Holomorphic transforms with application to affine processes

In a rather general setting of It\^o-L\'evy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on these extensions we develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multidimensional affine It\^o-L\'evy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform.Comment: 30 page

Evidence of reduced surface electron-phonon scattering in the conduction band of Bi_{2}Se_{3} by non-equilibrium ARPES

The nature of the Dirac quasiparticles in topological insulators calls for a direct investigation of the electron-phonon scattering at the \emph{surface}. By comparing time-resolved ARPES measurements of the TI Bi_{2}Se_{3} with different probing depths we show that the relaxation dynamics of the electronic temperature of the conduction band is much slower at the surface than in the bulk. This observation suggests that surface phonons are less effective in cooling the electron gas in the conduction band.Comment: 5 pages, 3 figure

Surface diffusion of Au on Si(111): A microscopic study

The direct evolution of submonolayer two-dimensional Au phases on the Si(111)-(7x7) surface was studied in real time using the spectroscopic photoemission and low energy electron microscope located at the synchrotron radiation source ELETTRA. A finite area covered by 1 monolayer (ML) of gold with a steplike transition zone was prepared by evaporation in situ. Subsequent annealing resulted in the spread of the Au layer and the formation of laterally extended Si(111)-(5x1)-Au and Si(111)-(√3x √3)R30°-Au surface reconstructions. At a temperature around 970 K, the boundary of the gold-covered region propagates on the clean Si(111)-(7x7) and exhibits a nonlinear dependence on time. The ordered Si(111)-(5x1)-Au plateau develops a separated front moving with constant velocity. Two values of the Au diffusion coefficients were estimated at a temperature of about 985 K: (1) D7x7=5,2x10-8 cm2 s-1 as the average diffusion coefficient for Au on a clean Si(111)-(7x7) surface in the concentration range from 0.4 ML up to 0.66 ML and (2) D5x1=1.2x10-7 cm2 s-1 as the lower limit for the diffusion of single Au atoms on the Si(111)-(5x1)-Au ordered phase

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

Modulation effect in the differential rate for Supersymmetric Dark Matter detection

The modulation effect in the direct detection of supersymmetric Cold Dark Matter (CDM) particles is investigated. It is shown that, while normally the modulation effect in the total event rate is small, $\leq 5$, in some special cases it becomes much larger. It also becomes more pronounced in the differential event rate. It may thus be exploited to discriminate against background.Comment: 17 LATEX pages, 4 Tables, 4 PostScript Figures included. Phys. Rev. D, to be publishe

Nuclear spin structure in dark matter search: The finite momentum transfer limit

Spin-dependent elastic scattering of weakly interacting massive dark matter particles (WIMP) off nuclei is reviewed. All available, within different nuclear models, structure functions S(q) for finite momentum transfer (q>0) are presented. These functions describe the recoil energy dependence of the differential event rate due to the spin-dependent WIMP-nucleon interactions. This paper, together with the previous paper ``Nuclear spin structure in dark matter search: The zero momentum transfer limit'', completes our review of the nuclear spin structure calculations involved in the problem of direct dark matter search.Comment: 39 pages, 12 figures, a review in revtex

Effects of CP Violation on Event Rates in the Direct Detection of Dark Matter

A full analytic analysis of the effects of CP violating phases on the event rates in the direct detection of dark matter in the scattering of neutralinos from nuclear targets is given. The analysis includes CP violating phases in softly broken supersymmetry in the framework of the minimal supersymmetric standard model (MSSM) when generational mixings are ignored. A numerical analysis shows that large CP violating phases including the constraints from the experimental limits on the neutron and the electron electric dipole moment (EDM) can produce substantial effects on the event rates in dark matter detectors.Comment: 17 pages, LaTex, including 2 figures; revised version to appear in the Physical Review

Observational Study Design in Veterinary Pathology, Part 2: Methodology

Observational studies are a basis for much of our knowledge of veterinary pathology, yet considerations for conducting pathology-based observational studies are not readily available. In part 1 of this series, we offered advice on planning and carrying out an observational study. Part 2 of the series focuses on methodology. Our general recommendations are to consider using already-validated methods, published guidelines, data from primary sources, and quantitative analyses. We discuss 3 common methods in pathology research—histopathologic scoring, immunohistochemistry, and polymerase chain reaction—to illustrate principles of method validation. Some aspects of quality control include use of clear objective grading criteria, validation of key reagents, assessing sample quality, determining specificity and sensitivity, use of technical and biologic negative and positive controls, blinding of investigators, approaches to minimizing operator-dependent variation, measuring technical variation, and consistency in analysis of the different study groups. We close by discussing approaches to increasing the rigor of observational studies by corroborating results with complementary methods, using sufficiently large numbers of study subjects, consideration of the data in light of similar published studies, replicating the results in a second study population, and critical analysis of the study findings

SEARCHING FOR COLD DARK MATTER

The differential cross-section for the elastic scattering of the lightest supersymmetric particle (LSP) with nuclear targets is calculated in the context of currently fashionable supersymmetric theories (SUSY). An effective four fermion interaction is constructed by considering i) $Z^0$ exchange ii)s-quark exchange and iii) Higgs exchange. It is expressed in terms of the form factors $f^0_V,f^0_A, f^0_S$ (isoscalar) and $f^1_V,f^1_A$ and $f^1_S$ (isovector) which contain all the information of the underlining theory. Numerical values were obtained using representative input parameters in the constrained parameter space of SUSY phenomenology. Both the coherent and for odd-A nuclei the incoherent (spin) nuclear matrix elements were evaluated for nuclei of experimental interest. The spin matrix elements tend to dominate for odd nuclei but the coherent matrix elements become more important in all other cases. For the coherent part the Higgs contribution competes with the Z- and s-quark contributions. Cross-sections as high as $10^{-37} cm^2$ have been obtained.Comment: Latex file, 25 pages , 2 figures (available by fax

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page