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

Actin assembly ruptures the nuclear envelope by prying the lamina away from nuclear pores and nuclear membranes in starfish oocytes.

The nucleus of oocytes (germinal vesicle) is unusually large and its nuclear envelope (NE) is densely packed with nuclear pore complexes (NPCs) stockpiled for embryonic development. We showed that breakdown of this specialized NE is mediated by an Arp2/3-nucleated F-actin 'shell' in starfish oocytes, in contrast to microtubule-driven tearing in mammalian fibroblasts. Here, we address the mechanism of F-actin-driven NE rupture by correlated live-cell, super-resolution and electron microscopy. We show that actin is nucleated within the lamina sprouting filopodia-like spikes towards the nuclear membranes. These F-actin spikes protrude pore-free nuclear membranes, whereas the adjoining membrane stretches accumulate NPCs associated with the still-intact lamina. Packed NPCs sort into a distinct membrane network, while breaks appear in ER-like, pore-free regions. Thereby, we reveal a new function for actin-mediated membrane shaping in nuclear rupture that is likely to have implications in other contexts such as nuclear rupture observed in cancer cells

Recombination-ready Sindbis replicon expression vectors for transgene expression

<p>Abstract</p> <p>Background</p> <p>Sindbis viruses have been widely used as tools to study gene function in cells. Despite the utility of these systems, the construction and production of alphavirus replicons is time consuming and inefficient due to potential additional restriction sites within the insert region and lack of directionality for insert ligation. In this report, we present a system useful for producing recombinant Sindbis replicons that uses lambda phage recombination technology to rapidly and specifically construct replicon expression plasmids that contain insert regions in the desired orientation.</p> <p>Results</p> <p>Recombination of the gene of interest with the replicon plasmid resulted in nearly 100% recombinants, each of which contained a correctly orientated insert. Replicons were easily produced in cell culture and packaged into pseudo-infectious viral particles. Insect and mammalian cells infected with pseudo-infectious viral particles expressed various transgenes at high levels. Finally, inserts from persistently replicating replicon RNA were easily isolated and recombined back into entry plasmids for sequencing and subsequent analysis.</p> <p>Conclusion</p> <p>Replication-ready replicon expression plasmids make the use of alphavirus replicons fast and easy as compared to traditional replicon production methods. This system represents a significant step forward in the utility and ease of use of alphavirus replicons in the study of gene function.</p

What is the benefit of ceilometers for aerosol remote sensing? An answer from EARLINET

With the establishment of ceilometer networks by national weather services, a discussion commenced to which extent these simple backscatter lidars can be used for aerosol research. Though primarily designed for the detection of clouds it was shown that at least observations of the vertical structure of the boundary layer might be possible. However, an assessment of the potential of ceilometers for the quantitative retrieval of aerosol properties is still missing. In this paper we discuss different retrieval methods to derive the aerosol backscatter coefficient beta(p),with special focus on the calibration of the ceilometers. Different options based on forward and backward integration methods are compared with respect to their accuracy and applicability. It is shown that advanced lidar systems such as those being operated in the framework of the European Aerosol Research Lidar Network (EARLINET) are excellent tools for the calibration, and thus beta(p) retrievals based on forward integration can readily be implemented and used for real-time applications. Furthermore, we discuss uncertainties introduced by incomplete overlap, the unknown lidar ratio, and water vapor absorption. The latter is relevant for the very large number of ceilometers operating in the spectral range around lambda = 905-910 nm. The accuracy of the retrieved beta(p) mainly depends on the accuracy of the calibration and the long-term stability of the ceilometer. Under favorable conditions, a relative error of beta(p) on the order of 10% seems feasible. In the case of water vapor absorption, corrections assuming a realistic water vapor distribution and laser spectrum are indispensable;otherwise errors on the order of 20% could occur. From case studies it is shown that ceilometers can be used for the reliable detection of elevated aerosol layers below 5 km, and can contribute to the validation of chemistry transport models, e. g.,the height of the boundary layer. However, the exploitation of ceilometer measurements is still in its infancy, so more studies are urgently needed to consolidate the present state of knowledge, which is based on a limited number of case studies

The Intrinsic Fundamental Group of a Linear Category

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.Comment: Final version, to appear in Algebras and Representation Theor

Our Sun. IV. The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismology provides a powerful tool to explore the deep interior of the Sun: for example, the adiabatic sound speed can be inferred with an accuracy of a few parts in 10,000. This has become a serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of sources of uncertainties in the standard solar model, which must be understood before the helioseismic observations can be used as constraints on theory. We find that the largest uncertainty in the sound speed in the solar interior, namely, 3 parts in 1000, arises from uncertainties in the observed photospheric abundances of the elements; uncertainties of 1 part in 1000 arise from (1) the 4% uncertainty in the OPAL opacities, (2) the 5% uncertainty in the basic pp nuclear reaction rate, (3) the 15% uncertainty in the diffusion constants for the gravitational settling of helium, and (4) the 50% uncertainties in diffusion constants for the heavier elements. (Other investigators have shown that similar uncertainties arise from uncertainties in the interior equation of state and in rotation-induced turbulent mixing.) The predicted pre-main-sequence solar lithium depletion is a factor of order 20 (an order of magnitude larger than that predicted by earlier models that neglected gravitational settling and used older opacities), and is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by 30% for the Cl-37 experiment and by 3% for the Ga-71 experiments (not including uncertainties in the capture cross sections), while the B-8 neutrino flux is uncertain by 30%.Comment: LaTeX, 38 pages (including 8 figures); ApJ, in press. Added figures/color figurea available at http://www.cita.utoronto.ca/~boothroy/sun4.htm

Dust detection by the wave instrument on STEREO: nanoparticles picked up by the solar wind?

The STEREO/WAVES instrument has detected a very large number of intense voltage pulses. We suggest that these events are produced by impact ionisation of nanoparticles striking the spacecraft at a velocity of the order of magnitude of the solar wind speed. Nanoparticles, which are half-way between micron-sized dust and atomic ions, have such a large charge-to-mass ratio that the electric field induced by the solar wind magnetic field accelerates them very efficiently. Since the voltage produced by dust impacts increases very fast with speed, such nanoparticles produce signals as high as do much larger grains of smaller speeds. The flux of 10-nm radius grains inferred in this way is compatible with the interplanetary dust flux model. The present results may represent the first detection of fast nanoparticles in interplanetary space near Earth orbit.Comment: In press in Solar Physics, 13 pages, 5 figure

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

Constraints from deuterium on the formation of icy bodies in the Jovian system and beyond

We consider the role of deuterium as a potential marker of location and ambient conditions during the formation of small bodies in our Solar system. We concentrate in particular on the formation of the regular icy satellites of Jupiter and the other giant planets, but include a discussion of the implications for the Trojan asteroids and the irregular satellites. We examine in detail the formation of regular planetary satellites within the paradigm of a circum-Jovian subnebula. Particular attention is paid to the two extreme potential subnebulae - "hot" and "cold". In particular, we show that, for the case of the "hot" subnebula model, the D:H ratio in water ice measured from the regular satellites would be expected to be near-Solar. In contrast, satellites which formed in a "cold" subnebula would be expected to display a D:H ratio that is distinctly over-Solar. We then compare the results obtained with the enrichment regimes which could be expected for other families of icy small bodies in the outer Solar system - the Trojan asteroids and the irregular satellites. In doing so, we demonstrate how measurements by Laplace, the James Webb Space Telescope, HERSCHEL and ALMA will play an important role in determining the true formation locations and mechanisms of these objects.Comment: Accepted and shortly to appear in Planetary and Space Science; 11 pages with 5 figure