Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity

Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find optimal solutions. Here, we investigate how the system's nonlinear transfer function can mitigate amplitude inhomogeneity and improve computational performance. By simulating Ising machines with polynomial, periodic, sigmoid and clipped transfer functions and benchmarking them with MaxCut optimization problems, we find the choice of transfer function to have a significant influence on the calculation time and solution quality. For periodic, sigmoid and clipped transfer functions, we report order-of-magnitude improvements in the time-to-solution compared to conventional polynomial models, which we link to the suppression of amplitude inhomogeneity induced by saturation of the transfer function. This provides insights into the suitability of systems for building Ising machines and presents an efficient way for overcoming performance limitations

Block Crossings in Storyline Visualizations

Storyline visualizations help visualize encounters of the characters in a story over time. Each character is represented by an x-monotone curve that goes from left to right. A meeting is represented by having the characters that participate in the meeting run close together for some time. In order to keep the visual complexity low, rather than just minimizing pairwise crossings of curves, we propose to count block crossings, that is, pairs of intersecting bundles of lines. Our main results are as follows. We show that minimizing the number of block crossings is NP-hard, and we develop, for meetings of bounded size, a constant-factor approximation. We also present two fixed-parameter algorithms and, for meetings of size 2, a greedy heuristic that we evaluate experimentally.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

From Equilibrium to Steady-State Dynamics after Switch-On of Shear

A relation between equilibrium, steady-state, and waiting-time dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semi-quantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios (Phys. Rev. Lett. 102, 135701). For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.Comment: 16 pages, 12 figures, submitted to Phys Rev

Automated detection and classification of nuclei in immunohistochemical stainings for Fuchs' endothelial corneal dystrophy

Fuchs’ endothelial corneal dystrophy (FECD) is a degenerative disease that affects the elderly population, and which lacks a unifying pathogenic theory and tangible drug targets. Immunohistochemical stainings can be used to identify proteins involved in the pathogenesis of FECD. We introduce a method for the automatic quantification of the ratio of stained cells starting from full high-resolution cornea images. First, the endothelium is extracted using entropy information in a low-resolution resampling. Then, within the endothelium, we heuristically detect and classify nuclei based on their size, color, and the color of the surrounding cytoplasm. This method achieves comparable results to manual evaluation in a set of corneas of patients with and without FECD.status: publishe

Recent X-ray Observations and the Evolution of Hot Gas in Elliptical Galaxies: Evidence for Circumgalactic Gas

X-ray emitting gaseous halos, such as that in elliptical galaxies like NGC 4472, cannot have been produced solely from gas expelled from galactic stars. In traditional models for the evolution of hot interstellar gas (cooling flows) in ellipticals, the galaxies are assumed to have been cleared of gas by SNII-driven winds at some early time then gas is subsequently replenished by mass loss from an evolving population of old stars. To test this, we accurately determine the stellar and dark halo mass of NGC 4472 using hydrostatic equilibrium, then solve the standard time-dependent cooling flow equations to recover the observed hot gas temperature and density distributions when evolved to the present time. This procedure fails: the computed gas density gradient is too steep, the total gas mass is too low, and the gas temperatures are much too low. All variants on this basic procedure also fail: increasing the SNIa rate, using the mass dropout assumption, arbitrarily adjusting uncertain coefficients, etc. However, agreement is achieved if the galaxy is supplied with additional, spatially-extended hot gas early in its evolution. This old ``circumgalactic'' gas can be retained to the present time and may be related to cosmological ``secondary infall''.Comment: 15 pages in two-column AASTEX LaTeX including 1 table and 8 figures; abstract corrected in replacement; accepted by Astrophysical Journa

Automated detection and classification of nuclei in immunohistochemical stainings for Fuchs\u27 endothelial corneal dystrophy

Fuchs’ endothelial corneal dystrophy (FECD) is a degenerative disease that affects the elderly population, and which lacks a unifying pathogenic theory and tangible drug targets. Immunohistochemical stainings can be used to identify proteins involved in the pathogenesis of FECD. We introduce a method for the automatic quantification of the ratio of stained cells starting from full high-resolution cornea images. First, the endothelium is extracted using entropy information in a low-resolution resampling. Then, within the endothelium, we heuristically detect and classify nuclei based on their size, color, and the color of the surrounding cytoplasm. This method achieves comparable results to manual evaluation in a set of corneas of patients with and without FECD

X-Ray Emission from Rotating Elliptical Galaxies

The slow inward flow of the hot gas in elliptical galaxy cooling flows is nearly impossible to detect directly due to instrumental limitations. However, in rotating galaxies, if the inflowing gas conserves angular momentum, it will eventually form a disk. The X-ray signature of this phenomenon is a flattening of the X-ray isophotes in the inner 1-10 kpc region. This effect is observable, so we have searched for it in X-ray observations of six rotating and non-rotating early-type galaxies, obtained mainly with the ROSAT PSPC and HRI imagers. The ellipticities of the X-ray emission never increase toward the central region, nor are the X-ray ellipticities significantly greater than the ellipticities for the optical stellar emission. Central ellipticities in excess of 0.5 were expected in rotating ellipticals whereas values of 0-0.2 are measured. The failure to detect the expected signature requires a modification to the standard cooling flow picture, possibly including partial galactic winds, rapid mass drop-out, or turbulent redistribution of angular momentum.Comment: 34 postscript pages; ApJ, in press (Feb 10,2000

An explanation for metallicity effects on X-ray Binary properties

We show that irradiation induced stellar winds can explain two important metallicity effects in X-ray binaries - the higher numbers and the softer spectra of the X-ray binaries in metal rich globular clusters compared to the metal poor ones. As has been previously noted by Iben, Tutukov and Fedorova, the winds should be stronger at lower metallicity due to less efficient line cooling. This will speed up the evolution of the LMXBs in metal poor clusters, hence reducing their numbers. These winds can also provide extra material near the accreting object which may create an intrinsic absorber to harden the X-ray spectra of the metal poor cluster systems relative to the metal rich ones, as suggested by observations. We outline some additional observational predictions of the model.Comment: 6 pages, no figures, accepted to Ap