On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and $v$ in $G$, the number of internal nodes on the shortest path between $u$ and $v$ in the subgraph of $G$ induced by $D \cup \{u,v\}$ is at most $\alpha$ times that in $G$. For general graphs, the only known previous approximability result is an $O(\log n)$-approximation algorithm ($n=|V|$) for $\alpha = 1$ by Ding et al. For any constant $\alpha > 1$, we give an $O(n^{1-\frac{1}{\alpha}}(\log n)^{\frac{1}{\alpha}})$-approximation algorithm. When $\alpha \geq 5$, we give an $O(\sqrt{n}\log n)$-approximation algorithm. Finally, we prove that, when $\alpha =2$, unless $NP \subseteq DTIME(n^{poly\log n})$, for any constant $\epsilon > 0$, the problem admits no polynomial-time $2^{\log^{1-\epsilon}n}$-approximation algorithm, improving upon the $\Omega(\log n)$ bound by Du et al. (albeit under a stronger hardness assumption)

A Novel Phenology Based Feature Subset Selection Technique Using Random Forest for Multitemporal PolSAR Crop Classification

Feature selection techniques intent to select a subset of features that minimizes redundancy and maximizes relevancy for classification problems in machine learning. Standard methods for feature selection in machine learning seldom take into account the domain knowledge associated with the data. Multitemporal crop classification studies with full-polarimetric synthetic aperture radar (PolSAR) data ought to consider the changes in the scattering mechanisms with their phenological growth stages. Hence, it is desirable to incorporate these changes while determining a feature subset for classification. In this study, a random forest (RF) based feature selection technique is proposed that takes into account the changes in the physical scattering mechanism with crop phenological stages for multitemporal PolSAR classification. The partial probability plot, which is an attribute of RF, provides information about the marginal effect of a polarimetric parameter on the desired crop class. Moreover, it is used to identify the specific range of a parameter where the probability of the presence of a particular crop class is high. The proposed technique identifies features that change significantly with crop phenology. The selected features are the ones whose ranges show maximum separation amongst crop classes. Additionally, the feature subset is refined by eliminating correlated features. The E-SAR L-band dataset of the AgriSAR-2006 campaign over the Demmin test site in Germany is used in this study. The classification accuracy using the novel feature selection technique is 99.12%. This is nominally better than using the features obtained from a standard feature selection method used in RF, such as mean decrease Gini (98.73%) and mean decrease accuracy (98.68%) that do not take into account the information based on crop phenology.This work was supported in part by the Spanish Ministry of Economy, Industry and Competitiveness, in part by the State Agency of Research (AEI), and in part by the European Funds for Regional Development under Projects TIN2014-55413-C2-2-P and TEC2017-85244-C2-1-P

Hardness and approximation for the geodetic set problem in some graph classes

In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of vertices from $S$. The \textsc{Minimum Geodetic Set (MGS)} problem is to find a geodetic set with minimum cardinality. In this paper, we prove that solving the \textsc{MGS} problem is NP-hard on planar graphs with a maximum degree six and line graphs. We also show that unless $P=NP$, there is no polynomial time algorithm to solve the \textsc{MGS} problem with sublogarithmic approximation factor (in terms of the number of vertices) even on graphs with diameter $2$. On the positive side, we give an $O\left(\sqrt[3]{n}\log n\right)$-approximation algorithm for the \textsc{MGS} problem on general graphs of order $n$. We also give a $3$-approximation algorithm for the \textsc{MGS} problem on the family of solid grid graphs which is a subclass of planar graphs

Dimensional Relationships in <i>Crassostrea madrasensis</i> (Preston) and <i>C. gryphoides</i> (Schlotheim) in Mangrove Ecosystem

559-566Mangrove influenced estuarine habits in the tropics are favor the settlement of oysters and their larval stages, which protect them from strong waves and speedy currents. Shell structure in Bivalves forms an important protective system. Description of the relationship between shell and soft body characteristics are essential in understanding ecological variations and productivity of oyster population. A total number of 627 oyster specimens were collected from different locations in Goa as case study for the tropical estuaries and studied for their allometric relationships. Data described in the present document could be of importance in monitoring the health of natural oyster beds. It also serves a baseline for planning sustainable management and understanding the aquaculture potential of Crassostrea spp. in mangrove influenced estuarine habitats

Distribution, abundance and diversity of phytoplankton in the inshore waters of Nizampatnam, South East coast of India

348-356Distribution, abundance and species assemblages of Phytoplankton were studied from inshore waters of Nizampatnam, South East coast of India in March 2007. <span style="mso-fareast-font-family:Calibri;mso-ansi-language:EN-US;mso-bidi-language: GU;mso-bidi-font-weight:bold" lang="EN-US">Significant spatial variations in temperature, pH, salinity, dissolved oxygen (DO), nitrites (NO2) –N)<span style="mso-fareast-font-family:Calibri;mso-ansi-language:EN-US;mso-bidi-language: GU;mso-bidi-font-weight:bold" lang="EN-US">, nitrates (NO3) – N)<span style="mso-fareast-font-family:Calibri;mso-ansi-language: EN-US;mso-bidi-language:GU;mso-bidi-font-weight:bold" lang="EN-US">, phosphate (PO4) –P),<span style="mso-fareast-font-family:Calibri;mso-ansi-language:EN-US;mso-bidi-language: GU;mso-bidi-font-weight:bold" lang="EN-US"> silicate (SiO4) – (Si)<span style="mso-fareast-font-family:Calibri; mso-ansi-language:EN-US;mso-bidi-language:GU;mso-bidi-font-weight:bold" lang="EN-US"> were monitored. A total of 90 species of phytoplankton (net hauls) represented by 5 groups were identified at nine stations, collected along three transects during low tide.<span style="mso-fareast-font-family: Calibri;mso-ansi-language:EN-US;mso-bidi-language:GU;mso-bidi-font-weight:bold" lang="EN-US"> Percentage contribution of each group of phytoplankton was in the order: Bacillariophyceans <span style="mso-fareast-font-family: Calibri;mso-ansi-language:EN-US;mso-bidi-language:GU;mso-bidi-font-weight:bold" lang="EN-US">> Dinophyceans <span style="mso-fareast-font-family: Calibri;mso-ansi-language:EN-US;mso-bidi-language:GU;mso-bidi-font-weight:bold" lang="EN-US">> Cyanophyceans <span style="mso-fareast-font-family: Calibri;mso-ansi-language:EN-US;mso-bidi-language:GU;mso-bidi-font-weight:bold" lang="EN-US">> Euglenophyceans<span style="mso-fareast-font-family:Calibri;mso-ansi-language:EN-US;mso-bidi-language: GU;mso-bidi-font-weight:bold" lang="EN-US">. Pleurosigma angulatum, Navicula sp. were dominant species in the study area. Bray - Curtis similarity and group average clustering, recommended identifying two assemblages of phytoplankton in the study area. High diversity of phytoplankton in the present area suggests stable environmental conditions. </span

Increased human MUC1 protein expression in Kras- and Pten- driven genital tract tumors of MUC1KrasPten triple transgenic mice triggers humoral immunity.

<p>(A) MUC1 immunohistochemistry staining of tumors occurring in the ovary (upper panel), oviduct (middle panel) or endometrium (lower panel). An antibody specific to the human MUC1 extracellular domain (clone HMPV, mouse IgG1) was used at 1∶100. Polarized MUC1 expression throughout the genital tract of healthy female mice at baseline is shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0102409#pone.0102409.s002" target="_blank">Fig. S2</a>. Mouse tumor MUC1 mimics human tumor expression (shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0102409#pone.0102409.s005" target="_blank">Fig. S5</a>). Representative immunohistochemical images shown. Scale bar −50 µm. (B) ELISA measurement of human MUC1 peptide-specific IgG antibodies in sera from MUC1KrasPten mice with tumors (n = 5 ovarian, n = 4 oviductal and n = 4 uterine). Upper panel: presence of antibodies at two different dilutions, using sing as target peptide a 100mer peptide comprising fie 20-aminoacid long peptide from the MUC1 extracellular domain of MUC1. Background levels were detected using sera from KrasPten mice with MUC1 negative tumors (i.e. wild -type for MUC1). Vehicle only was also included as an additional negative control. The assay was run in duplicate and values were plotted as means with standard deviations. Lower panel: box and whisker diagrams (min, Q1, median, Q3, max) of readings at 1∶20 dilution. Antibody levels are significantly higher (compared to control readings) in the ovarian and oviduct tumor group (one way ANOVA p<0.05; *two tail t test; p<0.05). Uterine tumors, p = 0.052.</p

Oviductal and endometrial tumors show endometrioid histology at both primary and satellite locations.

<p>Formalin fixed and paraffin embedded primary and metastatic tumor tissues were analyzed for histo-pathology. Representative images of H&E stained tumor sections are shown. Left column: primary tumors of the genital tract show endometrioid histology in the ovary, oviduct and endometrium. Right column: secondary tumors, including ovarian metastases to the diaphragm (upper), oviduct metastases to the pancreas (middle) and endometrial metastases to the diaphragm (lower) also show endometrioid histology. Scale bar −20 µm.</p

Primary tumors of the ovary, oviduct and uterus have epithelial origin.

<p>Immunohistochemistry staining of tumors occurring in the ovary (upper panels), oviduct (middle panels) or endometrium (lower panels). Antibodies to mouse cytokeratin 8 (an epithelial cell marker, left column) and mouse desmin (right column) were used at 1∶50 dilution. Representative images shown. Scale bar −50 µm.</p