Enumeration of rational plane curves tangent to a smooth cubic

We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.Comment: 27 pages, v2: typos corrected and references adde

Structure - property relationships of new polystyrene nanocomposites prepared from initiator-containing layered double hydroxides of zinc aluminum and magnesium aluminum

Polystyrene/layered double hydroxides (PS/LDHs) nanocomposites were prepared by free radical polymerization of styrene monomer in the presence of LDHs intercalated with 4,4′-azobis(4-cyanopentanoate) anions (LDH–ACPA). XRD and ATR-IR are used to confirm that the materials produced are layered and the presence of the azo-initiator anions in these LDHs. These LDHs were used successfully to polymerize styrene and both XRD and TEM images of the composites support the formation of a mixed exfoliated-intercalated nanocomposite for ZnAl–ACPA but a microcomposite for MgAl–ACPA. The magnesium-containing LDHs decreased the glass transition temperature (Tg) of the composites while ZnAl–ACPA did not affect Tg significantly. The Tg depression is related to enhanced polymer dynamics due to the extra free volume at the LDH additive-polymer interface. A reduction in the onset of thermal decomposition temperature was observed in PS/LDH compared to neat PS, likely due to the early decomposition of the LDH. The fire performance, as evaluated by the cone calorimeter, reveal that PS–ZnAl–ACPA shows enhanced fire properties compared to PS–MgAl–ACPA

A discriminative view of MRF pre-processing algorithms

While Markov Random Fields (MRFs) are widely used in computer vision, they present a quite challenging inference problem. MRF inference can be accelerated by pre-processing techniques like Dead End Elimination (DEE) or QPBO-based approaches which compute the optimal labeling of a subset of variables. These techniques are guaranteed to never wrongly label a variable but they often leave a large number of variables unlabeled. We address this shortcoming by interpreting pre-processing as a classification problem, which allows us to trade off false positives (i.e., giving a variable an incorrect label) versus false negatives (i.e., failing to label a variable). We describe an efficient discriminative rule that finds optimal solutions for a subset of variables. Our technique provides both per-instance and worst-case guarantees concerning the quality of the solution. Empirical studies were conducted over several benchmark datasets. We obtain a speedup factor of 2 to 12 over expansion moves without preprocessing, and on difficult non-submodular energy functions produce slightly lower energy.Comment: ICCV 201

The Effects of Intralayer Metal Composition of Layered Double Hydroxides on Glass Transition, Dispersion, Thermal and Fire Properties of Their PMMA Nanocomposites

A series of aluminum-containing layered double hydroxides (LDHs), containing Mg, Ca, Co, Ni, Cu and Zn as the divalent metals, have been prepared by the co-precipitation method and used to prepare nanocomposites of PMMA by in situ bulk polymerization. The additives were characterized by Fourier transform infrared spectroscopy, X-ray diffraction spectroscopy (XRD) and thermogravimetric analysis while the polymer composites were characterized by XRD, transmission electron microscopy, differential scanning calorimetry and cone calorimetry. Polymerization of methyl methacrylate in the presence of these undecenoate LDHs results in composites with enhanced thermal stability. The glass transition temperatures of the composites and the pristine polymers are found to be around 110 °C; this suggests that the presence of these additives has little effect on the polymer. It is found that the additive composition and the dispersion state of LDHs agglomerates in the polymer matrix influence the fire properties of composites as measured by cone calorimetry

A Numerical Approach to Virasoro Blocks and the Information Paradox

We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit corresponding to a light probe propagating in a BTZ black hole background. In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal $t^{-\frac{3}{2}}$ power-law decay. For the vacuum block the transition occurs at $t \approx \frac{\pi c}{6 h_L}$, confirming analytic predictions. In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the `forbidden singularities'. We emphasize that limitations on the reconstruction of a local bulk should ultimately stem from distinctions between semiclassical and exact correlators.Comment: 45 pages, 23 figure