Games That End in a Bang or a Whimper

Using truels, or three-person duels, as an example, we show that how players perceive a multiple-round game will end can make a big difference in whether it ends non-cooperatively (producing a "bang") or just peters out (producing a "whimper"): 1. If the players view the number of rounds as bounded-reasonable, because the game must end in a finite number of rounds-they will shoot from the start. 2. If the players view the number of rounds as unbounded-reasonable, because the horizon of the game is infinite-then a cooperative equilibrium, involving no shooting, can also occur. Real- life examples are given of players with bounded and unbounded outlooks in truel- like situations. Unbounded outlooks encourage cooperative play, foster hope, and lead to more auspicious outcomes. These outcomes are facilitated by institutions that put no bounds on play-including reprisals-thereby allowing for a day of reckoning for those who violate established norms. Eschatological implications of the analysis, especially for thinking about the future and how it might end, are also discussed.TRUELS; BACKWARD INDUCTION; INFINITE-HORIZON GAMES; ESCHATOLOGY

Single-Peakedness and Disconnected Coalitions

Ordinally single-peaked preferences are distinguished from cardinally singlepeaked preferences, in which all players have a similar perception of distances in some one-dimensional ordering. While ordinal single-peakedness can lead to disconnected coalitions that have a "hole" in the ordering, cardinal single-peakedness precludes this possibility, based on two models of coalition formation: ¥ Fallback (FB): Players seek coalition partners by descending lower and lower in their preference rankings until a majority coalition forms. ¥ Build-Up (BU): Similar to FB, except that when nonmajority subcoalitions form, they fuse into composite players, whose positions are defined cardinally and who are treated as single players in the convergence process. FB better reflects the unconstrained, or nonmyopic, possibilities of coalition formation, whereas BU-because all subcoalition members must be included in any majority coalition that forms-restricts combinatorial possibilities and tends to produce less compact majority coalitions. The "strange bedfellows" frequently observed in legislative coalitions and military alliances suggest that even when players agree on, say, a left-right ordering, their perceptions of exactly where players stand in this ordering may differ substantially. If so, a player may be acceptable to a coalition but may not find every member in it acceptable, causing that player not to join and possibly creating a disconnected coalition.COALITION FORMATION; SINGLE-PEAKEDNESS; LEGISLATURES; ALLIANCES

Cooperative vs. Non-Cooperative Truels: Little Agreement, But Does That Matter?

It is well-known that non-cooperative and cooperative game theory may yield different solutions to games. These differences are particularly dramatic in the case of truels, or three-person duels, in which the players may fire sequentially or simultaneously, and the games may be one-round or n-round. Thus, it is never a Nash equilibrium for all players to hold their fire in any of these games, whereas in simultaneous one-round and n-round truels such cooperation, wherein everybody survives, is in both the alpha-core and beta-core. On the other hand, both cores may be empty, indicating a lack of stability, when the unique Nash equilibrium is one survivor. Conditions under which each approach seems most applicable are discussed. Although it might be desirable to subsume the two approaches within a unified framework, such unification seems unlikely since the two approaches are grounded in fundamentally different notions of stability.COOPERATIVE GAME; NON-COOPERATIVE GAME; TRUEL; NASH EQUILIBRIUM; CORE

A light‐activated acyl carrier protein 'trap' for intermediate capture in type II iterative polyketide biocatalysis

A discrete acyl carrier protein (ACP) bearing a photolabile nonhydrolysable carba(dethia) malonyl pantetheine cofactor was chemoenzymatically prepared and utilized for the trapping of biosynthetic polyketide intermediates following light activation. From the in vitro assembly of the polyketides SEK4 and SEK4b by the type II actinorhodin ‘minimal’ polyketide synthase (PKS), a range of putative ACP-bound diketides, tetraketides, pentaketides and hexaketides were identified and characterised by FT-ICR-MS, providing direct insights on active site accessibility and substrate processing for this enzyme class

Autopiquer - a robust and reliable peak detection algorithm for mass spectrometry

We present a simple algorithm for robust and unsupervised peak detection by determining a noise threshold in isotopically resolved mass spectrometry data. Solving this problem will greatly reduce the subjective and time consuming manual picking of mass spectral peaks and so will prove beneficial in many research applications. The Autopiquer approach uses autocorrelation to test for the presence of (isotopic) structure in overlapping windows across the spectrum. Within each window, a noise threshold is optimized to remove the most unstructured data whilst keeping as much of the (isotopic) structure as possible. This algorithm has been successfully demonstrated for both peak detection and spectral compression on data from many different classes of mass spectrometer and for different sample types and this approach should also be extendible to other types of data that contain regularly spaced discrete peaks

Re-identification of c. 15 700 cal yr BP tephra bed at Kaipo Bog, eastern North Island: implications for dispersal of Rotorua and Puketarata tephra beds.

A 10 mm thick, c. 15 700 calendar yr BP (c. 13 100 14C yr BP) rhyolitic tephra bed in the well-studied montane Kaipo Bog sequence of eastern North Island was previously correlated with Maroa-derived Puketarata Tephra. We revise this correlation to Okataina-derived Rotorua Tephra based on new compositional data from biotite phenocrysts and glass. The new correlation limits the known dispersal of Puketarata Tephra (sensu stricto, c. 16 800 cal yr BP) and eliminates requirements to either reassess its age or to invoke dual Puketarata eruptive events. Our data show that Rotorua Tephra comprises two glass-shard types: an early-erupted low-K2O type that was dispersed mostly to the northwest, and a high-K2O type dispersed mostly to the south and southeast, contemporary with late-stage lava extrusion. Late-stage Rotorua eruptives contain biotite that is enriched in FeO compared with biotite from Puketarata pyroclastics. The occurrence of Rotorua Tephra in Kaipo Bog (100 km from the source) substantially extends its known distribution to the southeast. Our analyses demonstrate that unrecognised syn-eruption compositional and dispersal changes can cause errors in fingerprinting tephra deposits. However, the compositional complexity, once recognised, provides additional fingerprinting criteria, and also documents magmatic and dispersal processes

Rheological controls on the eruption potential and style of an andesite volcano:A case study from Mt. Ruapehu, New Zealand

The evolving magma rheology of three recent Ruapehu eruptions (1969, 1977, and 1995) is estimated using a combination of thermodynamic models and rheological calculations, supported by textural observations of the erupted scoria. We use a well-established thermodynamic model to determine the composition of these representative Ruapehu magmas from 300MPa to ∼30MPa. The outputs of the model provide the changing crystal and bubble content in a closed system (assuming no gas loss), as well as the fractionating melt compositions. We calculate the melt viscosity, and the effect of bubbles and crystals, to quantify the rheology of the magma during ascent (under assumed equilibrium conditions). The moderately high phenocryst content of Ruapehu scoria (∼30%) means that only a small amount of additional microlite crystallisation (∼5%) would result in a yield strength, which may lead the magma to stall. However, if the strain rates are high enough, more crystallisation would be possible without developing a yield stress. This suggests that microlite-rich magmas are almost certain to stall unless they encounter significant fluid addition from a source such as a hydrothermal system, groundwater, or surface water (i.e., Ruapehu's Crater Lake). Ruapehu magmas are initially H2O-undersaturated and as a consequence, crystallisation and bubble growth were suppressed until the magma achieved saturation, at ∼100 to 50 MPa. From this analysis, we suggest that Ruapehu magmas are more likely to erupt compared to magmas of a similar composition that are H2O-saturated. This partly explains the regular, albeit small-volume eruptions at Ruapehu and the propensity for phreatomagmatic eruptions when the magma:water ratio is low

The microanalysis of iron and sulphur oxidation states in silicate glass - Understanding the effects of beam damage

Quantifying the oxidation state of multivalent elements in silicate melts (e.g., Fe²⁺ versus Fe³⁺ or S²⁻ versus S⁶⁺) is fundamental for constraining oxygen fugacity. Oxygen fugacity is a key thermodynamic parameter in understanding melt chemical history from the Earth's mantle through the crust to the surface. To make these measurements, analyses are typically performed on small (<100 µm diameter) regions of quenched volcanic melt (now silicate glass) forming the matrix between crystals or as trapped inclusions. Such small volumes require microanalysis, with multiple techniques often applied to the same area of glass to extract the full range of information that will shed light on volcanic and magmatic processes. This can be problematic as silicate glasses are often unstable under the electron and photon beams used for this range of analyses. It is therefore important to understand any compositional and structural changes induced within the silicate glass during analysis, not only to ensure accurate measurements (and interpretations), but also that subsequent analyses are not compromised. Here, we review techniques commonly used for measuring the Fe and S oxidation state in silicate glass and explain how silicate glass of different compositions responds to electron and photon beam irradiation