Bounded Representations of Interval and Proper Interval Graphs

Klavik et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition for each vertex v two intervals L_v and R_v called bounds. We ask whether there exists a bounded representation in which each interval I_v has its left endpoint in L_v and its right endpoint in R_v. We show that the problem can be solved in linear time for interval graphs and in quadratic time for proper interval graphs. Robert's Theorem states that the classes of proper interval graphs and unit interval graphs are equal. Surprisingly the bounded representation problem is polynomially solvable for proper interval graphs and NP-complete for unit interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the proper and unit interval representations behave very differently. The bounded representation problem belongs to a wider class of restricted representation problems. These problems are generalizations of the well-understood recognition problem, and they ask whether there exists a representation of G satisfying some additional constraints. The bounded representation problems generalize many of these problems

Influence of germination on lectin in Lens culinaris seeds

The effect of germination conditions on the lectin of Lens culinaris var. Magda 20 seeds was studied. The seeds were germinated at 20 °C under different conditions of watering and light and for different periods of time. The seed lectin was assayed by haemagglutination and quantified by competitive ELISA. Changes in lectin content during germination were also monitored by SDS-PAGE and immunoblotting. Haemagglutinating activity and lectin content in the seeds were not changed during the first three days regardless of the conditions of the germination. However, lectin concentration was significantly higher after six days of germination; relative lectin levels being particularly high when germination was carried out in the light and with daily watering. The results of SDS-PAGE and immunoblotting have also shown that the lectin was not degraded during the first six days of germination however, other storage-proteins were broken down by proteolysis

Minimal Obstructions for Partial Representations of Interval Graphs

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. Two linear-time algorithms are known for solving this problem. In this paper, we characterize the minimal obstructions which make partial representations non-extendible. This generalizes Lekkerkerker and Boland's characterization of the minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible if and only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to a linear-time certifying algorithm for partial representation extension

Designed Azolopyridinium Salts Block Protective Antigen Pores In Vitro and Protect Cells from Anthrax Toxin

Background:Several intracellular acting bacterial protein toxins of the AB-type, which are known to enter cells by endocytosis, are shown to produce channels. This holds true for protective antigen (PA), the binding component of the tripartite anthrax-toxin of Bacillus anthracis. Evidence has been presented that translocation of the enzymatic components of anthrax-toxin across the endosomal membrane of target cells and channel formation by the heptameric/octameric PA63 binding/translocation component are related phenomena. Chloroquine and some 4-aminoquinolones, known as potent drugs against Plasmodium falciparium infection of humans, block efficiently the PA63-channel in a dose dependent way.Methodology/Principal Findings:Here we demonstrate that related positively charged heterocyclic azolopyridinium salts block the PA63-channel in the μM range, when both, inhibitor and PA63 are added to the same side of the membrane, the cis-side, which corresponds to the lumen of acidified endosomal vesicles of target cells. Noise-analysis allowed the study of the kinetics of the plug formation by the heterocycles. In vivo experiments using J774A.1 macrophages demonstrated that the inhibitors of PA63-channel function also efficiently block intoxication of the cells by the combination lethal factor and PA63 in the same concentration range as they block the channels in vitro.Conclusions/Significance:These results strongly argue in favor of a transport of lethal factor through the PA63-channel and suggest that the heterocycles used in this study could represent attractive candidates for development of novel therapeutic strategies against anthrax. © 2013 Beitzinger et al

A note on the factorization conjecture

We give partial results on the factorization conjecture on codes proposed by Schutzenberger. We consider finite maximal codes C over the alphabet A = {a, b} with C \cap a^* = a^p, for a prime number p. Let P, S in Z , with S = S_0 + S_1, supp(S_0) \subset a^* and supp(S_1) \subset a^*b supp(S_0). We prove that if (P,S) is a factorization for C then (P,S) is positive, that is P,S have coefficients 0,1, and we characterize the structure of these codes. As a consequence, we prove that if C is a finite maximal code such that each word in C has at most 4 occurrences of b's and a^p is in C, then each factorization for C is a positive factorization. We also discuss the structure of these codes. The obtained results show once again relations between (positive) factorizations and factorizations of cyclic groups

Resting-State Quantitative Electroencephalography Reveals Increased Neurophysiologic Connectivity in Depression

Symptoms of Major Depressive Disorder (MDD) are hypothesized to arise from dysfunction in brain networks linking the limbic system and cortical regions. Alterations in brain functional cortical connectivity in resting-state networks have been detected with functional imaging techniques, but neurophysiologic connectivity measures have not been systematically examined. We used weighted network analysis to examine resting state functional connectivity as measured by quantitative electroencephalographic (qEEG) coherence in 121 unmedicated subjects with MDD and 37 healthy controls. Subjects with MDD had significantly higher overall coherence as compared to controls in the delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), and beta (12–20 Hz) frequency bands. The frontopolar region contained the greatest number of “hub nodes” (surface recording locations) with high connectivity. MDD subjects expressed higher theta and alpha coherence primarily in longer distance connections between frontopolar and temporal or parietooccipital regions, and higher beta coherence primarily in connections within and between electrodes overlying the dorsolateral prefrontal cortical (DLPFC) or temporal regions. Nearest centroid analysis indicated that MDD subjects were best characterized by six alpha band connections primarily involving the prefrontal region. The present findings indicate a loss of selectivity in resting functional connectivity in MDD. The overall greater coherence observed in depressed subjects establishes a new context for the interpretation of previous studies showing differences in frontal alpha power and synchrony between subjects with MDD and normal controls. These results can inform the development of qEEG state and trait biomarkers for MDD

Evaluation of a Partial Genome Screening of Two Asthma Susceptibility Regions Using Bayesian Network Based Bayesian Multilevel Analysis of Relevance

Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls). The results were evaluated with traditional frequentist methods and we applied a new statistical method, called Bayesian network based Bayesian multilevel analysis of relevance (BN-BMLA). This method uses Bayesian network representation to provide detailed characterization of the relevance of factors, such as joint significance, the type of dependency, and multi-target aspects. We estimated posteriors for these relations within the Bayesian statistical framework, in order to estimate the posteriors whether a variable is directly relevant or its association is only mediated. With frequentist methods one SNP (rs3751464 in the FRMD6 gene) provided evidence for an association with asthma (OR = 1.43(1.2–1.8); p = 3×10−4). The possible role of the FRMD6 gene in asthma was also confirmed in an animal model and human asthmatics. In the BN-BMLA analysis altogether 5 SNPs in 4 genes were found relevant in connection with asthma phenotype: PRPF19 on chromosome 11, and FRMD6, PTGER2 and PTGDR on chromosome 14. In a subsequent step a partial dataset containing rhinitis and further clinical parameters was used, which allowed the analysis of relevance of SNPs for asthma and multiple targets. These analyses suggested that SNPs in the AHNAK and MS4A2 genes were indirectly associated with asthma. This paper indicates that BN-BMLA explores the relevant factors more comprehensively than traditional statistical methods and extends the scope of strong relevance based methods to include partial relevance, global characterization of relevance and multi-target relevance