On the Expressive Power of Multiple Heads in CHR

Constraint Handling Rules (CHR) is a committed-choice declarative language which has been originally designed for writing constraint solvers and which is nowadays a general purpose language. CHR programs consist of multi-headed guarded rules which allow to rewrite constraints into simpler ones until a solved form is reached. Many empirical evidences suggest that multiple heads augment the expressive power of the language, however no formal result in this direction has been proved, so far. In the first part of this paper we analyze the Turing completeness of CHR with respect to the underneath constraint theory. We prove that if the constraint theory is powerful enough then restricting to single head rules does not affect the Turing completeness of the language. On the other hand, differently from the case of the multi-headed language, the single head CHR language is not Turing powerful when the underlying signature (for the constraint theory) does not contain function symbols. In the second part we prove that, no matter which constraint theory is considered, under some reasonable assumptions it is not possible to encode the CHR language (with multi-headed rules) into a single headed language while preserving the semantics of the programs. We also show that, under some stronger assumptions, considering an increasing number of atoms in the head of a rule augments the expressive power of the language. These results provide a formal proof for the claim that multiple heads augment the expressive power of the CHR language.Comment: v.6 Minor changes, new formulation of definitions, changed some details in the proof

Decidability properties for fragments of CHR

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity >0). Both languages allow the use of the = built-in in the body of rules, thus are built on a host language that supports unification. However each imposes one further restriction. The first CHR dialect allows only range-restricted rules, that is, it does not allow the use of variables in the body or in the guard of a rule if they do not appear in the head. We show that the existence of an infinite computation is decidable for this dialect. The second dialect instead limits the number of atoms in the head of rules to one. We prove that in this case, the existence of a terminating computation is decidable. These results show that both dialects are strictly less expressive than Turing Machines. It is worth noting that the language (without function symbols) without these restrictions is as expressive as Turing Machines

Sparse integrative clustering of multiple omics data sets

High resolution microarrays and second-generation sequencing platforms are powerful tools to investigate genome-wide alterations in DNA copy number, methylation and gene expression associated with a disease. An integrated genomic profiling approach measures multiple omics data types simultaneously in the same set of biological samples. Such approach renders an integrated data resolution that would not be available with any single data type. In this study, we use penalized latent variable regression methods for joint modeling of multiple omics data types to identify common latent variables that can be used to cluster patient samples into biologically and clinically relevant disease subtypes. We consider lasso [J. Roy. Statist. Soc. Ser. B 58 (1996) 267-288], elastic net [J. R. Stat. Soc. Ser. B Stat. Methodol. 67 (2005) 301-320] and fused lasso [J. R. Stat. Soc. Ser. B Stat. Methodol. 67 (2005) 91-108] methods to induce sparsity in the coefficient vectors, revealing important genomic features that have significant contributions to the latent variables. An iterative ridge regression is used to compute the sparse coefficient vectors. In model selection, a uniform design [Monographs on Statistics and Applied Probability (1994) Chapman & Hall] is used to seek "experimental" points that scattered uniformly across the search domain for efficient sampling of tuning parameter combinations. We compared our method to sparse singular value decomposition (SVD) and penalized Gaussian mixture model (GMM) using both real and simulated data sets. The proposed method is applied to integrate genomic, epigenomic and transcriptomic data for subtype analysis in breast and lung cancer data sets.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS578 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Recognizing a relatively hyperbolic group by its Dehn fillings

Dehn fillings for relatively hyperbolic groups generalize the topological Dehn surgery on a non-compact hyperbolic $3$-manifold such as a hyperbolic knot complement. We prove a rigidity result saying that if two non-elementary relatively hyperbolic groups without suitable splittings have sufficiently many isomorphic Dehn fillings, then these groups are in fact isomorphic. Our main application is a solution to the isomorphism problem in the class of non-elementary relatively hyperbolic groups with residually finite parabolic groups and with no suitable splittings.Comment: Minor modification (including typesetting). 56 page

Expression of connexin genes in the human retina

Background: Gap junction channels allow direct metabolically and electrical coupling between adjacent cells in various mammalian tissues. Each channel is composed of 12 protein subunits, termed connexins (Cx). In the mouse retina, Cx43 could be localized mostly between astroglial cells whereas expression of Cx36, Cx45 and Cx57 genes has been detected in different neuronal subtypes. In the human retina, however, the expression pattern of connexin genes is largely unknown. Methods: Northern blot hybridizations, RT-PCR as well as immunofluorescence analyses helped to explore at least partially the expression pattern of the following human connexin genes GJD2 (hCx36), GJC1 (hCx45), GJA9 (hCx59) and GJA10 (hCx62) in the human retina. Results: Here we report that Northern blot hybridization signals of the orthologuous hCx36 and hCx45 were found in human retinal RNA. Immunofluorescence signals for both connexins could be located in both inner and outer plexiform layer (IPL, OPL). Expression of a third connexin gene denoted as GJA10 (Cx62) was also detected after Northern blot hybridization in the human retina. Interestingly, its gene structure is similar to that of Gja10 (mCx57) being expressed in mouse horizontal cells. RT-PCR analysis suggested that an additional exon of about 25 kb further downstream, coding for 12 amino acid residues, is spliced to the nearly complete reading frame on exon2 of GJA10 (Cx62). Cx59 mRNA, however, with high sequence identity to zebrafish Cx55.5 was only weakly detectable by RT-PCR in cDNA of human retina. Conclusion: In contrast to the neuron-expressed connexin genes Gjd2 coding for mCx36, Gjc1 coding for mCx45 and Gja10 coding for mCx57 in the mouse, a subset of 4 connexin genes, including the unique GJA9 (Cx59) and GJA10 (Cx62), could be detected at least as transcript isoforms in the human retina. First immunofluorescence analyses revealed a staining pattern of hCx36 and hCx45 expression both in the IPL and OPL, partially reminiscent to that in the mouse, although additional post-mortem material is needed to further explore their sublamina-specific distribution. Appropriate antibodies against Cx59 and Cx62 protein will clarify expression of these proteins in future studies

Reasoning about reversal-bounded counter machines

International audienceIn this paper, we present a short survey on reversal-bounded counter machines. It focuses on the main techniques for model-checking such counter machines with specifications expressed with formulae from some linear-time temporal logic. All the decision procedures are designed by translation into Presburger arithmetic. We provide a proof that is alternative to Ibarra's original one for showing that reachability sets are effectively definable in Presburger arithmetic. Extensions to repeated control state reachability and to additional temporal properties are discussed in the paper. The article is written to the honor of Professor Ewa Orłowska and focuses on several topics that are developped in her works