37,528 research outputs found
How to get a conservative well-posed linear system out of thin air. Part II. Controllability and stability
Published versio
Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction
For large, real-world inductive learning problems, the number of training
examples often must be limited due to the costs associated with procuring,
preparing, and storing the training examples and/or the computational costs
associated with learning from them. In such circumstances, one question of
practical importance is: if only n training examples can be selected, in what
proportion should the classes be represented? In this article we help to answer
this question by analyzing, for a fixed training-set size, the relationship
between the class distribution of the training data and the performance of
classification trees induced from these data. We study twenty-six data sets
and, for each, determine the best class distribution for learning. The
naturally occurring class distribution is shown to generally perform well when
classifier performance is evaluated using undifferentiated error rate (0/1
loss). However, when the area under the ROC curve is used to evaluate
classifier performance, a balanced distribution is shown to perform well. Since
neither of these choices for class distribution always generates the
best-performing classifier, we introduce a budget-sensitive progressive
sampling algorithm for selecting training examples based on the class
associated with each example. An empirical analysis of this algorithm shows
that the class distribution of the resulting training set yields classifiers
with good (nearly-optimal) classification performance
Decay of correlations in the dissipative two-state system
We study the equilibrium correlation function of the polaron-dressed
tunnelling operator in the dissipative two-state system and compare the
asymptoptic dynamics with that of the position correlations. For an Ohmic
spectral density with the damping strength , the correlation functions
are obtained in analytic form for all times at any and any bias. For ,
the asymptotic dynamics is found by using a diagrammatic approach within a
Coulomb gas representation. At T=0, the tunnelling or coherence correlations
drop as , whereas the position correlations show universal decay
. The former decay law is a signature of unscreened attractive
charge-charge interactions, while the latter is due to unscreened dipole-dipole
interactions.Comment: 5 pages, 5 figures, to be published in Europhys. Let
Characterization of coherent impurity effects in solid state qubits
We propose a characterisation of the effects of bistable coherent impurities
in solid state qubits. We introduce an effective impurity description in terms
of a tunable spin-boson environment and solve the dynamics for the qubit
coherences. The dominant rate characterizing the asymptotic time limit is
identified and signatures of non-Gaussian behavior of the quantum impurity at
intermediate times are pointed out. An alternative perspective considering the
qubit as a measurement device for the spin-boson impurity is proposed.Comment: 4 pages, 5 figures. Replaced with published version, minor change
Realizing vector meson dominance with transverse charge densities
The transverse charge density in a fast-moving nucleon is represented as a
dispersion integral of the imaginary part of the Dirac form factor in the
timelike region (spectral function). At a given transverse distance b the
integration effectively extends over energies in a range sqrt{t} ~< 1/b, with
exponential suppression of larger values. The transverse charge density at
peripheral distances thus acts as a low-pass filter for the spectral function
and allows one to select energy regions dominated by specific t-channel states,
corresponding to definite exchange mechanisms in the spacelike form factor. We
show that distances b ~ 0.5 - 1.5 fm in the isovector density are maximally
sensitive to the rho meson region, with only a ~10% contribution from
higher-mass states. Soft-pion exchange governed by chiral dynamics becomes
relevant only at larger distances. In the isoscalar density higher-mass states
beyond the omega are comparatively more important. The dispersion approach
suggests that the positive transverse charge density in the neutron at b ~ 1
fm, found previously in a Fourier analysis of spacelike form factor data, could
serve as a sensitive test of the the isoscalar strength in the ~1 GeV mass
region. In terms of partonic structure, the transverse densities in the vector
meson region b ~ 1 fm support an approximate mean-field picture of the motion
of valence quarks in the nucleon.Comment: 14 pages, 12 figure
Hopping conductivity in heavily doped n-type GaAs layers in the quantum Hall effect regime
We investigate the magnetoresistance of epitaxially grown, heavily doped
n-type GaAs layers with thickness (40-50 nm) larger than the electronic mean
free path (23 nm). The temperature dependence of the dissipative resistance
R_{xx} in the quantum Hall effect regime can be well described by a hopping law
(R_{xx} \propto exp{-(T_0/T)^p}) with p=0.6. We discuss this result in terms of
variable range hopping in a Coulomb gap together with a dependence of the
electron localization length on the energy in the gap. The value of the
exponent p>0.5 shows that electron-electron interactions have to be taken into
account in order to explain the occurrence of the quantum Hall effect in these
samples, which have a three-dimensional single electron density of states.Comment: 5 pages, 2 figures, 1 tabl
Scaling and data collapse for the mean exit time of asset prices
We study theoretical and empirical aspects of the mean exit time of financial
time series. The theoretical modeling is done within the framework of
continuous time random walk. We empirically verify that the mean exit time
follows a quadratic scaling law and it has associated a pre-factor which is
specific to the analyzed stock. We perform a series of statistical tests to
determine which kind of correlation are responsible for this specificity. The
main contribution is associated with the autocorrelation property of stock
returns. We introduce and solve analytically both a two-state and a three-state
Markov chain models. The analytical results obtained with the two-state Markov
chain model allows us to obtain a data collapse of the 20 measured MET profiles
in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
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