Meshfree Approximation for Multi-Asset Options

We price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX.Multi-asset options, radial basis function, meshfree approximation, collocation, multidimensional Lévy process, basket options, PIDE, PDE

Four-Hundred-and-Ninety-Million-Year Record of Bacteriogenic Iron Oxide Precipitation at Sea-Floor Hydrothermal Vents

Fe oxide deposits are commonly found at hydrothermal vent sites at mid-ocean ridge and back-arc sea floor spreading centers, seamounts associated with these spreading centers, and intra-plate seamounts, and can cover extensive areas of the seafloor. These deposits can be attributed to several abiogenic processes and commonly contain micron-scale filamentous textures. Some filaments are cylindrical casts of Fe oxyhydroxides formed around bacterial cells and are thus unquestionably biogenic. The filaments have distinctive morphologies very like structures formed by neutrophilic Fe oxidizing bacteria. It is becoming increasingly apparent that Fe oxidizing bacteria have a significant role in the formation of Fe oxide deposits at marine hydrothermal vents. The presence of Fe oxide filaments in Fe oxides is thus of great potential as a biomarker for Fe oxidizing bacteria in modern and ancient marine hydrothermal vent deposits. The ancient analogues of modern deep-sea hydrothermal Fe oxide deposits are jaspers. A number of jaspers, ranging in age from the early Ordovician to late Eocene, contain abundant Fe oxide filamentous textures with a wide variety of morphologies. Some of these filaments are like structures formed by modern Fe oxidizing bacteria. Together with new data from the modern TAG site, we show that there is direct evidence for bacteriogenic Fe oxide precipitation at marine hydrothermal vent sites for at least the last 490 Ma of the Phanerozoic

Pattern separation in the human hippocampus: Novel insights from natural lesion models and sleep-dependent memory consolidation

High demands on cognitive functions in daily life call for an efficient memory system that reduces interference between memories and enables generalizations across similar events. By means of pattern separation, similar memories are stored as distinct, non-overlapping representations, whereas during pattern completion, previously stored memories are reactivated by partial environmental cues. These two functions are critically reliant on the hippocampus. Evidence from computational models, studies in rodents, as well as human data support the idea that pattern separation and completion are mediated by the hippocampal dentate gyrus and CA3 regions. However, studies in humans lack information regarding mechanistic aspects of causality regarding the anatomical structures of the hippocampus and pattern separation and completion processes. The aim of this thesis was to elucidate the role of the human hippocampus and its subfield-specific contributions to pattern separation. We examined natural lesion models, by means of selective CA1 lesions during a transient global amnesia, and in a rare form of limbic encephalitis, where neurodegeneration preferentially shows in the dentate gyrus and CA3. The results showed that pattern separation measured by a mnemonic similarity task was best predicted by the volume of the dentate gyrus, whereas recognition memory was stronger associated with the volume of CA1. We also found a strong deficit in pattern separation associated with selective CA1 lesions. We then examined pattern separation performance after post-encoding sleep in healthy humans to clarify the neurobiological processes of memory consolidation. We demonstrated the relevance of hippocampal information processing during sleep in the stabilization of separated information. This might also suggest a link between pattern separation and completion processes during sleep-dependent memory consolidation.Hohe kognitive Anforderungen im Alltag benötigen ein effizientes Gedächtnissystem. Um zwischen ähnlichen Erlebnissen zu unterscheiden, aber auch Generalisierungen über Ereignisse zu schaffen, bietet das Gedächtnis zwei Funktionen. Erstens werden durch Musterseparation ähnliche Gedächtnisrepräsentationen unabhängig voneinander gespeichert. Zweitens können durch Musterkomplettierung zuvor gespeicherte Ereignisse durch Hinweisreize aus der Umwelt erinnert werden. Die Abhängigkeit dieser Funktionen vom Hippocampus, insbesondere von dessen Subregionen Gyrus Dentatus und CA3, wurde bereits in einer Vielzahl von theoretischen Modellen beschrieben, sowie anhand von Tier- und Humanstudien untersucht. Vergangenen Studien fehlen jedoch bezüglich des menschlichen Hippocampus eine mechanistische Aussage zur Kausalität zwischen Anatomie und Funktion. Zudem ist es bisher unklar, in welcher Weise Musterseparation und -komplettierung im Hinblick auf die Bildung von Langzeitgedächtnis stabilisiert werden können. Diese Arbeit hatte zum Ziel, die Rolle des menschlichen Hippocampus bezüglich der Musterseparation sowie der Gedächtniskonsolidierung zu präzisieren. Hierfür haben wir natürliche Läsionsmodelle des menschlichen Hippocampus, eine selektive Schädigung der CA1-Region bei Patienten mit Transienter Globaler Amnesie sowie eine seltene Form der limbischen Enzephalitis, bei der besonders der Gyrus Dentatus und CA3 betroffen sind, herangezogen. Weiterhin haben wir die Musterseparationsleistung bei gesunden Menschen nach Schlaf untersucht, um neurobiologische Prozesse der Gedächtniskonsolidierung zu erklären. Insgesamt stellt die Arbeit die Bedeutung der einzigartigen Struktur des Hippocampus für die Musterseparation und für die Beschreibung von Struktur-Funktions-Beziehungen in Gedächtnis und Konsolidierung heraus

Fine-Scale Coral Connectivity Pathways in the Florida Reef Tract: Implications for Conservation and Restoration

Connectivity between coral reefs is critical to ensure their resilience and persistence against disturbances. It is driven by ocean currents, which often have very complex patterns within reef systems. Only biophysical models that simulate both the fine-scale details of ocean currents and the life-history traits of larvae transported by these currents can help to estimate connectivity in large reef systems. Here we use the unstructured-mesh coastal ocean model SLIM that locally achieves a spatial resolution of ~100 m, 10 times finer than existing models, over the entire Florida Reef Tract (FRT). It allows us to simulate larval dispersal between the ~1,000 reefs composing the FRT. By using different connectivity measures and clustering methods, we have identified two major connectivity pathways, one originating on the westernmost end of the outer shelf and the other originating on the inner shelf, North of the Lower Keys. We introduce new connectivity indicators, based on the PageRank algorithm, to show that protection efforts should be focused on the most upstream reefs of each pathway, while reefs best suited for restoration are more evenly spread between the Lower and Upper Keys. We identify one particular reef, North of Vaca Key, that is a major stepping stone in the connectivity network. Our results are the first reef-scale connectivity estimates for the entire FRT. Such fine-scale information can provide knowledge-based decision support to allocate conservation and restoration resources optimally

Modelling of epithelial growth, fission and lumen formation during embryonic thyroid development : a combination of computational and experimental approaches

Organogenesis is the phase of embryonic development leading to the formation of fully functional organs. In the case of the thyroid, organogenesis starts from the endoderm and generates a multitude of closely packed independent spherical follicular units surrounded by a dense network of capillaries. Follicular organisation is unique and essential for thyroid function, i.e. thyroid hormone production. Previous in vivo studies showed that, besides their nutritive function, endothelial cells play a central role during thyroid gland morphogenesis. However, the precise mechanisms and biological parameters controlling the transformation of the multi-layered thyroid epithelial primordium into a multitude of single-layered follicles are mostly unknown. Animal studies used to improve understanding of organogenesis are costly and time-consuming, with recognised limitations. Here, we developed and used a 2-D vertex model of thyroid growth, angiogenesis and folliculogenesis, within the open-source Chaste framework. Our in silico model, based on in vivo images, correctly simulates the differential growth and proliferation of central and peripheral epithelial cells, as well as the morphogen-driven migration of endothelial cells, consistently with our experimental data. Our simulations further showed that reduced epithelial cell adhesion was critical to allow endothelial invasion and fission of the multi-layered epithelial mass. Finally, our model also allowed epithelial cell polarisation and follicular lumen formation by endothelial cell abundance and proximity. Our study illustrates how constant discussion between theoretical and experimental approaches can help us to better understand the roles of cellular movement, adhesion and polarisation during thyroid embryonic development. We anticipate that the use of in silico models like the one we describe can push forward the fields of developmental biology and regenerative medicine

Challenges and Prospects in Ocean Circulation Models

We revisit the challenges and prospects for ocean circulation models following Griffies et al. (2010). Over the past decade, ocean circulation models evolved through improved understanding, numerics, spatial discretization, grid configurations, parameterizations, data assimilation, environmental monitoring, and process-level observations and modeling. Important large scale applications over the last decade are simulations of the Southern Ocean, the Meridional Overturning Circulation and its variability, and regional sea level change. Submesoscale variability is now routinely resolved in process models and permitted in a few global models, and submesoscale effects are parameterized in most global models. The scales where nonhydrostatic effects become important are beginning to be resolved in regional and process models. Coupling to sea ice, ice shelves, and high-resolution atmospheric models has stimulated new ideas and driven improvements in numerics. Observations have provided insight into turbulence and mixing around the globe and its consequences are assessed through perturbed physics models. Relatedly, parameterizations of the mixing and overturning processes in boundary layers and the ocean interior have improved. New diagnostics being used for evaluating models alongside present and novel observations are briefly referenced. The overall goal is summarizing new developments in ocean modeling, including: how new and existing observations can be used, what modeling challenges remain, and how simulations can be used to support observations.Peer reviewe