1,970 research outputs found
Mapping correlated Gaussian patterns in a perceptron
The authors study the performance of a single-layer perceptron in realising a binary mapping of Gaussian input patterns. By introducing non-trivial correlations among the patterns, they generate a family of mappings including easier ones where similar inputs are mapped into the same output, and more difficult ones where similar inputs are mapped into different classes. The difficulty of the problem is gauged by the storage capacity of the network, which is higher for the easier problems
Enhancement of quantum dot peak-spacing fluctuations in the fractional q uantum Hall regime
The fluctuations in the spacing of the tunneling resonances through a quantum
dot have been studied in the quantum Hall regime. Using the fact that the
ground-state of the system is described very well by the Laughlin wavefunction,
we were able to determine accurately, via classical Monte Carlo calculations,
the amplitude and distribution of the peak-spacing fluctuations.
Our results clearly demonstrate a big enhancement of the fluctuations as the
importance of the electronic correlations increases, namely as the density
decreases and filling factor becomes smaller.
We also find that the distribution of the fluctuations approaches a Gaussian
with increasing density of random potentials.Comment: 6 pages, 3 figures all in gzipped tarred fil
Theory of Magneto-resistance of Disordered Superconducting Films
Recent experimental studies of magneto-resistance in disordered
superconducting thin films reveal a huge peak (about 5 orders of magnitude).
While it may be expected that magnetic field destroys superconductivity,
leading to an enhanced resistance, attenuation of the resistance at higher
magnetic fields is surprising.
We propose a model which accounts for the experimental results in the entire
range of magnetic fields, based on the formation of superconducting islands due
to fluctuations in the superconducting order parameter amplitude. At strong
magnetic fields Coulomb blockade in these islands gives rise to negative
magneto-resistance. As the magnetic field is reduced the effect of Coulomb
blockade diminishes and eventually the magneto-resistance changes sign.
Numerical calculations show good qualitative agreement with experimental data.Comment: 4 pages, 4 figure
Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling
We establish an exactly tight relation between reversible pebblings of graphs and Nullstellensatz refutations of pebbling formulas, showing that a graph G can be reversibly pebbled in time t and space s if and only if there is a Nullstellensatz refutation of the pebbling formula over G in size t+1 and degree s (independently of the field in which the Nullstellensatz refutation is made). We use this correspondence to prove a number of strong size-degree trade-offs for Nullstellensatz, which to the best of our knowledge are the first such results for this proof system
A New Spin-Orbit Induced Universality Class in the Quantum Hall Regime ?
Using heuristic arguments and numerical simulations it is argued that the
critical exponent describing the localization length divergence at the
quantum Hall transition is modified in the presence of spin-orbit scattering
with short range correlations. The exponent is very close to , the
percolation correlation length exponent, the prediction of a semi-classical
argument. In addition, a region of weakly localized regime, where the
localization length is exponentially large, is conjectured.Comment: 4 two-column pages including 4 eps figure
Epstein-Barr virus lytic gene expression is tightly linked to ER stress but not cytotoxicity with bortezomib or nelfinavir
Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling
We establish an exactly tight relation between reversible pebblings of graphs
and Nullstellensatz refutations of pebbling formulas, showing that a graph
can be reversibly pebbled in time and space if and only if there is a
Nullstellensatz refutation of the pebbling formula over in size and
degree (independently of the field in which the Nullstellensatz refutation
is made). We use this correspondence to prove a number of strong size-degree
trade-offs for Nullstellensatz, which to the best of our knowledge are the
first such results for this proof system
Orbital Magnetism and Current Distribution of Two-Dimensional Electrons under Confining Potential
The spatial distribution of electric current under magnetic field and the
resultant orbital magnetism have been studied for two-dimensional electrons
under a harmonic confining potential V(\vecvar{r})=m \omega_0^2 r^2/2 in
various regimes of temperature and magnetic field, and the microscopic
conditions for the validity of Landau diamagnetism are clarified. Under a weak
magnetic field (\omega_c\lsim\omega_0, \omega_c being a cyclotron frequency)
and at low temperature (T\lsim\hbar\omega_0), where the orbital magnetic
moment fluctuates as a function of the field, the currents are irregularly
distributed paramagnetically or diamagnetically inside the bulk region. As the
temperature is raised under such a weak field, however, the currents in the
bulk region are immediately reduced and finally there only remains the
diamagnetic current flowing along the edge. At the same time, the usual Landau
diamagnetism results for the total magnetic moment. The origin of this dramatic
temperature dependence is seen to be in the multiple reflection of electron
waves by the boundary confining potential, which becomes important once the
coherence length of electrons gets longer than the system length. Under a
stronger field (\omega_c\gsim\omega_0), on the other hand, the currents in
the bulk region cause de Haas-van Alphen effect at low temperature as
T\lsim\hbar\omega_c. As the temperature gets higher (T\gsim\hbar\omega_c)
under such a strong field, the bulk currents are reduced and the Landau
diamagnetism by the edge current is recovered.Comment: 15 pages, 11 figure
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