A numerical study of radial basis function based methods for option pricing under one dimension jump-diffusion model

The aim of this paper is to show how option prices in the Jump-diffusion model can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the Ameri- can put and the European vanilla call/put options on dividend-paying stocks in the Merton and Kou Jump-diffusion models. The radial basis function we select is the Cubic Spline. We also propose a simple numerical algorithm for finding a finite computational range of a global integral term in the PIDE so that the accuracy of approximation of the integral can be improved. Moreover, the solution functions of the PIDE are approximated explicitly by RBFs which have exact forms so we can easily compute the global intergal by any kind of numerical quadrature. Finally, we will also show numerically that our scheme is second order accurate in spatial variables in both American and European cases

Microscopic Investigation of Vortex Breakdown in a Dividing T-Junction Flow

3D-printed microfluidic devices offer new ways to study fluid dynamics. We present the first clear visualization of vortex breakdown in a dividing T-junction flow. By individual control of the inflow and two outflows, we decouple the effects of swirl and rate of vorticity decay. We show that even slight outflow imbalances can greatly alter the structure of vortex breakdown, by creating a net pressure difference across the junction. Our results are summarized in a dimensionless phase diagram, which will guide the use of vortex breakdown in T-junctions to achieve specific flow manipulation.Comment: 5 pages, 5 figure

A New Model of Trend Inflation

This paper introduces a new model of trend (or underlying) inflation. In contrast to many earlier approaches, which allow for trend inflation to evolve according to a random walk, ours is a bounded model which ensures that trend inflation is constrained to lie in an interval. The bounds of this interval can either be fixed or estimated from the data. Our model also allows for a time-varying degree of persistence in the transitory component of inflation. The bounds placed on trend inflation mean that standard econometric methods for estimating linear Gaussian state space models cannot be used and we develop a posterior simulation algorithm for estimating the bounded trend inflation model. In an empirical exercise with CPI inflation we find the model to work well, yielding more sensible measures of trend inflation and forecasting better than popular alternatives such as the unobserved components stochastic volatility model.

A Joint Analysis of GPS Displacement and GRACE Geopotential Data for Simultaneous Estimation of Geocenter Motion and Gravitational Field

Gravitational potential data from GRACE are being used to study mass redistribution within and between the atmosphere, hydrosphere, cryosphere, and solid Earth. The GRACE data are made available in a reference frame with its origin at the center of mass of the Earth system (geocenter) while many other geophysical models and data sets refer to a reference frame attached to the Earth's surface. Changes in the offset between these reference frames (geocenter motion) must be accounted for when GRACE data are used to quantify surface mass changes. In this study, we developed a technique for coestimation of geocenter motion and gravitational potential field seamlessly from degree 1 to 90 by simultaneously inverting a set of globallydistributed GPS displacement time series and the temporallyvarying GRACE gravity data. We found that the effect of geocenter motion was evident particularly in the GPS time series of horizontal displacements. Our estimates of geocenter motion are most consistent with the Satellite Laser Ranging (SLR) results within 1 mm in X and Z components and a submillimeter in Y component, when compared to monthly variability averaged over the period of 20032016. The overall magnitude of the degree1 (l = 1) surface mass load is estimated to be ~3 cm in equivalent water height annually migrating southwestward from Europe (DecemberJanuary) to the South Pacific (JuneJuly). Our results also show that dense GPS network data improve water storage recovery in major river basins in the United States and Europe by contributing significantly to the recovery of higherdegree (l ~20) geopotential coefficients

Flagellin induces β-defensin 2 in human colonic ex vivo infection with enterohemorrhagic Escherichia coli

Enterohemorrhagic E. coli (EHEC) is an important foodborne pathogen in the developed world and can cause life-threatening disease particularly in children. EHEC persists in the human gut by adhering intimately to colonic epithelium and forming characteristic attaching/effacing lesions. In this study, we investigated the innate immune response to EHEC infection with particular focus on antimicrobial peptide and protein expression by colonic epithelium. Using a novel human colonic biopsy model and polarized T84 colon carcinoma cells, we found that EHEC infection induced expression of human β-defensin 2 (hBD2), whereas hBD1, hBD3, LL-37 and lysozyme remained unchanged. Infection with specific EHEC deletion mutants demonstrated that this was dependent on flagellin, and apical exposure to purified flagellin was sufficient to stimulate hBD2 and also interleukin (IL)-8 expression ex vivo and in vitro. Flagellin-mediated hBD2 induction was significantly reduced by inhibitors of NF-κB, MAP kinase p38 and JNK but not ERK1/2. Interestingly, IL-8 secretion by polarized T84 cells was vectorial depending on the side of stimulation, and apical exposure to EHEC or flagellin resulted in apical IL-8 release. Our results demonstrate that EHEC only induces a modest immune response in human colonic epithelium characterized by flagellin-dependent induction of hBD2 and low levels of IL-8

Two Approaches to Building Time-Windowed Geometric Data Structures

Given a set of geometric objects each associated with a time value, we wish to determine whether a given property is true for a subset of those objects whose time values fall within a query time window. We call such problems time-windowed decision problems, and they have been the subject of much recent attention, for instance studied by Bokal, Cabello, and Eppstein [SoCG 2015]. In this paper, we present new approaches to this class of problems that are conceptually simpler than Bokal et al.\u27s, and also lead to faster algorithms. For instance, we present algorithms for preprocessing for the time-windowed 2D diameter decision problem in O(n log n) time and the time-windowed 2D convex hull area decision problem in O(n alpha(n) log n) time (where alpha is the inverse Ackermann function), improving Bokal et al.\u27s O(n log^2 n) and O(n log n loglog n) solutions respectively. Our first approach is to reduce time-windowed decision problems to a generalized range successor problem, which we solve using a novel way to search range trees. Our other approach is to use dynamic data structures directly, taking advantage of a new observation that the total number of combinatorial changes to a planar convex hull is near linear for any FIFO update sequence, in which deletions occur in the same order as insertions. We also apply these approaches to obtain the first O(n polylog n) algorithms for the time-windowed 3D diameter decision and 2D orthogonal segment intersection detection problems

Strictly local Union-Find

Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the growth and merger of data structures through nearest-neighbour steps; this naturally suggests the possibility of realising Union-Find using a lattice of very simple processors with strictly nearest-neighbour links. In this way the computational load can be distributed with near-ideal parallelism. Here we build on earlier work to show for the first time that this strict (rather than partial) locality is practical, with a worst-case runtime $\mathcal O(d^3)$ and mean runtime subquadratic in $d$ where $d$ is the surface code distance. A novel parity-calculation scheme is employed, which can also simplify previously proposed architectures. We compare our strictly local realisation with one augmented by long-range links; while the latter is of course faster, we note that local asynchronous logic could largely negate the difference.Comment: 15 pages, 12 figure

Two-dimensional phononic-photonic bandgap optomechanical crystal cavity

We present the fabrication and characterization of an artificial crystal structure formed from a thin-film of silicon which has a full phononic bandgap for microwave X-band phonons and a two-dimensional pseudo-bandgap for near-infrared photons. An engineered defect in the crystal structure is used to localize optical and mechanical resonances in the bandgap of the planar crystal. Two-tone optical spectroscopy is used to characterize the cavity system, showing a large vacuum coupling rate of 220kHz between the fundamental optical cavity resonance at 195THz and a co-localized mechanical resonance at 9.3GHz.Comment: 4 pages, 4 figure

Relationship between Insertion/Deletion (Indel) Frequency of Proteins and Essentiality

Background: In a previous study, we demonstrated that some essential proteins from pathogenicorganisms contained sizable insertions/deletions (indels) when aligned to human proteins of highsequence similarity. Such indels may provide sufficient spatial differences between the pathogenicprotein and human proteins to allow for selective targeting. In one example, an indel difference wastargeted via large scale in-silico screening. This resulted in selective antibodies and smallcompounds which were capable of binding to the deletion-bearing essential pathogen proteinwithout any cross-reactivity to the highly similar human protein. The objective of the current studywas to investigate whether indels were found more frequently in essential than non-essentialproteins.Results: We have investigated three species, Bacillus subtilis, Escherichia coli, and Saccharomycescerevisiae, for which high-quality protein essentiality data is available. Using these data, wedemonstrated with t-test calculations that the mean indel frequencies in essential proteins weregreater than that of non-essential proteins in the three proteomes. The abundance of indels in bothtypes of proteins was also shown to be accurately modeled by the Weibull distribution. However,Receiver Operator Characteristic (ROC) curves showed that indel frequencies alone could not beused as a marker to accurately discriminate between essential and non-essential proteins in thethree proteomes. Finally, we analyzed the protein interaction data available for S. cerevisiae andobserved that indel-bearing proteins were involved in more interactions and had greaterbetweenness values within Protein Interaction Networks (PINs).Conclusion: Overall, our findings demonstrated that indels were not randomly distributed acrossthe studied proteomes and were likely to occur more often in essential proteins and those thatwere highly connected, indicating a possible role of sequence insertions and deletions in theregulation and modification of protein-protein interactions. Such observations will provide newinsights into indel-based drug design using bioinformatics and cheminformatics tools