Analytic results and weighted Monte Carlo simulations for CDO pricing

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulae are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.Comment: 12 pages, 9 figure

NOTCH-mediated non-cell autonomous regulation of chromatin structure during senescence

Senescent cells interact with the surrounding microenvironment achieving diverse functional outcomes. We have recently identified that NOTCH1 can drive ‘lateral induction’ of a unique senescence phenotype in adjacent cells by specifically upregulating the NOTCH ligand JAG1. Here we show that NOTCH signalling can modulate chromatin structure autonomously and non-autonomously. In addition to senescence-associated heterochromatic foci (SAHF), oncogenic RAS-induced senescent (RIS) cells exhibit a massive increase in chromatin accessibility. NOTCH signalling suppresses SAHF and increased chromatin accessibility in this context. Strikingly, NOTCH-induced senescent cells, or cancer cells with high JAG1 expression, drive similar chromatin architectural changes in adjacent cells through cell–cell contact. Mechanistically, we show that NOTCH signalling represses the chromatin architectural protein HMGA1, an association found in multiple human cancers. Thus, HMGA1 is involved not only in SAHFs but also in RIS-driven chromatin accessibility. In conclusion, this study identifies that the JAG1–NOTCH–HMGA1 axis mediates the juxtacrine regulation of chromatin architecture

Spider Optimization: Probing the Systematics of a Large Scale B-Mode Experiment

Spider is a long-duration, balloon-borne polarimeter designed to measure large scale Cosmic Microwave Background (CMB) polarization with very high sensitivity and control of systematics. The instrument will map over half the sky with degree angular resolution in I, Q and U Stokes parameters, in four frequency bands from 96 to 275 GHz. Spider's ultimate goal is to detect the primordial gravity wave signal imprinted on the CMB B-mode polarization. One of the challenges in achieving this goal is the minimization of the contamination of B-modes by systematic effects. This paper explores a number of instrument systematics and observing strategies in order to optimize B-mode sensitivity. This is done by injecting realistic-amplitude, time-varying systematics in a set of simulated time-streams. Tests of the impact of detector noise characteristics, pointing jitter, payload pendulations, polarization angle offsets, beam systematics and receiver gain drifts are shown. Spider's default observing strategy is to spin continuously in azimuth, with polarization modulation achieved by either a rapidly spinning half-wave plate or a rapidly spinning gondola and a slowly stepped half-wave plate. Although the latter is more susceptible to systematics, results shown here indicate that either mode of operation can be used by Spider.Comment: 15 pages, 12 figs, version with full resolution figs available here http://www.astro.caltech.edu/~lgg/spider_front.ht

SPIDER: a balloon-borne CMB polarimeter for large angular scales

We describe SPIDER, a balloon-borne instrument to map the polarization of the millimeter-wave sky with degree angular resolution. Spider consists of six monochromatic refracting telescopes, each illuminating a focal plane of large-format antenna-coupled bolometer arrays. A total of 2,624 superconducting transition-edge sensors are distributed among three observing bands centered at 90, 150, and 280 GHz. A cold half-wave plate at the aperture of each telescope modulates the polarization of incoming light to control systematics. Spider's first flight will be a 20-30-day Antarctic balloon campaign in December 2011. This flight will map \sim8% of the sky to achieve unprecedented sensitivity to the polarization signature of the gravitational wave background predicted by inflationary cosmology. The Spider mission will also serve as a proving ground for these detector technologies in preparation for a future satellite mission.Comment: 12 pages, 6 figures; as published in the conference proceedings for SPIE Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy V (2010

Modeling and characterization of the SPIDER half-wave plate

Spider is a balloon-borne array of six telescopes that will observe the Cosmic Microwave Background. The 2624 antenna-coupled bolometers in the instrument will make a polarization map of the CMB with approximately one-half degree resolution at 145 GHz. Polarization modulation is achieved via a cryogenic sapphire half-wave plate (HWP) skyward of the primary optic. We have measured millimeter-wave transmission spectra of the sapphire at room and cryogenic temperatures. The spectra are consistent with our physical optics model, and the data gives excellent measurements of the indices of A-cut sapphire. We have also taken preliminary spectra of the integrated HWP, optical system, and detectors in the prototype Spider receiver. We calculate the variation in response of the HWP between observing the CMB and foreground spectra, and estimate that it should not limit the Spider constraints on inflation

A cryogenic rotation stage with a large clear aperture for the half-wave plates in the Spider instrument

We describe the cryogenic half-wave plate rotation mechanisms built for and used in Spider, a polarization-sensitive balloon-borne telescope array that observed the Cosmic Microwave Background at 95 GHz and 150 GHz during a stratospheric balloon flight from Antarctica in January 2015. The mechanisms operate at liquid helium temperature in flight. A three-point contact design keeps the mechanical bearings relatively small but allows for a large (305 mm) diameter clear aperture. A worm gear driven by a cryogenic stepper motor allows for precise positioning and prevents undesired rotation when the motors are depowered. A custom-built optical encoder system monitors the bearing angle to an absolute accuracy of +/- 0.1 degrees. The system performed well in Spider during its successful 16 day flight

A Simulation-Based Method for Correcting Mode Coupling in CMB Angular Power Spectra

Modern CMB analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo-$C_\ell$ based, MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, $F_{\ell}$, that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, $J_{\ell\ell'}$, which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the SPIDER balloon-borne CMB experiment.Comment: 14 pages, 7 figure