Computing Lengths of Shortest Non-Crossing Paths in Planar Graphs

Given a plane undirected graph $G$ with non-negative edge weights and a set of $k$ terminal pairs on the external face, it is shown in Takahashi et al., (Algorithmica, 16, 1996, pp. 339-357) that the lengths of $k$ non-crossing shortest paths joining the $k$ terminal pairs (if they exist) can be computed in $O(n \log n)$ worst-case time, where $n$ is the number of vertices of $G$. This technique only applies when the union $U$ of the computed shortest paths is a forest. We show that given a plane undirected weighted graph $U$ and a set of $k$ terminal pairs on the external face, it is always possible to compute the lengths of $k$ non-crossing shortest paths joining the $k$ terminal pairs in linear worst-case time, provided that the graph $U$ is the union of $k$ shortest paths, possibly containing cycles. Moreover, each shortest path $\pi$ can be listed in $O(\ell+\ell\log\lceil{\frac{k}{\ell}}\rceil)$, where $\ell$ is the number of edges in $\pi$. As a consequence, the problem of computing multi-terminal distances in a plane undirected weighted graph can always be solved in $O(n \log k)$ worst-case time in the general case.Comment: 17 pages, 11 figure

Network homophily via multi-dimensional extensions of Cantelli's inequality

Homophily is the principle whereby "similarity breeds connections". We give a quantitative formulation of this principle within networks. We say that a network is homophillic with respect to a given labeled partition of its vertices, when the classes of the partition induce subgraphs that are significantly denser than what we expect under a random labeled partition into classes maintaining the same cardinalities (type). This is the recently introduced \emph{random coloring model} for network homophily. In this perspective, the vector whose entries are the sizes of the subgraphs induced by the corresponding classes, is viewed as the observed outcome of the random vector described by picking labeled partitions at random among partitions with the same type.\,Consequently, the input network is homophillic at the significance level $\alpha$ whenever the one-sided tail probability of observing an outcome at least as extreme as the observed one, is smaller than $\alpha$. Clearly, $\alpha$ can also be thought of as a quantifier of homophily in the scale $[0,1]$. Since, as we show, even approximating this tail probability is an NP-hard problem, we resort multidimensional extensions of classical Cantelli's inequality to bound $\alpha$ from above. This upper bound is the homophily index we propose. It requires the knowledge of the covariance matrix of the random vector, which was not previously known within the random coloring model. In this paper we close this gap by computing the covariance matrix of subgraph sizes under the random coloring model. Interestingly, the matrix depends on the input partition only through its type and on the network only through its degrees. Furthermore all the covariances have the same sign and this sign is a graph invariant. Plugging this structure into Cantelli's bound yields a meaningful, easy to compute index for measuring network homophily

Max-flow vitality in undirected unweighted planar graphs

We show a fast algorithm for determining the set of relevant edges in a planar undirected unweighted graph with respect to the maximum flow. This is a special case of the \emph{max flow vitality} problem, that has been efficiently solved for general undirected graphs and $st$-planar graphs. The \emph{vitality} of an edge of a graph with respect to the maximum flow between two fixed vertices $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that edge. In this paper we show that the set of edges having vitality greater than zero in a planar undirected unweighted graph with $n$ vertices, can be found in $O(n \log n)$ worst-case time and $O(n)$ space.Comment: 9 pages, 4 figure

Evaluating homophily in networks via HONTO (HOmophily Network TOol): a case study of chromosomal interactions in human PPI networks

It has been observed in different kinds of networks, such as social or biological ones, a typical behavior inspired by the general principle 'similarity breeds connections'. These networks are defined as homophilic as nodes belonging to the same class preferentially interact with each other. In this work, we present HONTO (HOmophily Network TOol), a user-friendly open-source Python3 package designed to evaluate and analyze homophily in complex networks. The tool takes in input from the network along with a partition of its nodes into classes and yields a matrix whose entries are the homophily/heterophily z-score values. To complement the analysis, the tool also provides z-score values of nodes that do not interact with any other node of the same class. Homophily/heterophily z-scores values are presented as a heatmap allowing a visual at-a-glance interpretation of results. AVAILABILITY AND IMPLEMENTATION: Tool's source code is available at https://github.com/cumbof/honto under the MIT license, installable as a package from PyPI (pip install honto) and conda-forge (conda install -c conda-forge honto), and has a wrapper for the Galaxy platform available on the official Galaxy ToolShed (Blankenberg et al., 2014) at https://toolshed.g2.bx.psu.edu/view/fabio/honto

IMPLEMENTASI BUDAYA LITERASI DALAM PEMBENTUKAN KARAKTER INTEGRITAS SISWA DI SMA NEGERI 02 BATU

This study aims to describes the implementation of literacy culture in reporting the integrity character of students at SMA Negeri 02 Batu; mistakes and the solution of the problem in implementing literacy culture in order to characterize the integrity of students at SMA Negeri 02 Batu. The research method used qualitative research and descriptive approaches. This research consists of procedures, implementation and data analysis. The data technique are uses observation, interview and documentation. The data analysis technique consist of four stages of activity, namely data collection, data reduction, data presentation, and drawing conclusions. The data validity technique used source triangulation. The results showed that the implementation of Cultural Literacy was carried out through various stages, namely the habituation, development and learning stages. Constraints originating from GLS administrators and teachers are those who lack literacy training, students are low reading interest and different character of students, family is an understanding of the understanding of the character of education at home. Damage to GLS administrators and teachers, the solution is to provide training to improve competence, to students the solution is to motivate and approach each student, trust that comes from parents, the solution provides an understanding of character education at home

Clostridium botulinum spores and toxin in mascarpone cheese and other milk products

A total of 1,017 mascarpone cheese samples, collected at retail, were analyzed for Clostridium botulinum spores and toxin, aerobic mesophilic spore counts, as well as pH, a(w) (water activity), and Eh (oxidation-reduction potential). In addition 260 samples from other dairy products were also analyzed for spores and botulinum toxin. Experiments were carried out on naturally and artificially contaminated mascarpone to investigate the influence of different temperature conditions on toxin production by C. botulinum. Three hundred and thirty-one samples (32.5%) of mascarpone were positive for botulinal spores, and 7 (0.8%) of the 878 samples produced at the plant involved in an outbreak of foodborne botulism also contained toxin type A. The chemical-physical parameters (pH, a(w), Eh) of all samples were compatible with C. botulinum growth and toxinogenesis. Of the other milk products, 2.7% were positive for C. botulinum spores. Growth and toxin formation occurred in naturally and experimentally contaminated mascarpone samples after 3 and 4 days of incubation at 28 degrees C, respectively

Identification of Novel Linear Megaplasmids Carrying a ß-Lactamase Gene in Neurotoxigenic Clostridium butyricum Type E Strains

Since the first isolation of type E botulinum toxin-producing Clostridium butyricum from two infant botulism cases in Italy in 1984, this peculiar microorganism has been implicated in different forms of botulism worldwide. By applying particular pulsed-field gel electrophoresis run conditions, we were able to show for the first time that ten neurotoxigenic C. butyricum type E strains originated from Italy and China have linear megaplasmids in their genomes. At least four different megaplasmid sizes were identified among the ten neurotoxigenic C. butyricum type E strains. Each isolate displayed a single sized megaplasmid that was shown to possess a linear structure by ATP-dependent exonuclease digestion. Some of the neurotoxigenic C. butyricum type E strains possessed additional smaller circular plasmids. In order to investigate the genetic content of the newly identified megaplasmids, selected gene probes were designed and used in Southern hybridization experiments. Our results revealed that the type E botulinum neurotoxin gene was chromosome-located in all neurotoxigenic C. butyricum type E strains. Similar results were obtained with the 16S rRNA, the tetracycline tet(P) and the lincomycin resistance protein lmrB gene probes. A specific mobA gene probe only hybridized to the smaller plasmids of the Italian C. butyricum type E strains. Of note, a ß-lactamase gene probe hybridized to the megaplasmids of eight neurotoxigenic C. butyricum type E strains, of which seven from clinical sources and the remaining one from a food implicated in foodborne botulism, whereas this ß-lactam antibiotic resistance gene was absent form the megaplasmids of the two soil strains examined. The widespread occurrence among C. butyricum type E strains associated to human disease of linear megaplasmids harboring an antibiotic resistance gene strongly suggests that the megaplasmids could have played an important role in the emergence of C. butyricum type E as a human pathogen

Prevalence of Listeria species in camel sausages from retail markets in Aydin province in Turkey and RAPD analysis of Listeria monocytogenes isolates

Samples were taken from 100 camel sausages from the different retail markets in Aydin province in the south-west of Turkey and they were tested for the presence of Listeria spp by biochemical methods. Samples were enriched using Listeria Enrichment Broth and they were inoculated onto Listeria Selective Agar. Listeria monocytogenes was isolated from nine samples (9%), Listeria innocua from 14 samples (14%) and Listeria welshimeri from two samples(2%). A 701 bp fragment of listeriolysin O sequence for L. monocytogenes was amplified using specific primers by polymerase chain reaction (PCR) for confirmation of the identification. A random primer (OPA-11) was used in a random amplified polymorphic DNA (RAPD) assay. This detected five different band profiles amongst the L. monocytogenes isolates, indicating a relatively large amount of genetic heterogeneity amongst the nine isolates. The study has highlighted the need for improved strategies for food safety, in particular appropriate hygienic precautions to avoid contamination of sausage during the manufacturing process and appropriate preservation techniques during storage and transport, to prevent transmission of Listeria spp to consumers at home and abroad

Permutation criteria to evaluate multiple clinical endpoints in a proof-of-concept study: lessons from Pre-RELAX-AHF

Clinically relevant endpoints cannot be routinely targeted with reasonable power in a small study. Hence, proof-of-concept studies are often powered to a primary surrogate endpoint. However, in acute heart failure (AHF) effects on surrogates have not translated into clinical benefit in confirmatory studies. Although observing an effect on one of many endpoints due to chance is likely, observing concurrent positive trends across several outcomes by chance is usually unlikely. Pre-RELAX-AHF, which compared 4 relaxin doses with placebo in AHF, has shown favourable trends versus placebo (one-sided P <0.10) on six of nine clinical endpoints in the 30 mu g/kg/day group. To illustrate evaluation of multiple, correlated clinical endpoints for evidence of efficacy and for dose selection, a permutation method was applied retrospectively. By randomly re-assigning the treatment group to the actual data for each of the 229 subjects, 20,000 permutation samples were constructed. The permutation P value for at least six favourable trends among nine endpoints in any dose groups was 0.0073 (99.9% CI 0.0053-0.0093). This is higher than would be expected if the endpoints were uncorrelated (0.00026), but much lower than the probability of observing one of nine comparisons significant at the traditional two-sided P <0.05 (0.74). Thus, the result was unlikely due to correlated endpoints or to chance. Examining consistency of effect across multiple clinical endpoints in a proof-of-concept study may identify efficacious therapies and enable dose selection for confirmatory trials. The merit of the approach described requires confirmation through prospective application in designing future studies

High Density Microarray Analysis Reveals New Insights into Genetic Footprints of Listeria monocytogenes Strains Involved in Listeriosis Outbreaks

Listeria monocytogenes, a foodborne bacterial pathogen, causes invasive and febrile gastroenteritis forms of listeriosis in humans. Both invasive and febrile gastroenteritis listeriosis is caused mostly by serotypes 1/2a, 1/2b and 4b strains. The outbreak strains of serotype 1/2a and 4b could be further classified into several epidemic clones but the genetic bases for the diverse pathophysiology have been unsuccessful. DNA microarray provides an important tool to scan the entire genome for genetic signatures that may distinguish the L. monocytogenes strains belonging to different outbreaks. We have designed a pan-genomic microarray chip (Listeria GeneChip) containing sequences from 24 L. monocytogenes strains. The chip was designed to identify the presence/absence of genomic sequences, analyze transcription profiles and identify SNPs. Analysis of the genomic profiles of 38 outbreak strains representing 1/2a, 1/2b and 4b serotypes, revealed that the strains formed distinct genetic clusters adhering to their serotypes and epidemic clone types. Although serologically 1/2a and 1/b strains share common antigenic markers microarray analysis revealed that 1/2a strains are further apart from the closely related 1/2b and 4b strains. Within any given serotype and epidemic clone type the febrile gastroenteritis and invasive strains can be further distinguished based on several genetic markers including large numbers of phage genome, and intergenic sequences. Our results showed that the microarray-based data can be an important tool in characterization of L. monocytogenes strains involved in both invasive and gastroenteritis outbreaks. The results for the first time showed that the serotypes and epidemic clones are based on extensive pan-genomic variability and the 1/2b and 4bstrains are more closely related to each other than the 1/2a strains. The data also supported the hypothesis that the strains causing these two diverse outbreaks are genotypically different and this finding might be important in understanding the pathophysiology of this organism