Molecular and fossil evidence place the origin of cichlid fishes long after Gondwanan rifting.

Cichlid fishes are a key model system in the study of adaptive radiation, speciation and evolutionary developmental biology. More than 1600 cichlid species inhabit freshwater and marginal marine environments across several southern landmasses. This distributional pattern, combined with parallels between cichlid phylogeny and sequences of Mesozoic continental rifting, has led to the widely accepted hypothesis that cichlids are an ancient group whose major biogeographic patterns arose from Gondwanan vicariance. Although the Early Cretaceous (ca 135 Ma) divergence of living cichlids demanded by the vicariance model now represents a key calibration for teleost molecular clocks, this putative split pre-dates the oldest cichlid fossils by nearly 90 Myr. Here, we provide independent palaeontological and relaxed-molecular-clock estimates for the time of cichlid origin that collectively reject the antiquity of the group required by the Gondwanan vicariance scenario. The distribution of cichlid fossil horizons, the age of stratigraphically consistent outgroup lineages to cichlids and relaxed-clock analysis of a DNA sequence dataset consisting of 10 nuclear genes all deliver overlapping estimates for crown cichlid origin centred on the Palaeocene (ca 65-57 Ma), substantially post-dating the tectonic fragmentation of Gondwana. Our results provide a revised macroevolutionary time scale for cichlids, imply a role for dispersal in generating the observed geographical distribution of this important model clade and add to a growing debate that questions the dominance of the vicariance paradigm of historical biogeography

Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime

We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity $\sigma_{xy}^{AH}$. We show that $\sigma_{xy}^{AH}$ is proportional to the first derivative of the density of states $\varrho(\epsilon)$ and thus can be expected to change sign as a function of impurity band filling. We also show that $\sigma_{xy}^{AH}$ depends on temperature as the longitudinal conductivity $\sigma_{xx}$ within logarithmic accuracy.Comment: 4 pages, 1 eps figure, final versio

Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and superposition using a path integral. Deutsch's density matrix approach is causal but typically destroys coherence. For each of these formulations I demonstrate that there are yet further alternatives in prescribing the handling of information flow (inequivalent to previous analyses) that have implications for any system in which unitarity or coherence are not preserved.Comment: 25 pages, phyzzx, CALT-68-188

A Tverberg type theorem for matroids

Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.Comment: This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springe

Effects and Propositions

The quantum logical and quantum information-theoretic traditions have exerted an especially powerful influence on Bub's thinking about the conceptual foundations of quantum mechanics. This paper discusses both the quantum logical and information-theoretic traditions from the point of view of their representational frameworks. I argue that it is at this level, at the level of its framework, that the quantum logical tradition has retained its centrality to Bub's thought. It is further argued that there is implicit in the quantum information-theoretic tradition a set of ideas that mark a genuinely new alternative to the framework of quantum logic. These ideas are of considerable interest for the philosophy of quantum mechanics, a claim which I defend with an extended discussion of their application to our understanding of the philosophical significance of the no hidden variable theorem of Kochen and Specker.Comment: Presented to the 2007 conference, New Directions in the Foundations of Physic

The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine

We study the propagator of a non-relativistic, non-interacting particle in any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an external, flat spacetime in which two spatial regions, $V_-$ at time $t_-$ and $V_+$ at time $t_+$, are connected by two temporal wormholes, one leading from the past side of $V_-$ to t the future side of $V_+$ and the other from the past side of $V_+$ to the future side of $V_-$. We express the propagator explicitly in terms of those for ordinary, flat spacetime and for the two wormholes; and from that expression we show that the propagator satisfies completeness and unitarity in the initial and final ``chronal regions'' (regions without closed timelike curves) and its propagation from the initial region to the final region is unitary. However, within the time machine it satisfies neither completeness nor unitarity. We also give an alternative proof of initial-region-to-final-region unitarity based on a conserved current and Gauss's theorem. This proof can be carried over without change to most any non-relativistic time-machine spacetime; it is the non-relativistic version of a theorem by Friedman, Papastamatiou and Simon, which says that for a free scalar field, quantum mechanical unitarity follows from the fact that the classical evolution preserves the Klein-Gordon inner product

On the stability of two-chunk file-sharing systems

We consider five different peer-to-peer file sharing systems with two chunks, with the aim of finding chunk selection algorithms that have provably stable performance with any input rate and assuming non-altruistic peers who leave the system immediately after downloading the second chunk. We show that many algorithms that first looked promising lead to unstable or oscillating behavior. However, we end up with a system with desirable properties. Most of our rigorous results concern the corresponding deterministic large system limits, but in two simplest cases we provide proofs for the stochastic systems also.Comment: 19 pages, 7 figure

A stochastic perturbation of inviscid flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a \holderspace{k}{\alpha} local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.Comment: 13 pages, no figures

Isotopic Scaling in Nuclear Reactions

A three parameter scaling relationship between isotopic distributions for elements with Z$\leq 8$ has been observed that allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed iso-scaling) applies for a variety of reaction mechanisms that are dominated by phase space, including evaporation, multifragmentation and deeply inelastic scattering. The origins of this scaling behavior for the various reaction mechanisms are explained. For multifragmentation processes, the systematics is influenced by the density dependence of the asymmetry term of the equation of state.Comment: 10 Pages, 2 Figure

The photometric properties of a vast stellar substructure in the outskirts of M33

We have surveyed $\sim40$sq.degrees surrounding M33 with CFHT MegaCam in the g and i filters, as part of the Pan-Andromeda Archaeological Survey. Our observations are deep enough to resolve the top 4mags of the red giant branch population in this galaxy. We have previously shown that the disk of M33 is surrounded by a large, irregular, low-surface brightness substructure. Here, we quantify the stellar populations and structure of this feature using the PAndAS data. We show that the stellar populations of this feature are consistent with an old population with $<[Fe/H]>\sim-1.6$dex and an interquartile range in metallicity of $\sim0.5$dex. We construct a surface brightness map of M33 that traces this feature to $\mu_V\simeq33$mags\,arcsec$^{-2}$. At these low surface brightness levels, the structure extends to projected radii of $\sim40$kpc from the center of M33 in both the north-west and south-east quadrants of the galaxy. Overall, the structure has an "S-shaped" appearance that broadly aligns with the orientation of the HI disk warp. We calculate a lower limit to the integrated luminosity of the structure of $-12.7\pm0.5$mags, comparable to a bright dwarf galaxy such as Fornax or AndII and slightly less than $1\$ of the total luminosity of M33. Further, we show that there is tentative evidence for a distortion in the distribution of young stars near the edge of the HI disk that occurs at similar azimuth to the warp in HI. The data also hint at a low-level, extended stellar component at larger radius that may be a M33 halo component. We revisit studies of M33 and its stellar populations in light of these new results, and we discuss possible formation scenarios for the vast stellar structure. Our favored model is that of the tidal disruption of M33 in its orbit around M31.Comment: Accepted for publication in ApJ. 17 figures. ApJ preprint forma