A palaeoenvironmental reconstruction of the Middle Jurassic of Sardinia (Italy) based on integrated palaeobotanical, palynological and lithofacies data assessment

During the Jurassic, Sardinia was close to continental Europe. Emerged lands started from a single island forming in time a progressively sinking archipelago. This complex palaeogeographic situation gave origin to a diverse landscape with a variety of habitats. Collection- and literature-based palaeobotanical, palynological and lithofacies studies were carried out on the Genna Selole Formation for palaeoenvironmental interpretations. They evidence a generally warm and humid climate, affected occasionally by drier periods. Several distinct ecosystems can be discerned in this climate, including alluvial fans with braided streams (Laconi-Gadoni lithofacies), paralic swamps and coasts (Nurri-Escalaplano lithofacies), and lagoons and shallow marine environments (Ussassai-Perdasdefogu lithofacies). The non-marine environments were covered by extensive lowland and a reduced coastal and tidally influenced environment. Both the river and the upland/hinterland environments are of limited impact for the reconstruction. The difference between the composition of the palynological and palaeobotanical associations evidence the discrepancies obtained using only one of those proxies. The macroremains reflect the local palaeoenvironments better, although subjected to a transport bias (e.g. missing upland elements and delicate organs), whereas the palynomorphs permit to reconstruct the regional palaeoclimate. Considering that the flora of Sardinia is the southernmost of all Middle Jurassic European floras, this multidisciplinary study increases our understanding of the terrestrial environments during that period of time

Robot Kinematics INDUSTRIAL Classical Geometry Computer Vision GEOMETRY Computer Aided Geometric Design Image Processing Abstract Transforming Spanning Trees and Pseudo-Triangulations ∗

Let TS be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph TS where two members T and T ′ of TS are adjacent if T intersects T ′ only in points of S or in common edges. We prove that the diameter of TS is O(log k), where k denotes the number of convex layers of S. Based on this result, we show that the flip graph PS of pseudo-triangulations of S (where two pseudo-triangulations are adjacent if they differ in exactly one edge – either by replacement or by removal) has a diameter of O(n log k). This sharpens a known O(n log n) bound. Let � PS be the induced subgraph of pointed pseudo-triangulations of PS. We present an example showing that the distance between two nodes in � PS is strictly larger than the distance between the corresponding nodes in PS

Farthest Line Segment Voronoi Diagrams

The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restrictions are placed upon the n input line segments; they are allowed to touch or cross

On the number of plane graphs

We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs is minimized when S is in convex position, and that the same result holds for several relevant subfamilies. In addition we construct a new extremal configuration, the so-called double zig-zag chain. Most noteworthy this example bears Θ ∗ ( √ 72 n) = Θ ∗ (8.4853 n) triangulations and Θ ∗ (41.1889 n) plane graphs (omitting polynomial factors in both cases), improving the previously known best maximizing examples

Matching Edges and Faces in Polygonal Partitions

AbstractWe define general Laman (count) conditions for edges and faces of polygonal partitions in the plane. Several well-known classes, including k-regular partitions, k-angulations, and rank-k pseudo-triangulations, are shown to fulfill such conditions. As an implication, non-trivial perfect matchings exist between the edge sets (or face sets) of two such structures when they live on the same point set. We also describe a link to spanning tree decompositions that applies to quadrangulations and certain pseudo-triangulations