Galactic Punctuated Equilibrium: How to Undermine Carter's Anthropic Argument in Astrobiology

We investigate a new strategy which can defeat the (in)famous Carter's "anthropic" argument against extraterrestrial life and intelligence. In contrast to those already considered by Wilson, Livio, and others, the present approach is based on relaxing hidden uniformitarian assumptions, considering instead a dynamical succession of evolutionary regimes governed by both global (Galaxy-wide) and local (planet- or planetary system-limited) regulation mechanisms. This is in accordance with recent developments in both astrophysics and evolutionary biology. Notably, our increased understanding of the nature of supernovae and gamma-ray bursts, as well as of strong coupling between the Solar System and the Galaxy on one hand, and the theories of "punctuated equilibria" of Eldredge and Gould and "macroevolutionary regimes" of Jablonski, Valentine, et al. on the other, are in full accordance with the regulation- mechanism picture. The application of this particular strategy highlights the limits of application of Carter's argument, and indicates that in the real universe its applicability conditions are not satisfied. We conclude that drawing far-reaching conclusions about the scarcity of extraterrestrial intelligence and the prospects of our efforts to detect it on the basis of this argument is unwarranted.Comment: 3 figures, 26 page

Elementary amenable subgroups of R. Thompson's group F

The subgroup structure of Thompson's group F is not yet fully understood. The group F is a subgroup of the group PL(I) of orientation preserving, piecewise linear self homeomorphisms of the unit interval and this larger group thus also has a poorly understood subgroup structure. It is reasonable to guess that F is the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we explore the complexity of the elementary amenable subgroups of F in an attempt to understand the boundary between the elementary amenable subgroups and the non-elementary amenable. We construct an example of an elementary amenable subgroup up to class (height) omega squared, where omega is the first infinite ordinal.Comment: 20 page

Classical and quantum ergodicity on orbifolds

We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdi\`ere and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quantum ergodicity for the operator P. We also prove ergodicity of the geodesic flow on a compact Riemannian orbifold of negative sectional curvature.Comment: 14 page

Distributed Generation and Resilience in Power Grids

We study the effects of the allocation of distributed generation on the resilience of power grids. We find that an unconstrained allocation and growth of the distributed generation can drive a power grid beyond its design parameters. In order to overcome such a problem, we propose a topological algorithm derived from the field of Complex Networks to allocate distributed generation sources in an existing power grid.Comment: proceedings of Critis 2012 http://critis12.hig.no

Isomorphisms of Brin-Higman-Thompson groups

Let $m, m', r, r',t, t'$ be positive integers with $r, r' \ge 2$. Let $L_r$ denote the ring that is universal with an invertible $1 \times r$ matrix. Let $M_m(L_r^{\otimes t})$ denote the ring of $m \times m$ matrices over the tensor product of $t$ copies of $L_r$. In a natural way, $M_m(L_r^{\otimes t})$ is a partially ordered ring with involution. Let $PU_m(L_r^{\otimes t})$ denote the group of positive unitary elements. We show that $PU_m(L_r^{\otimes t})$ is isomorphic to the Brin-Higman-Thompson group $t V_{r,m}$; the case $t =1$ was found by Pardo, that is, $PU_m(L_r)$ is isomorphic to the Higman-Thompson group $V_{r,m}$. We survey arguments of Abrams, \'Anh, Bleak, Brin, Higman, Lanoue, Pardo, and Thompson that prove that $t' V_{r',m'} \cong tV_{r,m}$ if and only if $r' = r$, $t'=t$ and $\gcd(m',r'-1) = \gcd(m,r-1)$ (if and only if $M_{m'}(L_{r'}^{\otimes t'})$ and $M_m(L_r^{\otimes t})$ are isomorphic as partially ordered rings with involution).Comment: 24 page

Quantum cat maps with spin 1/2

We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map, which, according to the conjecture of Bohigas, Giannoni and Schmit, are expected to converge to those of the circular symplectic ensemble (CSE) of random matrices. In particular, we show that the diagonal approximation of the spectral form factor for small arguments agrees with the CSE prediction. The results are confirmed by numerical investigations.Comment: 26 pages, 3 figure

Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

Genomic and Evolutionary Features of the SPI-1 Type III Secretion System That Is Present in Xanthomonas albilineans but Is Not Essential for Xylem Colonization and Symptom Development of Sugarcane Leaf Scald

Xanthomonas albilineans is the causal agent of sugarcane leaf scald. Interestingly, this bacterium, which is not known to be insect or animal associated, possesses a type III secretion system (T3SS) belonging to the injectisome family Salmonella pathogenicity island 1 (SPI-1). The T3SS SPI-1 of X. albilineans shares only low similarity with other available T3SS SPI-1 sequences. Screening of a collection of 128 plant-pathogenic bacteria revealed that this T3SS SPI-1 is present in only two species of Xanthomonas: X. albilineans and X. axonopodis pv. phaseoli. Inoculation of sugarcane with knockout mutants showed that this system is not required by X. albilineans to spread within xylem vessels and to cause disease symptoms. This result was confirmed by the absence of this T3SS SPI-1 in an X. albilineans strain isolated from diseased sugarcane. To investigate the importance of the T3SS SPI-1 during the life cycle of X. albilineans, we analyzed T3SS SPI-1 sequences from 11 strains spanning the genetic diversity of this species. No nonsense mutations or frameshifting indels were observed in any of these strains, suggesting that the T3SS SPI-1 system is maintained within the species X. albilineans. Evolutionary features of T3SS SPI-1 based on phylogenetic, recombination, and selection analyses are discussed in the context of the possible functional importance of T3SS SPI-1 in the ecology of X. albilineans

Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la