72,674 research outputs found
On the spectral distribution of kernel matrices related to\ud radial basis functions
This paper focuses on the spectral distribution of kernel matrices related to radial basis functions. The asymptotic behaviour of eigenvalues of kernel matrices related to radial basis functions with different smoothness are studied. These results are obtained by estimated the coefficients of an orthogonal expansion of the underlying kernel function. Beside many other results, we prove that there are exactly (k+d−1/d-1) eigenvalues in the same order for analytic separable kernel functions like the Gaussian in Rd. This gives theoretical support for how to choose the diagonal scaling matrix in the RBF-QR method (Fornberg et al, SIAM J. Sci. Comput. (33), 2011) which can stably compute Gaussian radial basis function interpolants
Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron
In this article the framework for Parisi's spontaneous replica symmetry
breaking is reviewed, and subsequently applied to the example of the
statistical mechanical description of the storage properties of a
McCulloch-Pitts neuron. The technical details are reviewed extensively, with
regard to the wide range of systems where the method may be applied. Parisi's
partial differential equation and related differential equations are discussed,
and a Green function technique introduced for the calculation of replica
averages, the key to determining the averages of physical quantities. The
ensuing graph rules involve only tree graphs, as appropriate for a
mean-field-like model. The lowest order Ward-Takahashi identity is recovered
analytically and is shown to lead to the Goldstone modes in continuous replica
symmetry breaking phases. The need for a replica symmetry breaking theory in
the storage problem of the neuron has arisen due to the thermodynamical
instability of formerly given solutions. Variational forms for the neuron's
free energy are derived in terms of the order parameter function x(q), for
different prior distribution of synapses. Analytically in the high temperature
limit and numerically in generic cases various phases are identified, among
them one similar to the Parisi phase in the Sherrington-Kirkpatrick model.
Extensive quantities like the error per pattern change slightly with respect to
the known unstable solutions, but there is a significant difference in the
distribution of non-extensive quantities like the synaptic overlaps and the
pattern storage stability parameter. A simulation result is also reviewed and
compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi,
eepic), accepted for Physics Report
Continuous quantum phase transition in a Kondo lattice model
We study the magnetic quantum phase transition in an anisotropic Kondo
lattice model. The dynamical competition between the RKKY and Kondo
interactions is treated using an extended dynamic mean field theory (EDMFT)
appropriate for both the antiferromagnetic and paramagnetic phases. A quantum
Monte Carlo approach is used, which is able to reach very low temperatures, of
the order of 1% of the bare Kondo scale. We find that the finite-temperature
magnetic transition, which occurs for sufficiently large RKKY interactions, is
first order. The extrapolated zero-temperature magnetic transition, on the
other hand, is continuous and locally critical.Comment: 4 pages, 4 figures; updated, to appear in PR
Perturbation theory of von Neumann Entropy
In quantum information theory, von Neumann entropy plays an important role.
The entropies can be obtained analytically only for a few states. In continuous
variable system, even evaluating entropy numerically is not an easy task since
the dimension is infinite. We develop the perturbation theory systematically
for calculating von Neumann entropy of non-degenerate systems as well as
degenerate systems. The result turns out to be a practical way of the expansion
calculation of von Neumann entropy.Comment: 7 page
Reward Poisoning in Reinforcement Learning: Attacks Against Unknown Learners in Unknown Environments
We study black-box reward poisoning attacks against reinforcement learning (RL), in which an adversary aims to manipulate the rewards to mislead a sequence of RL agents with unknown algorithms to learn a nefarious policy in an environment unknown to the adversary a priori. That is, our attack makes minimum assumptions on the prior knowledge of the adversary: it has no initial knowledge of the environment or the learner, and neither does it observe the learner's internal mechanism except for its performed actions. We design a novel black-box attack, U2, that can provably achieve a near-matching performance to the state-of-the-art white-box attack, demonstrating the feasibility of reward poisoning even in the most challenging black-box setting
Spin and Current Variations in Josephson Junctions
We study the dynamics of a single spin embedded in the tunneling barrier
between two superconductors. As a consequence of pair correlations in the
superconducting state, the spin displays rich and unusual dynamics. To properly
describe the time evolution of the spin we derive the effective Keldysh action
for the spin. The superconducting correlations lead to an effective spin
action, which is non-local in time, leading to unconventional precession. We
further illustrate how the current is modulated by this novel spin dynamics
Electrohydrodynamic jet printing of PZT thick film micro-scale structures
This paper reports the use of a printing technique, called electrohydrodynamic jet printing, for producing PZT thick film micro-scale structures without additional material removing processes. The PZT powder was ball-milled and the effect of milling time on the particle size was examined. This ball-milling process can significantly reduce the PZT particle size and help to prepare stable composite slurry suitable for the E-Jet printing. The PZT micro-scale structures with different features were produced. The PZT lines with different widths and separations were fabricated through the control of the E-Jet printing parameters. The widths of the PZT lines were varied from 80 μm to 200 μm and the separations were changed from 5 μm to 200 μm. In addition, PZT walled structures were obtained by multi-layer E-Jet printing. The E-Jet printed PZT thick films exhibited a relative permittivity (ɛr) of ∼233 and a piezoelectric constant (d33, f) of ∼66 pC N−1
Proximity effect in atomic-scaled hybrid superconductor/ferromagnet structures: crucial role of electron spectra
We study the influence of the configuration of the majority and minority spin
subbands of electron spectra on the properties of atomic-scaled
superconductor-ferromagnet S-F-S and F-S-F hybrid structures. At low
temperatures, the S/F/S junction is either a 0 or junction depending on the
energy shift between S and F materials and the anisotropy of the Fermi
surfaces. We found that the spin switch effect in F/S/F system can be reversed
if the minority spin electron spectra in F metal is of the hole-like type
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