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Home Page of AM
CV & my interests:My early interests were radioelectronics, chemistry, rocket modelling, boat construction using self-made programs for calculations of boat shape and material expenses with programmable calculator (assembler), topography, shipping, diving, biking. It was in 80s.
When I took my undergraduate studies, I had got few narrow circles of interests: theory of adaptive control, modelling networks of enzymatic reactions, protein-made live machines. Generally my main interests were theoretical biology.
My diploma work was, in few words, "Problems of computational mathematics in modelling complex subsystems of metabolic processes, make building stable states diagramms invariant to the applied construction methods etc." It also contains theoretical derivation linking controlling coefficients to the global stability of the system. After that time I continued my work made turn to the distributed systems.
The object of my further studies is dynamical properties of short peptides by means of molecular dynamics methods. In concern with some statistical methods for aminoacid sentences correlations were developed. For instance, this are heap search for repeating sequences in large databases , pre-processing like fast reordering for the tables of the sequences frequencies and relative entropy -- proximity data analysis.
Now we try to test correlation dimention's procedure for the stochastic molecular dynamics data. New method of "cross-correlation dimension" was introduced for stochastic processes. Also, this when incorporated with new methods of generalized dimension (or multifractal spectrum) estimation can make hints about potential phase transitions even for "small" systems. Related literature is HERE.
Also I have interests in Neural Networks theory and practice.
See also:
An Introduction into correlation functions
Dedicated to N.A.Bernstein
Support Vector Machine
Comments:
Trajectory samples music synthesized by MLP(1/8sec) 3D-Eltsin synthesized by recurrent MLP Zaslavsky maps
1.Music 2D spectrogram first being sparsified then used as input-output data samples for NN training. Synthesized patterns undergoes IFFT transform while initial phases remain matter of choise.
2.Previously gray-scaled photo was full-face (en face). Then 3-D surface was evaluated by in-level-recurrent tensor neural network according to the shadow distribution.
3.It's p1-q2 plane of electron in power field trap. It is demo for Windows. (Calculates Generalized Dimension Spectrum).
