Fractional smoothness and applications in finance

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.Comment: Chapter of AMAMEF book. 20 pages

Charmonium Suppression with cc~ Dissociation by Strings

We study the production of cc~ pairs in nuclear reactions at SPS energies within the covariant transport approach HSD. The production of cc~ is treated perturbatively employing experimental cross sections while the interactions of cc~ pairs with baryons are included by conventional cascade-type two-body collisions. Adopting 6 mb for the cc~-baryon cross sections the data on J/\Psi suppression in p+A reactions are reproduced in line with calculations based on the Glauber model. Additionally the dissociation of the cc~ pairs by strings is included in a purely geometrical way. We find good agreement with experimental data from the NA38 and NA50 collaboration with an estimate for the string radius of ~0.2-0.3 fm.Comment: 9 pages (LaTeX), 5 PS figure

Can Galactic Cosmic Rays Account for Solar 6Li Without Overproducing Gamma Rays?

Cosmic-ray interactions with interstellar gas produces both 6Li, which accumulates in the interstellar medium (ISM), and $\pi^0$ mesons, which decay to gamma-rays which propagate throughout the cosmos. Local 6Li abundances and extragalactic gamma-rays thus have a common origin which tightly links them. We exploit this connection to use gamma-ray observations to infer the contribution to 6Li nucleosynthesis by standard Galactic cosmic-ray (GCR) interactions with the ISM. Our calculation uses a carefully propagated cosmic-ray spectrum and accounts for 6Li production from both fusion reactions ($\alpha \alpha \to ^6Li$) as well as from spallation channels ({p,\alpha+CNO \to ^6Li). We find that although extreme assumptions yield a consistent picture, more realistic ones indicate that solar 6Li cannot be produced by standard GCRs alone without overproducing the hadronic gamma rays. Implications for the primordial 6Li production by decaying dark matter and cosmic rays from cosmological structure formation are discussed. Upcoming gamma-ray observations by GLAST will be crucial for determining the resolution of this problem.Comment: 4 pages, 1 figure To be published in ApJ

Cluster structures on quantum coordinate rings

We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematic

Suppression of RNA interference increases alphavirus replication and virus-associated mortality in Aedes aegypti mosquitoes

<p>Abstract</p> <p>Background</p> <p>Arthropod-borne viruses (arboviruses) can persistently infect and cause limited damage to mosquito vectors. RNA interference (RNAi) is a mosquito antiviral response important in restricting RNA virus replication and has been shown to be active against some arboviruses. The goal of this study was to use a recombinant Sindbis virus (SINV; family <it>Togaviridae</it>; genus <it>Alphavirus</it>) that expresses B2 protein of Flock House virus (FHV; family <it>Nodaviridae</it>; genus <it>Alphanodavirus</it>), a protein that inhibits RNAi, to determine the effects of linking arbovirus infection with RNAi inhibition.</p> <p>Results</p> <p>B2 protein expression from SINV (TE/3'2J) inhibited the accumulation of non-specific small RNAs in <it>Aedes aegypti </it>mosquito cell culture and virus-specific small RNAs both in infected cell culture and <it>Ae. aegypti </it>mosquitoes. More viral genomic and subgenomic RNA accumulated in cells and mosquitoes infected with TE/3'2J virus expressing B2 (TE/3'2J/B2) compared to TE/3'2J and TE/3'2J virus expressing GFP. TE/3'2J/B2 exhibited increased infection rates, dissemination rates, and infectious virus titers in mosquitoes following oral bloodmeal. Following infectious oral bloodmeal, significantly more mosquitoes died when TE/3'2J/B2 was ingested. The virus was 100% lethal following intrathoracic inoculation of multiple mosquito species and lethality was dose-dependent in <it>Ae. aegypti</it>.</p> <p>Conclusion</p> <p>We show that RNAi is active in <it>Ae. aegypti </it>cell culture and that B2 protein inhibits RNAi in mosquito cells when expressed by a recombinant SINV. Also, SINV more efficiently replicates in mosquito cells when RNAi is inhibited. Finally, TE/3'2J/B2 kills mosquitoes in a dose-dependent manner independent of infection route and mosquito species.</p

IMAPS Observations of Interstellar Neutral Argon and the Implications for Partially Ionized Gas

We use the absorption features from neutral argon at 1048 and 1066 A to determine interstellar abundances or their lower limits toward nine early-type stars. These features were observed with the Interstellar Medium Absorption Profile Spectrograph (IMAPS) along sight lines with low reddening and low fractional abundances of molecular hydrogen. We find that the interstellar Ar I is below its solar and B-star abundance with respect to hydrogen toward zeta Pup, gamma2 Vel and beta Cen A with (logarithmic) reduction factors -0.37+/-0.09, -0.18+/-0.10, and -0.61+/-0.12 dex, respectively. While Ar can condense onto the surfaces of dust grains in the interiors of dense clouds, it is unlikely that argon atoms are depleted by this process in the low-density lines of sight considered in this study. Instead, we propose that the relatively large photoionization cross section of Ar makes it much easier to hide in its ionized form than H. In regions that are about half ionized, this effect can lower Ar I/H I by -0.11 to -0.96 dex, depending on the energy of the photoionizing radiation and its intensity divided by the local electron density. We apply this interpretation for the condition of the gas in front of beta Cen A, which shows the largest deficiency of Ar. Also, we determine the expected magnitudes of the differential ionizations for He, N, O, Ne and Ar in the partly ionized, warm gas in the local cloud around our solar system. For the local cloud and others that can be probed by UV studies, the observed Ar I to H I ratio may be a good discriminant between two possible alternatives, collisional ionization or photoionization, for explaining the existence of partly ionized regions.Comment: 36 pages, 3 figure

Dust in the Local Interstellar Wind

The gas-to-dust mass ratios found for interstellar dust within the Solar System, versus values determined astronomically for the cloud around the Solar System, suggest that large and small interstellar grains have separate histories, and that large interstellar grains preferentially detected by spacecraft are not formed exclusively by mass exchange with nearby interstellar gas. Observations by the Ulysses and Galileo satellites of the mass spectrum and flux rate of interstellar dust within the heliosphere are combined with information about the density, composition, and relative flow speed and direction of interstellar gas in the cloud surrounding the solar system to derive an in situ value for the gas-to-dust mass ratio, $R_{g/d} = 94^{+46}_{-38}$. Hubble observations of the cloud surrounding the solar system yield a gas-to-dust mass ratio of Rg/d=551+61-251 when B-star reference abundances are assumed. The exclusion of small dust grains from the heliosheath and heliosphere regions are modeled, increasing the discrepancy between interstellar and in situ observations. The shock destruction of interstellar grains is considered, and comparisons are made with interplanetary and presolar dust grains.Comment: 87 pages, 9 figures, 6 tables, accepted for publication in Astrophysical Journal. Uses AASTe

On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples

We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function can be non convex and needs not to satisfy global Lipschitz conditions in the jump integrand. We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a-priori $L^{\infty}$-bounds. Several examples and counter examples are discussed to shed light on the scope and applicability of different assumptions, and we provide an overview of major applications in finance and optimal control.Comment: 28 pages. Added DOI https://link.springer.com/chapter/10.1007%2F978-3-030-22285-7_1 for final publication, corrected typo (missing gamma) in example 4.1

Origin and evolution of the light nuclides

After a short historical (and highly subjective) introduction to the field, I discuss our current understanding of the origin and evolution of the light nuclides D, He-3, He-4, Li-6, Li-7, Be-9, B-10 and B-11. Despite considerable observational and theoretical progress, important uncertainties still persist for each and every one of those nuclides. The present-day abundance of D in the local interstellar medium is currently uncertain, making it difficult to infer the recent chemical evolution of the solar neighborhood. To account for the observed quasi-constancy of He-3 abundance from the Big Bang to our days, the stellar production of that nuclide must be negligible; however, the scarce observations of its abundance in planetary nebulae seem to contradict this idea. The observed Be and B evolution as primaries suggests that the source composition of cosmic rays has remained quasi-constant since the early days of the Galaxy, a suggestion with far reaching implications for the origin of cosmic rays; however, the main idea proposed to account for that constancy, namely that superbubbles are at the source of cosmic rays, encounters some serious difficulties. The best explanation for the mismatch between primordial Li and the observed "Spite-plateau" in halo stars appears to be depletion of Li in stellar envelopes, by some yet poorly understood mechanism. But this explanation impacts on the level of the recently discovered early ``Li-6 plateau'', which (if confirmed), seriously challenges current ideas of cosmic ray nucleosynthesis.Comment: 18 pages, 9 figs. Invited Review in "Symposium on the Composition of Matter", honoring Johannes Geiss on the occasion of his 80th birthday (Grindelwald, Switzerland, Sept. 2006), to be published in Space Science Series of ISS

Baryon stopping and strange baryon/antibaryon production at SPS energies

The amount of proton stopping in central Pb+Pb collisions from 20-160 AGeV as well as hyperon and antihyperon rapidity distributions are calculated within the UrQMD model in comparison to experimental data at 40, 80 and 160 AGeV taken recently from the NA49 collaboration. Furthermore, the amount of baryon stopping at 160 AGeV for Pb+Pb collisions is studied as a function of centrality in comparison to the NA49 data. We find that the strange baryon yield is reasonably described for central collisions, however, the rapidity distributions are somewhat more narrow than the data. Moreover, the experimental antihyperon rapidity distributions at 40, 80 and 160 AGeV are underestimated by up to factors of 3 - depending on the annihilation cross section employed - which might be addressed to missing multi-meson fusion channels in the UrQMD model.Comment: 18 pages, including 7 eps figures, to be published in Phys. Rev.