Posterior Contraction Rates of the Phylogenetic Indian Buffet Processes

By expressing prior distributions as general stochastic processes, nonparametric Bayesian methods provide a flexible way to incorporate prior knowledge and constrain the latent structure in statistical inference. The Indian buffet process (IBP) is such an example that can be used to define a prior distribution on infinite binary features, where the exchangeability among subjects is assumed. The phylogenetic Indian buffet process (pIBP), a derivative of IBP, enables the modeling of non-exchangeability among subjects through a stochastic process on a rooted tree, which is similar to that used in phylogenetics, to describe relationships among the subjects. In this paper, we study the theoretical properties of IBP and pIBP under a binary factor model. We establish the posterior contraction rates for both IBP and pIBP and substantiate the theoretical results through simulation studies. This is the first work addressing the frequentist property of the posterior behaviors of IBP and pIBP. We also demonstrated its practical usefulness by applying pIBP prior to a real data example arising in the field of cancer genomics where the exchangeability among subjects is violated

Lubricants

When liquids are confined into a nanometer-scale slit, the induced layering-like film structure allows the liquid to sustain non-isotropic stresses and thus be load-bearing. Such anisotropic characteristics of liquid under confinement arise naturally from the liquids’ wavenumber dependent compressibility, which does not need solidification to take place as a prerequisite. In other words, liquids under confinement can still retain fluidity with molecules being (sub-)diffusive. However, the extensively prolonged structural relaxation times can cause hysteresis of stress relaxation of confined molecules in response to the motions of confining walls and thereby rendering the quasi-static stress tensors history-dependent. In this work, by means of molecular dynamics, stress tensors of a highly confined key base-oil component, i.e., 1-decene trimer, are calculated after its relaxation from being compressed and decompressed. A maximum of 77.1 MPa normal stress discrepancy has been detected within a triple-layer boundary film. Analyses with respect to molecular morphology indicate that among the effects (e.g., confinement, molecular structure, and film density) that can potentially affect confined stresses, the ordering status of the confined molecules plays a predominant role

Absolute height measurement of specular surfaces with modified active fringe reflection photogrammetry

Deflectometric methods have existed for more than a decade for slope measurement of specular freeform surfaces through utilization of the deformation of a sample pattern after reflection from a test surface. Usually, these approaches require two-directional fringe patterns to be projected on a LCD screen or ground glass and require slope integration, which leads to some complexity for the whole measuring process. This paper proposes a new mathematical measurement model for measuring topography information of freeform specular surfaces, which integrates a virtual reference specular surface into the method of active fringe reflection delfectometry and presents a straight-forward relation between height and phase. This method only requires one direction of horizontal or vertical sinusoidal fringe patterns to be projected on a LCD screen, resulting in a significant reduction in capture time over established method. Assuming the whole system has been pre-calibrated, during the measurement process, the fringe patterns are captured separately via the virtual reference and detected freeform surfaces by a CCD camera. The reference phase can be solved according to spatial geometrical relation between LCD screen and CCD camera. The captured phases can be unwrapped with a heterodyne technique and optimum frequency selection method. Based on this calculated unwrapped-phase and that proposed mathematical model, absolute height of the inspected surface can be computed. Simulated and experimental results show that this methodology can conveniently calculate topography information for freeform and structured specular surfaces without integration and reconstruction processes

Non-fragile estimation for discrete-time T-S fuzzy systems with event-triggered protocol

summary:This paper investigates the non-fragile state estimation problem for a class of discrete-time T-S fuzzy systems with time-delays and multiple missing measurements under event-triggered mechanism. First of all, the plant is subject to the time-varying delays and the stochastic disturbances. Next, a random white sequence, the element of which obeys a general probabilistic distribution defined on $[0,1]$, is utilized to formulate the occurrence of the missing measurements. Also, an event generator function is employed to regulate the transmission of data to save the precious energy. Then, a non-fragile state estimator is constructed to reflect the randomly occurring gain variations in the implementing process. By means of the Lyapunov-Krasovskii functional, the desired sufficient conditions are obtained such that the Takagi-Sugeno (T-S) fuzzy estimation error system is exponentially ultimately bounded in the mean square. And then the upper bound is minimized via the robust optimization technique and the estimator gain matrices can be calculated. Finally, a simulation example is utilized to demonstrate the effectiveness of the state estimation scheme proposed in this paper

Propagation Characteristics of Seismic Wave While Transiting Interlining in Soil Medium

Based on the theory of wave and the Snell theorem, propagation characteristics of seismic wave, three kinds of elastic body waves, is studied when they pass through soil/elastic solid medium including elastic thin plan intercalation in half-space. The analytic solution of the amplitude rate is the rate of the amplitude of the wave behind the intercalation to that of the incident wave. Compared with the field data, the analytic results are beneficial, affected by soft clay stratum, at the Nankai District of Tianjin Municipality caused by the 1976 Tangshan earthquake (had a magnitude of 7.8). In this area, however, damage of the buildings was generally minor, about 50%, with the Heping District near Nankai