An adaptive way for improving noise reduction using local geometric projection
Abstract
We propose an adaptive way to improve noise reduction by local geometric projection. From the neighborhood of each candidate point in phase space, we identify the best subspace that the point will be orthogonally projected to. The signal subspace is formed by the most significant eigendirections of the neighborhood, while the less significant ones define the noise subspace. We provide a simple criterion to separate the most significant eigendirections from the less significant ones. This criterion is based on the maximum logarithmic difference between the neighborhood eigendirection lengths, and the assumption that there is at least one eigendirection that corresponds to the noise subspace. In this way, we take into account the special characteristics of each neighborhood and introduce a more successful noise reduction technique. Results are presented for a chaotic time series of the H�non map and Ikeda map, as well as on the Nasdaq Composite index.
Noise in chaotic data: Diagnosis and treatment
Abstract
A prominent limiting factor in the analysis of chaotic time series are measurement errors in the data. We show that this influence can be quite severe, depending on the nature of the noise, the complexity of the signal, and on the application one has in mind. Theoretical considerations yield general upper bounds on the tolerable noise level for dimension, entropy and Lyapunov estimates. We discuss methods to detect and analyze the noise present in a measured data set. We show how the situation can be improved by nonlinear noise reduction.
Arnold tongues in human cardiorespiratory systems
Abstract
Arnold tongues are phase-locking regions in parameter space, originally studied in circle-map models of cardiac arrhythmias. They show where a periodic system responds by synchronizing to an external stimulus. Clinical studies of resting or anesthetized patients exhibit synchronization between heart-beats and respiration. Here we show that these results are successfully modeled by a circle-map, neatly combining the phenomena of respiratory sinus arrhythmia (RSA), where inspiration modulates heart-rate and cardioventilatory coupling (CVC), where the heart is a pacemaker for respiration. Examination of the Arnold tongues reveals that while RSA can cause synchronization, the strongest mechanism for synchronization is CVC, so that the heart is acting as a pacemaker for respiration.
“We don’t support that”
Think again before calling tech support!
HyperDictionary.com
A good online dictionary:
http://www.hyperdictionary.com/index.html
I noticed that the definition of the candela is outdated. :( However, the Wikipedia entry gets it right.
Wikipedia
Found a great online encyclopedia, the Wikipedia:
http://en.wikipedia.org/wiki/Main_Page
It’s hosted by a company in San Diego. Articles must be considered Reader Beware, since they are publicly editable. However, in large part the community keeps the articles more or less accurate.
Monthly Report: 2004 January
Also located here.
Murison continued work on the adaptive optics (AO) front end for the FTS project. He and Brad Behr revised the optical design several times. The optical fiber is now imaged onto the same CCD camera as the starlight from the telescope, which makes calibration of the AO corrections much easier. The new design can be found here (click on “config 4” and on “hardware drawing 2"). Murison added refraction by ideal thin lenses into his computer algebra ray tracing package (AESOP) in order to trace the new AO design with misalignments. He wrote a memo describing how to ray trace an ideal thin lens in the paraxial approximation.
Behr, Hajian, and Murison redesigned the interferometer of the FTS. The new design has two major changes. First, the metrology laser light (red beam in the drawing) is injected directly into the starlight path via the first beam splitter cube, rather than via the notch filters of the previous design. This simplifies the system, improves throughput by about 25 percent, makes alignment easier, and is a “sweet” design. Second, the half of the starlight beam that used to get thrown away at the first beam splitter cube (required to polarize the starlight signal) has been fully recovered and sent through the system to wind up as a second signal on the CCD detector (yellow beam in the drawing), thereby effectively doubling our throughput. This was accomplished by clever use of transmitted and reflected polarized beam components, thus refuting the conventional wisdom that it is not possible to recover both halves of the starlight beam.
In response to several requests from colleagues of FTS members, Murison designed and implemented a web site for the FTS project. It is currently only a skeleton and not at all ready for public use. Content will be added by the FTS group as time allows, and it will “go public” when sufficiently ready. For now it serves as a useful repository for documentation of recent FTS work.
Murison and Efroimsky have decided on dynamics projects for presentation to the AAS Division on Dynamical Astronomy at its annual meeting in April. Their topics are on the dynamical stability of objects orbiting oblate, precessing planets, using the dynamical gauge formalism recently discovered by Efroimsky. Murison may, if time allows, also present recent results on calculation of orbit-orbit distances.
Murison’s student, Andrei Munteanu, has been announced as a Finalist in the Intel Science Talent Search. Andrei submitted a paper to the Intel STS describing his work (in collaboration with Murison) on orbit-orbit distances.
Monthly Report: 2003 December
Also available here.
Murison continued work on the adaptive optics (AO) front end for the FTS project. He implemented in Maple an analytic model of the relevant optics, including rotation and translation misalignments of each optical element, then used a computer algebra package he previously developed for other projects to analytically trace through the adaptive optics system. He successfully solved for the rotation angles required by the AO mirror to correct the location of the stellar image on the focal plane (specifically, to put the star on the end of the 50 micron fiber optic) for tip/tilt errors due to atmospheric fluctuations as measured by a separate video camera. The solution includes 28 separate misalignment parameters. This is one aspect of the AO mirror feedback loop model that will be incorporated in the AO control program that Murison is writing. Murison has partially completed a technical memorandum describing his AO work.
Murison designed and implemented a test configuration that will allow him to debug his AO control program using the actual AO hardware that will go into the FTS. The test rig is conveniently set up in Murison’s office.
Murison also came up with a modification that should solve a serious vibration problem due to the mechanical shutter employed by the FTS. The shutter vibration problem has always been present, but, due to the placement of the FTS optical bench on solid concrete at the USNO 24-inch, the vibrations damped quickly and did not interfere with observations. However, at the 25-inch telescope at the Clay Science Center, a resonance is now present and the vibrations do not damp quickly enough. (Either that or the shutter has begun a long slide toward failure.) Murison solved the problem by vibrationally isolating the shutter assembly from the rest of the FTS. He employed two of the most important problem-solving tools in scientific instrumentation: duct tape and a number 2 pencil.
The analytical ray tracing computer algebra package mentioned above that Murison wrote is described, in part, here. Web pages summarizing Murison’s FTS-related activities are here.