654 research outputs found
Groupoids and Wreath Products of Musical Transformations: a Categorical Approach from poly-Klumpenhouwer Networks
Transformational music theory, pioneered by the work of Lewin, shifts the
music-theoretical and analytical focus from the "object-oriented" musical
content to an operational musical process, in which transformations between
musical elements are emphasized. In the original framework of Lewin, the set of
transformations often form a group, with a corresponding group action on a
given set of musical objects. Klumpenhouwer networks have been introduced based
on this framework: they are informally labelled graphs, the labels of the
vertices being pitch classes, and the labels of the arrows being
transformations that maps the corresponding pitch classes. Klumpenhouwer
networks have been recently formalized and generalized in a categorical
setting, called poly-Klumpenhouwer networks. This work proposes a new
groupoid-based approach to transformational music theory, in which
transformations of PK-nets are considered rather than ordinary sets of musical
objects. We show how groupoids of musical transformations can be constructed,
and an application of their use in post-tonal music analysis with Berg's Four
pieces for clarinet and piano, Op. 5/2. In a second part, we show how groupoids
are linked to wreath products (which feature prominently in transformational
music analysis) through the notion of groupoid bisectionsComment: 16 pages, 9 figures; comments welcom
Finite size effects, super-and sub-poissonian noise in a nanotube connected to leads
The injection of electrons in the bulk of carbon nanotube which is connected
to ideal Fermi liquid leads is considered. While the presence of the leads
gives a cancellation of the noise cross-correlations, the auto-correlation
noise has a Fano factor which deviates strongly from the Schottky behavior at
voltages where finite size effects are expected. Indeed, as the voltage is
increased from zero, the noise is first super-poissonian, then sub-poissonian,
and eventually it reaches the Schottky limit. These finite size effects are
also tested using a diagnosis of photo-assisted transport, where a small AC
modulation is superposed to the DC bias voltage between the injection tip and
the nanotube. When finite size effects are at play, we obtain a stepwise
behavior for the noise derivative, as expected for normal metal systems,
whereas in the absence of finite size effects, due to the presence of Coulomb
interactions, a smoothed staircase is observed. The present work shows that it
is possible to explore finite size effects in nanotube transport via a zero
frequency noise measurement
A Quantitative Spectrographic Study of Magnesium Contamination in Calcium Oxalate Precipitates
Chemists have attempted quantitative spectrographic analysis repeatedly since 1863 when Miller first conducted his experiments. De Gramont added considerable information in a series of papers of about 1907. Leonard and Pollock, and Hartley also published much material about the same time. These methods depend on comparison with a standard of the same composition, containing the same elements. Gerlack and Schweitzer have recently developed a system which depends on comparison with lines of some other element which occur very nearby. The method used in our determinations is based on the earlier work
Controlling Light Through Optical Disordered Media : Transmission Matrix Approach
We experimentally measure the monochromatic transmission matrix (TM) of an
optical multiple scattering medium using a spatial light modulator together
with a phase-shifting interferometry measurement method. The TM contains all
information needed to shape the scattered output field at will or to detect an
image through the medium. We confront theory and experiment for these
applications and we study the effect of noise on the reconstruction method. We
also extracted from the TM informations about the statistical properties of the
medium and the light transport whitin it. In particular, we are able to isolate
the contributions of the Memory Effect (ME) and measure its attenuation length
Characterization of an imaging multimode optical fiber using digital micro-mirror device based single-beam system
This work demonstrates experimental approaches to characterize a single multimode fiber imaging system without a reference beam. Spatial light modulation is performed with a digital micro-mirror device that enables high-speed binary amplitude modulation. Intensity-only images are recorded by the camera and processed by a Bayesian inference based algorithm to retrieve the phase of the output optical field as well as the transmission matrix of the fiber. The calculated transmission matrix is validated by three standards: prediction accuracy, transmission imaging, and focus generation. Also, it is found that information on mode count and eigenchannels can be extracted from the transmission matrix by singular value decomposition. This paves the way for a more compact and cheaper single multimode fiber imaging system for many demanding imaging tasks
Focusing and Compression of Ultrashort Pulses through Scattering Media
Light scattering in inhomogeneous media induces wavefront distortions which
pose an inherent limitation in many optical applications. Examples range from
microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have
made the correction of spatial distortions possible by wavefront shaping
techniques. However, when ultrashort pulses are employed scattering induces
temporal distortions which hinder their use in nonlinear processes such as in
multiphoton microscopy and quantum control experiments. Here we show that
correction of both spatial and temporal distortions can be attained by
manipulating only the spatial degrees of freedom of the incident wavefront.
Moreover, by optimizing a nonlinear signal the refocused pulse can be shorter
than the input pulse. We demonstrate focusing of 100fs pulses through a 1mm
thick brain tissue, and 1000-fold enhancement of a localized two-photon
fluorescence signal. Our results open up new possibilities for optical
manipulation and nonlinear imaging in scattering media
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