Strong Ramsey Games in Unbounded Time

For two graphs $B$ and $H$ the strong Ramsey game $\mathcal{R}(B,H)$ on the board $B$ and with target $H$ is played as follows. Two players alternately claim edges of $B$. The first player to build a copy of $H$ wins. If none of the players win, the game is declared a draw. A notorious open question of Beck asks whether the first player has a winning strategy in $\mathcal{R}(K_n,K_k)$ in bounded time as $n\rightarrow\infty$. Surprisingly, in a recent paper Hefetz et al. constructed a $5$-uniform hypergraph $\mathcal{H}$ for which they proved that the first player does not have a winning strategy in $\mathcal{R}(K_n^{(5)},\mathcal{H})$ in bounded time. They naturally ask whether the same result holds for graphs. In this paper we make further progress in decreasing the rank. In our first result, we construct a graph $G$ (in fact $G=K_6\setminus K_4$) and prove that the first player does not have a winning strategy in $\mathcal{R}(K_n \sqcup K_n,G)$ in bounded time. As an application of this result we deduce our second result in which we construct a $4$-uniform hypergraph $G'$ and prove that the first player does not have a winning strategy in $\mathcal{R}(K_n^{(4)},G')$ in bounded time. This improves the result in the paper above. An equivalent formulation of our first result is that the game $\mathcal{R}(K_\omega\sqcup K_\omega,G)$ is a draw. Another reason for interest on the board $K_\omega\sqcup K_\omega$ is a folklore result that the disjoint union of two finite positional games both of which are first player wins is also a first player win. An amusing corollary of our first result is that at least one of the following two natural statements is false: (1) for every graph $H$, $\mathcal{R}(K_\omega,H)$ is a first player win; (2) for every graph $H$ if $\mathcal{R}(K_\omega,H)$ is a first player win, then $\mathcal{R}(K_\omega\sqcup K_\omega,H)$ is also a first player win.Comment: 18 pages, 46 figures; changes: fully reworked presentatio

Willingness to Pay for Improved Milk Sensory Characteristics and Assurances in Northern Kenya Using Experimental Auctions

Pastoralists in northern Kenya may be able to diversify income by selling milk in nearby towns and cities. However, milk sold in open-air markets in communities in northern Kenya is often of low quality in terms of its sensory characteristics. The milk is also often adulterated before sale. These markets are characterized by poor consumers who need to make choices about milk quality with virtually no information other than their own sensory perceptions. These conditions are similar in many parts of the world for many different commodities and products. An examination was undertaken using experimental auctions to determine if consumers in the border town of Moyale, Kenya are willing to pay for enhanced milk sensory characteristics and assurances. The results suggest that even poor consumers are willing to pay for enhanced sensory characteristics and assurances if these can be communicated in a trusted manner. Older, relatively well-informed women are the group most willing to pay the highest prices for milk quality.willingness-to-pay, milk, Kenya, Agribusiness, Agricultural Finance, Q10, Q14,

An Input Normal Form Homotopy for the L2 Optimal Model Order Reduction Problem

In control system analysis and design, finding a reduced order model, optimal in the L-squared sense, to a given system model is a fundamental problem. The problem is very difficult without the global convergence of homotopy methods, and a homotopy based approach has been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. A homotopy algorithm based on the input normal form characterization of the reduced order model is developed here and is compared with the homotopy algorithms based on Hyland and Bernstein's optimal projection equations. The main conclusions are that the input normal form algorithm can be very efficient, but can also be very ill conditioned or even fail

Decoupling of fluids and fluid-mobile elements during shallow subduction: Evidence from halogen-rich andesite melt inclusions from the Izu arc volcanic front

[1] Very rare, halogen-rich andesite melt inclusions (HRA) in bytownitic plagioclase phenocrysts (An89–90) from tephra fallout of the Izu arc volcanic front (Izu VF) provide new insights into the processes of fluid release from slab trenchward to the volcanic front in a cool subduction zone. These HRA are markedly enriched in Cl, F and Li - by factors of up to 8 (Cl, F) and 1.5 (Li) - but indistinguishable with respect to the fluid-mobile large-ion lithophile elements (LILE; K, Sr, Rb, Cs, Ba, Pb, U), rare earths (REE) or high field strength elements (HFSE) from the low-K tholeiitic magmas of the Izu VF. We suggest that the chemical signature of the HRA reflects the presence of a fluid in the mantle source that originated from the serpentinized mantle peridotite above the metacrust. This “wedge serpentinite” presumably formed by fluid infiltration beneath the forearc and was subsequently down-dragged with the slab to arc front depths. The combined evidence from the Izu VF (∼110 km above slab) and the outer forearc serpentinite seamounts (∼25 to 30 km above slab) suggests that the slab flux of B and Cl is highest beneath the forearc, and decreases with increasing slab depths. In contrast, the slab flux of Li is minor beneath the forearc, but increases with depth. Fluorine may behave similarly to Li, whereas the fluid-mobile LILE appear to be largely retained in the slab trenchward from the Izu VF. Consequently, the chemical signatures of both Izu trench sediments and basaltic rocks appear preserved until arc front depths

Comparison of microanalytical methods for estimating H20 contents of silicic volcanic glasses

Three methods of estimating H20 contents of geologic glasses are compared: (1) ion microprobe analysis (secondary ion mass spectrometry), (2) Fourier-transform infrared spectroscopy (FTIR), and (3) electron microprobe analysis using the Na decay-curve method. Each analytical method has its own advantages under certain conditions, depending on the relative importance of analytical accuracy, precision, sensitivity, spatial resolution,and convenience, and each is capable of providing reasonably accurate estimates of the H20, or total volatile, content of geologic glasses. The accuracy of ion microprobe analyses depends critically on the availability of well-characterized hydrous standard glasses. Precision is often better than 0,2 wt% (10). The method provides good spatial resolution (-15 #m) and the capability to determine simultaneously the abundance of other volatile species of interest (e.g., F, B). FTIR spectroscopy provides excellent analytical sensitivity (-10 ppm), accuracy and precision «0.1 wt%), and the capability to determine the abundance of H20 and C02 species (H20, OH-, C02' eOj-) in analyzed glasses, although the spatial resolution (> 25-35 #m) is not as good as that of the ion microprobe. The main advantages of the estimation of H20 contents of hydrous glasses using the electron microprobe are excellent spatial resolution (- 10 #m) and analytical convenience. The disadvantages are that accuracy and precision (>0.5 wt%) are not as good as those associated with the other methods, but, for certain applications, these uncertainties may be acceptable for the estimation of H20 contents of H20-rich (> 1 wt%) samples

Pb isotopic variability in melt inclusions from the EMI–EMII–HIMU mantle end-members and the role of the oceanic lithosphere

Melt inclusions from four individual lava samples representing the HIMU (Mangaia Island), EMI (Pitcairn Island) and EMII (Tahaa Island) end member components, have heterogeneous Pb isotopic composition larger than that defined by the erupted lavas in each island. The broad linear trend in ^(207)Pb/^(206)Pb–^(208)Pb/^(206)Pb space produced by the melt inclusions from Mangaia, Tahaa and fPitcairn samples reproduces the entire trend defined by the Austral chain, the Society islands and the Pitcairn island and seamount groups. The inclusions preserve a record of melt composition of far greater isotopic diversity than that sampled in whole rock basalts. These results can be explained by mixing of a common depleted component with the HIMU, EMI and EMII lavas, respectively. We favor a model that considers the oceanic lithosphere to be that common component. We suggest that the Pb isotopic compositions of the melt inclusions reflect wall rock reaction of HIMU, EMI and EMII melts during their percolation through the oceanic lithosphere. Under these conditions, the localized rapid crystallization of olivine from primitive basalt near the reaction zone would allow the entrapment of melt inclusions with different isotopic composition

Minimal Parameter Homotopies for the L2 Optimal Model Order Reduction Problem

The problem of finding a reduced order model, optimal in the L2 sense, to a given system model is a fundamental one in control system analysis and design. The problem is very difficult without the global convergence of homotopy methods, and a number of homotopy based approaches have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations are developed and compared here. The main conclusions are that dimensionality is inversely related to numerical well conditioning and algorithmic efficiency is inversely related to robustness of the algorithm

Stillbirth and loss: family practices and display

This paper explores how parents respond to their memories of their stillborn child over the years following their loss. When people die after living for several years or more, their family and friends have the residual traces of a life lived as a basis for an identity that may be remembered over a sustained period of time. For the parent of a stillborn child there is no such basis and the claim for a continuing social identity for their son or daughter is precarious. Drawing on interviews with the parents of 22 stillborn children, this paper explores the identity work performed by parents concerned to create a lasting and meaningful identity for their child and to include him or her in their families after death. The paper draws on Finch's (2007) concept of family display and Walter's (1999) thesis that links continue to exist between the living and the dead over a continued period. The paper argues that evidence from the experience of stillbirth suggests that there is scope for development for both theoretical frameworks