295 research outputs found
Learning algebraic structures with the help of Borel equivalence relations
We study algorithmic learning of algebraic structures. In our framework, a learner receives larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if the conjectures eventually stabilize to a correct guess. We prove that a family of structures is learnable if and only if its learning domain is continuously reducible to the relation E0 of eventual agreement on reals. This motivates a novel research program, that is, using descriptive set theoretic tools to calibrate the (learning) complexity of nonlearnable families. Here, we focus on the learning power of well-known benchmark Borel equivalence relations (i.e., E1, E2, E3, Z0, and Eset)
Mechanism of fragmentation and atomization of molecular ions in gasdynamic transport cell
The fragmentation of molecular ions formed upon the electrospraying of a sample and transported through the gasdynamic system of a mass spectrometer equipped with an IESAP (Ion Extraction from Solution at Atmospheric Pressure) source has been experimentally studied. It is established that ion fragmentation in a Kantorowicz-Gray type cell takes place in the immediate vicinity of a skimmer port, apparently, as a result of collisions between ions (accelerated in an electric field) and stagnant gas. Molecular mechanisms of fragmentation are considered and it is concluded that this process can take place in a single ion-molecule collision even
Creation, doubling, and splitting, of vortices in intracavity second harmonic generation
We demonstrate generation and frequency doubling of unit charge vortices in a
linear astigmatic resonator. Topological instability of the double charge
harmonic vortices leads to well separated vortex cores that are shown to
rotate, and become anisotropic, as the resonator is tuned across resonance
Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media
We demonstrate experimentally an optical process in which the spin angular
momentum carried by a circularly polarized light beam is converted into orbital
angular momentum, leading to the generation of helical modes with a wavefront
helicity controlled by the input polarization. This phenomenon requires the
interaction of light with matter that is both optically inhomogeneous and
anisotropic. The underlying physics is also associated with the so-called
Pancharatnam-Berry geometrical phases involved in any inhomogeneous
transformation of the optical polarization
Variations on the Deuteron
We consider few problems which are related to the deuteron and have simple
analytical solution. Relation is found between the deuteron electric quadrupole
moment and the -scattering amplitude. The degree of circular polarization
of photons is calculated for the radiative capture of longitudinally polarized
thermal neutrons. The anapole, electric dipole and magnetic quadrupole moments
of the deuteron are calculated.Comment: 14 pages, late
Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling
This paper investigates the dependence of synchronization transitions of
bursting oscillations on the information transmission delay over scale-free
neuronal networks with attractive and repulsive coupling. It is shown that for
both types of coupling, the delay always plays a subtle role in either
promoting or impairing synchronization. In particular, depending on the
inherent oscillation period of individual neurons, regions of irregular and
regular propagating excitatory fronts appear intermittently as the delay
increases. These delay-induced synchronization transitions are manifested as
well-expressed minima in the measure for spatiotemporal synchrony. For
attractive coupling, the minima appear at every integer multiple of the average
oscillation period, while for the repulsive coupling, they appear at every odd
multiple of the half of the average oscillation period. The obtained results
are robust to the variations of the dynamics of individual neurons, the system
size, and the neuronal firing type. Hence, they can be used to characterize
attractively or repulsively coupled scale-free neuronal networks with delays.Comment: 15 pages, 9 figures; accepted for publication in PLoS ONE [related
work available at http://arxiv.org/abs/0907.4961 and
http://www.matjazperc.com/
Triggered qutrits for Quantum Communication protocols
A general protocol in Quantum Information and Communication relies in the
ability of producing, transmitting and reconstructing, in general, qunits. In
this letter we show for the first time the experimental implementation of these
three basic steps on a pure state in a three dimensional space, by means of the
orbital angular momentum of the photons. The reconstruction of the qutrit is
performed with tomographic techniques and a Maximum-Likelihood estimation
method. In this way we also demonstrate that we can perform any transformation
in the three dimensional space
Polaronic optical absorption in electron-doped and hole-doped cuprates
Polaronic features similar to those previously observed in the photoinduced
spectra of cuprates have been detected in the reflectivity spectra of
chemically doped parent compounds of high-critical-temperature superconductors,
both -type and -type. In NdCuO these features, whose
intensities depend both on doping and temperature, include local vibrational
modes in the far infrared and a broad band centered at 1000 cm.
The latter band is produced by the overtones of two (or three) local modes and
is well described in terms of a small-polaron model, with a binding energy of
about 500 cm. Most of the above infrared features are shown to survive
in the metallic phase of NdCeCu0, BiSrCuO, and
YBaCuO, where they appear as extra-Drude peaks. The occurrence
of polarons is attributed to local modes strongly coupled to carriers, as shown
by a comparison with tunneling results.Comment: File latex, 31 p., submitted to Physical Review B. Figures may be
faxed upon reques
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