Feature selection for classification of medical images of human tissue for cancer recognition

A statistical pattern recognition system for ultrasound medical images of prostatic tissue for cancer has been proposed. Using the autocorrelation method, the correct size of a statistical sliding window for feature extraction was defined. Known texture discrimination features have been tested for effectiveness. Another set of discriminating features, based on edge value distribution, Fourier power spectrum and wavelet transform has been derived and investigated. The set can be used as an input to a neural net classifier

On a class of three-dimensional integrable Lagrangians

We characterize non-degenerate Lagrangians of the form $\int f(u_x, u_y, u_t) dx dy dt$ such that the corresponding Euler-Lagrange equations $(f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0$ are integrable by the method of hydrodynamic reductions. The integrability conditions constitute an over-determined system of fourth order PDEs for the Lagrangian density $f$, which is in involution and possess interesting differential-geometric properties. The moduli space of integrable Lagrangians, factorized by the action of a natural equivalence group, is three-dimensional. Familiar examples include the dispersionless Kadomtsev-Petviashvili (dKP) and the Boyer-Finley Lagrangians, $f=u_x^3/3+u_y^2-u_xu_t$ and $f=u_x^2+u_y^2-2e^{u_t}$, respectively. A complete description of integrable cubic and quartic Lagrangians is obtained. Up to the equivalence transformations, the list of integrable cubic Lagrangians reduces to three examples, $f=u_xu_yu_t, f=u_x^2u_y+u_yu_t, and f=u_x^3/3+u_y^2-u_xu_t ({\rm dKP}).$ There exists a unique integrable quartic Lagrangian, $f=u_x^4+2u_x^2u_t-u_xu_y-u_t^2.$ We conjecture that these examples exhaust the list of integrable polynomial Lagrangians which are essentially three-dimensional (it was verified that there exist no polynomial integrable Lagrangians of degree five). We prove that the Euler-Lagrange equations are integrable by the method of hydrodynamic reductions if and only if they possess a scalar pseudopotential playing the role of a dispersionless `Lax pair'. MSC: 35Q58, 37K05, 37K10, 37K25. Keywords: Multi-dimensional Dispersionless Integrable Systems, Hydrodynamic Reductions, Pseudopotentials.Comment: 12 pages A4 format, standard Latex 2e. In the file progs.tar we include the programs needed for computations performed in the paper. Read 1-README first. The new version includes two new section

The Assembly of Hierarchs in Krasnoyarsk: Historical and Architectural Study

The article examines the stages of construction history of the Assembly of Hierarchs in Krasnoyarsk that is a monument of architecture in the late XIX century. Archival documents and field studies of the object have been used for this research. On the basis of documentary material, the role of the first bishop of the Yenisei Diocese, Nicodemus, has been revealed in organizing and conducting activities related to site selection for the Hierarchs town church in Krasnoyarsk, with its buildings, as well as the design of interior decoration of residential buildings and chapel. A complex study design drawings of buildings in initial and final stages of formation have been presented for the first time; their architectural and planning analysis has been carried out. They allow us not only to discover creative proposals of architects, but also trace the techniques of architectural projects in the XIX century. The names of architects, who made up projects of structure and rebuilding homes for the Assembly of Hierarchs in Krasnoyarsk in the pre-revolutionary period, have been revealed. These materials given in the article make it possible to recreate an authentic architectural and planning structure of the Assembly of Hierarchs and chapel and the elements of the decor with great accuracy nowadays. The results of the study prove to have a great architectural and urban planning, historical and cultural value of the Assembly of Hierarchs in Krasnoyarsk.В статье рассмотрены этапы строительной истории Архиерейского дома в Красноярске - памятника архитектуры конца XIX века. Для исследования использованы архивные документы и натурное изучение объекта. На основе документальных материалов выявлена роль первого епископа Енисейской епархии, Никодима, в организации и проведении мероприятий, связанных с выбором участка для архиерейского подворья в Красноярске, с его застройкой, а также с оформлением внутреннего убранства жилых помещений и домовой церкви. Впервые представлены проектные чертежи комплекса исследуемых зданий начального и завершающего этапов формирования; проведен их архитектурно-планировочный анализ. Они позволяют раскрыть не только творческие предложения зодчих, но и методы составления архитектурных проектов в XIX веке. Выявлены фамилии архитекторов, составлявших в дореволюционный период проекты устройства и перестройки дома для Архиерея в Красноярске. Приведенные в статье материалы исследования позволяют с большой достоверностью воссоздать в настоящее время подлинную архитектурно-планировочную структуру Архиерейского дома и домовой церкви, элементы их декора. Результаты исследования подтверждают высокую архитектурно-градостроительную и историко-культурную ценность Архиерейского дома в Красноярске

Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets

This paper is devoted to description of the relationship among oriented associativity equations, symmetry consistent conjugate curvilinear coordinate nets, and the widest associated class of semi- Hamiltonian hydrodynamic-type systems.Comment: 19 page

Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2+1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page

Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions

We show how to generate coupled KdV hierarchies from Staeckel separable systems of Benenti type. We further show that solutions of these Staeckel systems generate a large class of finite-gap and rational solutions of cKdV hierarchies. Most of these solutions are new.Comment: 15 page

Integrable Systems and Metrics of Constant Curvature

In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature. Kaup-Boussinesq system has three local Hamiltonian structures and one nonlocal Hamiltonian structure associated with metric of constant curvature. Darboux theorem (reducing Hamiltonian structures to canonical form ''d/dx'' by differential substitutions and reciprocal transformations) for these Hamiltonian structures is proved