A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators

In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This result is a consequence of a new pointwise and weighted estimate for Laplace-Beltrami operators, a construction of some nonnegative function with arbitrary given critical point location in the manifold, and also two interpolation results for solutions of elliptic equations with lateral Robin boundary conditions

Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems

In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we study two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the history of a stochastic heat process through the observation at the final time T for which we obtain a conditional stability estimate. The other is an inverse source problem with observation on the lateral boundary. We derive the uniqueness of the source

On defining partition entropy by inequalities

Partition entropy is the numerical metric of uncertainty within a partition of a finite set, while conditional entropy measures the degree of difficulty in predicting a decision partition when a condition partition is provided. Since two direct methods exist for defining conditional entropy based on its partition entropy, the inequality postulates of monotonicity, which conditional entropy satisfies, are actually additional constraints on its entropy. Thus, in this paper partition entropy is defined as a function of probability distribution, satisfying all the inequalities of not only partition entropy itself but also its conditional counterpart. These inequality postulates formalize the intuitive understandings of uncertainty contained in partitions of finite sets.We study the relationships between these inequalities, and reduce the redundancies among them. According to two different definitions of conditional entropy from its partition entropy, the convenient and unified checking conditions for any partition entropy are presented, respectively. These properties generalize and illuminate the common nature of all partition entropies

Null controllability for some systems of two backward stochastic heat equations with one control force

The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system

The L∞-null controllability of parabolic equation with equivalued surface boundary conditions

In this paper, we obtain the L∞-null controllability of the parabolic equation with equivalued surface boundary conditions in Ω×[0,T]. The control is supported in the product of an open subset of Ω and a subset of [0,T] with positive measure. The main result is obtained by the method of Lebeau-Robbiano iteration, based on a new estimate for partial sum of the eigenfunctions of the elliptic operator with equivalued surface boundary conditions

Prediction of 8-state protein secondary structures by a novel deep learning architecture

© 2018 The Author(s). Background: Protein secondary structure can be regarded as an information bridge that links the primary sequence and tertiary structure. Accurate 8-state secondary structure prediction can significantly give more precise and high resolution on structure-based properties analysis. Results: We present a novel deep learning architecture which exploits an integrative synergy of prediction by a convolutional neural network, residual network, and bidirectional recurrent neural network to improve the performance of protein secondary structure prediction. A local block comprised of convolutional filters and original input is designed for capturing local sequence features. The subsequent bidirectional recurrent neural network consisting of gated recurrent units can capture global context features. Furthermore, the residual network can improve the information flow between the hidden layers and the cascaded recurrent neural network. Our proposed deep network achieved 71.4% accuracy on the benchmark CB513 dataset for the 8-state prediction; and the ensemble learning by our model achieved 74% accuracy. Our model generalization capability is also evaluated on other three independent datasets CASP10, CASP11 and CASP12 for both 8- and 3-state prediction. These prediction performances are superior to the state-of-the-art methods. Conclusion: Our experiment demonstrates that it is a valuable method for predicting protein secondary structure, and capturing local and global features concurrently is very useful in deep learning

Atomically flat interface between a single-terminated LaAlO3 substrate and SrTiO3 thin film is insulating

The surface termination of (100)-oriented LaAlO3 (LAO) single crystals was examined by atomic force microscopy and optimized to produce a single-terminated atomically flat surface by annealing. Then the atomically flat STO film was achieved on a single-terminated LAO substrate, which is expected to be similar to the n-type interface of two-dimensional electron gas (2DEG), i.e., (LaO)-(TiO2). Particularly, that can serve as a mirror structure for the typical 2DEG heterostructure to further clarify the origin of 2DEG. This newly developed interface was determined to be highly insulating. Additionally, this study demonstrates an approach to achieve atomically flat film growth based on LAO substrates.Comment: 4 pages, 3 figure

Study of f_0(980) and f_0(1500) from B_s \to f_0(980)K, f_0(1500)K Decays

In this paper, we calculate the branching ratios and CP-violating asymmetries for \bar B^0_s \to f_0(980)K, f_0(1500)K within Perturbative QCD approach based on k_T factorization. If the mixing angle $\theta$ falls into the range of 25^\circ<\theta<40^\circ, the branching ratio of \bar B^0_s\to f_0(980)K is 2.0\times 10^{-6}<{\cal B}(\bar B^0_s\to f_0(980)K)<2.6\times 10^{-6}, while $\theta$ lies in the range of 140^\circ<\theta<165^\circ, {\cal B}(\bar B^0_s\to f_0(980)K) is about 6.5\times 10^{-7}. As to the decay {\cal B}(\bar B^0_s\to f_0(1500)K), when the mixing scheme \mid f_0(1500)>=0.84\mid s\bar s>-0.54\mid n\bar n> for f_0(1500) is used, it is difficult to determine which scenario is more preferable than the other one from the branching ratios for these two scenarios, because they are both close to 1.0\times10^{-6}. But there exists large difference in the form factor F^{\bar B_s^0\to f_0(1500)} for two scenarios.Comment: 14 pages, 3 figures, submitted to J. Phys.