Generalized backward induction: Justification for a folk algorithm

I introduce axiomatically infinite sequential games that extend Kuhn’s classical framework. Infinite games allow for (a) imperfect information, (b) an infinite horizon, and (c) infinite action sets. A generalized backward induction (GBI) procedure is defined for all such games over the roots of subgames. A strategy profile that survives backward pruning is called a backward induction solution (BIS). The main result of this paper finds that, similar to finite games of perfect information, the sets of BIS and subgame perfect equilibria (SPE) coincide for both pure strategies and for behavioral strategies that satisfy the conditions of finite support and finite crossing. Additionally, I discuss five examples of well-known games and political economy models that can be solved with GBI but not classic backward induction (BI). The contributions of this paper include (a) the axiomatization of a class of infinite games, (b) the extension of backward induction to infinite games, and (c) the proof that BIS and SPEs are identical for infinite games

On massive dust clumps in the envelope of the red supergiant VY Canis Majoris

The envelope of the red supergiant VY CMa has long been considered an extreme example of episodic mass loss that is possibly taking place in other cool and massive evolved stars. Recent submm observations of the envelope revealed massive dusty clumps within 800 mas from the star which reinforce the picture of drastic mass-loss phenomena in VY CMa. We present new ALMA observations at an angular resolution of 0.1" and at an unprecedented sensitivity that reveal further details about the dusty clumps. We resolve more discrete features and identify a submm counterpart of a more distant Clump SW known from visual observations. The brightest clump, named C, is resolved in the observations. Gas seen against the resolved continuum emission of clump C produces a molecular spectrum in absorption. Except for SW Clump, no molecular emission is found to be associated with the dusty clumps and we propose that the dusty structures have an atypically low gas content. We attempt to reproduce the properties of the dusty clumps through three-dimensional radiative-transfer modeling. Although a clump configuration explaining the observations is found, it is not unique. A very high optical depth of all clumps to the stellar radiation make the modeling very challenging and requires unrealistically high dust masses. It is suggested that the dusty features have substructures, e.g. porosity, that allows deeper penetration of stellar photons within the clumps than in a homogeneous configuration. A comparison of the estimated clumps ages to variations in the stellar visual flux for over a century suggests that the mechanism responsible for their formation is not uniquely manifested by enhanced or strongly diminished visual light. The study demonstrates that the dusty mass-loss episodes of VY CMa are indeed unparalleled among all known non-explosive stars. The origin of these episodes remains an unsolved problem.Comment: accepted to A&

Tubular agglutinated foraminifera as indicators of organic carbon flux

The dimensions of tubular agglutinated foraminifera such as Rhizammina and Rhabdammina respond in a predictable manner to changes in the flux of organic carbon to the sea floor. In both the modern western North Atlantic and in an ancient example (the K/T boundary in Gubbio), the slender, finely-grained tubes (<100 μm diameter) dominate in oligotrophic regimes, whereas in eutrophic regimes the abundance of tubes is higher, and the mean and standard deviation of the tube diameter increases. Large tubes (> 500 μm) are present only when organic flux is comparatively high. Although our observations are at present not directly calibrated to primary productivity levels, we maintain that the potential for using tubular agglutinated foraminifera does exist

Remarks on the type locality and current status of the foraminiferal species Rzehakina epigona (Rzehak, 1895)

A likely topotype locality is proposed for Rzehakina epigona. As the type specimen of Silicina epigona Rzehak, 1895 is assumed to be lost, we undertook a search for new material in the type area, Zdounky village in Moravia. A single locality provided a total of 138 Rzehakina specimens. The greenish grey marly clays sampled here contain a rich fauna of both planktonic and benthic foraminifers belonging to the Abathomphalus mayaroensis Zone. In addition to R. epigona, rare specimens attributable to R. inclusa, R. lata, R. minima and even a typical form of R. fissistomata are present at the Zdounky locality. Biometrical analysis was carried out on 52 complete specimens using the involution value "Z" and the length/breadth ratio. Most of the Rzehakina epigona topotypes form a tight cluster with "Z" values between 4 and 15%, although forms that appear transitional to R. lata have Z values of around 20%. The length/breadth ratio is more variable, with values ranging between 1.2 and 2.0. However, the Z value measured from Rzehak's type figure is significantly higher and outside the range of variability of this cluster of specimens. We conclude that Rzehak's drawing may be imprecise. Unfortunately, we were not able to study the inner structure of these specimens owing to the lack of internal filling in these specimens. The unfavourable preservation and low abundance of specimens from the type locality do not enable a proper revision of the species Rzehakina epigona at this time