On the maximum order of graphs embedded in surfaces

The maximum number of vertices in a graph of maximum degree $\Delta\ge 3$ and fixed diameter $k\ge 2$ is upper bounded by $(1+o(1))(\Delta-1)^{k}$. If we restrict our graphs to certain classes, better upper bounds are known. For instance, for the class of trees there is an upper bound of $(2+o(1))(\Delta-1)^{\lfloor k/2\rfloor}$ for a fixed $k$. The main result of this paper is that graphs embedded in surfaces of bounded Euler genus $g$ behave like trees, in the sense that, for large $\Delta$, such graphs have orders bounded from above by begin{cases} c(g+1)(\Delta-1)^{\lfloor k/2\rfloor} & \text{if $k$ is even} c(g^{3/2}+1)(\Delta-1)^{\lfloor k/2\rfloor} & \text{if $k$ is odd}, \{cases} where $c$ is an absolute constant. This result represents a qualitative improvement over all previous results, even for planar graphs of odd diameter $k$. With respect to lower bounds, we construct graphs of Euler genus $g$, odd diameter $k$, and order $c(\sqrt{g}+1)(\Delta-1)^{\lfloor k/2\rfloor}$ for some absolute constant $c>0$. Our results answer in the negative a question of Miller and \v{S}ir\'a\v{n} (2005).Comment: 13 pages, 3 figure

Consumer shopping behavior: how much do consumers save?

This paper documents the potential and actual savings that consumers realize from four particular types of purchasing behavior: purchasing on sale; buying in bulk (at a lower per unit price); buying generic brands; and choosing outlets. How much can and do households save through each of these behaviors? How do these patterns vary with consumer demographics? We use data collected by a marketing firm on all food purchases brought into the home for a large, nationally representative sample of U.K. households in 2006. We are interested in how consumer choice affects the measurement of price changes. In particular, a standard price index based on a fixed basket of goods will overstate the rise in the true cost of living because it does not properly consider sales and bulk purchasing. According to our measures, the extent of this bias might be of the same or even greater magnitude than the better-known substitution and outlet biases

Parametric thermal analysis for the optimization of Double Walled Tubes layout in the Water Cooled Lithium Lead inboard blanket of DEMO fusion reactor

Within the roadmap that will lead to the nuclear fusion exploitation for electric energy generation, the construction of a DEMOnstration (DEMO) reactor is, probably, the most important milestone to be reached since it will demonstrate the technological feasibility and economic competitiveness of an industrial-scale nuclear fusion reactor. In order to reach this goal, several European universities and research centres have joined their efforts in the EUROfusion action, funded by HORIZON 2020 UE programme. Within the framework of EUROfusion research activities, ENEA and University of Palermo are involved in the design of the Water-Cooled Lithium Lead Breeding Blanket (WCLL BB), that is one of the two BB concepts under consideration to be adopted in the DEMO reactor. It is mainly characterized by a liquid lithium-lead eutectic alloy acting as breeder (lithium) and neutron multiplier (lead), as well as by subcooled pressurized water as coolant. Two separate circuits, both characterized by a pressure of 15.5 MPa and inlet/outlet temperatures of 295 °C/328 °C, are deputed to cool down the First Wall (FW) and the Breeder Zone (BZ). The former consists in a system of radial-toroidal-radial C-shaped squared channels where countercurrent water flow occurs while the latter relies in the use of bundles of poloidal-radial Double Walled Tubes (DWTs) housed within the breeder. A parametric thermal study has been carried out in order to assess the best DWTs' layout assuring that the structural material maximum temperature does not overcome the allowable limit of 550 °C and that the overall coolant thermal rise fulfils the design target value of 33 °C. The study has been performed following a theoretical-numerical approach based on the Finite Element Method (FEM) and adopting the quoted Abaqus FEM code. Main assumptions and models together with results obtained are herewith reported and critically discussed

A Survey of Best Monotone Degree Conditions for Graph Properties

We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.Comment: 25 page

Single exon skipping can address a multi-exon duplication in the dystrophin gene

Duchenne muscular dystrophy (DMD) is a severe muscle wasting disease typically caused by protein-truncating mutations that preclude synthesis of a functional dystrophin. Exonic deletions are the most common type of DMD lesion, however, whole exon duplications account for between 10–15% of all reported mutations. Here, we describe in vitro evaluation of antisense oligonucleotide-induced splice switching strategies to re-frame the transcript disrupted by a multi-exon duplication within the DMD gene. Phosphorodiamidate morpholino oligomers and phosphorodiamidate morpholino oligomers coupled to a cell penetrating peptide were evaluated in a Duchenne muscular dystrophy patient cell strain carrying an exon 14–17 duplication. Two strategies were employed; the conventional approach was to remove both copies of exon 17 in addition to exon 18, and the second strategy was to remove only the first copy of exon 17. Both approaches result in a larger than normal but in-frame DMD transcript, but surprisingly, the removal of only the first exon 17 appeared to be more efficient in restoring dystrophin, as determined using western blotting. The emergence of a normal sized DMD mRNA transcript that was not apparent in untreated samples may have arisen from back splicing and could also account for some of the dystrophin protein being produced

Natural Variation in Grain Selenium Concentration of Wild Barley, Hordeum spontaneum, Populations from Israel

Wild barley (Hordeum spontaneum), the progenitor of cultivated barley, is an important genetic resource for cereal improvement. Selenium (Se) is an essential trace mineral for humans and animals with antioxidant, anticancer, antiarthropathy, and antiviral effects. In the current study, the grain Se concentration (GSeC) of 92 H. spontaneum genotypes collected from nine populations representing different habitats in Israel was investigated in the central area of Guizhou Province, China. Remarkable variations in GSeC were found between and within populations, ranging from 0 to 0.387 mg kg−1 among the 92 genotypes with an average of 0.047 mg kg−1. Genotype 20_C from the Sede Boqer population had the highest GSeC, while genotype 25_1 from the Atlit population had the lowest. The mean value of GSeC in each population varied from 0.010 to 0.105 mg kg−1. The coefficient of variation for each population ranged from 12% to 163%. Significant correlations were found between GSeC and 12 ecogeographical factors out of 14 studied. Habitat soil type also significantly affected GSeC. The wild barley exhibited wider GSeC ranges and greater diversity than its cultivated counterparts. The higher Se grain concentrations found in H. spontaneum populations suggest that wild barley germplasm confer higher abilities for Se uptake and accumulation, which can be used for genetic studies of barley nutritional value and for further improvement of domesticated cereals

RELAP5/SIMMER-III code coupling development for PbLi-water interaction

A major safety issue in the Water-Cooled Lead-Lithium Breeding Blanket (WCLL-BB) system foreseen for fusion reactor is the interaction concerning the primary coolant (water) and the neutron multiplier (PbLi), due to a hypothetical tube rupture in the coolant circuit. This scenario involves an exothermic chemical reaction between PbLi and water with the production of hydrogen, in addition to critical interactions in a complex multiphase system in non-thermal equilibrium. In recent years the PbLi/water reaction was successfully implemented in the SIMMER-III code and validated against data from the LIFUS5/Mod3 experimental campaign. However, due to limitations of SIMMER-III, this work was restricted to the prediction of the phenomena inside the vessel, neglecting the simulation of the injection line. Nevertheless, since the injection line may actually have an important effect on the development of the transient, the simulation of the whole facility would be highly desirable. Indeed, the University of Pisa recently developed a coupling methodology between the SIMMER-III and RELAP5/Mod3.3 codes and applied it to simple single-phase cases. In this paper the complete simulation of the LIFUS5/Mod3 facility is presented, with the injection line modelled through RELAP5. Furthermore, all the complex aspects of the phenomena inside the reaction tank were included: the multiphase system and the interaction between water and PbLi with the chemical reaction and the production of hydrogen were modelled by SIMMER. Preliminary results are presented, showing that the coupling methodology can be effectively employed for the prediction of the chemical and thermal-hydraulic behaviour of complex loop experimental facilities