3,208 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
Explicit Learning Curves for Transduction and Application to Clustering and Compression Algorithms
Inductive learning is based on inferring a general rule from a finite data
set and using it to label new data. In transduction one attempts to solve the
problem of using a labeled training set to label a set of unlabeled points,
which are given to the learner prior to learning. Although transduction seems
at the outset to be an easier task than induction, there have not been many
provably useful algorithms for transduction. Moreover, the precise relation
between induction and transduction has not yet been determined. The main
theoretical developments related to transduction were presented by Vapnik more
than twenty years ago. One of Vapnik's basic results is a rather tight error
bound for transductive classification based on an exact computation of the
hypergeometric tail. While tight, this bound is given implicitly via a
computational routine. Our first contribution is a somewhat looser but explicit
characterization of a slightly extended PAC-Bayesian version of Vapnik's
transductive bound. This characterization is obtained using concentration
inequalities for the tail of sums of random variables obtained by sampling
without replacement. We then derive error bounds for compression schemes such
as (transductive) support vector machines and for transduction algorithms based
on clustering. The main observation used for deriving these new error bounds
and algorithms is that the unlabeled test points, which in the transductive
setting are known in advance, can be used in order to construct useful data
dependent prior distributions over the hypothesis space
Phase switching in a voltage-biased Aharonov-Bohm interferometer
Recent experiment [Sigrist et al., Phys. Rev. Lett. {\bf 98}, 036805 (2007)]
reported switches between 0 and in the phase of Aharonov-Bohm
oscillations of the two-terminal differential conductance through a two-dot
ring with increasing voltage bias. Using a simple model, where one of the dots
contains multiple interacting levels, these findings are explained as a result
of transport through the interferometer being dominated at different biases by
quantum dot levels of different "parity" (i.e. the sign of the overlap integral
between the dot state and the states in the leads). The redistribution of
electron population between different levels with bias leads to the fact that
the number of switching events is not necessarily equal to the number of dot
levels, in agreement with experiment. For the same reason switching does not
always imply that the parity of levels is strictly alternating. Lastly, it is
demonstrated that the correlation between the first switching of the phase and
the onset of the inelastic cotunneling, as well as the sharp (rather than
gradual) change of phase when switching occurs, give reason to think that the
present interpretation of the experiment is preferable to the one based on
electrostatic AB effect.Comment: 12 pages, 9 figure
Acyclic Games and Iterative Voting
We consider iterative voting models and position them within the general
framework of acyclic games and game forms. More specifically, we classify
convergence results based on the underlying assumptions on the agent scheduler
(the order of players) and the action scheduler (which better-reply is played).
Our main technical result is providing a complete picture of conditions for
acyclicity in several variations of Plurality voting. In particular, we show
that (a) under the traditional lexicographic tie-breaking, the game converges
for any order of players under a weak restriction on voters' actions; and (b)
Plurality with randomized tie-breaking is not guaranteed to converge under
arbitrary agent schedulers, but from any initial state there is \emph{some}
path of better-replies to a Nash equilibrium. We thus show a first separation
between restricted-acyclicity and weak-acyclicity of game forms, thereby
settling an open question from [Kukushkin, IJGT 2011]. In addition, we refute
another conjecture regarding strongly-acyclic voting rules.Comment: some of the results appeared in preliminary versions of this paper:
Convergence to Equilibrium of Plurality Voting, Meir et al., AAAI 2010;
Strong and Weak Acyclicity in Iterative Voting, Meir, COMSOC 201
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
Andreev Tunneling in Strongly Interacting Quantum Dots
We review recent work on resonant Andreev tunneling through a strongly
interacting quantum dot connected to a normal and to a superconducting lead. We
derive a general expression for the current flowing in the structure and
discuss the linear and non-linear transport in the nonperturbative regime. New
effects associated to the Kondo resonance combined with the two-particle
tunneling arise. The Kondo anomaly in the characteristics depends on the
relative size of the gap energy and the Kondo temperature.Comment: 8 pages, 4 figures; submitted to Superlattices and Microstructure
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