Gamma-Set Domination Graphs. I: Complete Biorientations of \u3cem\u3eq-\u3c/em\u3eExtended Stars and Wounded Spider Graphs

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes

Local Out-Tournaments with Upset Tournament Strong Components I: Full and Equal {0,1}-Matrix Ranks

A digraph D is a local out-tournament if the outset of every vertex is a tournament. Here, we use local out-tournaments, whose strong components are upset tournaments, to explore the corresponding ranks of the adjacency matrices. Of specific interest is the out-tournament whose adjacency matrix has boolean, nonnegative integer, term, and real rank all equal to the number of vertices, n. Corresponding results for biclique covers and partitions of the digraph are provided

Kings and Heirs: A Characterization of the (2,2)-domination Graphs of Tournaments

In 1980, Maurer coined the phrase king when describing any vertex of a tournament that could reach every other vertex in two or fewer steps. A (2,2)-domination graph of a digraph D, dom2,2(D), has vertex set V(D), the vertices of D, and edge uv whenever u and v each reach all other vertices of D in two or fewer steps. In this special case of the (i,j)-domination graph, we see that Maurer’s theorem plays an important role in establishing which vertices form the kings that create some of the edges in dom2,2(D). But of even more interest is that we are able to use the theorem to determine which other vertices, when paired with a king, form an edge in dom2,2(D). These vertices are referred to as heirs. Using kings and heirs, we are able to completely characterize the (2,2)-domination graphs of tournaments

Digraphs with Isomorphic Underlying and Domination Graphs: Pairs of Paths

A domination graph of a digraph D, dom (D), is created using thc vertex set of D and edge uv ϵ E (dom (D)) whenever (u, z) ϵ A (D) or (v, z) ϵ A (D) for any other vertex z ϵ A (D). Here, we consider directed graphs whose underlying graphs are isomorphic to their domination graphs. Specifically, digraphs are completely characterized where UGc (D) is the union of two disjoint paths

A Characterization of Connected (1,2)-Domination Graphs of Tournaments

Recently. Hedetniemi et aI. introduced (1,2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of D, dom1,2 (D), is defined to be the graph G = (V, E ) , where V (G) = V (D), and xy is an edge of G whenever x and y form a (1,2)-dominating pair in D. In this paper, we characterize all connected graphs that can be (I, 2)-dominating graphs of tournaments

ALMA Observations of Asymmetric Molecular Gas Emission from a Protoplanetary Disk in the Orion Nebula

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of molecular line emission from d216-0939, one of the largest and most massive protoplanetary disks in the Orion Nebula Cluster (ONC). We model the spectrally resolved HCO$^+$ (4--3), CO (3--2), and HCN (4--3) lines observed at 0\farcs5 resolution to fit the temperature and density structure of the disk. We also weakly detect and spectrally resolve the CS (7--6) line but do not model it. The abundances we derive for CO and HCO$^+$ are generally consistent with expected values from chemical modeling of protoplanetary disks, while the HCN abundance is higher than expected. We dynamically measure the mass of the central star to be $2.17\pm0.07\,M_\odot$ which is inconsistent with the previously determined spectral type of K5. We also report the detection of a spatially unresolved high-velocity blue-shifted excess emission feature with a measurable positional offset from the central star, consistent with a Keplerian orbit at $60\pm20\,\mathrm{au}$. Using the integrated flux of the feature in HCO$^+$ (4--3), we estimate the total H$_2$ gas mass of this feature to be at least $1.8-8\,M_\mathrm{Jupiter}$, depending on the assumed temperature. The feature is due to a local temperature and/or density enhancement consistent with either a hydrodynamic vortex or the expected signature of the envelope of a forming protoplanet within the disk.Comment: 19 pages, 12 figures, accepted for publication in A

A Cohort study evaluation of maternal PCB exposure related to time to pregnancy in daughters

Background: Polychlorinated biphenyls (PCBs) remain ubiquitous environmental contaminants. Developmental exposures are suspected to impact reproduction. Analysis of mixtures of PCBs may be problematic as components have a complex correlation structure, and along with limited sample sizes, standard regression strategies are problematic. We compared the results of a novel, empirical method to those based on categorization of PCB compounds by (1) hypothesized biological activity previously proposed and widely applied, and (2) degree of ortho- substitution (mono, di, tri), in a study of the relation of maternal serum PCBs and daughter’s time to pregnancy. Methods: We measured PCBs in maternal serum samples collected in the early postpartum in 289 daughters in the Child Health and Development Studies birth cohort. We queried time to pregnancy in these daughters 28–31 years later. We applied a novel weighted quantile sum approach to find the bad-actor compounds in the PCB mixture found in maternal serum. The approach includes empirical estimation of the weights through a bootstrap step which accounts for the variation in the estimated weights. Results: Bootstrap analyses indicated the dominant functionality groups associated with longer TTP were the dioxin-like, anti-estrogenic group (average weight, 22%) and PCBs not previously classified by biological activity (54%). In contrast, the unclassified PCBs were not important in the association with shorter TTP, where the anti-estrogenic groups and the PB-inducers group played a more important role (60% and 23%, respectively). The highly chlorinated PCBs (average weight, 89%) were mostly associated with longer TTP; in contrast, the degree of chlorination was less discriminating for shorter TTP. Finally, PCB 56 was associated with the strongest relationship with TTP with a weight of 47%. Conclusions: Our empirical approach found some associations previously identified by two classification schemes, but also identified other bad actors. This empirical method can generate hypotheses about mixture effects and mechanisms and overcomes some of the limitations of standard regression techniques

Development of All-Wood Connections with Plywood Flitch Plate and Oak Pegs

This paper proposes a new method for beam-beam connections, which include plywood as slot-in plates connected by oak pegs. A total of 96 specimens were fabricated for tests to explore the minimum required end distances and spacing between pegs parallel to the grain. A new failure mode, termed shear wedge that is different from those found in previous research, was found. A spring model was also proposed in this study to investigate the stiffness of the connections, and feasibility of EC5 to be applied on the new proposed connections was also examined. The effective number was discussed in this study and modified in accordance to the experimental results. The result of this study shows the new connections proposed do not lead to brittle failure unless failure in plywood occurred

Cognitive networks: brains, internet, and civilizations

In this short essay, we discuss some basic features of cognitive activity at several different space-time scales: from neural networks in the brain to civilizations. One motivation for such comparative study is its heuristic value. Attempts to better understand the functioning of "wetware" involved in cognitive activities of central nervous system by comparing it with a computing device have a long tradition. We suggest that comparison with Internet might be more adequate. We briefly touch upon such subjects as encoding, compression, and Saussurean trichotomy langue/langage/parole in various environments.Comment: 16 page