Asymptotic properties of solutions of certain third-order dynamic equations

AbstractIn this paper, the well known oscillation criteria due to Hille and Nehari for second-order linear differential equations will be generalized and extended to the third-order nonlinear dynamic equation (r2(t)((r1(t)xΔ(t))Δ)γ)Δ+q(t)f(x(t))=0 on time scale T, where γ≥1 is a ratio of odd positive integers. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. Two examples of dynamic equations on different time scales are given to show the applications of our main results

Higher-order Topology of Axion Insulator EuIn2_2As2_2

Based on first-principles calculations and symmetry analysis, we propose that EuIn$_2$As$_2$ is a long awaited axion insulator with antiferromagnetic (AFM) long range order. Characterized by the parity-based invariant $\mathbb Z_4=2$, the topological magneto-electric effect is quantized with $\theta=\pi$ in the bulk, with a band gap as large as 0.1 eV. When the staggered magnetic moment of the AFM phase is along $a/b$ axis, it's also a TCI phase. Gapless surface states emerge on (100), (010) and (001) surfaces, protected by mirror symmetries (nonzero mirror Chern numbers). When the magnetic moment is along $c$ axis, the (100) and (001) surfaces are gapped. As a consequence of a high-order topological insulator with $\mathbb Z_4=2$, the one-dimensional (1D) chiral state can exist on the hinge between those gapped surfaces. We have calculated both the topological surface states and hinge state in different phases of the system, respectively, which can be detected by ARPES or STM experiments

Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent

Abstract Background Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species. Results We propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD). We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC), and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models. Conclusions The SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is computationally efficient and is effective for both partially and fully observed systems. Automatic construction of reversible jump samplers and general formulation of the likelihood gradient function makes our method applicable to a wide range of stochastic models. Furthermore our derivations can be useful for other purposes such as using the gradient information for parametric sensitivity analysis or using the reversible jump samplers for full Bayesian inference. The software implementing the algorithms is publicly available at http://cbcl.ics.uci.edu/sg

Eye-Tracking Signals Based Affective Classification Employing Deep Gradient Convolutional Neural Networks

Utilizing biomedical signals as a basis to calculate the human affective states is an essential issue of affective computing (AC). With the in-depth research on affective signals, the combination of multi-model cognition and physiological indicators, the establishment of a dynamic and complete database, and the addition of high-tech innovative products become recent trends in AC. This research aims to develop a deep gradient convolutional neural network (DGCNN) for classifying affection by using an eye-tracking signals. General signal process tools and pre-processing methods were applied firstly, such as Kalman filter, windowing with hamming, short-time Fourier transform (SIFT), and fast Fourier transform (FTT). Secondly, the eye-moving and tracking signals were converted into images. A convolutional neural networks-based training structure was subsequently applied; the experimental dataset was acquired by an eye-tracking device by assigning four affective stimuli (nervous, calm, happy, and sad) of 16 participants. Finally, the performance of DGCNN was compared with a decision tree (DT), Bayesian Gaussian model (BGM), and k-nearest neighbor (KNN) by using indices of true positive rate (TPR) and false negative rate (FPR). Customizing mini-batch, loss, learning rate, and gradients definition for the training structure of the deep neural network was also deployed finally. The predictive classification matrix showed the effectiveness of the proposed method for eye moving and tracking signals, which performs more than 87.2% inaccuracy. This research provided a feasible way to find more natural human-computer interaction through eye moving and tracking signals and has potential application on the affective production design process

Technical Note: Melt Dispersion Technique for Preparing Paraffin Wax Microspheres for Cellulose Encapsulation

A practical and convenient approach for making paraffin wax microspheres with a melt dispersion technique was reported in this study. Surfactants were melted in water by water bath and then added to a flask after the wax was completely melted with stirring. Paraffin wax microspheres were generated by cooling. The obtained microspheres exhibited uniform diameters in the range of 10-60 μm observed with a scanning electrical microscope and were mainly dependent on the surfactant ratio. Encapsulated microcrystalline cellulose particles with the previously mentioned conditions were also generated and demonstrated the possibility of encapsulating microcrystalline cellulose with some acceptable agglomeration, although some encapsulated individually. Encapsulation of cellulose could be beneficial if agglomeration could be minimized and the encapsulated microcapsules could be dispersed during blending for wood composites manufacture