Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs

AbstractRobert E. Jamison characterized chordal graphs by the edge set of every k-cycle being the symmetric difference of k−2 triangles. Strongly chordal (and chordal bipartite) graphs can be similarly characterized in terms of the distribution of triangles (respectively, quadrilaterals). These results motivate a definition of ‘strongly chordal bipartite graphs’, forming a class intermediate between bipartite interval graphs and chordal bipartite graphs

Characterizing graph classes by intersections of neighborhoods

The interplay between maxcliques (maximal cliques) and intersections of closed neighborhoods leads to new types of characterizations of several standard graph classes. For instance, being hereditary clique-Helly is equivalent to every nontrivial maxclique $Q$ containing the intersection of closed neighborhoods of two vertices of $Q$, and also to, in all induced subgraphs, every nontrivial maxclique containing a simplicial edge (an edge in a unique maxclique). Similarly, being trivially perfect is equivalent to every maxclique $Q$ containing the closed neighborhood of a vertex of $Q$, and also to, in all induced subgraphs, every maxclique containing a simplicial vertex. Maxcliques can be generalized to maximal cographs, yielding a new characterization of ptolemaic graphs

Characterizing 2-Trees Relative to Chordal and Series-Parallel Graphs

The 2-connected 2-tree graphs are defined as being constructible from a single 3-cycle by recursively appending new degree-2 vertices so as to form 3-cycles that have unique edges in common with the existing graph. Such 2-trees can be characterized both as the edge-minimal chordal graphs and also as the edge-maximal series-parallel graphs. These are also precisely the 2-connected graphs that are simultaneously chordal and series-parallel, where these latter two better-known types of graphs have themselves been both characterized and applied in numerous ways that are unmotivated by their interaction with 2-trees and with each other. Toward providing such motivation, the present paper examines several simple, very closely-related characterizations of chordal graphs and 2-trees and, after that, of series-parallel graphs and 2-trees. This leads to showing a way in which chordal graphs and series-parallel graphs are special---indeed, extremal---in this regard

The leafage of a chordal graph

The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n - lg n - (1/2) lg lg n + O(1). The proper leafage l*(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and lower bounds on l*(G). Leafage equals proper leafage on claw-free chordal graphs. We use asteroidal sets and structural properties of chordal graphs.Comment: 19 pages, 3 figure

Maxclique and unit disk characterizations of strongly chordal graphs

Maxcliques (maximal complete subgraphs) and unit disks (closed neighborhoods of vertices) sometime play almost interchangeable roles in graph theory. For instance, interchanging them makes two existing characterizations of chordal graphs into two new characterizations. More intriguingly, these characterizations of chordal graphs can be naturally strengthened to new characterizations of strongly chordal graphs.Facultad de Ciencias Exacta

Benthic Foraminifera from the NECOP Study Area Impacted by the Mississippi River Plume and Seasonal Hypoxia

Benthic foraminifera influenced by the Mississippi River plume and seasonal hypoxia were assessed from Louisiana inner-continental shelf sediment samples. Surface foraminifera assemblages were representative of in-situ populations as established by staining techniques. Community diversity and richness/evenness analyses indicate three regimes: high stress (sediment dominated), intermediate stress (hypoxia dominated), and low stress (low sediment accumulation/high oxygen). Epistominella vitrea and Buliminella morgani are useful tracers of rapid sediment accumulation rate and hypoxia. A bottom-water productivity signal west of the Mississippi River plume is indicated by benthic and planktic foraminifera abundance peaks. Surface benthic foraminifera trends are utilized to interpret changes in historical community structure from hypoxic-area sediments deposited since the turn of the century. The hypoxia-tolerant species Buliminella morgani increases markedly upcore, while hypoxia intolerant species decrease or disappear. Diversity and dominance trends temporally correspond to a dramatic increase in U.S. fertilizer application. The results of this study have application to paleoenvironmental research spanning longer geologic timescales. The documented relationships between population structure and stressors in river-dominated marine systems may provide a useful analog for recognition of these conditions in the fossil record

Maxclique and unit disk characterizations of strongly chordal graphs

Maxcliques (maximal complete subgraphs) and unit disks (closed neighborhoods of vertices) sometime play almost interchangeable roles in graph theory. For instance, interchanging them makes two existing characterizations of chordal graphs into two new characterizations. More intriguingly, these characterizations of chordal graphs can be naturally strengthened to new characterizations of strongly chordal graphs.Facultad de Ciencias Exacta

Evaporative loss from irrigated interrows in a highly advective semi-arid agricultural area

Agricultural productivity has increased in the Texas High Plains at the cost of declining water tables, putting at risk the sustainability of the Ogallala Aquifer as a principal source of water for irrigated agriculture. This has led area producers to seek alternative practices that can increase water use efficiency (WUE) through more careful management of water. One potential way of improving WUE is by reducing soil evaporation (E), thus reducing overall evapotranspiration (ET). Before searching for ways to reduce E, it is first important to quantify E and understand the factors that determine its magnitude. The objectives of this study were (1) to quantify E throughout part of the growing season for irrigated cotton in a strongly advective semi-arid region; (2) to study the effects of LAI, days after irrigation, and measurement location within the row on the E/ET fraction; and (3) to study the ability of microlysimeter (ML) measures of E combined with sap flow gage measures of transpiration (T) to accurately estimate ET when compared with weighing lysimeter ET data and to assess the E/T ratio. The research was conducted in an irrigated cotton field at the Conservation & Production Research Laboratory of the USDA-ARS, Bushland, TX. ET was measured by a large weighing lysimeter, and E was measured by 10 microlysimeters that were deployed in two sets of 5 across the interrow. In addition, 10 heat balance sap flow gages were used to determine T. A moderately good agreement was found between the sum E + T and ET (SE = 1 mm or ~10% of ET). It was found that E may account for \u3e50% of ET during early stages of the growing season (LAI \u3c 0.2), significantly decreasing with increase in LAI to values near 20% at peak LAI of three. Measurement location within the north-south interrows had a distinct effect on the diurnal pattern of E, with a shift in time of peak E from west to east, a pattern that was governed by the solar radiation reaching the soil surface. However, total daily E was unaffected by position in the interrow. Under wet soil conditions, wind speed and direction affected soil evaporation. Row orientation interacted with wind direction in this study such that aerodynamic resistance to E usually increased when wind direction was perpendicular to row direction; but this interaction needs further study because it appeared to be lessened under higher wind speeds

Abnormal cognition, sleep, EEG and brain metabolism in a novel knock-in Alzheimer mouse, PLB1

Peer reviewedPublisher PD

LPS INHIBITION OF GLUCOSE PRODUCTION THROUGH THE TLR4, MYD88, NFκB PATHWAY

Acute exposure to lipopolysaccharide (LPS) can cause hypoglycemia and insulin resistance; the underlying mechanisms however, are unclear. We set out to determine whether insulin resistance is linked to hypoglycemia through TLR4, MyD88 and NFκB, a cell signaling pathway that mediates LPS induction of the proinflammatory cytokine TNFα. LPS induction of hypoglycemia was blocked in TLR4−/− and MyD88−/− mice but not in TNFα−/− mice. Both glucose production and glucose utilization were decreased during hypoglycemia. Hypoglycemia was associated with the activation of NFκB in the liver. LPS inhibition of glucose production was blocked in hepatocytes isolated from TLR4−/− and MyD88−/− mice and hepatoma cells expressing an IκB mutant that interferes with NFκB activation. Thus, LPS-induced hypoglycemia was mediated by the inhibition of glucose production from the liver through the TLR4, MyD88, NFκB pathway, independent of LPS induced TNFα. LPS inhibition of glucose production was not blocked by pharmacologic inhibition of the insulin signaling intermediate PI3K in hepatoma cells. Insulin injection caused a similar reduction of circulating glucose in TLR4−/− and TLR4+/+ mice. These two results suggest that LPS and insulin inhibit glucose production by separate pathways. Recovery from LPS induced hypoglycemia was linked to glucose intolerance and hyperinsulinemia in TLR4+/+ mice, but not in TLR4−/− mice