Jerzy Tiuryn

Applying dynamic Bayesian networks to perturbed gene expression data

BackgroundA central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments.ResultsWe extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed.ConclusionWe show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

Identification of functional modules from conserved ancestral protein–protein interactions

MOTIVATION The increasing availability of large-scale protein-protein interaction (PPI) data has fueled the efforts to elucidate the building blocks and organization of cellular machinery. Previous studies have shown cross-species comparison to be an effective approach in uncovering functional modules in protein networks. This has in turn driven the research for new network alignment methods with a more solid grounding in network evolution models and better scalability, to allow multiple network comparison. RESULTS We develop a new framework for protein network alignment, based on reconstruction of an ancestral PPI network. The reconstruction algorithm is built upon a proposed model of protein network evolution, which takes into account phylogenetic history of the proteins and the evolution of their interactions. The application of our methodology to the PPI networks of yeast, worm and fly reveals that the most probable conserved ancestral interactions are often related to known protein complexes. By projecting the conserved ancestral interactions back onto the input networks we are able to identify the corresponding conserved protein modules in the considered species. In contrast to most of the previous methods, our algorithm is able to compare many networks simultaneously. The performed experiments demonstrate the ability of our method to uncover many functional modules with high specificity. AVAILABILITY Information for obtaining software and supplementary results are available at http://bioputer.mimuw.edu.pl/papers/cappi.

Type reconstruction in the presence of polymorphic recursion

We study the problem of type-checking functional programs in three extensions of ML. One distinguishing feature of these extensions is that they allow recursive definitions to be polymorphically typed. Although the motivation for these extensions comes from pragmatic considerations of programming language design, we show that the typability problem for each one of these extensions is polynomial-time equivalent to the Semi-Unification Problem and, therefore, undecidable

An analysis of ML typability

We carry out an analysis of typability of terms in ML. Our main result is that this problem is DEXPTIME-hard, where by DEXPTIME we mean DTIME(2n0(1)). This, together with the known exponential-time algorithm that solves the problem, yields the DEXPTIME-completeness result. This settles an open problem of P. Kanellakis and J. C. Mitchell. Part of our analysis is an algebraic characterization of ML typability in terms of a restricted form of semi-unification, which we identify as acyclic semi-unification. We prove that ML typability and acyclic semi-unification can be reduced to each other in polynomial time. We believe this result is of independent interest.

Unique fixed points vs. least fixed points

Abstract The aim of this paper is to compare two approaches to the semantics of programming languages: the least fixed point approach, and the unique fixed point approach. Briefly speaking, we investigate here the problem of existence of extensions of algebras with the unique fixed point property to ordered algebras with the least fixed point property, that preserve the fixed point solutions. We prove that such extensions always exist, the construction of a free extension is given. It is also shown that in some cases there is no ‘faithful’ extension, i.e. some elements of a carrier are always collapsed.

A New Characterization of Lambda Definability

We give a new characterization of lambda definability in Henkin models using logical relations defined over ordered sets with varying arity. The advantage of this over earlier approaches by Plotkin and Statman is its simplicity and universality. Yet, decidability of lambda definability for hereditarily finite Henkin models remains an open problem. But if the variable set allowed in terms is also restricted to be finite then our techniques lead to a decision procedure.

ML typability is Dexptime-complete

We carry out an analysis of typability of terms in ML. Our main result is that this problem is DEXPTIME-hard, where by DEXPTIME we mean DTIME\((2^{n^{O(1)} } )\). This, together with the known exponential-time algorithm that solves the problem, yields the DEXPTIME-completeness result. This settles an open problem of P. Kanellakis and J.C. Mitchell.

Satisfiability of Inequalities in a Poset

We consider tractable and intractable cases of the satisfiability problem for conjunctions of inequalities between variables and constants in a fixed finite poset. We show that crowns are intractable. We study members and closure properties of the class of tractable posets. We define a feasible poset to be one whose potential obstacles to satisfiability are representable by a certain formula of the first-order extended by the least fixed operator. For bipartite posets we give a complete classification of hard posets and feasible ones.

Type inference problems: a survey

It is well recognized that types play an important role in programming. In strongly typed programming languages types serve as a device that helps to prevent the kind of errors as an application of an operator to an incompatible operand, such as indexing on a non-array variable. Hence, types in programming can be viewed as a safety mechanism. This is what types are good for. However, the price for working in a strongly typed environment is that the types can get very large. Hence, if types are to be explicit in every programming construct, then this may seriously affect readibility of a program, as well as it may cause severe difficulties when debugging the program. A possible solution to the above problem is to work in a system where types can be omitted from programs and retrieved from the program structure when needed.

The subtyping problem for second-order types is undecidable

We prove that the subtyping problem induced by Mitchells containment relation (1988) for second-order polymorphic types is undecidable. It follows that type-checking is undecidable for the polymorphic lambda-calculus extended by an appropriate subsumption rule.