1,428 research outputs found
Fractionally Predictive Spiking Neurons
Recent experimental work has suggested that the neural firing rate can be
interpreted as a fractional derivative, at least when signal variation induces
neural adaptation. Here, we show that the actual neural spike-train itself can
be considered as the fractional derivative, provided that the neural signal is
approximated by a sum of power-law kernels. A simple standard thresholding
spiking neuron suffices to carry out such an approximation, given a suitable
refractory response. Empirically, we find that the online approximation of
signals with a sum of power-law kernels is beneficial for encoding signals with
slowly varying components, like long-memory self-similar signals. For such
signals, the online power-law kernel approximation typically required less than
half the number of spikes for similar SNR as compared to sums of similar but
exponentially decaying kernels. As power-law kernels can be accurately
approximated using sums or cascades of weighted exponentials, we demonstrate
that the corresponding decoding of spike-trains by a receiving neuron allows
for natural and transparent temporal signal filtering by tuning the weights of
the decoding kernel.Comment: 13 pages, 5 figures, in Advances in Neural Information Processing
201
Consequences of the Pauli exclusion principle for the Bose-Einstein condensation of atoms and excitons
The bosonic atoms used in present day experiments on Bose-Einstein
condensation are made up of fermionic electrons and nucleons. In this Letter we
demonstrate how the Pauli exclusion principle for these constituents puts an
upper limit on the Bose-Einstein-condensed fraction. Detailed numerical results
are presented for hydrogen atoms in a cubic volume and for excitons in
semiconductors and semiconductor bilayer systems. The resulting condensate
depletion scales differently from what one expects for bosons with a repulsive
hard-core interaction. At high densities, Pauli exclusion results in
significantly more condensate depletion. These results also shed a new light on
the low condensed fraction in liquid helium II.Comment: 4 pages, 2 figures, revised version, now includes a direct comparison
with hard-sphere QMC results, submitted to Phys. Rev. Let
Engineering Local optimality in Quantum Monte Carlo algorithms
Quantum Monte Carlo algorithms based on a world-line representation such as
the worm algorithm and the directed loop algorithm are among the most powerful
numerical techniques for the simulation of non-frustrated spin models and of
bosonic models. Both algorithms work in the grand-canonical ensemble and have a
non-zero winding number. However, they retain a lot of intrinsic degrees of
freedom which can be used to optimize the algorithm. We let us guide by the
rigorous statements on the globally optimal form of Markov chain Monte Carlo
simulations in order to devise a locally optimal formulation of the worm
algorithm while incorporating ideas from the directed loop algorithm. We
provide numerical examples for the soft-core Bose-Hubbard model and various
spin-S models.Comment: replaced with published versio
Semiparametric multivariate volatility models
Estimation of multivariate volatility models is usually carried out by quasi maximum likelihood (QMLE), for which consistency and asymptotic normality have been proven under quite general conditions. However, there may be a substantial efficiency loss of QMLE if the true innovation distribution is not multinormal. We suggest a nonparametric estimation of the multivariate innovation distribution, based on consistent parameter estimates obtained by QMLE. We show that under standard regularity conditions the semiparametric efficiency bound can be attained. Without reparametrizing the conditional covariance matrix (which depends on the particular model used), adaptive estimation is not possible. However, in some cases the e?ciency loss of semiparametric estimation with respect to full information maximum likelihood decreases as the dimension increases. In practice, one would like to restrict the class of possible density functions to avoid the curse of dimensionality. One way of doing so is to impose the constraint that the density belongs to the class of spherical distributions, for which we also derive the semiparametric efficiency bound and an estimator that attains this bound. A simulation experiment demonstrates the e?ciency gain of the proposed estimator compared with QMLE. --Multivariate volatility,GARCH,semiparametric efficiency,adaptivity
Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices
The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard
model is studied in the canonical ensemble using a quantum Monte Carlo method.
We focus on the case where both species have half filling in order to maximize
the pairing correlations between the bosons and the fermions. In case of equal
hopping we distinguish between phase separation, a Luttinger liquid phase and a
phase characterized by strong singlet pairing between the species. True
long-range density waves exist with unequal hopping amplitudes.Comment: 5 pages, 5 figures, replaced with published versio
Integrable two-channel p_x+ip_y-wave superfluid model
We present a new two-channel integrable model describing a system of spinless
fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC
crossover of the s-wave case, the p-wave model has a third order quantum phase
transition. The critical point coincides with the deconfinement of a single
molecule within a BEC of bound dipolar molecules. The exact many-body
wavefunction provides a unique perspective of the quantum critical region
suggesting that the size of the condensate wavefunction, that diverges
logarithmically with the chemical potential, could be used as an experimental
indicator of the phase transition.Comment: 4 pages, 4 figure
Existence of Density Functionals for Excited States and Resonances
We show how every bound state of a finite system of identical fermions,
whether a ground state or an excited one, defines a density functional.
Degeneracies created by a symmetry group can be trivially lifted by a
pseudo-Zeeman effect. When complex scaling can be used to regularize a
resonance into a square integrable state, a DF also exists.Comment: 4 pages, no figure
Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime
Recent experiments on ultracold atomic alkali gases in a one-dimensional
optical lattice have demonstrated the transition from a gas of soft-core bosons
to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons
behave like fermions in many respects. We have studied the underlying many-body
physics through numerical simulations which accommodate both the soft-core and
hard-core limits in one single framework. We find that the Tonks-Girardeau gas
is reached only at the strongest optical lattice potentials. Results for
slightly higher densities, where the gas develops a Mott-like phase already at
weaker optical lattice potentials, show that these Mott-like short range
correlations do not enhance the convergence to the hard-core limit.Comment: 4 pages, 3 figures, replaced with published versio
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