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

Cloud Classification in Polar and Desert Regions and Smoke Classification from Biomass Burning Using a Hierarchical Neural Network

This research focuses on a new neural network scene classification technique. The task is to identify scene elements in Advanced Very High Resolution Radiometry (AVHRR) data from three scene types: polar, desert and smoke from biomass burning in South America (smoke). The ultimate goal of this research is to design and implement a computer system which will identify the clouds present on a whole-Earth satellite view as a means of tracking global climate changes. Previous research has reported results for rule-based systems (Tovinkere et at 1992, 1993) for standard back propagation (Watters et at. 1993) and for a hierarchical approach (Corwin et al 1994) for polar data. This research uses a hierarchical neural network with don't care conditions and applies this technique to complex scenes. A hierarchical neural network consists of a switching network and a collection of leaf networks. The idea of the hierarchical neural network is that it is a simpler task to classify a certain pattern from a subset of patterns than it is to classify a pattern from the entire set. Therefore, the first task is to cluster the classes into groups. The switching, or decision network, performs an initial classification by selecting a leaf network. The leaf networks contain a reduced set of similar classes, and it is in the various leaf networks that the actual classification takes place. The grouping of classes in the various leaf networks is determined by applying an iterative clustering algorithm. Several clustering algorithms were investigated, but due to the size of the data sets, the exhaustive search algorithms were eliminated. A heuristic approach using a confusion matrix from a lightly trained neural network provided the basis for the clustering algorithm. Once the clusters have been identified, the hierarchical network can be trained. The approach of using don't care nodes results from the difficulty in generating extremely complex surfaces in order to separate one class from all of the others. This approach finds pairwise separating surfaces and forms the more complex separating surface from combinations of simpler surfaces. This technique both reduces training time and improves accuracy over the previously reported results. Accuracies of 97.47%, 95.70%, and 99.05% were achieved for the polar, desert and smoke data sets