The evaluation of discrete barrier options in a path integral framework

The pricing of discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. A path integral approach to the evaluation of barrier options is developed. This leads to a backward recursion functional equation linking the pricing functions at successive barrier points. This functional equation is solved by expanding the pricing functions in Fourier-Hermite series. The backward recursion functional equation then becomes the backward recurrence relation for the coefficients in the Fourier-Hermite expansion of the pricing functions. A very efficient and accurate method for generating the pricing function at any barrier point is thus obtained. A number of numerical experiments with the method are performed in order to gain some understanding of the nature of convergence. Results for various volatility values and different numbers of basis functions in the Fourier-Hermite expansion are presented. Comparisons are given between pricing of discrete barrier option in the path integral framework and by use of finite difference methods

Open questions on prominences from coordinated observations by IRIS, Hinode, SDO/AIA, THEMIS, and the Meudon/MSDP

Context. A large prominence was observed on September 24, 2013, for three hours (12:12 UT -15:12 UT) with the newly launched (June 2013) Interface Region Imaging Spectrograph (IRIS), THEMIS (Tenerife), the Hinode Solar Optical Telescope (SOT), the Solar Dynamic Observatory Atmospheric Imaging Assembly (SDO/AIA), and the Multichannel Subtractive Double Pass spectrograph (MSDP) in the Meudon Solar Tower. Aims. The aim of this work is to study the dynamics of the prominence fine structures in multiple wavelengths to understand their formation. Methods. The spectrographs IRIS and MSDP provided line profiles with a high cadence in Mg II and in Halpha lines. Results. The magnetic field is found to be globally horizontal with a relatively weak field strength (8-15 Gauss). The Ca II movie reveals turbulent-like motion that is not organized in specific parts of the prominence. On the other hand, the Mg II line profiles show multiple peaks well separated in wavelength. Each peak corresponds to a Gaussian profile, and not to a reversed profile as was expected by the present non-LTE radiative transfer modeling. Conclusions. Turbulent fields on top of the macroscopic horizontal component of the magnetic field supporting the prominence give rise to the complex dynamics of the plasma. The plasma with the high velocities (70 km/s to 100 km/s if we take into account the transverse velocities) may correspond to condensation of plasma along more or less horizontal threads of the arch-shape structure visible in 304 A. The steady flows (5 km/s) would correspond to a more quiescent plasma (cool and prominence-corona transition region) of the prominence packed into dips in horizontal magnetic field lines. The very weak secondary peaks in the Mg II profiles may reflect the turbulent nature of parts of the prominence.Comment: 15 pages, 14 figure

Evaluating the performance of low-energy feed forward osmosis system for desalination using impaired and saline water sources

Forward Osmosis (FO) is a natural process of treating water or wastewater due to the difference in osmotic pressures. FO is a membrane separation technology, applicable to food processing, industrial wastewater treatment and seawater or brackish water desalination. The phenomena of FO processes occur whereby water molecules are driven across a semi-permeable membrane by an osmotic pressure gradient that is generated from a higher concentrate draw solution. FO processes can recover potable water resources from wastewater streams through the flow of pure water from a lower concen-trated feed solution towards higher concentrated draw solutions leaving behind pollutants, impurities, and salts in the semi-permeable membrane. This paper assesses the design, build and testing of a laboratory scaled Feed Forward Osmosis (FFO) system for treating river water collected from the River Medway, Kent, England. The FO process was a highly effective form of river water treatment and able to treat the River Water with high rejection rates of solutes (>90%). Experimental results showed that the FFO system can achieve a better performance when the molarity of the draw solution is higher. The average solute rejection rate of the FO membrane for both inorganic and organic compounds was 94.83 %. Moreover, the operation of the forward osmosis membrane illustrated that it has a lower fouling propensity and higher solute rejection ca-pabilities. The pilot scaled FFO system has the ability for greater salt rejection and lower electronic conductivity levels which resulted from the successful desalination of river water. A sodium chloride (NaCl) or saltwater draw solution performed posi-tively in inducing higher osmotic pressures with a substantial effect of lower energy requirements for the system. Lower en-ergy consumptions of the FFO system allow similar water treatment possibilities with energy savings potential. The FFO system showed to be an environmentally viable and economically feasible river water treatment technology

Kinetic analysis of ASIC1a delineates conformational signaling from proton-sensing domains to the channel gate.

Acid-sensing ion channels (ASICs) are neuronal Na <sup>+</sup> channels that are activated by a drop in pH. Their established physiological and pathological roles, involving fear behaviors, learning, pain sensation, and neurodegeneration after stroke, make them promising targets for future drugs. Currently, the ASIC activation mechanism is not understood. Here, we used voltage-clamp fluorometry (VCF) combined with fluorophore-quencher pairing to determine the kinetics and direction of movements. We show that conformational changes with the speed of channel activation occur close to the gate and in more distant extracellular sites, where they may be driven by local protonation events. Further, we provide evidence for fast conformational changes in a pathway linking protonation sites to the channel pore, in which an extracellular interdomain loop interacts via aromatic residue interactions with the upper end of a transmembrane helix and would thereby open the gate

Random Tensors and Planted Cliques

The r-parity tensor of a graph is a generalization of the adjacency matrix, where the tensor's entries denote the parity of the number of edges in subgraphs induced by r distinct vertices. For r=2, it is the adjacency matrix with 1's for edges and -1's for nonedges. It is well-known that the 2-norm of the adjacency matrix of a random graph is O(\sqrt{n}). Here we show that the 2-norm of the r-parity tensor is at most f(r)\sqrt{n}\log^{O(r)}n, answering a question of Frieze and Kannan who proved this for r=3. As a consequence, we get a tight connection between the planted clique problem and the problem of finding a vector that approximates the 2-norm of the r-parity tensor of a random graph. Our proof method is based on an inductive application of concentration of measure

Measurement of Electromagnetic Activity of Yeast Cells at 42 GHz

This paper discusses the possibility of using a device composed of a resonant cavity, preamplifiers, and a spectrum analyzer to detect electromagnetic emission of yeast cells at a frequency of about 42 GHz. Measurement in this frequency range is based on the Frohlich\'s postulate of coherent polar oscillations as a fundamental biophysical property of biological systems and on the experiments of Grundler and Keilmann who disclosed effects of exposure to the electromagnetic field at 42 GHz on the growth rate of yeast cells. This article includes a detailed description of the laboratory equipment and the methods used to evaluate the obtained results

Generalised resultants, dynamic polynomial combinants and the minimal design problem

The theory of dynamic polynomial combinants is linked to the linear part of the dynamic determinantal assignment problems (DAP), which provides the unifying description of the dynamic, as well as static pole and zero dynamic assignment problems in linear systems. The assignability of spectrum of polynomial combinants provides necessary conditions for solution of the original DAP. This paper demonstrates the origin of dynamic polynomial combinants from linear systems, examines issues of their representation and the parameterisation of dynamic polynomial combinants according to the notions of order and degree, and examines their spectral assignment. Central to this study is the link of dynamic combinants to the theory of generalised resultants, which provide the matrix representation of the dynamic combinants. The paper considers the case of coprime set of polynomials for which spectral assignability is always feasible and provides a complete characterisation of all assignable combinants with order above and below the Sylvester order. A complete parameterisation of combinants and respective generalised resultants is given and this leads naturally to the characterisation of the minimal degree and order combinant for which spectrum assignability may be achieved, which is referred to as the dynamic combinant minimal design (DCMD) problem. An algorithmic approach based on rank tests of Sylvester matrices is given, which produces the minimal order and degree solution in a finite number of steps. Such solutions provide low bounds for the respective dynamic assignment control problems

Centennial-scale evolution of Dansgaard-Oeschger events in the northeast Atlantic Ocean between 39.5 and 56.5 ka B.P

There is much uncertainty surrounding the mechanisms that forced the abrupt climate fluctuations found in many palaeoclimate records during Marine Isotope Stage (MIS)-3. One of the processes thought to be involved in these events is the Atlantic Meridional Overturning Circulation (MOC), which exhibited large changes in its dominant mode throughout the last glacial period. Giant piston core MD95-2006 from the northeast Atlantic Ocean records a suite of palaeoceanographic proxies related to the activity of both surface and deep water masses through a period of MIS-3 when abrupt climate fluctuations were extremely pronounced. A two-stage progression of surface water warming during interstadial warm events is proposed, with initial warming related to the northward advection of a thin warm surface layer within the North Atlantic Current, which only extended into deeper surface layers as the interstadial progressed. Benthic foraminifera isotope data also show millennial-scale oscillations but of a different structure to the abrupt surface water changes. These changes are argued to partly be related to the influence of low-salinity deepwater brines. The influence of deepwater brines over the site of MD95-2006 reached a maximum at times of rapid warming of surface waters. This observation supports the suggestion that brine formation may have helped to destabilize the accumulation of warm, saline surface waters at low latitudes, helping to force the MOC into a warm mode of operation. The contribution of deepwater brines relative to other mechanisms proposed to alter the state of the MOC needs to be examined further in future studies