Explicit generating functional for pions and virtual photons

We construct the explicit one-loop functional of chiral perturbation theory for two light flavours, including virtual photons. We stick to contributions where 1 or 2 mesons and at most one photon are running in the loops. With the explicit functional at hand, the evaluation of the relevant Green functions boils down to performing traces over the flavour matrices. For illustration, we work out the pi+ pi- -> pi0 pi0 scattering amplitude at threshold at order p^4, e^2p^2.Comment: 20 pages, 2 figures; version accepted for publication, minor typographical changes, acknowledgments adde

Discovery of a Small Central Disk of CO and HI in the Merger Remnant NGC 34

We present CO(1-0) and HI(21-cm) observations of the central region of the wet merger remnant NGC 34. The Combined Array for Research in Millimeter-wave Astronomy (CARMA) observations detect a regularly rotating disk in CO with a diameter of 2.1 kpc and a total molecular hydrogen mass of ($2.1 \pm 0.2) \times10^9~M_\odot$. The rotation curve of this gas disk rises steeply, reaching maximum velocities at 1" (410 pc) from the center. Interestingly, HI observations done with the Karl G. Jansky Very Large Array show that the absorption against the central continuum has the exact same velocity range as the CO in emission. This strongly suggests that the absorbing HI also lies within 1" from the center, is mixed in and corotates with the molecular gas. A comparison of HI absorption profiles taken at different resolutions (5"-45") shows that the spectra at lower resolutions are less deep at the systemic velocity. This provides evidence for HI emission in the larger beams, covering the region from 1 kpc to 9 kpc from the center. The central rapidly rotating disk was likely formed either during the merger or from fall-back material. Lastly, the radio continuum flux of the central source at mm wavelengths ($5.4\pm1.8$ mJy) is significantly higher than expected from an extrapolation of the synchrotron spectrum, indicating the contribution of thermal free-free emission from the central starburst.Comment: Accepted for publication in A

Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading

It is widely acknowledge that there has been a major breakthrough in the mathematical theory of option trading. This breakthrough, which is usually summarized by the Black-Scholes formula, has generated a lot of excitement and a certain mystique. On the mathematical side, it involves advanced probabilistic techniques from martingale theory and stochastic calculus which are accessible only to a small group of experts with a high degree of mathematical sophistication; hence the mystique. In its practical implications it offers exciting prospects. Its promise is that, by a suitable choice of a trading strategy, the risk involved in handling an option can be eliminated completely. Since October 1987, the mood has become more sober. But there are also mathematical reasons which suggest that expectations should be lowered. This will be the main point of the present expository account. We argue that, typically, the risk involved in handling an option has an irreducible intrinsic part. This intrinsic risk may be much smaller than the a priori risk, but in general one should not expect it to vanish completely. In this more sober perspective, the mathematical technique behind the Black-Scholes formula does not lose any of its importance. In fact, it should be seen as a sequential regression scheme whose purpose is to reduce the a priori risk to its intrinsic core. We begin with a short introduction to the Black-Scholes formula in terms of currency options. Then we develop a general regression scheme in discrete time, first in an elementary two-period model, and then in a multiperiod model which involves martingale considerations and sets the stage for extensions to continuous time. Our method is based on the interpretation and extension of the Black-Scholes formula in terms of martingale theory. This was initiated by Kreps and Harrison; see, e.g. the excellent survey of Harrison and Pliska (1981,1983). The idea of embedding the Black-Scholes approach into a sequential regression scheme goes back to joint work of the first author with D. Sondermann. In continuous time and under martingale assumptions, this was worked out in Schweizer (1984) and Föllmer and Sondermann (1986). Schweizer (1988) deals with these problems in a general semimartingale mode

Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading

It is widely acknowledge that there has been a major breakthrough in the mathematical theory of option trading. This breakthrough, which is usually summarized by the Black-Scholes formula, has generated a lot of excitement and a certain mystique. On the mathematical side, it involves advanced probabilistic techniques from martingale theory and stochastic calculus which are accessible only to a small group of experts with a high degree of mathematical sophistication; hence the mystique. In its practical implications it offers exciting prospects. Its promise is that, by a suitable choice of a trading strategy, the risk involved in handling an option can be eliminated completely. Since October 1987, the mood has become more sober. But there are also mathematical reasons which suggest that expectations should be lowered. This will be the main point of the present expository account. We argue that, typically, the risk involved in handling an option has an irreducible intrinsic part. This intrinsic risk may be much smaller than the a priori risk, but in general one should not expect it to vanish completely. In this more sober perspective, the mathematical technique behind the Black-Scholes formula does not lose any of its importance. In fact, it should be seen as a sequential regression scheme whose purpose is to reduce the a priori risk to its intrinsic core. We begin with a short introduction to the Black-Scholes formula in terms of currency options. Then we develop a general regression scheme in discrete time, first in an elementary two-period model, and then in a multiperiod model which involves martingale considerations and sets the stage for extensions to continuous time. Our method is based on the interpretation and extension of the Black-Scholes formula in terms of martingale theory. This was initiated by Kreps and Harrison; see, e.g. the excellent survey of Harrison and Pliska (1981,1983). The idea of embedding the Black-Scholes approach into a sequential regression scheme goes back to joint work of the first author with D. Sondermann. In continuous time and under martingale assumptions, this was worked out in Schweizer (1984) and Föllmer and Sondermann (1986). Schweizer (1988) deals with these problems in a general semimartingale mode

Inter-molecular structure factors of macromolecules in solution: integral equation results

The inter-molecular structure of semidilute polymer solutions is studied theoretically. The low density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of random phase (RPA) like structure are derived for the inter-molecular structure factor on large distances when inter-molecular excluded volume is incorporated at the microscopic level. This leads to a non-linear equation for the excluded volume interaction parameter. For macromolecular size-mass scaling exponents, $\nu$, above a spatial-dimension dependent value, $\nu_c=2/d$, mean field like density scaling is recovered, but for $\nu<\nu_c$ the density scaling becomes non-trivial in agreement with field theoretic results and justifying phenomenological extensions of RPA. The structure of the polymer mesh in semidilute solutions is discussed in detail and comparisons with large scale Monte Carlo simulations are added. Finally a new possibility to determine the correction to scaling exponent $\omega_{12}$ is suggested.Comment: 11 pages, 5 figures; to be published in Phys. Rev. E (1999

Arabidopsis glucosinolates trigger a contrasting transcriptomic response in a generalist and a specialist herbivore.

Phytophagous insects have to deal with toxic defense compounds from their host plants. Although it is known that insects have evolved genes and mechanisms to detoxify plant allochemicals, how specialist and generalist precisely respond to specific secondary metabolites at the molecular level is less understood. Here we studied the larval performance and transcriptome of the generalist moth Heliothis virescens and the specialist butterfly Pieris brassicae feeding on Arabidopsis thaliana genotypes with different glucosinolate (GS) levels. H. virescens larvae gained significantly more weight on the GS-deficient mutant quadGS compared to wild-type (Col-0) plants. On the contrary, P. brassicae was unaffected by the presence of GS and performed equally well on both genotypes. Strikingly, there was a considerable differential gene expression in H. virescens larvae feeding on Col-0 compared to quadGS. In contrast, compared to H. virescens, P. brassicae displayed a much-reduced transcriptional activation when fed on both plant genotypes. Transcripts coding for putative detoxification enzymes were significantly upregulated in H. virescens, along with digestive enzymes and transposable elements. These data provide an unprecedented view on transcriptional changes that are specifically activated by GS and illustrate differential molecular responses that are linked to adaptation to diet in lepidopteran herbivores