Optimal stopping via pathwise dual empirical maximisation

The optimal stopping problem arising in the pricing of American options can be tackled by the so called dual martingale approach. In this approach, a dual problem is formulated over the space of martingales. A feasible solution of the dual problem yields an upper bound for the solution of the original primal problem. In practice, the optimization is performed over a finite-dimensional subspace of martingales. A sample of paths of the underlying stochastic process is produced by a Monte-Carlo simulation, and the expectation is replaced by the empirical mean. As a rule the resulting optimization problem, which can be written as a linear program, yields a martingale such that the variance of the obtained estimator can be large. In order to decrease this variance, a penalizing term can be added to the objective function of the path-wise optimization problem. In this paper, we provide a rigorous analysis of the optimization problems obtained by adding different penalty functions. In particular, a convergence analysis implies that it is better to minimize the empirical maximum instead of the empirical mean. Numerical simulations confirm the variance reduction effect of the new approach

Identifying a gender-inclusive pedagogy from Maltese science teachers' personal practical knowledge

Teachers bring with them into the science classrooms their own gendered identitities and their views and perceptions about how boys and girls learn and achieve in science. This paper tries to explore the way in which fourteen Maltese science teachers use their own 'personal practical knowledge' to identify their views about gender and science and create their own individual gender-inclusive pedagogy. The study suggests that the science teachers focus more on the individuality of students and on the social and cultural background of the students in their classrooms rather than on gender. The teachers try to develop pedagogies and assessment practices which take into consideration the personal constructs of individual learners. The ideas for such a gender-inclusive pedagogy emerge from their common-sense experience in the classroom, their training as teachers and are closely interrelated to current ideas of social constructivism

GluN2B and GluN2D NMDARs dominate synaptic responses in the adult spinal cord

The composition of the postsynaptic ionotropic receptors that receive presynaptically released transmitter is critical not only for transducing and integrating electrical signals but also for coordinating downstream biochemical signaling pathways. At glutamatergic synapses in the adult CNS an overwhelming body of evidence indicates that the NMDA receptor (NMDAR) component of synaptic responses is dominated by NMDARs containing the GluN2A subunit, while NMDARs containing GluN2B, GluN2C, or GluN2D play minor roles in synaptic transmission. Here, we discovered NMDAR-mediated synaptic responses with characteristics not described elsewhere in the adult CNS. We found that GluN2A-containing receptors contribute little to synaptic NMDAR responses while GluN2B dominates at synapses of lamina I neurons in the adult spinal cord. In addition, we provide evidence for a GluN2D-mediated synaptic NMDAR component in adult lamina I neurons. Strikingly, the charge transfer mediated by GluN2D far exceeds that of GluN2A and is comparable to that of GluN2B. Lamina I forms a disti

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277

Consistent patterns of common species across tropical tree communities

Trees structure the Earth’s most biodiverse ecosystem, tropical forests. The vast number of tree species presents a formidable challenge to understanding these forests, including their response to environmental change, as very little is known about most tropical tree species. A focus on the common species may circumvent this challenge. Here we investigate abundance patterns of common tree species using inventory data on 1,003,805 trees with trunk diameters of at least 10 cm across 1,568 locations1,2,3,4,5,6 in closed-canopy, structurally intact old-growth tropical forests in Africa, Amazonia and Southeast Asia. We estimate that 2.2%, 2.2% and 2.3% of species comprise 50% of the tropical trees in these regions, respectively. Extrapolating across all closed-canopy tropical forests, we estimate that just 1,053 species comprise half of Earth’s 800 billion tropical trees with trunk diameters of at least 10 cm. Despite differing biogeographic, climatic and anthropogenic histories7, we find notably consistent patterns of common species and species abundance distributions across the continents. This suggests that fundamental mechanisms of tree community assembly may apply to all tropical forests. Resampling analyses show that the most common species are likely to belong to a manageable list of known species, enabling targeted efforts to understand their ecology. Although they do not detract from the importance of rare species, our results open new opportunities to understand the world’s most diverse forests, including modelling their response to environmental change, by focusing on the common species that constitute the majority of their trees

Insights into the high-energy γ-ray emission of Markarian 501 from extensive multifrequency observations in the Fermi era

We report on the γ-ray activity of the blazar Mrk 501 during the first 480 days of Fermi operation. We find that the average Large Area Telescope (LAT) γ-ray spectrum of Mrk 501 can be well described by a single power-law function with a photon index of 1.78 ± 0.03. While we observe relatively mild flux variations with the Fermi-LAT (within less than a factor of two), we detect remarkable spectral variability where the hardest observed spectral index within the LAT energy range is 1.52 ± 0.14, and the softest one is 2.51 ± 0.20. These unexpected spectral changes do not correlate with the measured flux variations above 0.3 GeV. In this paper, we also present the first results from the 4.5 month long multifrequency campaign (2009 March 15-August 1) on Mrk 501, which included the Very Long Baseline Array (VLBA), Swift, RXTE, MAGIC, and VERITAS, the F-GAMMA, GASP-WEBT, and other collaborations and instruments which provided excellent temporal and energy coverage of the source throughout the entire campaign. The extensive radio to TeV data set from this campaign provides us with the most detailed spectral energy distribution yet collected for this source during its relatively low activity. The average spectral energy distribution of Mrk 501 is well described by the standard one-zone synchrotron self-Compton (SSC) model. In the framework of this model, we find that the dominant emission region is characterized by a size ≲0.1 pc (comparable within a factor of few to the size of the partially resolved VLBA core at 15-43 GHz), and that the total jet power (≃1044 erg s-1) constitutes only a small fraction (∼10-3) of the Eddington luminosity. The energy distribution of the freshly accelerated radiating electrons required to fit the time-averaged data has a broken power-law form in the energy range 0.3 GeV-10 TeV, with spectral indices 2.2 and 2.7 below and above the break energy of 20 GeV. We argue that such a form is consistent with a scenario in which the bulk of the energy dissipation within the dominant emission zone of Mrk 501 is due to relativistic, proton-mediated shocks. We find that the ultrarelativistic electrons and mildly relativistic protons within the blazar zone, if comparable in number, are in approximate energy equipartition, with their energy dominating the jet magnetic field energy by about two orders of magnitude. © 2011. The American Astronomical Society

Exploratory Web Searching with Dynamic Taxonomies and Results Clustering

Abstract. This paper proposes exploiting both explicit and mined metadata for enriching Web searching with exploration services. On-line results clustering is useful for providing users with overviews of the results and thus allowing them to restrict their focus to the desired parts. On the other hand, the various metadata that are available to a WSE (Web Search Engine), e.g. domain/language/date/filetype, are commonly exploited only through the advanced (form-based) search facilities that some WSEs offer (and users rarely use). We propose an approach that combines both kinds of metadata by adopting the interaction paradigm of dynamic taxonomies and faceted exploration. This combination results to an effective, flexible and efficient exploration experience.