# Projects on mathematical modelling and data analysis

## 1. Optimal regression model generation

Computing Center of RAS, author, leader

A mathematical model creation technique was developed. It is intended for modelling of engineering systems. There are set of smooth functions that is given by expert. The sought regression model is an element of the functions superposition set. To make superpositions the stochastic optimization algorithms were used.

## 2. Nonparametric regression model synthesis for the oxygen sensor forecasting

STMicroelectronics, author

To forecast the oxygen lambda sensor values the system of non-parametric regression models was created. The system make trial linear combination of the unit non-parametric models to find out a model with the best forecast ability.

## 3. Modelling of the pressure in the combusting camera of a diesel engine

STMicroelectronics, author

To make a model of the pressure a set of linear and arbitrary superpositions of given smooth function was generated. Three model were selected from the set of more than 10.000 automatically-generated models. The selected models were stable, precise and they satisfy experts in the field.

## 4. Mathematical modeling of the biomarkers of patients with cardio-vascular disease

Immunoclin Ltd., author

The classification algorithm for different groups of patients was created. The set of biomarkers, which could bring a good classification was discovered. To do this a system of classification algorithms generation was created.

## 5. Protein geometric structure dependencies discovering

Institute of Bioorganic Chemistry of RAS, author

A pair of informational units of a protein sequence is given. A distance between the units is calculated using their physicochemical features. The distance function could be chosen such that the units with the same conformation state are placed in the neighborhood. The set of algorithms to prove this hypothesis was developed.

## 6. Revelation behavior patterns of institutional owners at the world markets

RusAtom Group, author, leader

A technique to discovering hidden interrelation between the institutional owners trading was created, it works with a large number of time series and concerns the most valuable stock shares at the biggest markets in the world. Algorithms of hidden interrelations between the stock shares pricing and owners’ portfolio alteration were developed.

## 7. The optimal strategy for continuous auctions

Forecsys Ltd., author

Web systems hold continuous auctions on trading advertising places for a given set of words. An approach to the optimal client strategy was proposed.

## 8. The decision support system for the Russian Electricity Generation Industry

RAO ES Russia, author, leader

The Russian power plants, utilities and supply networks have states, which are described by series of reports. Methodology of integral state estimation was created, software system for decision support was developed. Projects on mathematical modelling and data analysis Vadim Strizhov

## 9. The options fare price estimation problem

Forecsys Ltd., author

Two stochastic process models were compared: the Black-Scholes option pricing model versus Mordecki model. The goal was to specify given model according to nonferrous metal trading data.

## 10. Multi-objective problem stochastic optimization software

STMicroelectronics, co-author

The Matlab software toolbox for single- and multi-objective optimization was created. It includes genetic and evolution algorithms, response-surface algorithms, approximators, visualizers and test problems.

## 11. The model for scenario analysis of the Russian macro-economical parameters

Computing Center of RAS, co-author

The model is based on the vector auto-regression technique. It is tuned using the main econometrical feature data for the last ten years. The forecast and the scenario analysis are included using the feed-back control model.

## 12. Expert estimations concordance methodology

Author of the methodology

Quality of a complex featured object one can estimate in two ways: using direct expert estimates and using weighted sum of feature values. In general case these two accepted quality estimates are different. A method for concordance of expert estimates was proposed.

The indexes based on this technique are:

- Integral indicators of the quality of life in Russian regions, CEMI RAS,
- Human development index in Russia, Moscow State University,
- Kyoto-index: the measure of power plant ecological footprints in the USA, Gaia Ltd.,
- Protected area management effectiveness in Russia, WWF, World Wildlife Fund,
- Index of the rare and Red List species in Russia, Ministry of Natural Resources,
- Econometrical index of the Russian economy state, Computing Center of RAS,
- The high school scientific research effectiveness, The Russian Ministry of Education.

## 13. Modelling on the Russian state protected areas management

IUCN . The World Conservation Union, co-author

A methodology of the state of the protected areas assessment and the management effectiveness evaluation was proposed. A set of algorithms of the IUCN database processing were created.

## 14. Dynamic system phase trajectory analysis algorithms

Computing Center of RAS, author

The mathematical model for living systems under extreme conditions was described. To classify a system state a phase trajectory of the system should be represented as a sequence of clusters. The algorithm for partitioning a phase trajectory into clusters was developed.

## 15. Case history phase trajectories comparison

Computing Center of RAS, author

Algorithms for patients case history clustering were proposed. They are based on the Dynamic Time Warping technique. The minimal cost DTW path of is approximated by a parametric model. The model’s parameters are used for the clustering.

## 16. Pulse wave analysis for non-invasive diagnostics

Niteq Ltd., USA, co-author

Algorithms for low-frequency waveform analysis were designed. The created algorithms are based on a cardiac system mathematical model and statistical description of the heart pulse wave. The goal was to recover a signal from real-time input data and estimate model parameters.