Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks

We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability within a sublinear factor. We show that this is a tight bound, as we can find an approximation within a linear factor in networks of height two. We then show that, in trees of height three, it is NP-hard to approximate the problem within a factor $2^{f(n)}$ for any sublinear function $f$ of the size of the input $n$. Again, this bound is tight, as we prove that the usual max-product algorithm finds (in any network) approximations within factor $2^{c \cdot n}$ for some constant $c < 1$. Last, we present a simple algorithm, and show that it provably produces solutions at least as good as, and potentially much better than, the max-product algorithm. We empirically analyze the proposed algorithm against max-product using synthetic and realistic networks.Comment: 18 page

Prospects and status of quark mass renormalization in three-flavour QCD

We present the current status of a revised strategy to compute the running of renormalized quark masses in QCD with three flavours of massless O(a) improved Wilson quarks. The strategy employed uses the standard finite-size scaling method in the Schr\"odinger functional and accommodates for the non-perturbative scheme-switch which becomes necessary at intermediate renormalized couplings as discussed in [arXiv:1411.7648].Comment: 7 pages, 3 figures, 1 table; Proceedings of the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japa

White Dwarfs In Ngc6397 And M4: Constraints On The Physics Of Crystallization

We explore the physics of crystallization in the dense Coulomb plasma of the deep interiors of white dwarf stars using the color-magnitude diagram and luminosity function constructed from Hubble Space Telescope photometry of the globular cluster M 4 and compare it with our results for proper motion cleaned Hubble Space Telescope photometry of the globular cluster NGC 6397. We demonstrate that the data are consistent with a binary mixture of carbon and oxygen crystallizing at a value of Gamma higher than the theoretical value for a One Component Plasma (OCP). We show that this result is in line with the latest Molecular Dynamics simulations for binary mixtures of C/O. We discuss implications for future work.Astronom

Finding the Higgs Boson through Supersymmetry

The study of displaced vertices containing two b--jets may provide a double discovery at the Large Hadron Collider (LHC): we show how it may not only reveal evidence for supersymmetry, but also provide a way to uncover the Higgs boson necessary in the formulation of the electroweak theory in a large region of the parameter space. We quantify this explicitly using the simplest minimal supergravity model with bilinear breaking of R-parity, which accounts for the observed pattern of neutrino masses and mixings seen in neutrino oscillation experiments.Comment: 7 pages, 7 figures. Final version to appear at PRD. Discussion and results were enlarge

Phenomenological Analysis of pppp and pˉp\bar{p}p Elastic Scattering Data in the Impact Parameter Space

We use an almost model-independent analytical parameterization for $pp$ and $\bar{p}p$ elastic scattering data to analyze the eikonal, profile, and inelastic overlap functions in the impact parameter space. Error propagation in the fit parameters allows estimations of uncertainty regions, improving the geometrical description of the hadron-hadron interaction. Several predictions are shown and, in particular, the prediction for $pp$ inelastic overlap function at $\sqrt{s}=14$ TeV shows the saturation of the Froissart-Martin bound at LHC energies.Comment: 15 pages, 16 figure

Ultrahigh Transmission Optical Nanofibers

We present a procedure for reproducibly fabricating ultrahigh transmission optical nanofibers (530 nm diameter and 84 mm stretch) with single-mode transmissions of 99.95 $\pm$ 0.02%, which represents a loss from tapering of 2.6 $\,\times \,$ 10$^{-5}$ dB/mm when normalized to the entire stretch. When controllably launching the next family of higher-order modes on a fiber with 195 mm stretch, we achieve a transmission of 97.8 $\pm$ 2.8%, which has a loss from tapering of 5.0 $\,\times \,$ 10$^{-4}$ dB/mm when normalized to the entire stretch. Our pulling and transfer procedures allow us to fabricate optical nanofibers that transmit more than 400 mW in high vacuum conditions. These results, published as parameters in our previous work, present an improvement of two orders of magnitude less loss for the fundamental mode and an increase in transmission of more than 300% for higher-order modes, when following the protocols detailed in this paper. We extract from the transmission during the pull, the only reported spectrogram of a fundamental mode launch that does not include excitation to asymmetric modes; in stark contrast to a pull in which our cleaning protocol is not followed. These results depend critically on the pre-pull cleanliness and when properly following our pulling protocols are in excellent agreement with simulations.Comment: 32 pages, 10 figures, accepted to AIP Advance