arXiv subjects

Aigul Khakimova

Publications and source records attributed to Aigul Khakimova.

4 recordsLinked to original sources

arXiv2020

Lipophilicity Prediction with Multitask Learning and Molecular Substructures Representation

Lipophilicity is one of the factors determining the permeability of the cell membrane to a drug molecule. Hence, accurate lipophilicity prediction is an essential step in the development of new drugs. In this paper, we introduce a novel approach to encoding additional graph information by extracting molecular substructures. By adding a set of generalized atomic features of these substructures to an established Direct Message Passing Neural Network (D-MPNN) we were able to achieve a new state-of-the-art result at the task of prediction of two main lipophilicity coefficients, namely logP and logD descriptors. We further improve our approach by employing a multitask approach to predict logP and logD values simultaneously. Additionally, we present a study of the model performance on symmetric and asymmetric molecules, that may yield insight for further research.

cs.LG↗

arXiv2019

Integrable boundary conditions for the Hirota-Miwa equation and Lie algebras

Systems of discrete equations on a quadrilateral graph related to the series $D^{(2)}_N$ of the affine Lie algebras are studied. The systems are derived from the Hirota-Miwa equation by imposing boundary conditions compatible with the integrability property. The Lax pairs for the systems are presented. It is shown that in the continuum limit the quad systems tend to the corresponding systems of the differential equations belonging to the well-know Drinfeld-Sokolov hierarchies. The problem of finding the formal asymptotic expansion of the solutions to the Lax equations is studied. Generating functions for the local conservation laws are found for the systems corresponding to $D^{(2)}_3$. An example of the higher symmetry is presented.

nlin.SI↗

arXiv2018

Invariant manifolds for the hyperbolic type integrable equations and their applications

We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference) equation compatible with the linearized equation for any choice of $u$. This equation defines a surface called a generalized invariant manifold. In a sense, the manifold generalizes the symmetry, which is also a solution to the linearized equation. In this paper, we concentrate on continuous and discrete models of hyperbolic type. It is known that such kind equations have two hierarchies of symmetries, corresponding to the characteristic directions. We have shown that properly chosen generalized invariant manifold allows one to construct recursion operators that generate these symmetries. It is surprising that both recursion operators are related to different parametrizations of the same invariant manifold. Therefore, knowing one of the recursion operators for the hyperbolic type integrable equation (having no pseudo-constants) we can immediately find the second one.

nlin.SI↗

arXiv2017

On a method for constructing the Lax pairs for integrable models via quadratic ansatz

A method for constructing the Lax pairs for nonlinear integrable models is suggested. First we look for a nonlinear invariant manifold to the linearization of the given equation. Examples show that such invariant manifold does exist and can effectively be found. Actually it is defined by a quadratic form. As a result we get a nonlinear Lax pair consisting of the linearized equation and the invariant manifold. Our second step consists of finding an appropriate change of the variables to linearize the found nonlinear Lax pair. The desired change of the variables is again defined by a quadratic form. The method is illustrated by the well-known KdV equation and the modified Volterra chain. New Lax pairs are found. The formal asymptotic expansions for their eigenfunctions are constructed around the singular values of the spectral parameter. By applying the method of the formal diagonalization to these Lax pairs the infinite series of the local conservation laws are obtained for the corresponding nonlinear models.

nlin.SI↗