Critical connectedness of thin arithmetical discrete planes

An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version of the usual notion of substitution acting on words. We associate with the fully subtractive algorithm a set of substitutions whose incidence matrix is provided by the matrices of the algorithm, and prove that their geometric counterparts generate arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of the DGCI extended abstrac

Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

Damaged DNA Binding Protein 2 Plays a Role in Breast Cancer Cell Growth

The Damaged DNA binding protein 2 (DDB2), is involved in nucleotide excision repair as well as in other biological processes in normal cells, including transcription and cell cycle regulation. Loss of DDB2 function may be related to tumor susceptibility. However, hypothesis of this study was that DDB2 could play a role in breast cancer cell growth, resulting in its well known interaction with the proliferative marker E2F1 in breast neoplasia. DDB2 gene was overexpressed in estrogen receptor (ER)-positive (MCF-7 and T47D), but not in ER-negative breast cancer (MDA-MB231 and SKBR3) or normal mammary epithelial cell lines. In addition, DDB2 expression was significantly (3.0-fold) higher in ER-positive than in ER-negative tumor samples (P = 0.0208) from 16 patients with breast carcinoma. Knockdown of DDB2 by small interfering RNA in MCF-7 cells caused a decrease in cancer cell growth and colony formation. Inversely, introduction of the DDB2 gene into MDA-MB231 cells stimulated growth and colony formation. Cell cycle distribution and 5 Bromodeoxyuridine incorporation by flow cytometry analysis showed that the growth-inhibiting effect of DDB2 knockdown was the consequence of a delayed G1/S transition and a slowed progression through the S phase of MCF-7 cells. These results were supported by a strong decrease in the expression of S phase markers (Proliferating Cell Nuclear Antigen, cyclin E and dihydrofolate reductase). These findings demonstrate for the first time that DDB2 can play a role as oncogene and may become a promising candidate as a predictive marker in breast cancer

On Model Checking Boolean BI

The logic of bunched implications (BI), introduced by O'Hearn and Pym, is a substructural logic which freely combines additive and multiplicative implications. Boolean BI (BBI) denotes BI with classical interpretation of additives and its model is the commutative monoid. We show that when the monoid is finitely generated and propositions are recursively defined, or the monoid is infinitely generated and propositions are restricted to generator propositions, the model checking problem is undecidable. In the case of finitely related monoid and,generator propositions. the model checking problem is EXPSPACE-complete.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000270711900021&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Computer Science, Theory & MethodsEICPCI-S(ISTP)

The 3′ Splice Site of Influenza A Segment 7 mRNA Can Exist in Two Conformations: A Pseudoknot and a Hairpin

The 3′ splice site of influenza A segment 7 is used to produce mRNA for the M2 ion-channel protein, which is critical to the formation of viable influenza virions. Native gel analysis, enzymatic/chemical structure probing, and oligonucleotide binding studies of a 63 nt fragment, containing the 3′ splice site, key residues of an SF2/ASF splicing factor binding site, and a polypyrimidine tract, provide evidence for an equilibrium between pseudoknot and hairpin structures. This equilibrium is sensitive to multivalent cations, and can be forced towards the pseudoknot by addition of 5 mM cobalt hexammine. In the two conformations, the splice site and other functional elements exist in very different structural environments. In particular, the splice site is sequestered in the middle of a double helix in the pseudoknot conformation, while in the hairpin it resides in a two-by-two nucleotide internal loop. The results suggest that segment 7 mRNA splicing can be controlled by a conformational switch that exposes or hides the splice site

Building and Combining Matching Algorithms

International audienceThe concept of matching is ubiquitous in declarative programming and in automated reasoning. For instance, it is a key mechanism to run rule-based programs and to simplify clauses generated by theorem provers. A matching problem can be seen as a particular conjunction of equations where each equation has a ground side. We give an overview of techniques that can be applied to build and combine matching algorithms. First, we survey mutation-based techniques as a way to build a generic matching algorithm for a large class of equational theories. Second, combination techniques are introduced to get combined matching algorithms for disjoint unions of theories. Then we show how these combination algorithms can be extended to handle non-disjoint unions of theories sharing only constructors. These extensions are possible if an appropriate notion of normal form is computable

Facet Connectedness of Arithmetic Discrete Hyperplanes with Non-Zero Shift

International audienceWe present a criterion for the arithmetic discrete hyperplane Open image in new window to be facet connected when θ is the connecting thickness Open image in new window . We encode the shift μ in a numeration system associated with the normal vector Open image in new window and we describe an incremental construction of the plane based on this encoding. We deduce a connectedness criterion and we show that when the Fully Subtractive algorithm applied to Open image in new window has a periodic behaviour, the encodings of shifts μ for which the plane is connected may be recognised by a finite state automaton

On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System

We investigate the computational complexity of counting the Hilbert basis of a homogeneous system of linear Diophantine equations. We establish lower and upper bounds on the complexity of this problem by showing that counting the Hilbert basis is #P-hard and belongs to the class #NP. Moreover, we investigate the complexity of variants obtained by restricting the number of occurrences of the variables in the system

Inhibitory synaptic release properties are topographically distributed in auditory circuitry

By definition Timed Automata have an infinite state-space, thus for verification purposes, an exact finite abstraction is required. We propose a location-based finite zone abstraction, which computes an abstraction based on the relevant guards for a particular state of the model (as opposed to all guards). We show that the location-based zone abstraction is sound and complete with respect to location reachability; that it generalises active-clock reduction, in the sense that an inactive clock has no relevant guards at all; that it enlarges the class of timed automata, that can be verified. We generalise the new abstraction to the case of networks of timed automata, and experimentally demonstrate a potentially exponential speedup compared to the usual abstraction