Competing orders and inter-layer tunnelling in cuprate superconductors: A finite temperature Landau theory

We propose a finite temperature Landau theory that describes competing orders and interlayer tunneling in cuprate superconductors as an important extension to a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)], where the superconducting transition temperature $T_c$ is defined in three possible ways as a function of the zero temperature order parameter. For given parameters, our theory determines $T_c$ without any ambiguity. In mono- and double-layer systems we discuss the relation between zero temperature order parameter and the associated transition temperature in the presence of competing orders, and draw a connection to the puzzling experimental fact that the pseudo-gap temperature is much higher than the corresponding energy scale near optimum doping. Applying the theory to multi-layer systems, we calculate the layer-number dependence of $T_c$. In a reasonable parameter space the result turns out to be in agreement with experiments.Comment: 5 pages, 3 figure

Tunable Frequency Comb Generation from a Microring with a Thermal Heater

We demonstrate a novel comb tuning method for microresonator-based Kerr comb generators. Continuously tunable, low-noise, and coherent comb generation is achieved in a CMOS-compatible silicon nitride microring resonator.Comment: submitted to CLEO201

Aqua­(2,9-dimethyl-1,10-phenanthroline-κ2 N,N′)bis­(2-hydroxy­benzoato-κO)manganese(II) 2,9-dimethyl-1,10-phenanthroline hemisolvate

In the asymmetric unit of the title complex, [Mn(C7H5O3)2(C14H12N2)(H2O)]·0.5C14H12N2, the MnII ion is coordinated by a bidentate 2,9-dimethyl-1,10-phenanthroline (dmphen) mol­ecule, one water mol­ecule and two monodentate 2-hydroxy­benzoate anions in a distorted trigonal-bipyramidal geometry. The OH group of the 2-hydroxy­benzoate anion is disordered over two positions with site-occupancy factors of 0.5. The asymmetric unit is completed with by an uncoordinated half-mol­ecule of dmphen, disordered about a crystallographic twofold axis. In the crystal structure, mol­ecules are linked into a two-dimensional framework by O—H⋯N, O—H⋯O and C—H⋯O hydrogen bonds. The packing of the structure is further stabilized by π–π stacking inter­actions involving dmphen mol­ecules, with centroid–centroid separations of 3.8027 (3) and 3.6319 (3) Å

Exact and Consistent Interpretation for Piecewise Linear Neural Networks: A Closed Form Solution

Strong intelligent machines powered by deep neural networks are increasingly deployed as black boxes to make decisions in risk-sensitive domains, such as finance and medical. To reduce potential risk and build trust with users, it is critical to interpret how such machines make their decisions. Existing works interpret a pre-trained neural network by analyzing hidden neurons, mimicking pre-trained models or approximating local predictions. However, these methods do not provide a guarantee on the exactness and consistency of their interpretation. In this paper, we propose an elegant closed form solution named $OpenBox$ to compute exact and consistent interpretations for the family of Piecewise Linear Neural Networks (PLNN). The major idea is to first transform a PLNN into a mathematically equivalent set of linear classifiers, then interpret each linear classifier by the features that dominate its prediction. We further apply $OpenBox$ to demonstrate the effectiveness of non-negative and sparse constraints on improving the interpretability of PLNNs. The extensive experiments on both synthetic and real world data sets clearly demonstrate the exactness and consistency of our interpretation.Comment: KDD 201