283 research outputs found
Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging
We propose a general method to study dependent data in a binary tree, where
an individual in one generation gives rise to two different offspring, one of
type 0 and one of type 1, in the next generation. For any specific
characteristic of these individuals, we assume that the characteristic is
stochastic and depends on its ancestors' only through the mother's
characteristic. The dependency structure may be described by a transition
probability which gives the probability that the pair of
daughters' characteristics is around , given that the mother's
characteristic is . Note that , the characteristic of the daughter of
type 0, and , that of the daughter of type 1, may be conditionally dependent
given , and their respective conditional distributions may differ. We then
speak of bifurcating Markov chains. We derive laws of large numbers and central
limit theorems for such stochastic processes. We then apply these results to
detect cellular aging in Escherichia Coli, using the data of Stewart et al. and
a bifurcating autoregressive model.Comment: Published in at http://dx.doi.org/10.1214/105051607000000195 the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Euler Scheme and Tempered Distributuions
Given a smooth R^d-valued diffusion, we study how fast the Euler scheme with
time step 1/n converges in law. To be precise, we look for which class of test
functions f the approximate expectation E[f(X^{n,x}_1)] converges with speed
1/n to E[f(X^x_1)]. If X is uniformly elliptic, we show that this class
contains all tempered distributions, and all measurable functions with
exponential growth. We give applications to option pricing and hedging, proving
numerical convergence rates for prices, deltas and gammas.Comment: 26 page
Short communication: inversion of convex ordering: local volatility does not maximise the price of VIX futures
It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is incorrect: we build a continuous stochastic volatility model in which a VIX future is strictly more expensive than in its associated local volatility model. More generally, in our model, strictly convex payoffs on a squared VIX are strictly cheaper than in the associated local volatility model. This corresponds to an inversion of convex ordering between local and stochastic variances, when moving from instantaneous variances to squared VIX, as convex payoffs on instantaneous variances are always cheaper in the local volatility model. We thus prove that this inversion of convex ordering, which is observed in the S&P 500 market for short VIX maturities, can be produced by a continuous stochastic volatility model. We also prove that the model can be extended so that, as suggested by market data, the convex ordering is preserved for long maturities
Experimental study of a low-order wavefront sensor for the high-contrast coronagraphic imager EXCEDE
The mission EXCEDE (EXoplanetary Circumstellar Environments and Disk
Explorer), selected by NASA for technology development, is designed to study
the formation, evolution and architectures of exoplanetary systems and
characterize circumstellar environments into stellar habitable zones. It is
composed of a 0.7 m telescope equipped with a Phase-Induced Amplitude
Apodization Coronagraph (PIAA-C) and a 2000-element MEMS deformable mirror,
capable of raw contrasts of 1e-6 at 1.2 lambda/D and 1e-7 above 2 lambda/D. One
of the key challenges to achieve those contrasts is to remove low-order
aberrations, using a Low-Order WaveFront Sensor (LOWFS). An experiment
simulating the starlight suppression system is currently developed at NASA Ames
Research Center, and includes a LOWFS controlling tip/tilt modes in real time
at 500 Hz. The LOWFS allowed us to reduce the tip/tilt disturbances to 1e-3
lambda/D rms, enhancing the previous contrast by a decade, to 8e-7 between 1.2
and 2 lambda/D. A Linear Quadratic Gaussian (LQG) controller is currently
implemented to improve even more that result by reducing residual vibrations.
This testbed shows that a good knowledge of the low-order disturbances is a key
asset for high contrast imaging, whether for real-time control or for post
processing.Comment: 12 pages, 20 figures, proceeding of the SPIE conference
Optics+Photonics, San Diego 201
High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation
The Phase-Induced Amplitude Apodization (PIAA) coronagraph is a high
performance coronagraph concept able to work at small angular separation with
little loss in throughput. We present results obtained with a laboratory PIAA
system including active wavefront control. The system has a 94.3% throughput
(excluding coating losses) and operates in air with monochromatic light.
Our testbed achieved a 2.27e-7 raw contrast between 1.65 lambda/D (inner
working angle of the coronagraph configuration tested) and 4.4 lambda/D (outer
working angle). Through careful calibration, we were able to separate this
residual light into a dynamic coherent component (turbulence, vibrations) at
4.5e-8 contrast and a static incoherent component (ghosts and/or polarization
missmatch) at 1.6e-7 contrast. Pointing errors are controlled at the 1e-3
lambda/D level using a dedicated low order wavefront sensor.
While not sufficient for direct imaging of Earth-like planets from space, the
2.27e-7 raw contrast achieved already exceeds requirements for a ground-based
Extreme Adaptive Optics system aimed at direct detection of more massive
exoplanets. We show that over a 4hr long period, averaged wavefront errors have
been controlled to the 3.5e-9 contrast level. This result is particularly
encouraging for ground based Extreme-AO systems relying on long term stability
and absence of static wavefront errors to recover planets much fainter than the
fast boiling speckle halo.Comment: 18 pages, 12 figures. Accepted for publication in PASP. The pointing
control scheme for this system is described in a separate paper
(Coronagraphic Low-Order Wave-Front Sensor: Principle and Application to a
Phase-Induced Amplitude Coronagraph, The Astrophysical Journal, Volume 693,
Issue 1, pp. 75-84 (2009)
Diffraction-limited polarimetric imaging of protoplanetary disks and mass-loss shells with VAMPIRES
Both the birth and death of a stellar system are areas of key scientific importance. Whether it's understanding the process of planetary formation in a star's early years, or uncovering the cause of the enormous mass-loss that takes place during a star's dying moments, a key to scientific understanding lies in the inner few AU of the circumstellar environment. Corresponding to scales of 10s of milli-arcseconds, these observations pose a huge technical challenge due to the high angular-resolutions and contrasts required. A major stumbling block is the problem of the Earth's own atmospheric turbulence. The other difficulty is that precise calibration is required to combat the extremely high contrast ratios and high resolutions faced. By taking advantage of the fact that starlight scattered by dust in the circumstellar region is polarized, differential polarimetry can help achieve this calibration. Spectral features can also be utilized
On-sky demonstration of low-order wavefront sensing and control with focal plane phase mask coronagraphs
The ability to characterize exoplanets by spectroscopy of their atmospheres
requires direct imaging techniques to isolate planet signal from the bright
stellar glare. One of the limitations with the direct detection of exoplanets,
either with ground- or space-based coronagraphs, is pointing errors and other
low-order wavefront aberrations. The coronagraphic detection sensitivity at the
diffraction limit therefore depends on how well low-order aberrations upstream
of the focal plane mask are corrected. To prevent starlight leakage at the
inner working angle of a phase mask coronagraph, we have introduced a
Lyot-based low-order wavefront sensor (LLOWFS), which senses aberrations using
the rejected starlight diffracted at the Lyot plane. In this paper, we present
the implementation, testing and results of LLOWFS on the Subaru Coronagraphic
Extreme Adaptive Optics system (SCExAO) at the Subaru Telescope.
We have controlled thirty-five Zernike modes of a H-band vector vortex
coronagraph in the laboratory and ten Zernike modes on sky with an integrator
control law. We demonstrated a closed-loop pointing residual of 0.02 mas in the
laboratory and 0.15 mas on sky for data sampled using the minimal 2-second
exposure time of the science camera. We have also integrated the LLOWFS in the
visible high-order control loop of SCExAO, which in closed-loop operation has
validated the correction of the non-common path pointing errors between the
infrared science channel and the visible wavefront sensing channel with
pointing residual of 0.23 mas on sky.Comment: 12 pages, 15 figures, Accepted and scheduled for publication in
September 2015 issue of the PAS
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