9,850 research outputs found
Fractional norms and quasinorms do not help to overcome the curse of dimensionality
The curse of dimensionality causes the well-known and widely discussed
problems for machine learning methods. There is a hypothesis that using of the
Manhattan distance and even fractional quasinorms lp (for p less than 1) can
help to overcome the curse of dimensionality in classification problems. In
this study, we systematically test this hypothesis. We confirm that fractional
quasinorms have a greater relative contrast or coefficient of variation than
the Euclidean norm l2, but we also demonstrate that the distance concentration
shows qualitatively the same behaviour for all tested norms and quasinorms and
the difference between them decays as dimension tends to infinity. Estimation
of classification quality for kNN based on different norms and quasinorms shows
that a greater relative contrast does not mean better classifier performance
and the worst performance for different databases was shown by different norms
(quasinorms). A systematic comparison shows that the difference of the
performance of kNN based on lp for p=2, 1, and 0.5 is statistically
insignificant
Stress-dependent electrical transport and its universal scaling in granular materials
We experimentally and numerically examine stress-dependent electrical
transport in granular materials to elucidate the origins of their universal
dielectric response. The ac responses of granular systems under varied
compressive loadings consistently exhibit a transition from a resistive plateau
at low frequencies to a state of nearly constant loss at high frequencies. By
using characteristic frequencies corresponding to the onset of conductance
dispersion and measured direct-current resistance as scaling parameters to
normalize the measured impedance, results of the spectra under different stress
states collapse onto a single master curve, revealing well-defined
stress-independent universality. In order to model this electrical transport, a
contact network is constructed on the basis of prescribed packing structures,
which is then used to establish a resistor-capacitor network by considering
interactions between individual particles. In this model the
frequency-dependent network response meaningfully reproduces the experimentally
observed master curve exhibited by granular materials under various normal
stress levels indicating this universal scaling behaviour is found to be
governed by i) interfacial properties between grains and ii) the network
configuration. The findings suggest the necessity of considering contact
morphologies and packing structures in modelling electrical responses using
network-based approaches.Comment: 12 pages, 4 figure
A model study of present-day Hall-effect circulators
Stimulated by the recent implementation of a three-port Hall-effect microwave
circulator of Mahoney et al. (MEA), we present model studies of the performance
of this device. Our calculations are based on the capacitive-coupling model of
Viola and DiVincenzo (VD). Based on conductance data from a typical Hall-bar
device obtained from a two-dimensional electron gas (2DEG) in a magnetic field,
we numerically solve the coupled field-circuit equations to calculate the
expected performance of the circulator, as determined by the parameters of
the device when coupled to 50 ports, as a function of frequency and
magnetic field. Above magnetic fields of 1.5T, for which a typical 2DEG enters
the quantum Hall regime (corresponding to a Landau-level filling fraction
of 20), the Hall angle always
remains close to , and the parameters are close to the analytic
predictions of VD for . As anticipated by VD, MEA find the
device to have rather high (k) impedance, and thus to be extremely
mismatched to , requiring the use of impedance matching. We
incorporate the lumped matching circuits of MEA in our modeling and confirm
that they can produce excellent circulation, although confined to a very small
bandwidth. We predict that this bandwidth is significantly improved by working
at lower magnetic field when the Landau index is high, e.g. , and the
impedance mismatch is correspondingly less extreme. Our modeling also confirms
the observation of MEA that parasitic port-to-port capacitance can produce very
interesting countercirculation effects
Constrained pre-equalization accounting for multi-path fading emulated using large RC networks: applications to wireless and photonics communications
Multi-path propagation is modelled assuming a multi-layer RC network with randomly allocated resistors and capacitors to represent the transmission medium. Due to frequency-selective attenuation, the waveforms associated with each propagation path incur path-dependent distortion. A pre-equalization procedure that takes into account the capabilities of the transmission source as well as the transmission properties of the medium is developed. The problem is cast within a Mixed Integer Linear Programming optimization framework that uses the developed nominal RC network model, with the excitation waveform customized to optimize signal fidelity from the transmitter to the receiver. The objective is to match a Gaussian pulse input accounting for frequency regions where there would be pronounced fading. Simulations are carried out with different network realizations in order to evaluate the sensitivity of the solution with respect to changes in the transmission medium mimicking the multi-path propagation. The proposed approach is of relevance where equalization techniques are difficult to implement. Applications are discussed within the context of emergent communication modalities across the EM spectrum such as light percolation as well as emergent indoor communications assuming various modulation protocols or UWB schemes as well as within the context of space division multiplexing
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