Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models

We study two planar square lattice Heisenberg models with explicit dimerization or quadrumerization of the couplings in the form of ladder and plaquette arrangements. We investigate the quantum critical points of those models by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\alpha = J^\prime/J$. The critical point of the order-disorder quantum phase transition in the ladder model is determined as $\alpha_\mathrm{c} = 1.9096(2)$ improving on previous studies. For the plaquette model we obtain $\alpha_\mathrm{c} = 1.8230(2)$ establishing a first benchmark for this model from quantum Monte Carlo simulations. Based on those values we give further convincing evidence that the models are in the three-dimensional (3D) classical Heisenberg universality class. The results of this contribution shall be useful as references for future investigations on planar Heisenberg models such as concerning the influence of non-magnetic impurities at the quantum critical point.Comment: 10+ pages, 7 figures, 4 table

Suggestive Annotation: A Deep Active Learning Framework for Biomedical Image Segmentation

Image segmentation is a fundamental problem in biomedical image analysis. Recent advances in deep learning have achieved promising results on many biomedical image segmentation benchmarks. However, due to large variations in biomedical images (different modalities, image settings, objects, noise, etc), to utilize deep learning on a new application, it usually needs a new set of training data. This can incur a great deal of annotation effort and cost, because only biomedical experts can annotate effectively, and often there are too many instances in images (e.g., cells) to annotate. In this paper, we aim to address the following question: With limited effort (e.g., time) for annotation, what instances should be annotated in order to attain the best performance? We present a deep active learning framework that combines fully convolutional network (FCN) and active learning to significantly reduce annotation effort by making judicious suggestions on the most effective annotation areas. We utilize uncertainty and similarity information provided by FCN and formulate a generalized version of the maximum set cover problem to determine the most representative and uncertain areas for annotation. Extensive experiments using the 2015 MICCAI Gland Challenge dataset and a lymph node ultrasound image segmentation dataset show that, using annotation suggestions by our method, state-of-the-art segmentation performance can be achieved by using only 50% of training data.Comment: Accepted at MICCAI 201

Research on nonlinear optical materials: an assessment. IV. Photorefractive and liquid crystal materials

This panel considered two separate subject areas: photorefractive materials used for nonlinear optics and liquid crystal materials used in light valves. Two related subjects were not considered due to lack of expertise on the panel: photorefractive materials used in light valves and liquid crystal materials used in nonlinear optics. Although the inclusion of a discussion of light valves by a panel on nonlinear optical materials at first seems odd, it is logical because light valves and photorefractive materials perform common functions

Optical homodyne tomography with polynomial series expansion

We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner function and the marginal distribution and discretize Fourier space. We show that this technique solves most technical difficulties encountered with kernel deconvolution based methods and reconstructs overall better and smoother Wigner functions. We also give estimators of the reconstruction errors for both methods and show improvement in noise handling properties and resilience to statistical errors.Comment: v3: 3 typos were corrected in some mathematical expressions. v2: Many typos corrected. Added a paragraph on distance to target state in Sec. I

Design strategies for optimizing holographic optical tweezers setups

We provide a detailed account of the construction of a system of holographic optical tweezers. While much information is available on the design, alignment and calibration of other optical trapping configurations, those based on holography are relatively poorly described. Inclusion of a spatial light modulator in the setup gives rise to particular design trade-offs and constraints, and the system benefits from specific optimization strategies, which we discuss.Comment: 16 pages, 15 figure

Variability and multi-periodic oscillations in the X-ray light curve of the classical nova V4743 Sgr

The classical nova V4743 Sgr was observed with XMM-Newton for about 10 hours on April 4 2003, 6.5 months after optical maximum. At this time, this nova had become the brightest supersoft X-ray source ever observed. We present the results of a time series analysis performed on the X-ray light curve obtained in this observation, and in a previous shorter observation done with Chandra 16 days earlier. Intense variability, with amplitude as large as 40% of the total flux, was observed both times. Similarities can be found between the two observations in the structure of the variations. Most of the variability is well represented as a combination of oscillations at a set of discrete frequencies lower than 1.7 mHz. At least five frequencies are constant over the 16 day time interval between the two observations. We suggest that a periods in the power spectrum of both light curves at the frequency of 0.75 mHz and its first harmonic are related to the spin period of the white dwarf in the system, and that other observed frequencies are signatures of nonradial white dwarf pulsations. A possible signal with a 24000 sec period is also found in the XMM-Newton light curve: a cycle and a half are clearly identified. This period is consistent with the 24278 s periodicity discovered in the optical light curve of the source and thought to be the orbital period of the nova binary system.Comment: In press in Monthly Notices of the Royal Astronomical Societ

A manually reconfigurable reflective spatial sound modulator for ultrasonic waves in air

Precise control of ultrasonic acoustic waves with frequencies f ≳ 20 kHz is useful in a range of applications from ultrasonic scanners to nondestructive testing and consumer haptic devices. A spatial sound modulator (SSM) is the acoustic analogy to the spatial light modulator (SLM) in optics and is highly sought after by acoustics researchers. A spatial sound modulator is constrained by very distinct practical conditions. Namely, it must be a reconfigurable device which modulates sound arbitrarily from a decoupled source. Here a reflective phase modulating device is realized, whose local units can be tuned to imprint a phase signature to an incoming wave. It is manually reconfigurable and consists of 1024 rigidly ended square waveguides with sliding bottom surfaces to provide variable phase delays. Experiments demonstrate the ability of this device to focus ultrasonic waves in air at different points in space, generate accurate pressure landscapes, and perform multiplane holography. Moreover, thanks to the subwavelength nature of the unit cells, this device outperforms state‐of‐the‐art phased‐array transducers of the same size in the quality and energy distribution of generated acoustic holographic images. These results pave the way for the construction of electronically controlled reflective SSM

Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents $\nu,\alpha,\beta,\gamma, \eta$ from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to $100^3$ spins. This enables us to compute independent estimates of $\nu$ and $\gamma$ from power-law fits of their critical divergencies.Comment: 33 pages, 12 figures (not included, available on request). Preprint FUB-HEP 19/92, HLRZ 77/92, September 199

A Path Algorithm for Constrained Estimation

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new path following algorithm for quadratic programming based on exact penalization. Similar penalties arise in $l_1$ regularization in model selection. Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the lasso and generalized lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well chosen examples illustrate the mechanics and potential of path following.Comment: 26 pages, 5 figure

Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths

We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function $G_{diam}(x)$, which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter $x$, $G_{diam} \propto \exp(-x/\xi)$, where $\xi$ is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with $q=10$, 15, and $20$ on large square lattices of size $300 \times 300$, $120 \times 120$, and $80 \times 80$, respectively, clearly confirm the theoretically predicted behavior. Moreover, using this observable we are able to verify an exact formula for the correlation length $\xi_d(\beta_t)$ in the disordered phase at the first-order transition point $\beta_t$ with an accuracy of about $1$ for all considered values of $q$. This is a considerable improvement over estimates derived from the large-distance behavior of standard (projected) two-point correlation functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm