Bounds on the Chabauty--Kim Locus of Hyperbolic Curves

Conditionally on the Tate--Shafarevich and Bloch--Kato Conjectures, we give an explicit upper bound on the size of the $p$-adic Chabauty--Kim locus, and hence on the number of rational points, of a smooth projective curve $X/\mathbb{Q}$ of genus $g\geq2$ in terms of $p$, $g$, the Mordell--Weil rank $r$ of its Jacobian, and the reduction types of $X$ at bad primes. This is achieved using the effective Chabauty--Kim method, generalising bounds found by Coleman and Balakrishnan--Dogra using the abelian and quadratic Chabauty methods.Comment: 24 pages, comments welcom

Double-Mode RR Lyrae Variables in the Globular Cluster M3

We present new B-band CCD photometry for five double-mode RR Lyrae (RRd) variables (V68, V79, V87, V99, and V166) in the globular cluster M3. The pulsational behavior of the RRd variables is described. V68 and V87 have been known as RRd variables since 1982, V79 was recently discovered as an RRd (Clement et al.), and our data have identified V99 and V166 as RRd variables (Corwin et al.). Earlier studies of V79 and V166 do not show double-mode behavior, which indicates that these stars have only recently become RRd stars. V166 changed its dominant pulsation mode from fundamental to first overtone in the interval 1992 to 1993. The candidate double-mode variables V28 and V126 do not exhibit clear RRd behavior in the 1992–1993 data

The Role of Legal Services in the Antipoverty Program

Large-scale adaptive radiations might explain the runaway success of a minority of extant vertebrate clades. This hypothesis predicts, among other things, rapid rates of morphological evolution during the early history of major groups, as lineages invade disparate ecological niches. However, few studies of adaptive radiation have included deep time data, so the links between extant diversity and major extinct radiations are unclear. The intensively studied Mesozoic dinosaur record provides a model system for such investigation, representing an ecologically diverse group that dominated terrestrial ecosystems for 170 million years. Furthermore, with 10,000 species, extant dinosaurs (birds) are the most speciose living tetrapod clade. We assembled composite trees of 614-622 Mesozoic dinosaurs/birds, and a comprehensive body mass dataset using the scaling relationship of limb bone robustness. Maximum-likelihood modelling and the node height test reveal rapid evolutionary rates and a predominance of rapid shifts among size classes in early (Triassic) dinosaurs. This indicates an early burst niche-filling pattern and contrasts with previous studies that favoured gradualistic rates. Subsequently, rates declined in most lineages, which rarely exploited new ecological niches. However, feathered maniraptoran dinosaurs (including Mesozoic birds) sustained rapid evolution from at least the Middle Jurassic, suggesting that these taxa evaded the effects of niche saturation. This indicates that a long evolutionary history of continuing ecological innovation paved the way for a second great radiation of dinosaurs, in birds. We therefore demonstrate links between the predominantly extinct deep time adaptive radiation of non-avian dinosaurs and the phenomenal diversification of birds, via continuing rapid rates of evolution along the phylogenetic stem lineage. This raises the possibility that the uneven distribution of biodiversity results not just from large-scale extrapolation of the process of adaptive radiation in a few extant clades, but also from the maintenance of evolvability on vast time scales across the history of life, in key lineages

Measurement of ionospheric total electron content using single frequency geostationary satellite observations

The ionised upper portion of the atmosphere, the ionosphere, affects radio signals travelling between satellites and the ground. This degrades the performance of satellite navigation, surveillance and communication systems. Techniques to measure and mitigate ionospheric effects and in particular to measure the total electron content, the TEC, are therefore required. TEC is usually determined by analysing the differential delay experienced by dual‐frequency signals. Here, we demonstrate a technique which enables TEC to be derived using single frequency signals passing between geostationary satellites and terrestrial Global Positioning System (GPS) receivers. Geostationary satellites offer the key advantage that the ray‐paths are not moving and hence are easier to interpret than standard GPS TEC. Daily TEC time series are derived for three ground receivers from Europe over the year 2015. The technique is validated by correlation analysis both between pairs of ground receiver observations and between ground receivers and independent ionosonde observations. The correlation between pairs of receivers over a year shows good agreement. Good agreement was also seen between the TEC time series and ionosonde data, suggesting the technique is reliable and routinely produces realistic ionospheric information. The technique is not suitable for use on every GPS receiver type because drift in derived TEC values was observed for profiles calculated using receivers without links to highly stable clocks. The demonstrated technique has the potential to become a routine method to derive TEC, helping to map the ionosphere in real time and to mitigate ionospheric effects on radio systems.<br/