Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice

In first-passage percolation on the integer lattice, the Shape Theorem provides precise conditions for convergence of the set of sites reachable within a given time from the origin, once rescaled, to a compact and convex limiting shape. Here, we address convergence towards an asymptotic shape for cone-like subgraphs of the $\Z^d$ lattice, where $d\ge2$. In particular, we identify the asymptotic shapes associated to these graphs as restrictions of the asymptotic shape of the lattice. Apart from providing necessary and sufficient conditions for $L^p$- and almost sure convergence towards this shape, we investigate also stronger notions such as complete convergence and stability with respect to a dynamically evolving environment.Comment: 23 pages. Together with arXiv:1305.6260, this version replaces the old. The main results have been strengthened and an earlier error in the statement corrected. To appear in J. Theoret. Proba

Polycyclic aromatic hydrocarbons and molecular hydrogen in oxygen-rich planetary nebulae: the case of NGC6720

Evolved stars are primary sources for the formation of polycyclic aromatic hydrocarbons (PAHs) and dust grains. Their circumstellar chemistry is usually designated as either oxygen-rich or carbon-rich, although dual-dust chemistry objects, whose infrared spectra reveal both silicate- and carbon-dust features, are also known. The exact origin and nature of this dual-dust chemistry is not yet understood. Spitzer-IRS mid-infrared spectroscopic imaging of the nearby, oxygen-rich planetary nebula NGC6720 reveals the presence of the 11.3 micron aromatic (PAH) emission band. It is attributed to emission from neutral PAHs, since no band is observed in the 7 to 8 micron range. The spatial distribution of PAHs is found to closely follow that of the warm clumpy molecular hydrogen emission. Emission from both neutral PAHs and warm H2 is likely to arise from photo-dissociation regions associated with dense knots that are located within the main ring. The presence of PAHs together with the previously derived high abundance of free carbon (relative to CO) suggest that the local conditions in an oxygen-rich environment can also become conducive to in-situ formation of large carbonaceous molecules, such as PAHs, via a bottom-up chemical pathway. In this scenario, the same stellar source can enrich the interstellar medium with both oxygen-rich dust and large carbonaceous molecules.Comment: Accepted by MNRAS. 5 page

On alpha stable distribution of wind driven water surface wave slope

We propose a new formulation of the probability distribution function of wind driven water surface slope with an $\alpha$-stable distribution probability. The mathematical formulation of the probability distribution function is given under an integral formulation. Application to represent the probability of time slope data from laboratory experiments is carried out with satisfactory results. We compare also the $\alpha$-stable model of the water surface slopes with the Gram-Charlier development and the non-Gaussian model of Liu et al\cite{Liu}. Discussions and conclusions are conducted on the basis of the data fit results and the model analysis comparison.Comment: final version of the manuscript: 25 page

Pressure-Induced Insulating State in Ba1-xRExIrO3 (RE = Gd, Eu) Single Crystals

BaIrO3 is a novel insulator with coexistent weak ferromagnetism, charge and spin density wave. Dilute RE doping for Ba induces a metallic state, whereas application of modest pressure readily restores an insulating state characterized by a three-order-of-magnitude increase of resistivity. Since pressure generally increases orbital overlap and broadens energy bands, a pressure-induced insulating state is not commonplace. The profoundly dissimilar responses of the ground state to light doping and low hydrostatic pressures signal an unusual, delicate interplay between structural and electronic degrees of freedom in BaIrO3

Consistency of the Shannon entropy in quantum experiments

The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.Comment: 12 pages, LaTeX2e/REVTeX4. V5: slightly different than the published versio

Anomalous aging phenomena caused by drift velocities

We demonstrate via several examples that a uniform drift velocity gives rise to anomalous aging, characterized by a specific form for the two-time correlation functions, in a variety of statistical-mechanical systems far from equilibrium. Our first example concerns the oscillatory phase observed recently in a model of competitive learning. Further examples, where the proposed theory is exact, include the voter model and the Ohta-Jasnow-Kawasaki theory for domain growth in any dimension, and a theory for the smoothing of sandpile surfaces.Comment: 7 pages, 3 figures. To appear in Europhysics Letter

Strong electron correlations in cobalt valence tautomers

We have examined cobalt based valence tautomer molecules such as Co(SQ)$_2$(phen) using density functional theory (DFT) and variational configuration interaction (VCI) approaches based upon a model Hamiltonian. Our DFT results extend earlier work by finding a reduced total energy gap (order 0.6 eV) between high temperature and low temperature states when we fully relax the coordinates (relative to experimental ones). Futhermore we demonstrate that the charge transfer picture based upon formal valence arguments succeeds qualitatively while failing quantitatively due to strong covalency between the Co 3$d$ orbitals and ligand $p$ orbitals. With the VCI approach, we argue that the high temperature, high spin phase is strongly mixed valent, with about 30 % admixture of Co(III) into the predominantly Co(II) ground state. We confirm this mixed valence through a fit to the XANES spectra. Moreover, the strong electron correlations of the mixed valent phase provide an energy lowering of about 0.2-0.3 eV of the high temperature phase relative to the low temperature one. Finally, we use the domain model to account for the extraordinarily large entropy and enthalpy values associated with the transition.Comment: 10 pages, 4 figures, submitted to J. Chem. Phy

Multichannel pseudogap Kondo model: Large-N solution and quantum-critical dynamics

We discuss a multichannel SU(N) Kondo model which displays non-trivial zero-temperature phase transitions due to a conduction electron density of states vanishing with a power law at the Fermi level. In a particular large-N limit, the system is described by coupled integral equations corresponding to a dynamic saddle point. We exactly determine the universal low-energy behavior of spectral densities at the scale-invariant fixed points, obtain anomalous exponents, and compute scaling functions describing the crossover near the quantum-critical points. We argue that our findings are relevant to recent experiments on impurity-doped d-wave superconductors.Comment: 4 pages, 3 figs; extended discussion of large-N spin representations, added references; accepted for publication in PR

Collaborative Layer-wise Discriminative Learning in Deep Neural Networks

Intermediate features at different layers of a deep neural network are known to be discriminative for visual patterns of different complexities. However, most existing works ignore such cross-layer heterogeneities when classifying samples of different complexities. For example, if a training sample has already been correctly classified at a specific layer with high confidence, we argue that it is unnecessary to enforce rest layers to classify this sample correctly and a better strategy is to encourage those layers to focus on other samples. In this paper, we propose a layer-wise discriminative learning method to enhance the discriminative capability of a deep network by allowing its layers to work collaboratively for classification. Towards this target, we introduce multiple classifiers on top of multiple layers. Each classifier not only tries to correctly classify the features from its input layer, but also coordinates with other classifiers to jointly maximize the final classification performance. Guided by the other companion classifiers, each classifier learns to concentrate on certain training examples and boosts the overall performance. Allowing for end-to-end training, our method can be conveniently embedded into state-of-the-art deep networks. Experiments with multiple popular deep networks, including Network in Network, GoogLeNet and VGGNet, on scale-various object classification benchmarks, including CIFAR100, MNIST and ImageNet, and scene classification benchmarks, including MIT67, SUN397 and Places205, demonstrate the effectiveness of our method. In addition, we also analyze the relationship between the proposed method and classical conditional random fields models.Comment: To appear in ECCV 2016. Maybe subject to minor changes before camera-ready versio

Crystal Field Triplets: A New Route to Non-Fermi Liquid Physics

A model for crystal field triplet ground states on rare earth or actinide ions with dipolar and quadrupolar couplings to conduction electrons is studied for the first time with renormalization group methods. The quadrupolar coupling leads to a new nontrivial, non-Fermi liquid fixed point, which survives in an intermediate valence Anderson model. The calculated magnetic susceptibility displays one parameter scaling, going as $T^{-\alpha}$ ($\alpha \approx 0.4$) at intermediate temperatures, reminiscent of the non-Fermi liquid alloy UCu_{5-x}Pd_x.Comment: 4 pages, 3 figures, REVTe