Leaps: an approach to the block structure of a graph

To study the block structure of a connected graph G=(V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V. These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define the operation +G as well as the set of leaps LG of the connected graph G. The underlying graph of +G , as well as that of LG , turns out to be just the block closure of G (i.e. the graph obtained by making each block of G into a complete subgraph).

Microtubule length distributions in the presence of protein-induced severing

Microtubules are highly regulated dynamic elements of the cytoskeleton of eukaryotic cells. One of the regulation mechanisms observed in living cells is the severing by the proteins katanin and spastin. We introduce a model for the dynamics of microtubules in the presence of randomly occurring severing events. Under the biologically motivated assumption that the newly created plus end undergoes a catastrophe, we investigate the steady state length distribution. We show that the presence of severing does not affect the number of microtubules, regardless of the distribution of severing events. In the special case in which the microtubules cannot recover from the depolymerizing state (no rescue events) we derive an analytical expression for the length distribution. In the general case we transform the problem into a single ODE that is solved numerically.Comment: 9 pages, 4 figure

Validating and optimizing the effects of model progression in simulation-based inquiry learning

Model progression denotes the organization of the inquiry learning process in successive phases of increasing complexity. This study investigated the effectiveness of model progression in general, and explored the added value of either broadening or narrowing students’ possibilities to change model progression phases. Results showed that high-school students in the ‘standard’ model progression condition (n = 19), who could enter subsequent phases at will, outperformed students from a control condition (n = 30) without model progression. The unrestricted condition (n = 22) had the additional option of returning to previous phases, whereas the restricted condition (n = 20) disallowed such downward progressions as well as upward progressions in case insufficient knowledge was acquired. Both variants were found to be more effective in terms of performance than the ‘standard’ form of model progression. However, as performance in all three model progression conditions was still rather weak, additional support is needed for students to reach full understanding of the learning content

Soil-borne microorganisms and soil-type affect pyrrolizidine alkaloids in Jacobaea vulgaris

Secondary metabolites like pyrrolizidine alkaloids (PAs) play a crucial part in plant defense. We studied the effects of soil-borne microorganisms and soil-type on pyrrolizidine alkaloids in roots and shoots of Jacobaea vulgaris. We used clones of two genotypes from a dune area (Meijendel), propagated by tissue culture and grown on two sterilized soils and sterilized soils inoculated with 5% of non-sterilized soil of either of the two soil-types. Soil-borne microorganisms and soil-type affected the composition of PAs. By changing the composition rather than the total concentration below and aboveground, plants have a more complex defense strategy than formerly thought. Interestingly, a stronger negative effect on plant growth was found in sterilized soils inoculated with their ‘own’ microbial community suggesting that pathogenic and/or other plant inhibiting microorganisms were adapted to their ‘own’ soil conditions

Ambient Geochemical and Isotopic Variations in Groundwaters Across an Area of Accelerating Shale Gas Development

One of the main challenges associated with Marcellus Formation shale gas development is to ensure proper management and disposal of flowback water produced as a result of hydraulic fracturing of gas wells. The flowback water consists of a mixture of returned frac\u27ing fluids and highly saline formation brines. As a result, improper management or disposal of this flowback can potentially contaminate the fresh surface waters and groundwaters of the area. To better assess any detrimental effect on water quality, there is need to understand the natural geochemical variations prior to the rapid expansion of gas drilling in the area.;This study focuses on documenting the baseline geochemical characteristics of groundwaters in different formations lying stratigraphically above the Marcellus Formation. 41 groundwater well sites in north central West Virginia were sampled with the USGS Water Science Center of West Virginia. These private and public sampling locations were chosen from within the United States Geological Survey database and represent different formation aquifers with differing well depths. Geochemical data was obtained for major cations and anions, dissolved gas concentrations of methane, oxygen and hydrogen isotopic compositions of water (delta18OH2O and delta 2HH2O), carbon isotopic compositions of dissolved inorganic carbon (delta13CDIC), sulfur and oxygen isotope compositions of dissolved sulfate (delta34SSO4 and delta18OSO4) and carbon and hydrogen isotope compositions of dissolved methane (delta13CCH4 and delta2HCH4). Field parameters of temperature, conductivity, pH, dissolved oxygen, turbidity, and oxidation reduction potential were also collected. I hypothesize that the baseline variations of stable isotopes can be used in conjunction with other geochemical parameters to identify groundwater aquifers that have received significant contribution from frac flowback waters

Guides and Shortcuts in Graphs

The geodesic structure of a graphs appears to be a very rich structure. There are many ways to describe this structure, each of which captures only some aspects. Ternary algebras are for this purpose very useful and have a long tradition. We study two instances: signpost systems, and a special case of which, step systems. Signpost systems were already used to characterize graph classes. Here we use these for the study of the geodesic structure of a spanning subgraph F with respect to its host graph G. Such a signpost system is called a guide to (F,G). Our main results are: the characterization of the step system of a cycle, the characterization of guides for spanning trees and hamiltonian cycles