MaskDensity14: an R package for the density approximant of a univariate based on noise multiplied data

Lin (2014) developed a framework of the method of the sample-moment-based density approximant, for estimating the probability density function of microdata based on noise multiplied data. Theoretically, it provides a promising method for data users in generating the synthetic data of the original data without accessing the original data; however, technical issues can cause problems implementing the method. In this paper, we describe a software package called MaskDensity14, written in the R language, that uses a computational approach to solve the technical issues and makes the method of the sample-moment-based density approximant feasible. MaskDensity14 has applications in many areas, such as sharing clinical trial data and survey data without releasing the original data

Analytic continuation by averaging Pad\'e approximants

The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pad\'{e} approximants technique. We propose to remedy the well-known problems of the Pad\'{e} approximants by performing an average of several continuations, obtained by varying the number of fitted input points and Pad\'{e} coefficients independently. The suggested approach is then applied to several test cases, including Sm and Pr atomic self-energies, the Green's functions of the Hubbard model for a Bethe lattice and of the Haldane model for a nano-ribbon, as well as two special test functions. The sensitivity to numerical noise and the dependence on the precision of the numerical libraries are analysed in detail. The present approach is compared to a number of other techniques, i.e. the non-negative least-square method, the non-negative Tikhonov method and the maximum entropy method, and is shown to perform well for the chosen test cases. This conclusion holds even when the noise on the input data is increased to reach values typical for quantum Monte Carlo simulations. The ability of the algorithm to resolve fine structures is finally illustrated for two relevant test functions.Comment: 10 figure

Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations

We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.Comment: 15 pages, corrected typos, updated references, improvements in discussio

Finite Density Algorithm in Lattice QCD -- a Canonical Ensemble Approach

I will review the finite density algorithm for lattice QCD based on finite chemical potential and summarize the associated difficulties. I will propose a canonical ensemble approach which projects out the finite baryon number sector from the fermion determinant. For this algorithm to work, it requires an efficient method for calculating the fermion determinant and a Monte Carlo algorithm which accommodates unbiased estimate of the probability. I shall report on the progress made along this direction with the Pad\'{e} - Z$_2$ estimator of the determinant and its implementation in the newly developed Noisy Monte Carlo algorithm.Comment: Invited talk at Nankai Symposium on Mathematical Physics, Tianjin, Oct. 2001, 18 pages, 3 figures; expanded and references adde

Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries

Frequency-domain filters for time-windowed gravitational waves from inspiralling compact binaries are constructed which combine the excellent performance of our previously developed time-domain P-approximants with the analytic convenience of the stationary phase approximation without a serious loss in event rate. These Fourier-domain representations incorporate the ``edge oscillations'' due to the (assumed) abrupt shut-off of the time-domain signal caused by the relativistic plunge at the last stable orbit. These new analytic approximations, the SPP-approximants, are not only `effectual' for detection and `faithful' for parameter estimation, but are also computationally inexpensive to generate (and are `faster' by factors up to 10, as compared to the corresponding time-domain templates). The SPP approximants should provide data analysts the Fourier-domain templates for massive black hole binaries of total mass m less than about 40 solar mases, the most likely sources for LIGO and VIRGO.Comment: 50 Pages, 10 Postscript figures, 7 Tables, Revtex, Typos corrected, References updated, Additions on pages 25, 26 and 3

The Co-Ni distribution in decagonal Al69.7(4)Co10.0(4)Ni20.3(4)

The Co—Ni distribution in d-Al69.7(4)Co10.0(4)Ni20.3(4) was investigated based on X-ray and neutron diffraction data. The structure was modelled in higher dimensional space using the ‘charge-flipping' and ‘low-density elimination' methods and it was quantitatively refined in three-dimensional space employing a pseudo-approximant approach. In higher-dimensional description, the Co atoms are found at the centre of one of the two symmetry independent occupation domains, enclosed by regions mainly occupied by Ni. The other occupation domain is mostly occupied by Al. In physical space Co atoms are located in the centres of small Al pentagons and form pentagonal units, which are arranged in decagonal rings. On these sites Co is partly substituted by Ni, while all other transition metal sites are occupied by Ni and to a minor degree by Al. The fraction of Co found on transition metal sites decreases with decreasing Co-Co distances, whereby Co is replaced by N

Low Photon Count Phase Retrieval Using Deep Learning

Imaging systems' performance at low light intensity is affected by shot noise, which becomes increasingly strong as the power of the light source decreases. In this paper we experimentally demonstrate the use of deep neural networks to recover objects illuminated with weak light and demonstrate better performance than with the classical Gerchberg-Saxton phase retrieval algorithm for equivalent signal over noise ratio. Prior knowledge about the object is implicitly contained in the training data set and feature detection is possible for a signal over noise ratio close to one. We apply this principle to a phase retrieval problem and show successful recovery of the object's most salient features with as little as one photon per detector pixel on average in the illumination beam. We also show that the phase reconstruction is significantly improved by training the neural network with an initial estimate of the object, as opposed as training it with the raw intensity measurement.Comment: 8 pages, 5 figure