Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications

In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve large-scale problems. However, general nonsubmodular problems are significantly more challenging to solve. Finding a solution when the problem is of large size to be of practical interest, however, typically requires relaxation. Two standard relaxation methods are widely used for solving general BQPs--spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high, especially for large scale problems. In this work, we present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton methods, for the dual problem. Both of them are significantly more efficiently than standard interior-point methods. In practice, the smoothing Newton solver is faster than the quasi-Newton solver for dense or medium-sized problems, while the quasi-Newton solver is preferable for large sparse/structured problems. Our experiments on a few computer vision applications including clustering, image segmentation, co-segmentation and registration show the potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern Analysis and Machine Intelligenc

A Helium-Surface Interaction Potential of Bi2_2Te3_3(111) from Ultrahigh-Resolution Spin-Echo Measurements

We have determined an atom-surface interaction potential for the He$-$Bi$_2$Te$_3$(111) system by analysing ultrahigh resolution measurements of selective adsorption resonances. The experimental measurements were obtained using $^3$He spin-echo spectrometry. Following an initial free-particle model analysis, we use elastic close-coupling calculations to obtain a three-dimensional potential. The three-dimensional potential is then further refined based on the experimental data set, giving rise to an optimised potential which fully reproduces the experimental data. Based on this analysis, the He$-$Bi$_2$Te$_3$(111) interaction potential can be described by a corrugated Morse potential with a well depth $D=(6.22\pm0.05)~\mathrm{meV}$, a stiffness $\kappa =(0.92\pm0.01)~\mathrm{\AA}^{-1}$ and a surface electronic corrugation of $(9.6\pm0.2)$% of the lattice constant. The improved uncertainties of the atom-surface interaction potential should also enable the use in inelastic close-coupled calculations in order to eventually study the temperature dependence and the line width of selective adsorption resonances

Counterpropagating beams in biased photorefractive crystals: anisotropic theory

We formulate an anisotropic nonlocal theory of the space charge field induced by the coherent counterpropagating beams in biased photorefractive crystals. We establish that the competition between the drift and diffusion terms has to be taken into account when the crystal cˆ axis is tilted with respect to the propagation direction of the beams. We demonstrate that this configuration combines the features of both spatial soliton formation without energy exchange and two-wave mixing with energy exchange leading to pattern formation

The SFR-M _∗ Correlation Extends to Low Mass at High Redshift

To achieve a fuller understanding of galaxy evolution, SED fitting can be used to recover quantities beyond stellar masses (M$_*$) and star formation rates (SFRs). We use Star Formation Histories (SFHs) reconstructed via the Dense Basis method of Iyer \& Gawiser (2017) for a sample of $17,873$ galaxies at $0.5<z<6$ in the CANDELS GOODS-S field to study the nature and evolution of the SFR-M$_*$ correlation. The reconstructed SFHs represent trajectories in SFR-M$_*$ space, enabling us to study galaxies at epochs earlier than observed by propagating them backwards in time along these trajectories. We study the SFR-M$_*$ correlation at $z=1,2,3,4,5,6$ using both direct fits to galaxies observed at those epochs and SFR-M$_*$ trajectories of galaxies observed at lower redshifts. The SFR-M$_*$ correlations obtained using the two approaches are found to be consistent with each other through a KS test. Validation tests using SFHs from semi-analytic models and cosmological hydrodynamical simulations confirm the sensitivity of the method to changes in the slope, normalization and shape of the SFR-M$_*$ correlation. This technique allows us to further probe the low-mass regime of the correlation at high-z by $\sim 1$ dex and over an effective volume of $\sim 10\times$ larger than possible with just direct fits. We find that the SFR-M$_*$ correlation is consistent with being linear down to M$_*\sim 10^7 M_\odot$ at $z>4$. The evolution of the correlation is well described by $\log SFR= (0.80\pm 0.029 - 0.017\pm 0.010\times t_{univ})\log M_*$ $- (6.487\pm 0.282-0.039\pm 0.008\times t_{univ})$, where $t_{univ}$ is the age of the universe in Gyr.Comment: 22 pages, 10 figures. Accepted for publication in Ap

Heralded generation of entangled photon pairs

Entangled photons are a crucial resource for quantum communication and linear optical quantum computation. Unfortunately, the applicability of many photon-based schemes is limited due to the stochastic character of the photon sources. Therefore, a worldwide effort has focused in overcoming the limitation of probabilistic emission by generating two-photon entangled states conditioned on the detection of auxiliary photons. Here we present the first heralded generation of photon states that are maximally entangled in polarization with linear optics and standard photon detection from spontaneous parametric down-conversion. We utilize the down-conversion state corresponding to the generation of three photon pairs, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state. This controlled generation of entangled photon states is a significant step towards the applicability of a linear optics quantum network, in particular for entanglement swapping, quantum teleportation, quantum cryptography and scalable approaches towards photonics-based quantum computing

Comparison of Different Approaches to Surface Functionalization of Biodegradable Polycaprolactone Scaffolds

Due to their good mechanical stability compared to gelatin, collagen or polyethylene glycol nanofibers and slow degradation rate, biodegradable poly-epsilon-caprolactone (PCL) nanofibers are promising material as scaffolds for bone and soft-tissue engineering. Here, PCL nanofibers were prepared by the electrospinning method and then subjected to surface functionalization aimed at improving their biocompatibility and bioactivity. For surface modification, two approaches were used: (i) COOH-containing polymer was deposited on the PCL surface using atmospheric pressure plasma copolymerization of CO2 and C2H4, and (ii) PCL nanofibers were coated with multifunctional bioactive nanostructured TiCaPCON film by magnetron sputtering of TiC-CaO-Ti3POx target. To evaluate bone regeneration ability in vitro, the surface-modified PCL nanofibers were immersed in simulated body fluid (SBF, 1x) for 21 days. The results obtained indicate different osteoblastic and epithelial cell response depending on the modification method. The TiCaPCON-coated PCL nanofibers exhibited enhanced adhesion and proliferation of MC3T3-E1 cells, promoted the formation of Ca-based mineralized layer in SBF and, therefore, can be considered as promising material for bone tissue regeneration. The PCL-COOH nanofibers demonstrated improved adhesion and proliferation of IAR-2 cells, which shows their high potential for skin reparation and wound dressing

No More Active Galactic Nuclei in Clumpy Disks Than in Smooth Galaxies at z~2 in CANDELS / 3D-HST

We use CANDELS imaging, 3D-HST spectroscopy, and Chandra X-ray data to investigate if active galactic nuclei (AGNs) are preferentially fueled by violent disk instabilities funneling gas into galaxy centers at 1.3<z<2.4. We select galaxies undergoing gravitational instabilities using the number of clumps and degree of patchiness as proxies. The CANDELS visual classification system is used to identify 44 clumpy disk galaxies, along with mass-matched comparison samples of smooth and intermediate morphology galaxies. We note that, despite being being mass-matched and having similar star formation rates, the smoother galaxies tend to be smaller disks with more prominent bulges compared to the clumpy galaxies. The lack of smooth extended disks is probably a general feature of the z~2 galaxy population, and means we cannot directly compare with the clumpy and smooth extended disks observed at lower redshift. We find that z~2 clumpy galaxies have slightly enhanced AGN fractions selected by integrated line ratios (in the mass-excitation method), but the spatially resolved line ratios indicate this is likely due to extended phenomena rather than nuclear AGNs. Meanwhile the X-ray data show that clumpy, smooth, and intermediate galaxies have nearly indistinguishable AGN fractions derived from both individual detections and stacked non-detections. The data demonstrate that AGN fueling modes at z~1.85 - whether violent disk instabilities or secular processes - are as efficient in smooth galaxies as they are in clumpy galaxies.Comment: ApJ accepted. 17 pages, 17 figure

Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems

Quantum simulators are controllable quantum systems that can reproduce the dynamics of the system of interest, which are unfeasible for classical computers. Recent developments in quantum technology enable the precise control of individual quantum particles as required for studying complex quantum systems. Particularly, quantum simulators capable of simulating frustrated Heisenberg spin systems provide platforms for understanding exotic matter such as high-temperature superconductors. Here we report the analog quantum simulation of the ground-state wavefunction to probe arbitrary Heisenberg-type interactions among four spin-1/2 particles . Depending on the interaction strength, frustration within the system emerges such that the ground state evolves from a localized to a resonating valence-bond state. This spin-1/2 tetramer is created using the polarization states of four photons. The single-particle addressability and tunable measurement-induced interactions provide us insights into entanglement dynamics among individual particles. We directly extract ground-state energies and pair-wise quantum correlations to observe the monogamy of entanglement

Antioxidant intervention in rheumatoid arthritis: results of an open pilot study

There is evidence that reactive oxygen species play a causal role in auto-immune diseases, such as rheumatoid arthritis (RA). Despite the supporting evidence for a beneficial effect of antioxidants on clinical characteristics of RA, the right balance for optimal effectiveness of antioxidants is largely unknown. To determine the potential beneficial effects of an antioxidant intervention on clinical parameters for RA, an open pilot study was designed. Eight non-smoking female patients with rheumatoid factor + RA and a Disease Activity Score (DAS 28) higher than 2.5 were enrolled in the study. Patients had to be receiving stable non-steroidal anti-inflammatory drug treatment and/or ‘second line’ medication for at least 3 months. The pilot group consumed 20 g of antioxidant-enriched spread daily during a period of 10 weeks. The intervention was stopped after 10 weeks and was followed by a ‘wash-out’ period of 4 weeks. At t = 0, t = 10 weeks and t = 14 weeks, patients’ condition was assessed by means of DAS. In addition, standard laboratory analyses were performed, and blood-samples for antioxidants were taken. The antioxidant-enriched spread was well tolerated. All laboratory measures of inflammatory activity and oxidative modification were generally unchanged. However, the number of swollen and painful joints were significantly decreased and general health significantly increased, as reflected by a significantly improved (1.6) DAS at t = 10 weeks. The antioxidant effect was considered beneficial as, compared to the scores at t = 0, the DAS significantly reduced at t = 10 weeks. Increase of the DAS (0.7) after the “wash-out period” at t = 14 confirmed a causal relation between changes in clinical condition and antioxidants. This open pilot study aimed to assess the clinical relevance of an antioxidant intervention as a first step in assessing potential beneficial effects of antioxidants on rheumatoid arthritis. These conclusions need to be validated in a larger controlled study population