Vasilii Gromov - Profile on Academia.edu (original) (raw)

E-mail: stroller@rambler.ru

Google Scholar: https://scholar.google.com.ua/citations?user=nw7Gm6gAAAAJ&hl=ru
Research Gate: https://www.researchgate.net/profile/Vasilii\_Gromov
ORCID: http://orcid.org/0000-0001-5891-6597
LinkedIn

Degrees:
Ph. D. in Computational Mathematics
(Dnepropetrovsk National University, 2006).
Title: Post-critical behaviour and solution branching for the cylindrical shell theory non-linear problems.
The theses deal with creating complex real-word non-linear systems models (thin-walled shells) and sophisticated computational methods to analyze them. Also catastrophe theory methods were applied to the problem.

M. Sc. in Applied Mathematics
(Dnepropetrovsk National University, 2000).
Title: Catastrophe of spherical shell.
The theses deal with developing sophisticated computational methods
for non-linear boundary problems.

Honours:

Marquis Who’s who in the world 2014, 2015.
Marquis Who’s who in Science and Engineering 2016-2017 (12th Edition).
The International Biographical Centre:
Cambridge Certificate for Outstanding Scientific Achievement 2015
the Leading Professionals of the World 2014 - A Lifetime of Scientific Achievement 2014
Experience: Science:
Seniour researcher of Center for Reliability and Sustainability of Structures (Dnipropetrovsk National University, since 2007), research officer of the same center (since 2000).
Visiting professor of Universite du Maine (Faculty of Science and Technologies, May 2011).
Visiting lecturer of Universite du Maine (Engineering Higher School, November 2011). I deliver lectures on Data Mining.

Experience: Teaching:
Supervised Ph.D. thesis: Anastasia V. Kabeshova (2015, co-supervision with Prof. Olivier Beauchet, geriatrist), University of Angers (France). Title: Predire la chute de la personne agee: apports des modeles mathematiques non-lineaires (Предсказание падений у пожилых людей: преимущества нелинейных моделей)

Expert of Ukrainian Ministry of Science and Education in charge with licensing of mastership and bachelorship programmes in the field of Computer Science and Applied Mathematics (since 2011).
Advanced professor of Computational Mathematics and Mathematical Cybernetics Department (since 2006); associate professor (the same department, since 2002).
I deliver (or delivered) lectures on:

For Masters in AI and System Analysis:
- Data Mining;
- Non-linear time series forecasting;
- Theory of self-organizing systems;
- Theory of Statistical Complexity;
- Catastrophe theory;
- Foresighting;
- Complex Networks;

For Bachelors in System Analysis:

- Statistical forecasting of Economical Process;
- Neural networks.
- Mathematical models of biology, ecology, and sociology;
- Theory of complex systems;
- Design patterns;
- Self-organized systems;
- Object-oriented programming.

Experience: Reviewer: Artificial intelligence review (AIR) (Canada)
Journal of Intelligent and Fuzzy Systems

https://publons.com/institution/7879/

International cooperation:

I am a coordinator and a founder of double diploma mastership programme (computer science) between Dnepropetrovsk National University (Ukraine) and Universite du Maine (France)

Skills:
Statistical and mathematical packages: SPSS 13.0, Mathematica 10.0,
NeuroSolutions 5.07.
Language: Fluent in English, Russian, and Ukrainian; conversant in Japanese.
Programming: Delphi.

Background: philosophy, figure skating, swimming.
Supervisors: Natalia I. Obodan

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Papers by Vasilii Gromov

IMA Journal of Management Mathematics

This article deals with the logistics of a Ukrainian food and consumer goods distributor. Our mai... more This article deals with the logistics of a Ukrainian food and consumer goods distributor. Our main goal is to reduce the field costs of the company, which comprise the agent labour costs and company's transportation charges. The mathematical model used is an integer programming optimization one. The problem is heuristically decomposed into subproblems; methods to solve these subproblems are presented. In order to reduce company costs one is able to reduce company agents' staff, to optimize agents' daily routes, to minimize overall goods delivery charges and to reduce the number of rented vehicles. The developed software system offers considerable field costs reduction (28%), decision-making transparency for the planning group and a less prominent influence of human factors on decisions and schedules.

Modern state-of-the-art algorithms to process words and sentences of natural languages make it po... more Modern state-of-the-art algorithms to process words and sentences of natural languages make it possible to map each word of a literary work, in one way or another, into a real scalar or vector, and thereby the text is represented as a path in singleor multidimensional phase space. If one employs a word-to-vec or similar procedures, the texts are mapped into semantic paths; in doing so one may vary the dimension of the phase space. Hence, there are a number of semantic paths associated with a given literary piece. In the framework of another approach, one may map a word into its emotional characteristic, either negative or positive; the approach relies on expert assessments. The resulting series is what is known an emotional path.

Inverse bifurcation problem for von Karman-type elliptic equations

2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET), 2018

Typical solution sequences similar to those of post-bifurcation solutions observed along the bifu... more Typical solution sequences similar to those of post-bifurcation solutions observed along the bifurcation paths of the nonlinear boundary problem for von Karman equations are extracted to serve as precursors of bifurcation (tools to solve the problem). The method allows one to divide all operations required to solve the problem under study into two non-equal parts. The most time-consuming part (to trace bifurcation paths and cluster the respective solution) is performed off-line, while the part of the algorithm that is carried out on-line (the identification algorithm) requires a relatively small number of arithmetic operations. This allows development of the efficient system of rapid identification of pre-buckling states.

Prediction and Control of Buckling: The Inverse Bifurcation Problems for von Karman Equations

Applied Mathematical Analysis: Theory, Methods, and Applications, 2019

The chapter presents novel approaches to predict and control buckling of thin-walled structures; ... more The chapter presents novel approaches to predict and control buckling of thin-walled structures; mathematically, these approaches are formalized as the first and second inverse bifurcation problems for von Karman equations. Both approaches are based upon the method employed to solve the direct bifurcation problem for the equations in question. The approach considered was applied to several difficult problems of actual practice, viz., for the first inverse problem, to the problems of optimal thickness distribution and optimal external pressure distribution for a cylindrical shell, optimal curvature for a cylindrical panel as well; for the second inverse problem, to the problem to predict buckling of a cylindrical shell under an external pressure.

Chaotic Time Series Prediction: Run for the Horizon

The present paper deals with behaviour of approximate solution sequence of boundary problems for ... more The present paper deals with behaviour of approximate solution sequence of boundary problems for the nonlinear elliptic equations of von Karman type constructed with the employment of the iterative generalized Kantorovich method; the relations for the generalized solution of equations in question is used as the governing ones. We revealed correctness of the relations as well as strongly continuity of the method operator in specific ’weighted’ space that makes it possible to state sufficient conditions for strong convergence.

Generalized Relational Tensors For Irregularly Sampled Time Series: Methods To Store, Re-generate, And Predict

The paper deals with a generalized relational tensor, a novel discrete structure to store informa... more The paper deals with a generalized relational tensor, a novel discrete structure to store information about a time series, and algorithms (1) to fill the structure, (2) to generate a time series from the structure, and (3) to predict a time series, for both regularly and irregularly sampled time series. The algorithms combine the concept of generalized z-vectors with ant colony optimization techniques. In order to estimate quality of the storing/re-generating procedure, a difference between characteristics of the initial and regenerated time series is used. The structure allows working with a multivariate time series, with an irregularly sampled time series, and with a number of series as well. For chaotic time series, a difference between characteristics of the initial time series (the highest Lyapunov exponent, the auto-correlation function) and those of the time series re-generated from a structure is used to assess the effectiveness of the algorithms in question. The approach ha...

A Language as a Self-organized Critical System

Prime Archives in Complex Systems

Asian Research Journal of Mathematics

This paper considers the coefficient inverse problem for the nonlinear boundary problem of von Ka... more This paper considers the coefficient inverse problem for the nonlinear boundary problem of von Karman equations. The Fréchet differentiability of the inverse operator is proved and its neural network approximation is constructed with neuroevolution augmented topology model. The model used proves efficient to solve the coefficient inverse problem even for the parameters values close to those corresponding to singular solutions of the direct problem.

Rapid identification of pre-buckling states: A case of cylindrical shell

Thin-Walled Structures

Artificial Intelligence Research

The paper deals with a novel algorithm used to improve identification quality of clusters generat... more The paper deals with a novel algorithm used to improve identification quality of clusters generated by predictive clustering algorithm as a tool to identify states preceding to bifurcations for a system governed by von Karman equations. To construct bifurcation precursors, solutions (of the equations) observed on bifurcation paths are clustered; centers of the clusters constitute a set of bifurcation precursors. To decrease identification error rate, quality of each precursor is assessed with the employment of an additional, validation set. The paper concerns with two approaches to this procedure; the first one employs a single number to assess identification value of a cluster in order to delete those with low identification values. The second approach uses proposed knowledge extraction procedure to ascertain rules of replacement of the precursors chosen by the algorithm (active) by more efficient one. A wide-ranging simulation reveals that the best variant (provided that the Wisha...

The complete bifurcation structure of nonlinear boundary problem for cylindrical panel subjected to uniform external pressure

Thin-Walled Structures

Complexity

A natural language (represented by texts generated by native speakers) is considered as a complex... more A natural language (represented by texts generated by native speakers) is considered as a complex system, and the type thereof to which natural languages belong is ascertained. Namely, the authors hypothesize that a language is a self-organized critical system and that the texts of a language are “avalanches” flowing down its word cooccurrence graph. The respective statistical characteristics for distributions of the number of words in the texts of English and Russian languages are calculated; the samples were constructed on the basis of corpora of literary texts and of a set of social media messages (as a substitution to the oral speech). The analysis found that the number of words in the texts obeys power-law distribution.

Вісник Дніпропетровського університету. Серія: Моделювання

The present paper deals with behaviour of approximate solution sequence of boundary problems for ... more The present paper deals with behaviour of approximate solution sequence of boundary problems for the nonlinear elliptic equations of von Karman type constructed with the employment of the iterative generalized Kantorovich method; the relations for the generalized solution of equations in question is used as the governing ones. We revealed correctness of the relations as well as strongly continuity of the method operator in specific 'weighted' space that makes it possible to state sufficient conditions for strong convergence.

System research and information technologies

Аннотация. В рамках нелинейного обобщённого метода Канторовича предложен новый подход к локализац... more Аннотация. В рамках нелинейного обобщённого метода Канторовича предложен новый подход к локализации и анализу особых точек решения нелинейной краевой задачи для уравнений Кармана: решение нелинейной краевой задачи сводится к решению последовательности нелинейных краевых задач для обыкновенных дифференциальных уравнений. Одномерные краевые задачи решаются с помощью метода сведения нелинейной краевой задачи к эквивалентной задаче Коши, в процессе реализации которого строится матрица Фреше, вырожденность которой является необходимым и достаточным условием существования ветвления. Численное построение уравнений разветвления позволяет построить ветви, исходящие из точки бифуркации. Вычислительный эксперимент позволил установить бифуркационную картину для случая уравнения Кармана с обобщенной правой частью: решение характеризуются существованием ветвей первичного и вторичного ветвлений. Ключевые слова: уравнения Кармана, ветвление решений нелинейных краевых задач для уравнений в частных производных, нелинейный обобщённый метод Канторовича, первичное ветвление, вторичное ветвление.

Falling in the elderly: Do statistical models matter for performance criteria of fall prediction? Results from two large population-based studies

European Journal of Internal Medicine, 2016

To compare performance criteria (i.e., sensitivity, specificity, positive predictive value, negat... more To compare performance criteria (i.e., sensitivity, specificity, positive predictive value, negative predictive value, area under receiver operating characteristic curve and accuracy) of linear and non-linear statistical models for fall risk in older community-dwellers. Participants were recruited in two large population-based studies, "Prévention des Chutes, Réseau 4" (PCR4, n=1760, cross-sectional design, retrospective collection of falls) and "Prévention des Chutes Personnes Agées" (PCPA, n=1765, cohort design, prospective collection of falls). Six linear statistical models (i.e., logistic regression, discriminant analysis, Bayes network algorithm, decision tree, random forest, boosted trees), three non-linear statistical models corresponding to artificial neural networks (multilayer perceptron, genetic algorithm and neuroevolution of augmenting topologies [NEAT]) and the adaptive neuro fuzzy interference system (ANFIS) were used. Falls ≥1 characterizing fallers and falls ≥2 characterizing recurrent fallers were used as outcomes. Data of studies were analyzed separately and together. NEAT and ANFIS had better performance criteria compared to other models. The highest performance criteria were reported with NEAT when using PCR4 database and falls ≥1, and with both NEAT and ANFIS when pooling data together and using falls ≥2. However, sensitivity and specificity were unbalanced. Sensitivity was higher than specificity when identifying fallers, whereas the converse was found when predicting recurrent fallers. Our results showed that NEAT and ANFIS were non-linear statistical models with the best performance criteria for the prediction of falls but their sensitivity and specificity were unbalanced, underscoring that models should be used respectively for the screening of fallers and the diagnosis of recurrent fallers.

Postcritical Branching Patterns for Cylindrical Shell Subjected to Uniform External Loading

Solid Mechanics and Its Applications, 2013

ABSTRACT The classical problem of stability and postbuckling behaviour of a cylindrical shell und... more ABSTRACT The classical problem of stability and postbuckling behaviour of a cylindrical shell under external pressure is studied from the standpoint of branching of nonlinear boundary problem solutions. Complete branching patterns for the case of a cylindrical shell subjected to uniform external pressure and for the case of a cylindrical shell subjected to uniform axial compression are presented. The case of external pressure comprises the trunk (originated from zero point—undeformed state), primary bifurcation paths (branches) (with deformed shapes regular circumferentially—corresponding to classical eigenforms), and secondary bifurcation paths (with deformed shapes local circumferentially). The case of axial compression comprises the trunk, primary bifurcation paths (with deformed shapes regular circumferentially and longitudinally—corresponding to classical eigenforms), secondary bifurcation paths (with deformed shapes regular circumferentially and local longitudinally that are “single or many belts of dents” shape), and tertiary bifurcation paths (with deformed shapes local both circumferentially and longitudinally that are “solitary dent” or “group of adjacent dents” shape). Typical load-deflection diagrams for general pressure patterns are presented and associated with postcritical branches for the uniformly loaded cases. Respective critical loads estimates are shown. The cylindrical panels represent another branching pattern; the presence of longitudinal edges as discontinuities coinciding with asymptotic lines of shell surface induces the state of generalized edge effect (prominent bending with essentially nonlinear properties).

Branching of Nonlinear Boundary Problem Solutions

Solid Mechanics and Its Applications, 2013

ABSTRACT Branching, i.e., the splitting of solutions into two or more branches, is considered to ... more ABSTRACT Branching, i.e., the splitting of solutions into two or more branches, is considered to be the essential feature of nonlinear boundary problems solutions behaviour for deformation of thin shells. The types of branching and branching (singular) points are distinguished as bifurcation points and limit points. Such special cases as multiple branching, symmetric bifurcation points, and isolated branches are considered as well. The static and energy criteria of stability and expected behaviour of shell structure are presented. The vector–matrix formulation of a bifurcation problem as the instrument to reveal the non-uniqueness of the solution is presented. The connection between the bifurcation problem for boundary and Cauchy problems is demonstrated. The properties of the correspondent Frechet matrix as the key parameters of branching are considered. The specifics of eigenvalues and eigenforms (obtained in the frameworks of linear theory) for most typical shell loading cases which demonstrate the buckling modes of behaviour—external pressure and axial compression—are presented.

In Lieu of Introduction

Solid Mechanics and Its Applications, 2013

ABSTRACT Thin shells are often the best and only choice for designers of flying vehicles, naval v... more ABSTRACT Thin shells are often the best and only choice for designers of flying vehicles, naval vehicles and civil engineering structures. Shell behaviour under a growing load demonstrates its essential nonlinearity, manifesting itself in buckling, in a variety of postbuckling shapes, and in rapid transitions from one shape to another. Nonuniformity of shell structure and loading appeared to be the key factors influencing shell instability (that is the possibility for rapid change of deformed shape, for development of large deflections). The classical Euler approach to stability analysis presumes an ideal undeformed initial state and considers possibility of the solution non-uniqueness in its small vicinity, narrowing the scope of analysis and often delivering improper critical loads. Full nonlinear analysis and its efficient numerical implementation are needed for an investigation of shell behaviour. Typical shell behaviour patterns are studied and the complicated branching of the respective nonlinear boundary problems (including primary, secondary, and tertiary bifurcation paths) are revealed and analyzed. Such important factors as nonuniformity of load and structure (non-symmetric load pattern, structural defects and imperfections, anisotropy, etc.) are to be studied as the causes of initially nonlinear behaviour, transformations of stress-strain state during shell uploading, and a variety of postbuckling forms. Such analysis is performed on the basis of wide-scale numerical analysis. The technical progress of recent decades has placed before designers the paramount task of perceiving complicated loads for structures with minimal structural weight. For aerospace and naval vehicles, as well as civil engineering structures, thin shells, mostly cylindrical and spherical, have been accepted as the best solutions.

Boundary Problem of Thin Shells Theory

Solid Mechanics and Its Applications, 2013

IMA Journal of Management Mathematics

This article deals with the logistics of a Ukrainian food and consumer goods distributor. Our mai... more This article deals with the logistics of a Ukrainian food and consumer goods distributor. Our main goal is to reduce the field costs of the company, which comprise the agent labour costs and company's transportation charges. The mathematical model used is an integer programming optimization one. The problem is heuristically decomposed into subproblems; methods to solve these subproblems are presented. In order to reduce company costs one is able to reduce company agents' staff, to optimize agents' daily routes, to minimize overall goods delivery charges and to reduce the number of rented vehicles. The developed software system offers considerable field costs reduction (28%), decision-making transparency for the planning group and a less prominent influence of human factors on decisions and schedules.

Modern state-of-the-art algorithms to process words and sentences of natural languages make it po... more Modern state-of-the-art algorithms to process words and sentences of natural languages make it possible to map each word of a literary work, in one way or another, into a real scalar or vector, and thereby the text is represented as a path in singleor multidimensional phase space. If one employs a word-to-vec or similar procedures, the texts are mapped into semantic paths; in doing so one may vary the dimension of the phase space. Hence, there are a number of semantic paths associated with a given literary piece. In the framework of another approach, one may map a word into its emotional characteristic, either negative or positive; the approach relies on expert assessments. The resulting series is what is known an emotional path.

Inverse bifurcation problem for von Karman-type elliptic equations

2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET), 2018

Typical solution sequences similar to those of post-bifurcation solutions observed along the bifu... more Typical solution sequences similar to those of post-bifurcation solutions observed along the bifurcation paths of the nonlinear boundary problem for von Karman equations are extracted to serve as precursors of bifurcation (tools to solve the problem). The method allows one to divide all operations required to solve the problem under study into two non-equal parts. The most time-consuming part (to trace bifurcation paths and cluster the respective solution) is performed off-line, while the part of the algorithm that is carried out on-line (the identification algorithm) requires a relatively small number of arithmetic operations. This allows development of the efficient system of rapid identification of pre-buckling states.

Prediction and Control of Buckling: The Inverse Bifurcation Problems for von Karman Equations

Applied Mathematical Analysis: Theory, Methods, and Applications, 2019

The chapter presents novel approaches to predict and control buckling of thin-walled structures; ... more The chapter presents novel approaches to predict and control buckling of thin-walled structures; mathematically, these approaches are formalized as the first and second inverse bifurcation problems for von Karman equations. Both approaches are based upon the method employed to solve the direct bifurcation problem for the equations in question. The approach considered was applied to several difficult problems of actual practice, viz., for the first inverse problem, to the problems of optimal thickness distribution and optimal external pressure distribution for a cylindrical shell, optimal curvature for a cylindrical panel as well; for the second inverse problem, to the problem to predict buckling of a cylindrical shell under an external pressure.

Chaotic Time Series Prediction: Run for the Horizon

The present paper deals with behaviour of approximate solution sequence of boundary problems for ... more The present paper deals with behaviour of approximate solution sequence of boundary problems for the nonlinear elliptic equations of von Karman type constructed with the employment of the iterative generalized Kantorovich method; the relations for the generalized solution of equations in question is used as the governing ones. We revealed correctness of the relations as well as strongly continuity of the method operator in specific ’weighted’ space that makes it possible to state sufficient conditions for strong convergence.

Generalized Relational Tensors For Irregularly Sampled Time Series: Methods To Store, Re-generate, And Predict

The paper deals with a generalized relational tensor, a novel discrete structure to store informa... more The paper deals with a generalized relational tensor, a novel discrete structure to store information about a time series, and algorithms (1) to fill the structure, (2) to generate a time series from the structure, and (3) to predict a time series, for both regularly and irregularly sampled time series. The algorithms combine the concept of generalized z-vectors with ant colony optimization techniques. In order to estimate quality of the storing/re-generating procedure, a difference between characteristics of the initial and regenerated time series is used. The structure allows working with a multivariate time series, with an irregularly sampled time series, and with a number of series as well. For chaotic time series, a difference between characteristics of the initial time series (the highest Lyapunov exponent, the auto-correlation function) and those of the time series re-generated from a structure is used to assess the effectiveness of the algorithms in question. The approach ha...

A Language as a Self-organized Critical System

Prime Archives in Complex Systems

Asian Research Journal of Mathematics

This paper considers the coefficient inverse problem for the nonlinear boundary problem of von Ka... more This paper considers the coefficient inverse problem for the nonlinear boundary problem of von Karman equations. The Fréchet differentiability of the inverse operator is proved and its neural network approximation is constructed with neuroevolution augmented topology model. The model used proves efficient to solve the coefficient inverse problem even for the parameters values close to those corresponding to singular solutions of the direct problem.

Rapid identification of pre-buckling states: A case of cylindrical shell

Thin-Walled Structures

Artificial Intelligence Research

The paper deals with a novel algorithm used to improve identification quality of clusters generat... more The paper deals with a novel algorithm used to improve identification quality of clusters generated by predictive clustering algorithm as a tool to identify states preceding to bifurcations for a system governed by von Karman equations. To construct bifurcation precursors, solutions (of the equations) observed on bifurcation paths are clustered; centers of the clusters constitute a set of bifurcation precursors. To decrease identification error rate, quality of each precursor is assessed with the employment of an additional, validation set. The paper concerns with two approaches to this procedure; the first one employs a single number to assess identification value of a cluster in order to delete those with low identification values. The second approach uses proposed knowledge extraction procedure to ascertain rules of replacement of the precursors chosen by the algorithm (active) by more efficient one. A wide-ranging simulation reveals that the best variant (provided that the Wisha...

The complete bifurcation structure of nonlinear boundary problem for cylindrical panel subjected to uniform external pressure

Thin-Walled Structures

Complexity

A natural language (represented by texts generated by native speakers) is considered as a complex... more A natural language (represented by texts generated by native speakers) is considered as a complex system, and the type thereof to which natural languages belong is ascertained. Namely, the authors hypothesize that a language is a self-organized critical system and that the texts of a language are “avalanches” flowing down its word cooccurrence graph. The respective statistical characteristics for distributions of the number of words in the texts of English and Russian languages are calculated; the samples were constructed on the basis of corpora of literary texts and of a set of social media messages (as a substitution to the oral speech). The analysis found that the number of words in the texts obeys power-law distribution.

Вісник Дніпропетровського університету. Серія: Моделювання

The present paper deals with behaviour of approximate solution sequence of boundary problems for ... more The present paper deals with behaviour of approximate solution sequence of boundary problems for the nonlinear elliptic equations of von Karman type constructed with the employment of the iterative generalized Kantorovich method; the relations for the generalized solution of equations in question is used as the governing ones. We revealed correctness of the relations as well as strongly continuity of the method operator in specific 'weighted' space that makes it possible to state sufficient conditions for strong convergence.

System research and information technologies

Аннотация. В рамках нелинейного обобщённого метода Канторовича предложен новый подход к локализац... more Аннотация. В рамках нелинейного обобщённого метода Канторовича предложен новый подход к локализации и анализу особых точек решения нелинейной краевой задачи для уравнений Кармана: решение нелинейной краевой задачи сводится к решению последовательности нелинейных краевых задач для обыкновенных дифференциальных уравнений. Одномерные краевые задачи решаются с помощью метода сведения нелинейной краевой задачи к эквивалентной задаче Коши, в процессе реализации которого строится матрица Фреше, вырожденность которой является необходимым и достаточным условием существования ветвления. Численное построение уравнений разветвления позволяет построить ветви, исходящие из точки бифуркации. Вычислительный эксперимент позволил установить бифуркационную картину для случая уравнения Кармана с обобщенной правой частью: решение характеризуются существованием ветвей первичного и вторичного ветвлений. Ключевые слова: уравнения Кармана, ветвление решений нелинейных краевых задач для уравнений в частных производных, нелинейный обобщённый метод Канторовича, первичное ветвление, вторичное ветвление.

Falling in the elderly: Do statistical models matter for performance criteria of fall prediction? Results from two large population-based studies

European Journal of Internal Medicine, 2016

To compare performance criteria (i.e., sensitivity, specificity, positive predictive value, negat... more To compare performance criteria (i.e., sensitivity, specificity, positive predictive value, negative predictive value, area under receiver operating characteristic curve and accuracy) of linear and non-linear statistical models for fall risk in older community-dwellers. Participants were recruited in two large population-based studies, "Prévention des Chutes, Réseau 4" (PCR4, n=1760, cross-sectional design, retrospective collection of falls) and "Prévention des Chutes Personnes Agées" (PCPA, n=1765, cohort design, prospective collection of falls). Six linear statistical models (i.e., logistic regression, discriminant analysis, Bayes network algorithm, decision tree, random forest, boosted trees), three non-linear statistical models corresponding to artificial neural networks (multilayer perceptron, genetic algorithm and neuroevolution of augmenting topologies [NEAT]) and the adaptive neuro fuzzy interference system (ANFIS) were used. Falls ≥1 characterizing fallers and falls ≥2 characterizing recurrent fallers were used as outcomes. Data of studies were analyzed separately and together. NEAT and ANFIS had better performance criteria compared to other models. The highest performance criteria were reported with NEAT when using PCR4 database and falls ≥1, and with both NEAT and ANFIS when pooling data together and using falls ≥2. However, sensitivity and specificity were unbalanced. Sensitivity was higher than specificity when identifying fallers, whereas the converse was found when predicting recurrent fallers. Our results showed that NEAT and ANFIS were non-linear statistical models with the best performance criteria for the prediction of falls but their sensitivity and specificity were unbalanced, underscoring that models should be used respectively for the screening of fallers and the diagnosis of recurrent fallers.

Postcritical Branching Patterns for Cylindrical Shell Subjected to Uniform External Loading

Solid Mechanics and Its Applications, 2013

ABSTRACT The classical problem of stability and postbuckling behaviour of a cylindrical shell und... more ABSTRACT The classical problem of stability and postbuckling behaviour of a cylindrical shell under external pressure is studied from the standpoint of branching of nonlinear boundary problem solutions. Complete branching patterns for the case of a cylindrical shell subjected to uniform external pressure and for the case of a cylindrical shell subjected to uniform axial compression are presented. The case of external pressure comprises the trunk (originated from zero point—undeformed state), primary bifurcation paths (branches) (with deformed shapes regular circumferentially—corresponding to classical eigenforms), and secondary bifurcation paths (with deformed shapes local circumferentially). The case of axial compression comprises the trunk, primary bifurcation paths (with deformed shapes regular circumferentially and longitudinally—corresponding to classical eigenforms), secondary bifurcation paths (with deformed shapes regular circumferentially and local longitudinally that are “single or many belts of dents” shape), and tertiary bifurcation paths (with deformed shapes local both circumferentially and longitudinally that are “solitary dent” or “group of adjacent dents” shape). Typical load-deflection diagrams for general pressure patterns are presented and associated with postcritical branches for the uniformly loaded cases. Respective critical loads estimates are shown. The cylindrical panels represent another branching pattern; the presence of longitudinal edges as discontinuities coinciding with asymptotic lines of shell surface induces the state of generalized edge effect (prominent bending with essentially nonlinear properties).

Branching of Nonlinear Boundary Problem Solutions

Solid Mechanics and Its Applications, 2013

ABSTRACT Branching, i.e., the splitting of solutions into two or more branches, is considered to ... more ABSTRACT Branching, i.e., the splitting of solutions into two or more branches, is considered to be the essential feature of nonlinear boundary problems solutions behaviour for deformation of thin shells. The types of branching and branching (singular) points are distinguished as bifurcation points and limit points. Such special cases as multiple branching, symmetric bifurcation points, and isolated branches are considered as well. The static and energy criteria of stability and expected behaviour of shell structure are presented. The vector–matrix formulation of a bifurcation problem as the instrument to reveal the non-uniqueness of the solution is presented. The connection between the bifurcation problem for boundary and Cauchy problems is demonstrated. The properties of the correspondent Frechet matrix as the key parameters of branching are considered. The specifics of eigenvalues and eigenforms (obtained in the frameworks of linear theory) for most typical shell loading cases which demonstrate the buckling modes of behaviour—external pressure and axial compression—are presented.

In Lieu of Introduction

Solid Mechanics and Its Applications, 2013

ABSTRACT Thin shells are often the best and only choice for designers of flying vehicles, naval v... more ABSTRACT Thin shells are often the best and only choice for designers of flying vehicles, naval vehicles and civil engineering structures. Shell behaviour under a growing load demonstrates its essential nonlinearity, manifesting itself in buckling, in a variety of postbuckling shapes, and in rapid transitions from one shape to another. Nonuniformity of shell structure and loading appeared to be the key factors influencing shell instability (that is the possibility for rapid change of deformed shape, for development of large deflections). The classical Euler approach to stability analysis presumes an ideal undeformed initial state and considers possibility of the solution non-uniqueness in its small vicinity, narrowing the scope of analysis and often delivering improper critical loads. Full nonlinear analysis and its efficient numerical implementation are needed for an investigation of shell behaviour. Typical shell behaviour patterns are studied and the complicated branching of the respective nonlinear boundary problems (including primary, secondary, and tertiary bifurcation paths) are revealed and analyzed. Such important factors as nonuniformity of load and structure (non-symmetric load pattern, structural defects and imperfections, anisotropy, etc.) are to be studied as the causes of initially nonlinear behaviour, transformations of stress-strain state during shell uploading, and a variety of postbuckling forms. Such analysis is performed on the basis of wide-scale numerical analysis. The technical progress of recent decades has placed before designers the paramount task of perceiving complicated loads for structures with minimal structural weight. For aerospace and naval vehicles, as well as civil engineering structures, thin shells, mostly cylindrical and spherical, have been accepted as the best solutions.

Boundary Problem of Thin Shells Theory

Solid Mechanics and Its Applications, 2013