Stability of the periodic Toda lattice under short range perturbations

We consider the stability of the periodic Toda lattice (and slightly more generally of the algebro-geometric finite-gap lattice) under a short range perturbation. We prove that the perturbed lattice asymptotically approaches a modulated lattice. More precisely, let $g$ be the genus of the hyperelliptic curve associated with the unperturbed solution. We show that, apart from the phenomenon of the solitons travelling on the quasi-periodic background, the $n/t$-pane contains $g+2$ areas where the perturbed solution is close to a finite-gap solution in the same isospectral torus. In between there are $g+1$ regions where the perturbed solution is asymptotically close to a modulated lattice which undergoes a continuous phase transition (in the Jacobian variety) and which interpolates between these isospectral solutions. In the special case of the free lattice ($g=0$) the isospectral torus consists of just one point and we recover the known result. Both the solutions in the isospectral torus and the phase transition are explicitly characterized in terms of Abelian integrals on the underlying hyperelliptic curve. Our method relies on the equivalence of the inverse spectral problem to a matrix Riemann--Hilbert problem defined on the hyperelliptic curve and generalizes the so-called nonlinear stationary phase/steepest descent method for Riemann--Hilbert problem deformations to Riemann surfaces.Comment: 38 pages, 1 figure. This version combines both the original version and arXiv:0805.384

Effects of a strategy to improve offender assessment practices: Staff perceptions of implementation outcomes

Background: This implementation study examined the impact of an organizational process improvement intervention (OPII) on a continuum of evidence based practices related to assessment and community reentry of drug-involved offenders: Measurement/Instrumentation, Case Plan Integration, Conveyance/Utility, and Service Activation/Delivery. Methods: To assess implementation outcomes (staff perceptions of evidence-based assessment practices), a survey was administered to correctional and treatment staff (n = 1509) at 21 sites randomly assigned to an Early- or Delayed-Start condition. Hierarchical linear models with repeated measures were used to examine changes in evidence-based assessment practices over time, and organizational characteristics were examined as covariates to control for differences across the 21 research sites. Results: Results demonstrated significant intervention and sustainability effects for three of the four assessment domains examined, although stronger effects were obtained for intra- than inter-agency outcomes. No significant effects were found for Conveyance/Utility. Conclusions: Implementation interventions such as the OPII represent an important tool to enhance the use of evidence-based assessment practices in large and diverse correctional systems. Intra-agency assessment activities that were more directly under the control of correctional agencies were implemented most effectively. Activities in domains that required cross-systems collaboration were not as successfully implemented, although longer follow-up periods might afford detection of stronger effects

On Fourier transforms of radial functions and distributions

We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier transform of any radial function $f(r)$ in any dimension, provided one knows the Fourier transform of the one-dimensional function $t\to f(|t|)$ and the two-dimensional function $(x_1,x_2)\to f(|(x_1,x_2)|)$. We prove analogous results for radial tempered distributions.Comment: 12 page

Eclipses During the 2010 Eruption of the Recurrent Nova U Scorpii

The eruption of the recurrent nova U Scorpii on 28 January 2010 is now the all-time best observed nova event. We report 36,776 magnitudes throughout its 67 day eruption, for an average of one measure every 2.6 minutes. This unique and unprecedented coverage is the first time that a nova has any substantial amount of fast photometry. With this, two new phenomena have been discovered: the fast flares in the early light curve seen from days 9-15 (which have no proposed explanation) and the optical dips seen out of eclipse from days 41-61 (likely caused by raised rims of the accretion disk occulting the bright inner regions of the disk as seen over specific orbital phases). The expanding shell and wind cleared enough from days 12-15 so that the inner binary system became visible, resulting in the sudden onset of eclipses and the turn-on of the supersoft X-ray source. On day 15, a strong asymmetry in the out-of-eclipse light points to the existence of the accretion stream. The normal optical flickering restarts on day 24.5. For days 15-26, eclipse mapping shows that the optical source is spherically symmetric with a radius of 4.1 R_sun. For days 26-41, the optical light is coming from a rim-bright disk of radius 3.4 R_sun. For days 41-67, the optical source is a center-bright disk of radius 2.2 R_sun. Throughout the eruption, the colors remain essentially constant. We present 12 eclipse times during eruption plus five just after the eruption.Comment: ApJ in press. 60 pages, 17 figure

First Evidence of Reproductive Adaptation to “Island Effect” of a Dwarf Cretaceous Romanian Titanosaur, with Embryonic Integument In Ovo

<div><h3>Background</h3><p>The Cretaceous vertebrate assemblages of Romania are famous for geographically endemic dwarfed dinosaur taxa. We report the first complete egg clutches of a dwarf lithostrotian titanosaur, from Toteşti, Romania, and its reproductive adaptation to the “island effect”.</p> <h3>Methodology/Findings</h3><p>The egg clutches were discovered in sequential sedimentary layers of the Maastrichtian Sânpetru Formation, Toteşti. The occurrence of 11 homogenous clutches in successive strata suggests philopatry by the same dinosaur species, which laid clutches averaging four ∼12 cm diameters eggs. The eggs and eggshells display numerous characters shared with the positively identified material from egg-bearing level 4 of the Auca Mahuevo (Patagonia, Argentina) nemegtosaurid lithostrotian nesting site. Microscopic embryonic integument with bacterial evidences was recovered in one egg. The millimeter-size embryonic integument displays micron size dermal papillae implying an early embryological stage at the time of death, likely corresponding to early organogenesis before the skeleton formation.</p> <h3>Conclusions/Significance</h3><p>The shared oological characters between the Haţeg specimens and their mainland relatives suggest a highly conservative reproductive template, while the nest decrease in egg numbers per clutch may reflect an adaptive trait to a smaller body size due to the “island effect”. The combined presence of the lithostrotian egg and its embryo in the Early Cretaceous Gobi coupled with the oological similarities between the Haţeg and Auca Mahuevo oological material evidence that several titanosaur species migrated from Gondwana through the Haţeg Island before or during the Aptian/Albian. It also suggests that this island might have had episodic land bridges with the rest of the European archipelago and Asia deep into the Cretaceous.</p> </div

The evolution of the plastid chromosome in land plants: gene content, gene order, gene function

This review bridges functional and evolutionary aspects of plastid chromosome architecture in land plants and their putative ancestors. We provide an overview on the structure and composition of the plastid genome of land plants as well as the functions of its genes in an explicit phylogenetic and evolutionary context. We will discuss the architecture of land plant plastid chromosomes, including gene content and synteny across land plants. Moreover, we will explore the functions and roles of plastid encoded genes in metabolism and their evolutionary importance regarding gene retention and conservation. We suggest that the slow mode at which the plastome typically evolves is likely to be influenced by a combination of different molecular mechanisms. These include the organization of plastid genes in operons, the usually uniparental mode of plastid inheritance, the activity of highly effective repair mechanisms as well as the rarity of plastid fusion. Nevertheless, structurally rearranged plastomes can be found in several unrelated lineages (e.g. ferns, Pinaceae, multiple angiosperm families). Rearrangements and gene losses seem to correlate with an unusual mode of plastid transmission, abundance of repeats, or a heterotrophic lifestyle (parasites or myco-heterotrophs). While only a few functional gene gains and more frequent gene losses have been inferred for land plants, the plastid Ndh complex is one example of multiple independent gene losses and will be discussed in detail. Patterns of ndh-gene loss and functional analyses indicate that these losses are usually found in plant groups with a certain degree of heterotrophy, might rendering plastid encoded Ndh1 subunits dispensable