

Mathematical methods of data processing
Illposed problems, methods of consideration of
a priori expert information
A.V. Kryanev, G.V. Lukin. The metric analysis and data processing. M.: Fizmatlit, 2010.

The book main objective is to acquaint the reader with the most effective both approved classical and new stochastic and determined methods of estimation and forecasting, to learn to use these methods at the solution of specific targets of data processing. In the book the basic concepts of parametrical and nonparametric statistics, including concepts of estimations, and also the requirements shown to properties of estimations from the point of view of their calculation at data processing on the computer are stated. Some new methods of robust estimation are presented to book, the account of the aprioristic information and forecasting, including algorithms of their numerical realization. Bases of a new direction of data processing  the metric analysis are presented, allowing to solve problems of interpolation and forecasting of one and various variables functions on the basis of an effective utilization of the information of the stochastic and determined characters about investigated functional dependence. It is supposed, that the reader has preliminary mastered a course of probability theory and the mathematical statistics. This book is intended science officers, postgraduate students, students of older years of the various specialities using mathematical methods of data processing.

Arsenin V.Ya., Kryanev A.V. Generalized
Maximum Likelihood Method and its Application for IllPosed
Problems Solving. IllPosed Problems in Natural Sciences. A.
Tikhanov(Ed.). VSP BV, Netherlands, pp.312, 1992. 

Arsenin
V.Ya., Kryanev A.V. Generalized maximum likelihood method for
finite dimensional illposed problems solving. USSR Computational
Mathematics and Mathematical Physics, v.31, N5, pp.643653,
1991. (In Russian)(581 kb) 
This paper proposes a method of
consideration of a priori information about the desired
solution of finitedimensional illposed problems, which
is based on the maximumlikelihood method. The method allows
considering available information as a stochastic character
as well as deterministic one and to get the best approximated
solution.

Kryanev
A.V. Statistical form of A.N. Tihonov's regularized leastsquares
method,  Dokl. Acad. Nauk SSSR, Tom 219, N4, Moscow, 1986.
(In Russian) (217 Kb) 

Kryanev
A.V. Iterational methods of illposed problems solving. USSR
Computational Mathematics and Mathematical Physics, v. 14, N1,
1974. (In Russian) (516 kb) 
This paper concentrates on one of the methods of illposed
problems solving. The described method is convenient for
a computer realization.

Krjanev A.V. The solution of incorrectly posed problem by methods
of successive approximations,  Dokl. Añad. Nauk SSSR, Tom 210,
¹ 1, Ì.: 1973 (174 Kb) 

Robust methods
I.Antoniou, P.Akritas, D.A.Burak, V.V.Ivanov, A.V.Kryanev, G.V.Lukin. Robust methods for stock market data analysis. Physica A, Vol 336, pp. 538 – 548. 2004.
(402 Kb)
We consider the problem of extraction of trend and chaotic components from irregular stock market time series. The proposed methods also permit to extract a part of chaotic component, the socalled anomalous term, caused by the transient shorttime surges with high amplitudes. This provides more accurate determination of the trend component. The methods are based on the Mevaluation with decision functions of Huber and Tukey type. The iterative numerical schemes for determination of trend and chaotic components are briefly presented, resulting in an acceptable solution within a finite number of iterations. The optimal level for extraction of the chaotic component is determined by a new numerical scheme based on the fractal dimension of the chaotic component of the analyzed series. Forecasting from the realized part of the analyzed series and a priori expert information is also discussed.

A.V. Kryanev, G.V. Lukin The metric analysis and data processing
(40 Kb)

Borog V.V., Kryanev A.V., Udumyan D.K. Syntheticmethod determination of latent anomalies in variations of galactic space beams. Geomagnetism and aeronomy. Vol. 51, Issue 4, pp. 475 – 482. 2011.
(111 Kb)
A method has been proposed for detecting hidden periodicities in nonstationary finite time series with strong noise. The successive application of the spectral singular expansion and wavelet transform makes it possible to calculate the energy of short signals with an arbitrary form against a suppressing noise background, the amplitude of which is several times as large as that of a useful signal. This method has been used to identify variations in the galactic cosmic ray (GCR) flux related to IMF disturbances due to the earthward propagation of solar magnetic clouds in the heliosphere.

Kryanev A.V. Application of modern methods of mathematical
statistics for regression analysis on computer. MEPhI,
1988. (in Russian) (3,236 kb) Additions and changes,
2001. (in Russian)
(127 Kb)

This manual is based on the material of the course
for fiveyear students, 'Mathematical methods of data
processing'. The manual states methods and algorithms
of regression dependence recovery, including solutions
of planning optimal experiments problem. The main
purpose of the manual is to familiarize the reader
with the most effective and approved classic and new
statistical methods of recovery, and to learn using
these methods for specific problems solving.

Kryanev A.V. Application of Modern Methods of Parametric and
NonParametric Statistics in Case of Experiment Data Processing
on Computer. MEPhI, 1987. (in Russian) (3,137 Kb) Additions
and changes, 2001. (in Russian)
(108 Kb) 
This manual is based on the material of the first part
of the course 'Mathematical methods of data processing'.
The manual introduces the reader to the most effective and
approved modern methods of mathematical statistic, it shows
how to apply these methods to the specific problems solving.
The manual states basic notions of parametric and nonparametric
statistics, including notions of estimation and properties,
producing to estimation from the calculation point of view
at the data processing on computer.

Arsenin V.Ya., Kryanev A.V., TsupkoSitnikov M.V. Application
of Robust Methods for IllPosed Problems Solving. USSR Computational
Mathematics and Mathematical Physics, v.29, N5, pp.653661,
1989. (in Russian) (439 Kb) 
We propose the robust method of
illposed problems solving for integral first kind equations
and liner algebraic equation systems. The described method
is robust to data errors, which exceed the bound of set
mistake. We suggest the effective algorithm of robust smoothing
functional minimization and describe the application of
this method for charged beam diagnostics problem solving.

Methods of extraction of time series chaotic
and deterministic components
A.V. Kryanev, G.V. Lukin The metric analysis and data processing
(40 Kb)

Ivanov V.V., Kryanev A.V., Lukin G.V. NONSTATIONARY SINGULARSPECTRUM ANALYSIS OF DETERMINED AND CHAOTIC TIME PROCESS
(95 Kb)

A.V. Kryanev, G.V.Lukin, D.K.Udumyan. Metric Analysis and Applications. Numerical Methods and Programming, Vol.10, pp. 408 – 414. 2009. http://srcc.msu.su/nummeth/english/
(354 Kb)
A new approach to the interpolation of functions of one or several variables and to the time series forecasting (extrapolation) as well as some schemes and algorithms based on it are proposed. This approach is called the metric analysis. The metric analysis shows a high accuracy in interpolating the functions of several variables, even in the case of a comparatively small number of points with known function values. It is found that the metric analysis allows one to extrapolate and forecast the values of functions of a wider class than the known singular spectrum analysis.

Kryanev A.V., Chernyi A.I. Robust linear smoothing splines
and their applications. MEPhI Preprint, 00697, 1997. (In
Russian) 

Kryanev A.V. Robust methods for
extraction of trend, anomalous and cycle components from chaotic
timeseries. Paper work of ISIPC, 1999. 

Time series forecasting
models
A.V. Kryanev, G.V. Lukin The metric analysis and data processing
(40 Kb)

Ivanov V.V., Kryanev A.V., Lukin G.V. NONSTATIONARY SINGULARSPECTRUM ANALYSIS OF DETERMINED AND CHAOTIC TIME PROCESS
(95 Kb)

A.V. Kryanev, G.V.Lukin, D.K.Udumyan. Metric Analysis and Applications. Numerical Methods and Programming, Vol.10, pp. 408 – 414. 2009. http://srcc.msu.su/nummeth/english/
(354 Kb)
A new approach to the interpolation of functions of one or several variables and to the time series forecasting (extrapolation) as well as some schemes and algorithms based on it are proposed. This approach is called the metric analysis. The metric analysis shows a high accuracy in interpolating the functions of several variables, even in the case of a comparatively small number of points with known function values. It is found that the metric analysis allows one to extrapolate and forecast the values of functions of a wider class than the known singular spectrum analysis.

I.
Antoniou, Yu.S. Gorshkov, V.V.
Ivanov, A.V. Kryanev. Forecasting financial derivative
prices. Chaos, Solitons and Fractals 11, 2000.

In this paper we consider the
problem of forecasting the prices of financial market
derivatives. A model of changing the underlying asset
prices in the form of general Ito stochastic process is
developed. The derivative prices can be obtained from
the solution of the reverse Cauchy problem for appropriate
parabolic equations on the basis of the reverse Kolmogorov
equation. We present here the numerical scheme for solving
the reverse Cauchy problem for call option and put option
prices based on the implicit finite element difference
method.

Optimisation problems and solution
methods
Optimisation
problems in economics
I.Antoniou, V.V.Ivanov, A.V.Kryanev, V.V.Matokhin, M.V.Shapovalov. On the efficient resources distribution in economics based on entropy. Physica A Vol. 336, pp. 549  562. 2004.
http://www.sciencedirect.com/science/article/pii/S0378437103012329
(799 Kb)
We generalize the approach developed in our previous work on the efficient resources distribution in economic systems with a small number of elements based on entropy. In order to take into account the asymmetric resources distribution, a new set of twoparameter interpolating functions is introduced. We demonstrate that the maximal value of entropy is reached only in case of asymmetric distribution of resources. First results on application of the generalized approach to the analysis of incomes distribution for Sweden and Russia populations have shown that the new scheme permits to estimate effectively the state of the analyzed system and control the resources distribution process.

V. V. Haritonov, A.V. Kryanev, V.V. Matokhin. Adaptable potential of economic systems. International Journal of Nuclear Governance, Economy and Ecology. Vol. 2, pp. 131 – 145. 2008
(21 Kb)
This paper describes an analysis of the stability of economic systems and the preferable distributions of resources. The approach describes the adaptable potential of numerical sequences corresponding to the distribution of resources in economic systems, and can be used for the analysis of the stability of economic systems and in forecasting the occurrence of crisis situations.

N.I. Geraskin, V.V.Haritonov, S.G.Klimanov, A.V. Kryanev and V.I. Savander. Dynamic behavior of fuel cost component in total electricity cost of nuclear power plants with WWERtype power units. International Journal of Nuclear Energy Science and Technology. Vol. 3, pp. 314 – 323. 2007
(21 Kb)
This paper describes the technical and economic analyses of changes in the fuel component of prime electrical energy cost that are caused by implementing various versions of nuclear fuel design and nuclear fuel cycle schemes in WWER440 power reactors.

I.Antoniou,
V.V.
Ivanov, Yu.L. Korolev, A.V.Kryanev, V.V.Matokhin, Z.Suchanecki.
Analysis of resources distribution in economics based on entropy
Physica A: Statistical Mechanics and its Applications, 304
(34) (2002) pp. 525534

We propose a new approach to the problem
of efficient resources distribution in different types of
economic systems. We also propose to use entropy as an indicator
of the efficiency of resources distribution. Our approach
is based on methods of statistical physics in which the
states of economic systems are described in terms of the
density functions rho(g,alpha) of the variable g parameterised
by alpha. The parameter alpha plays a role of the integral
characteristic of the state of the economic system. Having
the density function rho(g,alpha) we can use the corresponding
entropy to evaluate the efficiency of the resources distribution.
Our theoretical study have been tested on real data related
to the portfolio investment.

Kharitonov
V.V., Kryanev A.V., Matokhin V.V. Technology of Making of
Investment Attractive Packs of Innovation Projects. MEPhI Scientific
digest2002. (in Russian) 

Simonov B.P., Matokhin V.V., Sobolev
A.U., Anisimov K.V., Grigoriev A.U. Technology of R&D Results
Commercialisation. 'Scientific session in MEPhI2001', Digest,
v.6, 2001 (in Russian) 

Kharitonov
V.V., Kryanev A.V., Korolev Yu.L., Matokhin V.V. Informational
Internet Technology of Innovation Projects Initial Examination
for Optimal Portfolio (Pack) Making. Report on conference, Obninsk,
2001. (in Russian) 

Kharitonov V.V.,
Kryanev A.V., Matokhin V.V. Technology of R&D Packs Commercialisation
and Its Financing Optimisation. Economics and Forecasting in
Nuclear Energy, Digest N3, 2001. (in Russian) 

Korolev Yu.L., Kryanev A.V., Malginova E.G.,
Matokhin V.V. Dynamic Changes Analysis of Consumption Structure,
MEPhI, 2000. (in Russian) 

Matokhin V.V., Simonov B.P., Yunev D.A., Shchurov
A.M., Ananiev A.A. Estimation of Innovation Project Commercialisation.
Innovation magazine, SaintPetersburg: 'Transfer', N910, 1999.
(in Russian) 

Kryanev A.V., Matokhin V.V., Klimanov S.G. Statistical functions
of resources distribution in economy, MEPhI Preprint, 1998.
(In Russian) (450 Kb) 
We propose the development of statistical
functions of resource distribution from control function
used for Lorenz diagram interpolation. It is shown that
smoothing change of resource distribution nonlinear power
leads to distinctions in kind of statistical functions.
It proves the special significance of distribution corresponding
to the circle on Lorenz plane. The material of the preprint
is using as a studybook in EconomicAnalytical Institute
of the MEPhI.

Dudyrev K., Kryanev A.V., Nekrasov V.I. Monitoring
Optimisation in Surface Contamination Reconstruction. MEPhI
Preprint, 1994. (in Russian) 

Optimisation
problems in finance
Kryanev A.V., Lukin G.V. MATHEMATICAL SIMULATION OF INVESTMENT PORTFOLIOS OPTIMIZATION PROBLEMS
(99 Kb)

I. Antoniou, V.V. Ivanov, A.V. Kryanev On a Binomial Model of Option Pricing
(99 Kb)
The conventional models of option pricing are based on the artificial proposition of the market neutrality to the risk, which is equivalent to the assumption that the expected return µ equals the riskfree return r. However, in real markets µ may significantly differ from r. This may lead to the noticeable difference between model and real values of option prices. We consider here a modiffcation of the CoxRossRubenstein binomial model that takes into account the dependence of option prices on µ.

I. Antoniou, Yu. Gorshkov, V.V. Ivanov, A.V. Kryanev. Forecasting financial derivative prices. Chaos, Solitons & Fractals, Vol. 11, pp. 223 – 229. 2000
(14 Kb)
In this paper we consider the problem of forecasting the prices of financial market derivatives. A model of changing the underlying asset prices in the form of general Ito stochastic process is developed. The derivative prices can be obtained from the solution of the reverse Cauchy problem for appropriate parabolic equations on the basis of the reverse Kolmogorov equation. We present here the numerical scheme for solving the reverse Cauchy problem for call option and put option prices based on the implicit finite element difference method.

I.Antoniou,
V.V.
Ivanov, A.V.Kryanev. On a binomial model of option pricing.
Journal of Computational Methods in Sciences and Engineering
vol. 2, no. 1s2s, 2002, pp. 105109

The conventional models of option pricing are
based on the artificial propositionof the market neutrality
to the risk, which is equivalent to the assumption that the
expected return mu equals the riskfree return r. However,
in real markets mu may significantly differ from r. This may
lead to the noticeable difference between model and real values
of option prices. We consider here a modification of the CoxRossRubenstein
binomial model that takes into account the dependence of option
prices on mu.


Kryanev A.V. Basis of Financial Analysis and Portfolio Investments
in Market Economy. MEPhI, 2001. (in Russian) 
This manual proposes a summary of basis of mathematical
theory for portfolio investment. Here you can find the basic
elements of financial analysis, cash flow analysis, description
of Markowitz scheme for portfolio investment and its application
to the Russian reality. Also tasks for selfcontrol are
presented.
The manual means for students of EconomicAnalytical Institute
and extension course.

Gorchkov Yu.S., Klimanov S.G., Kryanev
A.V. Investment Portfolio Optimisation with Expert Efficiency
Forecasting, Digest of Scientific session MEPhI1998, 1998.
(in Russian) 

Kryanev A.V., Chernyi A.I. Mathematical Models of Investment
Portfolio Optimisation Problems, MEPhI Preprint, 1997. (in Russian)
(508 Kb) 
This preprint proposes schemes of
formulation and solving the portfolio investment optimisation
problem, which are different from Markowitz scheme and advise
a new risk definition. In particular a new portfolio optimisation
problem formulation considers for largescale portfolio.

Kryanev A.V., Chernyi A.I. Numerical Solutions of Optimisation
Problems for Mathematical Models in Investment Theory, Mathematical
modelling magazine, v.8, N8, 1996. (in Russian) (277 Kb) 

Kryanev A.V., Chernyi A.I. Mathematical Models of Efficiency
Investments Interaction, MEPhI Preprint, 1996. (in Russian)
(373 Kb) 
This preprint proposes mathematical model, which help
to link effectiveness of different classes, including reconstruction
of class effectiveness covariance matrix. Mathematical models
take into account the presence of effectiveness link through
regions and industries that helps to detect among parameters
of issuers those who connected with regions and industries
along with own parameters.

Optimisation
problems in radiation therapy
Klimanov
V.A., Kryanev A.V., Klimanov S.G., Beliakov A.I., Golovkin
Yu.V. Impact of Errors in Input Data on Value of Probability
of Control over Tumour under Optimal Irradiation Plan. Scientific
works of MEPhI2002. (in Russian) (129 Kb) 
This paper considers basic profile beams optimisation
problem with taking into account constraints on dose distribution
in risk organs and tumour.

Klimanov V.A.,
Kryanev A.V. Profiles Beams Optimisation Problem with Application
of Physical Criterion Functions. Thesis of Intern. conf. Inverse
and illposed problems, MSU, p.37. (in Russian) (69 Kb) 
This paper considers basic profile beams optimisation
problem with taking into account constraints on dose distribution
in risk organs and tumour.

Rubinsky D.A., Klimanov
V.A., Klimanov S.G., Krianev A.V. Profiles beams optimization
problem for remote radiation therapy as multicriterion problem.
Proceeding of IX Mediterranean Conference on Medical and Biological
Engineering and Computing, Croatia, 2001. (151 Kb) 
Profiles beams optimisation problem for tumours in remote
radiation therapy has been researched in lot of papers during
last years. This paper deals with formulation of profiles
intensity optimisation problem as a multicriterion one
and application of finitesize pencil beam algorithm and
largescaled elements method for its numeric solution.

Klimanov
V.A., Klimanov S.G., Kryanev A.V. Formulation and Numerical
Solution of the Radiation Intensity Profile Optimisation Problem
as MultiCriteria Problem Using Physical and Biological Objective
Function. Medical Physics, 11, 2001. 

Kryanev A.V., Klimanov
V.A., Klimanov S.G., Rubinsky D.A., Zrajun A.G. Profiles
Beams Optimization Problems for Remote Radiation Therapy as
Multicriterion Problem. Chicago2000 World Congress. (409 Kb) 
Profiles beams optimisation problem for tumours in remoteradiation
therapy has been researched in lot of papers during last
years. This paper deals with formulation of profiles intensity
optimisation problem as a multicriterion one and application
of finitesize pencil beam algorithm and largescaled elements
method for its numeric solution.

Klimanov V.A.,
Kryanev A.V. Formulation of Radiation Therapy Planning Optimisation
Problem. Medical Physics, N7, 2000. (in Russian) (160 Kb) 
Radiation therapy optimisation is one of the modern
research directions in physical medicine. This paper researches
lot of papers for last ten years, which deal with formulation
and solving of radiation therapy optimisation problems as
radiation intensity profiling. It is emphasising that now
three schemes of radiation intensity profile optimisation
problem formulation is used: with and without using physical
or biological criterion functions. Advantages and disadvantages
of each of foregoing possible scheme are analysed here.
Some formulation recommendations are given.

Klimanov
V.A., Klimanov S.G., Kryanev A.V., Rubinsky D.A. Mathematical
Modelling of Radiation Therapy Dose Planning Optimisation Problem
Based on the Pencil Beam Algorithm and LargeScaled Elements
Methods. MEPhI Scientific digest2000. (in Russian) 

Klimanov V.A.,
Klimanov S.G., Kryanev A.V. Choice of Optimal Solution for Set
Radiation Ports Placement with Use of Physical Criterion Functions.
MEPhI Scientific digest2000. (in Russian) (114 Kb) 
We developed an algorithm of set radiation ports optimal
placement choice that we propose in this paper. This algorithm
use physical criterion functions. As a directing parameter
in the ports choice optimisation problem the geometrical
placement of radiation intensity ports is used in conditions
of its constancy.

Klimanov
V.A., Kryanev A.V., Rubinsky D.A. Numeric Solution for
Radiation Therapy Dose Planning Optimization Problem Based
on the Pencil Beam Algorithm and LargeScaled Elements Methods.
Physica Medica, v.15, p. 166, 1999.


Klimanov V.A.,
Klimanov S.G., Kryanev A.V., Rubinsky D.A., Zrajun A.G. Profiles
Beams Optimisation Problems for Remote Radiation Therapy. (in
Russian) (91 Kb) 

Klimanov
V.A., Kryanev A.V., Rubinsky D.A. Radiation therapy dose
planning optimization based on the pencil beam algorithm and
largescaled elements method. Third "Medical Physics97"
International Conference meeting reports theses. Obninsk, p.11,
1997 

Klimanov V.A., Klimanov
S.G., Kryanev A.V., Rubinsky D.A., Zrajun A.G. Profiles Beams Optimisation
Problems for Remote Radiation Therapy.  2 (in Russian) (110 Kb)
Profiles beams optimisation problem for tumours in remote
radiation therapy has been researched in lot of papers during
last years. This paper deals with formulation of profiles
intensity optimisation problem as a multicriterion one
and application of finitesize pencil beam algorithm and
largescaled elements method for its numeric solution.

Mathematical theory of nuclear reactors
Vdovina O.P., Kryanev A.V., Sevostianov A.E.
Numeric Solutions of Inverse Problem Solving for SteadyState
Transport Equation and ComputerAided Tomography Problems Using
Worth Function. Mathematical modelling, v.6, N9, 1994. (in Russian) 

Kryanev A.V. Analytical and Numerical Methods of Mathematical
Transport Theory. MEPhI Preprint, 1991. (in Russian) (6,682
Kb) 
This manual is based on the material of the year course
'Questions of mathematical transport theory'. Here formulation
and decision methods of basic mathematical transport theory
are presented. As analytical as well as numerical methods
of transport theory problems solving are considered. The
purpose of the manual is to introduce reader to basic mathematical
transport theory results, which help to solve many transport
particles and emissions applications.

Shchikhov S.B., Kryanev A.V. Research of Stationary
Temperature and Neutron Fields Stability of Reactor Core in
Distributed Models. Atomic energy, v.68, issue 2, 1990. (in
Russian) 

Kryanev A.V. Qualitative and Numerical Methods
for Correction Problems of Mathematical Reactors Theory Problems.
Abstract form doctoral thesis, MEPhI, 1989. (in Russian). 

Kryanev A.V. Existence, Uniqueness
and Stability of Stationary TemperatureNeurone Distributions
in Multiplying Mediums, Preprint, USSR Academy of Science, 1986.
(in Russian) 

Kryanev A.V., Shchikhov S.B. Questions of Mathematical Theory
of Reactors. Nonlinear Analysis. Energoatomisdat, 1983. (in
Russian) (12,615 Kb) 
This work deals with basic nuclear reactor nonlinear
distribution research qualitative methods. We got the conditions
guaranteeing existence and uniqueness of stationary regimes
with taking into account feedbacks including the temperature
ones. Such properties of nonstationary regimes as duration,
stability, and periodicity are researched here. We used
cone theory methods, in particular, stability on cone. Methods,
developed in the work, apply for direct nuclear reactors
models research.


