1,065 research outputs found
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
Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal
Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of photon production due to changes in the properties
of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric
bubble. This mechanism can be re-phrased in terms of the Casimir effect and has
recently been the subject of considerable controversy. The present paper probes
Schwinger's suggestion in detail: Using the sudden approximation we calculate
Bogolubov coefficients relating the QED vacuum in the presence of the expanded
bubble to that in the presence of the collapsed bubble. In this way we derive
an estimate for the spectrum and total energy emitted. We verify that in the
sudden approximation there is an efficient production of photons, and further
that the main contribution to this dynamic Casimir effect comes from a volume
term, as per Schwinger's original calculation. However, we also demonstrate
that the timescales required to implement Schwinger's original suggestion are
not physically relevant to sonoluminescence. Although Schwinger was correct in
his assertion that changes in the zero-point energy lead to photon production,
nevertheless his original model is not appropriate for sonoluminescence. In
other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018,
quant-ph/9905034) we have developed a variant of Schwinger's model that is
compatible with the physically required timescales.Comment: 18 pages, ReV_TeX 3.2, 9 figures. Major revisions: This document is
now limited to providing a probe of Schwinger's original suggestion for
sonoluminescence. For details on our own variant of Schwinger's ideas see
quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/990503
Stress Tensor Correlators in the Schwinger-Keldysh Formalism
We express stress tensor correlators using the Schwinger-Keldysh formalism.
The absence of off-diagonal counterterms in this formalism ensures that the +-
and -+ correlators are free of primitive divergences. We use dimensional
regularization in position space to explicitly check this at one loop order for
a massless scalar on a flat space background. We use the same procedure to show
that the ++ correlator contains the divergences first computed by `t Hooft and
Veltman for the scalar contribution to the graviton self-energy.Comment: 14 pages, LaTeX 2epsilon, no figures, revised for publicatio
Sonoluminescence as a QED vacuum effect. I: The Physical Scenario
Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of changes in the properties of the
quantum-electrodynamic (QED) vacuum state. This mechanism is most often phrased
in terms of changes in the Casimir Energy: changes in the distribution of
zero-point energies and has recently been the subject of considerable
controversy. The present paper further develops this quantum-vacuum approach to
sonoluminescence: We calculate Bogolubov coefficients relating the QED vacuum
states in the presence of a homogeneous medium of changing dielectric constant.
In this way we derive an estimate for the spectrum, number of photons, and
total energy emitted. We emphasize the importance of rapid spatio-temporal
changes in refractive indices, and the delicate sensitivity of the emitted
radiation to the precise dependence of the refractive index as a function of
wavenumber, pressure, temperature, and noble gas admixture. Although the
physics of the dynamical Casimir effect is a universal phenomenon of QED,
specific experimental features are encoded in the condensed matter physics
controlling the details of the refractive index. This calculation places rather
tight constraints on the possibility of using the dynamical Casimir effect as
an explanation for sonoluminescence, and we are hopeful that this scenario will
soon be amenable to direct experimental probes. In a companion paper we discuss
the technical complications due to finite-size effects, but for reasons of
clarity in this paper we confine attention to bulk effects.Comment: 25 pages, LaTeX 209, ReV-TeX 3.2, eight figures. Minor revisions:
Typos fixed, references updated, minor changes in numerical estimates, minor
changes in some figure
The basophil activation test differentiates between patients with wheat-dependent exercise-induced anaphylaxis and control subjects using gluten and isolated gluten protein types
Background: Oral food challenge using gluten and cofactors is the gold standard to diagnose wheat-dependent exercise-induced anaphylaxis (WDEIA), but this procedure puts patients at risk of an anaphylactic reaction. Specific IgE to ω5-gliadins as major allergens and skin prick tests to wheat may yield negative results. Thus, we designed a proof-of-principle study to investigate the utility of the basophil activation test (BAT) for WDEIA diagnosis. Methods: Different gluten protein types (GPT; α-, γ-, ω1,2- and ω5-gliadins, high-molecular-weight glutenin subunits [HMW-GS] and low-molecular-weight glutenin subunits [LMW-GS]) and gluten were used in different concentrations to measure basophil activation in 12 challenge-confirmed WDEIA patients and 10 control subjects. The results were compared to routine allergy diagnostics. Parameters analyzed include the percentage of CD63+ basophils, the ratio of %CD63+ basophils induced by GPT/gluten to %CD63+ basophils induced by anti-FcεRI antibody, area under the dose-response curve and test sensitivity and specificity. Results: GPT and gluten induced strong basophil activation for %CD63+ basophils and for %CD63+/anti-FcɛRI ratio in a dose-dependent manner in patients, but not in controls (p < 0.001, respectively). BAT performance differed from acceptable (0.73 for LMW-GS) to excellent (0.91 for ω5-gliadins) depending on the specific GPT as evaluated by the area under the receiver operating characteristic curve. Patients showed individual sensitization profiles. After determination of the best cut-off points, ω5-gliadins and HMW-GS showed the best discrimination between patients and controls with a sensitivity/specificity of 100/70 and 75/100, respectively. Conclusion: This study shows the alternative role of BAT in better defining WDEIA and the causative wheat allergens. The best BAT parameters to distinguish WDEIA patients from controls were %CD63+ basophil values for ω5-gliadins and HMW-GS
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
Diffusion, peer pressure and tailed distributions
We present a general, physically motivated non-linear and non-local advection
equation in which the diffusion of interacting random walkers competes with a
local drift arising from a kind of peer pressure. We show, using a mapping to
an integrable dynamical system, that on varying a parameter, the steady state
behaviour undergoes a transition from the standard diffusive behavior to a
localized stationary state characterized by a tailed distribution. Finally, we
show that recent empirical laws on economic growth can be explained as a
collective phenomenon due to peer pressure interaction.Comment: RevTex: 4 pages + 3 eps-figures. Minor Revision and figure 3
replaced. To appear in Phys. Rev. Letter
Quantum radiation in external background fields
A canonical formalism is presented which allows for investigations of quantum
radiation induced by localized, smooth disturbances of classical background
fields by means of a perturbation theory approach. For massless,
non-selfinteracting quantum fields at zero temperature we demonstrate that the
low-energy part of the spectrum of created particles exhibits a non-thermal
character. Applied to QED in varying dielectrics the response theory approach
facilitates to study two distinct processes contributing to the production of
photons: the squeezing effect due to space-time varying properties of the
medium and of the velocity effect due to its motion. The generalization of this
approach to finite temperatures as well as the relation to sonoluminescence is
indicated.Comment: 20 page
New Spirometry Indices for Detecting Mild Airflow Obstruction.
The diagnosis of chronic obstructive pulmonary disease (COPD) relies on demonstration of airflow obstruction. Traditional spirometric indices miss a number of subjects with respiratory symptoms or structural lung disease on imaging. We hypothesized that utilizing all data points on the expiratory spirometry curves to assess their shape will improve detection of mild airflow obstruction and structural lung disease. We analyzed spirometry data of 8307 participants enrolled in the COPDGene study, and derived metrics of airflow obstruction based on the shape on the volume-time (Parameter D), and flow-volume curves (Transition Point and Transition Distance). We tested associations of these parameters with CT measures of lung disease, respiratory morbidity, and mortality using regression analyses. There were significant correlations between FEV1/FVC with Parameter D (r = -0.83; p < 0.001), Transition Point (r = 0.69; p < 0.001), and Transition Distance (r = 0.50; p < 0.001). All metrics had significant associations with emphysema, small airway disease, dyspnea, and respiratory-quality of life (p < 0.001). The highest quartile for Parameter D was independently associated with all-cause mortality (adjusted HR 3.22,95% CI 2.42-4.27; p < 0.001) but a substantial number of participants in the highest quartile were categorized as GOLD 0 and 1 by traditional criteria (1.8% and 33.7%). Parameter D identified an additional 9.5% of participants with mild or non-recognized disease as abnormal with greater burden of structural lung disease compared with controls. The data points on the flow-volume and volume-time curves can be used to derive indices of airflow obstruction that identify additional subjects with disease who are deemed to be normal by traditional criteria
Quantum radiation in a plane cavity with moving mirrors
We consider the electromagnetic vacuum field inside a perfect plane cavity
with moving mirrors, in the nonrelativistic approximation. We show that low
frequency photons are generated in pairs that satisfy simple properties
associated to the plane geometry. We calculate the photon generation rates for
each polarization as functions of the mechanical frequency by two independent
methods: on one hand from the analysis of the boundary conditions for moving
mirrors and with the aid of Green functions; and on the other hand by an
effective Hamiltonian approach. The angular and frequency spectra are discrete,
and emission rates for each allowed angular direction are obtained. We discuss
the dependence of the generation rates on the cavity length and show that the
effect is enhanced for short cavity lengths. We also compute the dissipative
force on the moving mirrors and show that it is related to the total radiated
energy as predicted by energy conservation.Comment: 17 pages, 1 figure, published in Physical Review
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