation theory (Basilevsky, M. V., Grigoriev, F. V., Nikitina, E. A., Leszczynski, J., J. Phys. Chem. B 2010, 114, 2457), which is based on the exact solution of the electrostatic Poisson equation with the space-dependent dielectric permittivity. Its present modification ensures the property curl E = 0 for the electric strength field E inherent to this solution, which is the obligatory condition imposed by Maxwell equations. The illustrative computation is made for the model system of the point dipole immersed in a spherical cavity of excluded volume.

physics.chem-ph↗