A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation.Comment: 26 page

A 233 km Tunnel for Lepton and Hadron Colliders

A decade ago, a cost analysis was conducted to bore a 233 km circumference Very Large Hadron Collider (VLHC) tunnel passing through Fermilab. Here we outline implementations of $e^+e^-$, $p \bar{p}$, and $\mu^+ \mu^-$ collider rings in this tunnel using recent technological innovations. The 240 and 500 GeV $e^+e^-$ colliders employ Crab Waist Crossings, ultra low emittance damped bunches, short vertical IP focal lengths, superconducting RF, and low coercivity, grain oriented silicon steel/concrete dipoles. Some details are also provided for a high luminosity 240 GeV $e^+ e^-$ collider and 1.75 TeV muon accelerator in a Fermilab site filler tunnel. The 40 TeV $p \bar{p}$ collider uses the high intensity Fermilab $\bar{p}$ source, exploits high cross sections for $p \bar{p}$ production of high mass states, and uses 2 Tesla ultra low carbon steel/YBCO superconducting magnets run with liquid neon. The 35 TeV muon ring ramps the 2 Tesla superconducting magnets at 9 Hz every 0.4 seconds, uses 250 GV of superconducting RF to accelerate muons from 1.75 to 17.5 TeV in 63 orbits with 71% survival, and mitigates neutrino radiation with phase shifting, roller coaster motion in a FODO lattice.Comment: LaTex, 6 pages, 1 figure, Advanced Accelerator Concepts Workshop, Austin, TX, 10-15 June 201

A Visual Environment for Real-Time Image Processing in Hardware (VERTIPH)

Real-time video processing is an image-processing application that is ideally suited to implementation on FPGAs. We discuss the strengths and weaknesses of a number of existing languages and hardware compilers that have been developed for specifying image processing algorithms on FPGAs. We propose VERTIPH, a new multiple-view visual language that avoids the weaknesses we identify. A VERTIPH design incorporates three different views, each tailored to a different aspect of the image processing system under development; an overall architectural view, a computational view, and a resource and scheduling view

Adaptive constraints for feature tracking

In this paper extensions to an existing tracking algorithm are described. These extensions implement adaptive tracking constraints in the form of regional upper-bound displacements and an adaptive track smoothness constraint. Together, these constraints make the tracking algorithm more flexible than the original algorithm (which used fixed tracking parameters) and provide greater confidence in the tracking results. The result of applying the new algorithm to high-resolution ECMWF reanalysis data is shown as an example of its effectiveness

Late Quaternary climatic changes revealed by luminescence dating, mineral magnetism and diffuse reflectance spectroscopy of river terrace palaeosols: a new form of geoproxy data for the southern African interior

AbstractThe nature, spatial patterns and forcing mechanisms of Quaternary climatic changes across southern Africa remain unresolved and contentious, principally due to the scarcity of continuous and robustly-dated proxy records. We present what we interpret to be a broadly continuous record of late Quaternary climatic change based on optically stimulated luminescence (OSL) dating, and mineral magnetic and diffuse reflectance spectroscopy (DRS) analyses of stacked palaeosols within an overbank alluvial succession along the Modder River, central South Africa. The OSL ages indicate that alluvial sedimentation occurred at a fairly steady rate, averaging ∼0.15 mm/yr from at least 44 ka until ∼0.83 ka. This suggests that the palaeosols are accretionary, having formed contemporaneously with sedimentation. Climate is identified as the key soil-forming factor controlling the intensity of pedogenesis and is reflected in the changing concentration of pedogenic ferrimagnetic minerals (magnetite/maghemite) of single domain and superparamagnetic dimensions, and by variations in the amount of hematite compared to goethite. These data indicate that the climate was generally dry (rainfall ∼200–400 mm/yr) from ∼46 to 32 ka, except for a brief peak in humidity at ∼42 ka. There was then a period of greater humidity (rainfall ∼400–600 mm/yr) from ∼32 to 28 ka, possibly reflecting enhanced moisture supply from the Atlantic Ocean associated with the equatorward migration and intensification of westerly storm tracks. Although the precise mechanism remains unresolved, this climatic change may have been linked to an obliquity minimum at ∼29 ka. After ∼28 ka, the climate became progressively cooler and drier, especially between ∼18 and 15.5 ka when rainfall was as low as ∼100–200 mm/yr. Temperatures and rainfall then increased from ∼15.5 ka onwards, with the latter possibly linked to rising sea-surface temperatures in the SW Indian Ocean and enhanced moisture supply from easterly circulation. At ∼0.83 ka, a time corresponding with part of the Medieval Climatic Anomaly (MCA, ∼900–1300 AD), rainfall reached ∼600–700 mm/yr and was higher than at present (∼400–500 mm/yr). Fluvial landforms have previously been overlooked as a source of palaeoenvironmental information in southern Africa, but this study clearly demonstrates the potential to extract robust palaeoenvironmental data from alluvial-palaeosol successions in the arid to semi-arid interior where other forms of proxy record are scarce

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.Comment: 12 pages, 10 figures, supplementary informatio

The free energy in the Derrida--Retaux recursive model

We are interested in a simple max-type recursive model studied by Derrida and Retaux (2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime