**
Bioinformatics**

Currently the main area of my research. The topics in which
I am particularly interested/involved include:

This is focused around Finite State Linear Model (FSLM) proposed by A.Brazma. The model incorporates biologically intuitive gene regulatory mechanism similar to that in Boolean networks, but can describe also the continuous changes in protein concentrations. The model exhibits some quite interesting (and even somewhat contradictory features). The model is very general regarding its abilities to describe the behaviour of gene regulatory networks - we have shown that the problem whether a concrete gene will reach an active state in general is algorithmically unsolvable.Similarly, also such problems as the equivalence of two networks in general are algorithmically unsolvable.*Modelling of gene regulatory networks.*

At the same time the same time the problem of reconstruction of network that is consistent with a given gahaviour (series of measurements of protein concentrations in given time points) turned out to be computationally unexpectedly easy (comparable to that of reconstration of Boolean networks).

Even more interestengly, it was possible to develop symbolic methods for analysis of the dynamics of FSLM networks. Although this can't be guaranteed, these methods often allow to draw conclusions about network stability and automatically identify possible "stable behaviours" of such network.This was done on topological level of protein structure (so called TOPS diagrams). Several new algorithms for comparison and motif search have been developed here S protein database and for matching of existing patterns aginst new instances. Mathematically these can be reduced to finding maximal common subgraph and subgraph isomorphism algorithm for graphs that satisfy certain additional constraints (most importantly, the vertices are ordered); it is also interesting that the particular subclass of graphs seems not to be studied before.*Motif search in protein structures.*

A database of topological motifs as well as tools for searching for these motifs in protein structures (given as PDB files) has also been developed.The approach is based on assumption that evolution of structures at least partially can be described as a stepwise process, where each step is a result of accumulating sequence changes and results in comparatively small but noticeable change in protein structure. One of the aims of this work is to estimate the probabilities with which different types of such small "structural mutations" might occur (that is, to obtain for structures something similar to scoring matrices for protein sequences).*Evolution of protein structures.*

Large part of this is done at the same topological level as motif search, however some work is done also by using coordinate-based structure comparisons.I am involved in database desing for a number of collaborative European Projects:*Database design for biomolecular data.*,*MolPAGE*,*ENGAGE*. The focus is on development of Data Werahouse for integrated storing and analysis of data obtained by different experimental techniques from the same data samples. The project also involves a development of a system for annotation and storage of data for management of biomedical samples as well as assay data produced for these samples. The system contains two main components -*CAGEKID*(patient and Sample Information Management System) and*SIMS*(Assay Information Management System) that are inetegrated within SIMBIOMS open source project.*AIMS*

**
Computational Learning**

This is the subject I have started my research carrier with (I have
been fortunate to work on my
Dr.sc. thesis as one of the students of
Rusins Freivalds) and
the one in which I still feel interested. My research is mainly focussed
on probabilistic aspects of inductive inference - on realations between
classes of functions identifiable with different probabilities according
to some criterion of identification. The focus of interest in computational
learning has somewhat changed since the time I have been very active in
the field, however probabilistic identification of limiting functions
and identification up to small (according to measure) sets
probably still might be of some interest.

**
Automated verification of formal systems**

I have never been an expert in this field in general, however I have enjoyed working
on several problems related to reachability of particular states in some kind of formal systems.
In joint work with K.Cerans we genaralized a famous result by O.Maler and A.Pnueli for
multi-polynomial systems.

Another subfield of this area in which I have been involved is the use
of Higman lemma to prove that reachability problem in particular systems is decidable (this
research was originated by A.Parosh, B.Jonsson and K.Cerans). Unfortunately, the attempts to
generalize Higmans result to other practically interesting cases so far have led only to negative
results.

Somewhat unexpectedly state reachability problems become an important topic also in recent
work also in recent work in bioinformatics in applying Finite State Linear Models for modelling
the behaviour of gene regulatory networks.