Stochastic methods for solving high-dimensional partial differential equations

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms

Automatic Generation of Cognitive Theories using Genetic Programming

Cognitive neuroscience is the branch of neuroscience that studies the neural mechanisms underpinning cognition and develops theories explaining them. Within cognitive neuroscience, computational neuroscience focuses on modeling behavior, using theories expressed as computer programs. Up to now, computational theories have been formulated by neuroscientists. In this paper, we present a new approach to theory development in neuroscience: the automatic generation and testing of cognitive theories using genetic programming. Our approach evolves from experimental data cognitive theories that explain “the mental program” that subjects use to solve a specific task. As an example, we have focused on a typical neuroscience experiment, the delayed-match-to-sample (DMTS) task. The main goal of our approach is to develop a tool that neuroscientists can use to develop better cognitive theories

Community structure detection in the evolution of the United States airport network

This is the post-print version of the Article. Copyright © 2013 World Scientific PublishingThis paper investigates community structure in the US Airport Network as it evolved from 1990 to 2010 by looking at six bi-monthly intervals in 1990, 2000 and 2010, using data obtained from the Bureau of Transportation Statistics of the US Department of Transport. The data contained monthly records of origin-destination pairs of domestic airports and the number of passengers carried. The topological properties and the volume of people traveling are both studied in detail, revealing high heterogeneity in space and time. A recently developed community structure detection method, accounting for the spatial nature of these networks, is applied and reveals a picture of the communities within. The patterns of communities plotted for each bi-monthly interval reveal some interesting seasonal variations of passenger flows and airport clusters that do not occupy a single US region. The long-term evolution of the network between those years is explored and found to have consistently improved its stability. The more recent structure of the network (2010) is compared with migration patterns among the four US macro-regions (West, Midwest, Northeast and South) in order to identify possible relationships and the results highlight a clear overlap between US domestic air travel and migration

Cognitive modelling of language acquisition with complex networks

ABSTRACT Cognitive modelling is a well-established computational intelligence tool, which is very useful for studying cognitive phenomena, such as young children's first language acquisition. Specifically, linguistic modelling has recently benefited greatly from complex network theory by modelling large sets of empirical linguistic data as complex networks, thereby illuminating interesting new patterns and trends. In this chapter, we show how simple network analysis techniques can be applied to the study of language acquisition, and we argue that they reveal otherwise hidden information. We also note that a key network parameter -the ranked frequency distribution of the links -provides useful knowledge about the data, even though it had been previously neglected in this domain

Fractional smoothness and applications in finance

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.Comment: Chapter of AMAMEF book. 20 pages

Conservative management of significant epidural haematomas in children

Objective: A significant epidural haematoma (EDH) is generally treated by craniotomy and evacuation. This is a report of conservative management following an EDH on computerized tomography (CT) in a paediatric population. The authors examined whether conservative treatment of radiologically significant EDH is a successful and safe therapeutic option. Methods: Retrospective data were collected from charts of patients with conservatively treated EDH in the Department of Surgery of the University Children's Hospital Zurich between September 1993 and January 2004. Included were patients without focal neurological deficits, with a Glasgow Coma Scale (GCS) of 15 and an initial CT demonstrating an EDH with a minimal thickness of 1cm. Mild clinical symptoms of raised intracranial pressure such as headache, nausea or vomiting were treated symptomatically. Follow-up included a standardized interview, a neuropaediatric examination and CT. Results: Thirteen children with EDH had successful conservative management. Only one 12-year-old female patient with a delayed diagnosed frontal EDH required surgical intervention 24h after admission and 5 days after the accident. Clinical follow-up showed patients without neurological deficits, a Glasgow Outcome Scale of 5 and no post-traumatic sequelae over an average of 4 4/12 years (range 4 months to 10 4/12 years). Follow-up CT showed complete resolution of the EDH within 2 to 3 months. Conclusions: Our results demonstrate that significant EDH can be treated non-operatively in neurologically normal children. We recommend that such treatment be performed in specialised paediatric centres under adequate neurological observation since prompt emergency operation in case of neurological deterioration should be provide

Middle to Late Holocene vegetation history of the Upper Engadine (Swiss Alps): the role of man and fire

To reconstruct the vegetation and fire history of the Upper Engadine, two continuous sediment cores from Lej da Champfèr and Lej da San Murezzan (Upper Engadine Valley, southeastern Switzerland) were analysed for pollen, plant macrofossils, charcoal and kerogen. The chronologies of the cores are based on 38 radiocarbon dates. Pollen and macrofossil data suggest a rapid afforestation with Betula, Pinus sylvestris, Pinus cembra, and Larix decidua after the retreat of the glaciers from the lake catchments 11,000cal years ago. This vegetation type persisted until ca. 7300cal b.p. (5350b.c.) when Picea replaced Pinus cembra. Pollen indicative of human impact suggests that in this high-mountain region of the central Alps strong anthropogenic activities began during the Early Bronze Age (3900cal b.p., 1950b.c.). Local human settlements led to vegetational changes, promoting the expansion of Larix decidua and Alnus viridis. In the case of Larix, continuing land use and especially grazing after fire led to the formation of Larix meadows. The expansion of Alnus viridis was directly induced by fire, as evidenced by time-series analysis. Subsequently, the process of forest conversion into open landscapes continued for millennia and reached its maximum at the end of the Middle Ages at around 500cal b.p. (a.d.1450

Influence of human impact and bedrock differences on the vegetational history of the Insubrian Southern Alps

Vegetation history for the study region is reconstructed on the basis of pollen, charcoal and AMS14C investigations of lake sediments from Lago del Segrino (calcareous bedrock) and Lago di Muzzano (siliceous bedrock). Late-glacial forests were characterised byBetula andPinus sylvestris. At the beginning of the Holocene they were replaced by temperate continental forest and shrub communities. A special type of temperate lowland forest, withAbies alba as the most important tree, was present in the period 8300 to 4500 B.P. Subsequently,Fagus, Quercus andAlnus glutinosa were the main forest components andA. alba ceased to be of importance.Castanea sativa andJuglans regia were probably introduced after forest clearance by fire during the first century A.D. On soils derived from siliceous bedrock,C. sativa was already dominant at ca. A.D. 200 (A.D. dates are in calendar years). In limestone areas, however,C. sativa failed to achieve a dominant role. After the introduction ofC. sativa, the main trees were initially oak (Quercus spp.) and later the walnut (Juglans regia). Ostrya carpinifolia became the dominant tree around Lago del Segrino only in the last 100-200 years though it had spread into the area at ca. 5000 cal. B.C. This recent expansion ofOstrya is confirmed at other sites and appears to be controlled by human disturbances involving especially clearance. It is argued that these forests should not be regarded as climax communities. It is suggested that under undisturbed succession they would develop into mixed deciduous forests consisting ofFraxinus excelsior, Tilia, Ulmus, Quercus andAce

Surgical treatment versus medical treatment in hypertrophic obstructive cardiomyopathy

Sixty-three patients operated upon for HOCM and 49 patients selected for non-surgical treatment have been followed-up for 15 years. Pre-operatively, surgical patients had a higher left ventricular outflow tract gradient at rest and, on the average, more severe symptoms than non-surgical patients. Septal myectomy relieved the pressure gradient and symptoms more consistently than long-term treatment with β-blockers or verapamil. Within an average observation time of 7½ years, there was late deterioration or death in almost half of the non-surgical patients but in less than one-quarter in the operated patients. The 10 year mortality rate was 80% in the surgical series and 71% in the non-surgical series. In operated patients, pre-operative symptomatic status was significantly related to early and late mortality. In medically treated patients, mortality was unrelated to symptoms; however, it was significantly lower in patients receiving long term treatment with β-blockers or verapamil. In conclusion, a high basal pressure gradient associated to limiting symptoms is a clear-cut indication for surgery. Other indications are more debatable. In medically treated patients, long-term administration of β-blockers or verapamil is beneficial even without symptoms as it appears to improve prognosi

The Euler-Maruyama approximation for the absorption time of the CEV diffusion

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme