Theropod dinosaur diversity and palaeobiology in the Wealden Group (Early Cretaceous) of England: evidence from a previously undescribed tibia
A robust, partial right tibia of a theropod dinosaur (Natural History Museum London collections, BMNH R9385) is described for the first time. The specimen was collected at Hastings, Sussex (England) in the last century, and is among the oldest known of English Wealden Group theropods. It represents a tetanuran theropod that may have been about 3 m in total length, and is distinct from all currently known Wealden theropods for which tibiae have been described. The present specimen is significant palaeobiologically in exhibiting a series of theropod tooth marks on its caudal surface, indicating predation or scavenging by another theropod.
Magnetostratigraphy of the Lower Cretaceous Vectis Formation (Wealden Group) on the Isle of Wight, Southern England
Magnetostratigraphic results are described from two sections within the Lower Cretaceous Vectis Formation (formerly Wealden Shales) of the Isle of Wight, Southern England. The sections are located at Shepherd's Chine and Yaverland, respectively. In both of these sections a reliably-established reverse polarity magnetozone, herein defined as the Vectis magnetozone, occurs within the Shepherd's Chine Member. This magnetozone has a thickness of some 15 m and its upper boundary is well defined in the Yaverland section but is obscured in the Shepherd's Chine Section due to cliff slumping. The lower boundary is well established in both sections and lies some 15 m above the Barnes High Sandstone Member in the Shepherd's Chine section and 12 m above this unit at Yaverland. This boundary provides a useful chron-stratigraphic datum. A comparison with established geomagnetic polarity timescales for the Cretaceous indicates that the Vectis magnetozone may be correlated either with Lower Aptian reverse polarity Chron CM-0 or with Lower Barremian Chron CM-1, with the former being the more likely. An important implication of this interpretation is that the base of the Aptian stage, as defined from Tethyan foraminiferal zones, must lie within the Vectis Formation, at least 25-30 m beneath the top of the Shepherd's Chine Member, rather than at the top of this member as hitherto commonly accepted. Beds characterized by anomalously high intensities of magnetization, which occur at the base of the Vectis Formation and a few metres above the Barnes High Sandstone in the two sections, are tentatively interpreted as having a volcanogenic origin.
When to Cross the Spread? Trading in Two-Sided Limit Order Books
In this paper the problem of optimal trading in illiquid markets is addressed when the deviations from a given stochastic target function describing, for instance, external aggregate client flow are penalized. Using techniques of singular stochastic control, we extend the results of [F. Naujokat and N. Westray, Math. Financ. Econ., 4 (2011), pp. 299--335] to a two-sided limit order market with temporary market impact and resilience, where the bid ask spread is now also controlled. In addition to using market orders, the trader can also submit orders to a dark pool. We first show existence and uniqueness of an optimal control. In a second step, a suitable version of the stochastic maximum principle is derived which yields a characterization of the optimal trading strategy in terms of a nonstandard coupled forward-backward stochastic differential equation (FBSDE). We show that the optimal control can be characterized via buy, sell, and no-trade regions. The new feature is that we now get a nondegenerate no-...