Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

The M Dwarf GJ 436 and its Neptune-Mass Planet

We determine stellar parameters for the M dwarf GJ 436 that hosts a Neptune-mass planet. We employ primarily spectral modeling at low and high resolution, examining the agreement between model and observed optical spectra of five comparison stars of type, M0-M3. Modeling high resolution optical spectra suffers from uncertainties in TiO transitions, affecting the predicted strengths of both atomic and molecular lines in M dwarfs. The determination of Teff, gravity, and metallicity from optical spectra remains at ~10%. As molecules provide opacity both in lines and as an effective continuum, determing molecular transition parameters remains a challenge facing models such as the PHOENIX series, best verified with high resolution and spectrophotometric spectra. Our analysis of GJ 436 yields an effective temperature of Teff = 3350 +/- 300 K and a mass of 0.44 Msun. New Doppler measurements for GJ 436 with a precision of 3 m/s taken during 6 years improve the Keplerian model of the planet, giving a minimum mass, M sin i = 0.0713 Mjup = 22.6 Mearth, period, P = 2.6439 d, and e = 0.16 +/- 0.02. The noncircular orbit contrasts with the tidally circularized orbits of all close-in exoplanets, implying either ongoing pumping of eccentricity by a more distant companion, or a higher Q value for this low-mass planet. The velocities indeed reveal a long term trend, indicating a possible distant companion.Comment: 27 pages, 7 figures, accepted to PAS

Unified View of Scaling Laws for River Networks

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.Comment: 14 pages, 9 figures, 4 tables (converted to Revtex4, PRE ref added

Excitons in a Photosynthetic Light-Harvesting System: A Combined Molecular Dynamics/Quantum Chemistry and Polaron Model Study

The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with a novel approach which combines molecular dynamics (MD) simulations with quantum chemistry (QC) calculations. The MD simulations of an LH-II complex, solvated and embedded in a lipid bilayer at physiological conditions (with total system size of 87,055 atoms) revealed a pathway of a water molecule into the B800 binding site, as well as increased dimerization within the B850 BChl ring, as compared to the dimerization found for the crystal structure. The fluctuations of pigment (B850 BChl) excitation energies, as a function of time, were determined via ab initio QC calculations based on the geometries that emerged from the MD simulations. From the results of these calculations we constructed a time-dependent Hamiltonian of the B850 exciton system from which we determined the linear absorption spectrum. Finally, a polaron model is introduced to describe quantum mechanically both the excitonic and vibrational (phonon) degrees of freedom. The exciton-phonon coupling that enters into the polaron model, and the corresponding phonon spectral function are derived from the MD/QC simulations. It is demonstrated that, in the framework of the polaron model, the absorption spectrum of the B850 excitons can be calculated from the autocorrelation function of the excitation energies of individual BChls, which is readily available from the combined MD/QC simulations. The obtained result is in good agreement with the experimentally measured absorption spectrum.Comment: REVTeX3.1, 23 pages, 13 (EPS) figures included. A high quality PDF file of the paper is available at http://www.ks.uiuc.edu/Publications/Papers/PDF/DAMJ2001/DAMJ2001.pd

Topological self-similarity on the random binary-tree model

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented

Evolution of Plasma Flow Shear and Stability in the ZaP Flow Z-Pinch

Abstract. The stabilizing effect of an axial flow on the m = 1 kink instability in Z-pinches has been studied numerically with a linearized ideal MHD model to reveal that a sheared axial flow stabilizes the kink mode when the shear exceeds a threshold. The sheared flow stabilizing effect is investigated with the ZaP Flow Zpinch experiment. An azimuthal array of surface mounted magnetic probes measures the fluctuation levels of the azimuthal modes m = 1, 2, and 3. After pinch assembly a quiescent period is found where the mode activity is significantly reduced. The quiescent period lasts for over 2000 times the expected instability growth time in a static Z-pinch. Optical images from a fast framing camera, a two-chord HeNe interferometer, and a ruby holographic interferometer indicate a stable, discrete pinch plasma during this time. Multichord Doppler shift measurements of impurity lines show a large, sheared flow during the quiescent period and low, uniform flow profiles during periods of high mode activity. The value of the velocity shear satisfies the theoretical threshold for stability during the quiescent period and does not satisfy the threshold during the high mode activity. Experiments are conducted with varying amounts of injected neutral gas to gain an understanding of the Z-pinch formation and lifetime

Evaluation of 18F-2-deoxy-2-fluoro-glucose positron emission tomography for gastric cancer screening in asymptomatic individuals undergoing endoscopy

18F-2-deoxy-2-fluoro-glucose Positron Emission Tomography (FDG-PET) has been recently proposed as a promising cancer-screening test. However, the validity of FDG-PET in cancer screening has not been evaluated. We investigated the sensitivity of FDG-PET compared with upper gastric endoscopy in gastric cancer screening for asymptomatic individuals. A total of 2861 consecutive subjects (1600 men and 1261 women) who were asymptomatic and who underwent both FDG-PET and upper gastrointestinal endoscopy between 1 February 2004 and 31 January 2005 were included in this study. Both endoscopists and a radiologist were unaware of the results of the other diagnostic tests. The FDG-PET images were examined using criteria determined by the pattern of FDG accumulation. Sensitivity and specificity of FDG-PET were calculated compared with endoscopic diagnosis as the gold standard. Among 2861 subjects enrolled in the study, there were 20 subjects with gastric cancer, of whom 18 were T1 in depth of cancer invasion. Positive FDG-PET results were obtained only in 2 of the 20 cancer subjects. The calculated sensitivity and specificity for overall gastric cancers were 10.0% (95% confidence interval (CI): 1.2–31.7%) and 99.2% (95% CI: 98.8–99.5%), respectively. 18F-2-deoxy-2-fluoro-glucose Positron Emission Tomography was poorly sensitive for detection of gastric cancer in the early stages

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice

Developing an Informatics Tool To Advance Supportive Care: The Veterans Health Care Administration Palliative Care National Clinical Template

BACKGROUND: Increasing emphasis in performance-based payment, public reporting, and quality improvement (QI) has led to widespread interest in measuring and improving the quality of care. By 2014, hospice programs will be required to report quality data to the federal government or incur financial penalties. With this increased interest in quality reporting comes an opportunity to develop informatics tools to capture data that reflect the complex practices involved in palliative care (PC). Therefore, there is a need to disseminate information on developing tools that facilitate capturing data and fostering improved performance. The Veterans Health Care Administration, a national leader in health information technology (HIT) and PC, established the Quality Improvement Resource Center (QuIRC) to develop innovative HIT tools to standardize and improve PC practices throughout the 153 Department of Veterans Affairs (VA) medical centers nationwide. OBJECTIVE: The aim of the paper is to describe the development of the Palliative Care-National Clinical Template (PC-NCT) for documenting initial PC consults. RESULTS: Domains of quality of life provided the foundation for this template. Principles of user-centered informatics design guided development activities. A national consensus panel of PC experts prioritized quality indicators as targets for QI. An interdisciplinary team of PC providers identified desired aspects of template functionality. QuIRC balanced PC providers' desired aspects of functionality against the feasibility within the VA HIT system. Formal pilot and usability testing contributed to numerous iterations of the PC-NCT currently piloted in five geographically distributed sites. CONCLUSION: This paper presents a robust approach to developing an informatics tool for PC practice. Data collected via the PC-NCT will bring variations in current practice into view and assist in directing resources at "important targets" for QI. Although the development of HIT tools to quantify PC practice is complex, there is enormous potential to improve the quality of care for patients and families facing serious illnesses