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

Mechanisms of degassing at Nevado del Ruiz volcano, Colombia

Author Posting. © Geological Society, 2003. This article is posted here by permission of Geological Society for personal use, not for redistribution. The definitive version was published in Journal of the Geological Society 160 (2003): 507-521, doi:10.1144/0016-764902-028.Nevado del Ruiz volcano is an andesite stratovolcano located in the northern Andes of Colombia. The volcano erupted on 11 September 1985, 13 November 1985, and 1 September 1989. The last two eruptions emitted juvenile solid material. This paper examines the volatile and light lithophile trace element contents of melt inclusions and matrix glasses from this juvenile material, and proposes a model for degassing within the volcano. Major element distributions in the glasses show two evolutionary trends, with subsidiary points that lie between the two trends. The data suggest the existence of two separate magmas, which have interacted, mingled, and mixed during their ascent and eruption. Water contents in melt inclusions, as determined by secondary ionization mass spectrometric analysis, are generally low, averaging between 1.6 and 3.3 wt.%. Halogen concentrations in the glasses range from 400 to 1200 ppm for fluorine and from 1100 to 1500 ppm for chlorine. Sulphur contents are low, not exceeding 500 ppm, with most glasses containing <200 ppm. Lithium concentrations range from 20 to 40 ppm, beryllium from 1.5 to 2 ppm, and boron exhibits high variability from 30 to 100 ppm. The only significant difference between melt inclusions and matrix glasses is for water, with matrix glasses having significantly lower concentrations (<0.5 wt.%) than the melt inclusions. The generally elevated concentrations of boron in the magma may be a consequence of enrichment in the source region of the magma, i.e. by subduction of altered oceanic crust and/or sediments. Yet the large degree of boron heterogeneity in both melt inclusions and matrix glasses necessitates subsequent addition of boron at shallower depths as well, by the assimilation of crustal sedimentary rocks or by interaction with hydrothermal fluids. Evidence for pre-eruptive magma emplacement at shallow levels is provided by (1) anhydrous mineral assemblages of plagioclase and pyroxene, (2) high silica contents of glasses, and (3) low water contents in melt inclusions. When combined, these observations suggest a period of magma residence at shallow depths, probably <3 km beneath the summit of the volcano. A multistage model of magma transport and degassing involves alternating periods of magma ascent and magma ponding. Initially, volatile-bearing magma ascends from depths of 9–15 km, driven by buoyancy. During decompression, the magma loses gas, particularly CO2 and sulphur. The magma eventually ponds at its neutral buoyancy level. At this point, the gas-saturated magma cools and crystallizes, thereby liberating gas under isobaric conditions. As a result, CO2 is depleted from the magma whereas H2O and SiO2 are enriched. The H2O enrichment is caused by its increased solubility in the magma as CO2 is degassed, whereas SiO2 is enriched by fractional crystallization. The density of the magma decreases as the level of dissolved H2O increases, eventually causing the magma to become buoyant once more and to continue its ascent, either to erupt or to freeze at shallow depths.This work was funded with grants to J.S. by the Natural Sciences and Engineering Research Council of Canada and by the Fonds pour la formation de chercheurs et l’aide a` la recherche (Que´bec)

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,

Volcanic glasses at the Izu arc volcanic front : new perspectives on fluid and sediment melt recycling in subduction zones

Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 5 (2004): Q01007, doi:10.1029/2002GC000408.Volcanic glasses contained in distal fallout tephras from the Izu arc volcanic front (Izu VF) provide unique perspectives on general problems of arc volcanism. Unlike cogenetic lavas, these glasses are liquid compositions where element concentrations as well as ratios have significance. Isotopic evidence and previous work show that there is no sediment melt contribution to the sources of the Izu VF tephras, and hence their trace element characteristics permit determination of the trace element contents of slab fluids. The slab fluid is a composite of metasediment (∼5% of total fluid) and metabasalt (∼95%) component fluids, and carries large ion lithophile elements (LILE) with high LILE/Th and LILE/U, and low Th and U relative to source. Except for Sr and K, the metabasalt fluid is much less enriched than the metasediment fluid, but its large relative proportions make it an important carrier of many trace elements. The metabasalt fluid has the characteristics of the arc trace element signature, obviating the need for ubiquitous involvement of sediment in arc magma genesis. The fluid component in the tephras is remarkably constant in composition over fifteen million years, and hence appears to be a robust composition that may be applicable to other convergent margins. Assuming that the metabasalt fluid is a common component, and that distribution coefficients between sediment and fluid are similar from one arc to another, composite fluid compositions can be estimated for other arcs. Differences from this composition then would likely result from a sediment melt component. Comparison to arcs with sediment melt components in their source (Marianas, eastern Aleutians) shows that partial sediment melts may be so enriched, that they can completely mask the signature of the comingling slab fluids. Hence sediment melts can easily dominate the trace element and isotopic signature of many convergent margins. Since sediment melts inherit the LILE/LILE ratios of the trench sediment, Earth's surface processes must eventually influence the compositional diversity of arcs.This study was funded by the “Deutsche Forschungsgemeinschaft” (grants Str 441/3 and 441/4). The Northeast National Ion Microprobe Facility at WHOI was supported by grants EAR-9628749 and EAR-990440 from the National Science Foundation

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

Efficacy of Stochastic Vestibular Stimulation to Improve Locomotor Performance in a Discordant Sensory Environment

Astronauts exposed to microgravity face sensorimotor challenges incurred when readapting to a gravitational environment. Sensorimotor Adaptability (SA) training has been proposed as a countermeasure to improve locomotor performance during re-adaptation, and it is suggested that the benefits of SA training may be further enhanced by improving detection of weak sensory signals via mechanisms such as stochastic resonance when a non-zero level of stochastic white noise based electrical stimulation is applied to the vestibular system (stochastic vestibular stimulation, SVS). The purpose of this study was to test the efficacy of using SVS to improve short-term adaptation in a sensory discordant environment during performance of a locomotor task

A multidisciplinary stroke clinic for outpatient care of veterans with cerebrovascular disease

Background: Managing cerebrovascular risk factors is complex and difficult. The objective of this program evaluation was to assess the effectiveness of an outpatient Multidisciplinary Stroke Clinic model for the clinical management of veterans with cerebrovascular disease or cerebrovascular risk factors. Methods: The Multidisciplinary Stroke Clinic provided care to veterans with cerebrovascular disease during a one-half day clinic visit with interdisciplinary evaluations and feedback from nursing, health psychology, rehabilitation medicine, internal medicine, and neurology. We conducted a program evaluation of the clinic by assessing clinical care outcomes, patient satisfaction, provider satisfaction, and costs. Results: We evaluated the care and outcomes of the first consecutive 162 patients who were cared for in the clinic. Patients had as many as six clinic visits. Systolic and diastolic blood pressure decreased: 137.2 ± 22.0 mm Hg versus 128.6 ± 19.8 mm Hg, P = 0.007 and 77.9 ± 14.8 mm Hg versus 72.0 ± 10.2 mm Hg, P = 0.004, respectively as did low-density lipoprotein (LDL)-cholesterol (101.9 ± 23.1 mg/dL versus 80.6 ± 25.0 mg/dL, P = 0.001). All patients had at least one major change recommended in their care management. Both patients and providers reported high satisfaction levels with the clinic. Veterans with stroke who were cared for in the clinic had similar or lower costs than veterans with stroke who were cared for elsewhere. Conclusion: A Multidisciplinary Stroke Clinic model provides incremental improvement in quality of care for complex patients with cerebrovascular disease at costs that are comparable to usual post-stroke care

A study of patent thickets

Report analysing whether entry of UK enterprises into patenting in a technology area is affected by patent thickets in the technology area