A. Verschoren

SynTReN: a generator of synthetic gene expression data for design and analysis of structure learning algorithms

BackgroundThe development of algorithms to infer the structure of gene regulatory networks based on expression data is an important subject in bioinformatics research. Validation of these algorithms requires benchmark data sets for which the underlying network is known. Since experimental data sets of the appropriate size and design are usually not available, there is a clear need to generate well-characterized synthetic data sets that allow thorough testing of learning algorithms in a fast and reproducible manner.ResultsIn this paper we describe a network generator that creates synthetic transcriptional regulatory networks and produces simulated gene expression data that approximates experimental data. Network topologies are generated by selecting subnetworks from previously described regulatory networks. Interaction kinetics are modeled by equations based on Michaelis-Menten and Hill kinetics. Our results show that the statistical properties of these topologies more closely approximate those of genuine biological networks than do those of different types of random graph models. Several user-definable parameters adjust the complexity of the resulting data set with respect to the structure learning algorithms.ConclusionThis network generation technique offers a valid alternative to existing methods. The topological characteristics of the generated networks more closely resemble the characteristics of real transcriptional networks. Simulation of the network scales well to large networks. The generator models different types of biological interactions and produces biologically plausible synthetic gene expression data.

Prediction of kinase-specific phosphorylation sites using conditional random fields

Motivation: Phosphorylation is a crucial post-translational protein modification mechanism with important regulatory functions in biological systems. It is catalyzed by a group of enzymes called kinases, each of which recognizes certain target sites in its substrate proteins. Several authors have built computational models trained from sets of experimentally validated phosphorylation sites to predict these target sites for each given kinase. All of these models suffer from certain limitations, such as the fact that they do not take into account the dependencies between amino acid motifs within protein sequences in a global fashion. Results: We propose a novel approach to predict phosphorylation sites from the protein sequence. The method uses a positive dataset to train a conditional random field (CRF) model. The negative training dataset is used to specify the decision threshold corresponding to a desired false positive rate. Application of the method on experimentally verified benchmark phosphorylation data (Phospho.ELM) shows that it performs well compared to existing methods for most kinases. This is to our knowledge that the first report of the use of CRFs to predict post-translational modification sites in protein sequences. Availability: The source code of the implementation, called CRPhos, is available from http://www.ptools.ua.ac.be/CRPhos/ Contact: kris.laukens@ua.ac.be Suplementary Information: Supplementary data are available at http://www.ptools.ua.ac.be/CRPhos/

Exact sequences for relative Brauer groups and Picard groups

Abstract Relative Brauer groups and Picard groups have been introduced in [19] resp. [17]. In both papers we restricted atteention to the Brauer group resp. Picard group of a single couple ( R , σ ) consisting of a commutative ring R and an indempotent kernel funktor σ in R -mod. Here we answer the question: what happens to these invariants if we change R or σ ? The exact sequences describing this functional behaviour have several applications in ring theory and algebraic geometry, some of which have been included.

Strongly normalizing extensions

Abstract In this paper, we introduce strongly normalizing extensions as a natural generalization of centralizing extensions between rings. We show that these extensions behave in a much nicer way than normalizing extensions, both from the geometric and localization theoretic point of view.

Local cohomology and quasicoherent sheaves

Local cohomology is usually defined only with respect to locally closed subsets of a (locally) noetherian scheme, which is amply sufficient for most applications in algebraic geometry. When dealing with ring theoretic problems more general subsets are needed, however. As a matter of fact, if one wishes to investigate the structure of reflexive sheaves on a Krull scheme, say, then one is inevitably led to consider the subset of all codimension 1 points, which is not necessarily locally closed. What all of these different types of subsets have in common is that they are so-called “generically closed” subsets ( = closed under generization). The behaviour of quasicoherent and coherent sheaves on generically closed subsets has been amply studied in [VVZ, VV3, V], where we have also introduced the localization of quasicoherent sheaves with respect to these. On the other hand, in [Sul, K. Suominen has introduced local cohomology with respect to arbitrary subsets of a scheme (actually, of an arbitrary ringed space!), with the purpose of applying this to general duality theory. The local cohomology groups and sheaves he obtains are also constructed through some localization in the category of sheaves on X. We will briefly recall the essentials about this below. One may of course wonder whether the two theories are connected in some way. At first glance, this may seem rather unlikely, since, e.g., the former theory only deals with quasicoherent sheaves, whereas the latter uses resolutions by arbitrary, not necessarily quasicoherent, injective sheaves. In this note, we prove the (maybe surprising) fact that on a locally noetherian scheme X the two “local cohomologies” with respect to an arbitrary closed subset Y coincide for any quasicoherent sheaf of modules on X. Actually, we prove a somewhat stronger result: in fact it suffices to

Walsh transforms, balanced sum theorems and partition coefficients over multary alphabets

In this note, we indicate how the basic machinery of Walsh transforms can be generalized from the binary case ([3, 4]) to multary alphabets. Our main results show how Walsh coefficients are related to partition coefficients and how they may be used to calculate schema averages.

FULLY BOUNDED GROTHENDIECK CATEGORIES PART I: LOCALLY NOETHERIAN CATEGORIES

In this paper we aim to generalize some well-known properties of left noetherian fully left bounded rings to locally noetherian Grothendieck categories. For technical reasons the general theory will only be developed for locally noetherian categories having a noetherian generator. However, to show that the theory works in much more general situations as well, similar results will be proved to hold in other categories, e.g. the category of graded left modules over a graded noetherian ring, which will be dealt with in Part II of this paper. In the first paragraphs we recall some properties of locally noetherian categories and localization in Grothendieck categories. Next, we will introduce prime kernel functors in Grothendieck categories. Once the technical machinery developed we generalize results of Krause and Gabriel to Grothendieck categories with a noetherian generator. We conclude by giving some relations between symmetric kernel functors and fully bounded Grothendieck categories.

Fully bounded grothendieck categories part II: Graded modules

In Part I of this paper the second author studies boundedness conditions in Grothendieck categories with a Noetherian generator. However, if R is a Z-graded ring, then R is not necessarily a generator for R-gr, the Grothendieck category of graded left R-modules. As a matter of fact, we may consider G = @&R(n) as a generator for R-gr but G is neither a ring, nor is G Noetherian in R-gr even if R is a left Noetherian graded ring. Thus the graded case does not fall into the cases dealt with in Part I. Another new feature here is that in the graded case the existence of a functor R -gr + R-mod is evident, whereas in the locally Noetherian case substantial use has to be made of the Gabriel-Popescu embedding theorem, in order to obtain a somewhat similar situation. Although the functor R-gr --, R-mod is not as nice as one might hope after a first optimistic glance, we aim to study graded fully boundedness properties and relate these to phenomena in R-mod. A similar philosophy is behind the first author’s results on graded rings and modules of quotients, and it may thus be expected that the graded boundedness conditions may be brought to bear on certain properties of graded localizations, exactly as in the ungraded case. The final section of the paper characterizes graded fully left bounded rings that are fully left bounded. For basic theory on graded rings we refer to [l, 171. Some of the less known results have been summarized in Section 1.

Localization of presheaves of modules

cf. [31, WI. In this paper we look at the problem in a different way. We want to consider torsion theories in the category of presheaves of modules over a fixed presheaf of rings. The functorial character of torsion theory, as set up by P. Gabriel, cf. [l], and 0. Goldman, cf. [4], invites direct generalization. On the other hand we also want earlier constructed structure (pre-) sheaves, cf. [3], [6], [7], to be the result of localization of a constant presheaf. Because of this we are forced to consider certain special torsion theories, called local torsion theories. These are locally defined by common kernel functors in module categories.

On the Brauer group of a projective variety

This paper presents a direct, torsion-theoretic description of the Brauer group of a projective schemeX. IfX is a regular projective variety of dimension at most two, then Br(X) reduces to the relative Brauer group of the homogeneous coordinate ring ofX, based on pseudo Azumaya algebras.