Estimation in semi-parametric regression with non-stationary regressors

In this paper, we consider a partially linear model of the form $Y_t=X_t^{\tau}\theta_0+g(V_t)+\epsilon_t$, $t=1,...,n$, where $\{V_t\}$ is a $\beta$ null recurrent Markov chain, $\{X_t\}$ is a sequence of either strictly stationary or non-stationary regressors and $\{\epsilon_t\}$ is a stationary sequence. We propose to estimate both $\theta_0$ and $g(\cdot)$ by a semi-parametric least-squares (SLS) estimation method. Under certain conditions, we then show that the proposed SLS estimator of $\theta_0$ is still asymptotically normal with the same rate as for the case of stationary time series. In addition, we also establish an asymptotic distribution for the nonparametric estimator of the function $g(\cdot)$. Some numerical examples are provided to show that our theory and estimation method work well in practice.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ344 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Corrections to holographic entanglement plateau

We investigate the robustness of the Araki-Lieb inequality in a two-dimensional (2D) conformal field theory (CFT) on torus. The inequality requires that $\Delta S=S(L)-|S(L-\ell)-S(\ell)|$ is nonnegative, where $S(L)$ is the thermal entropy and $S(L-\ell)$, $S(\ell)$ are the entanglement entropies. Holographically there is an entanglement plateau in the BTZ black hole background, which means that there exists a critical length such that when $\ell \leq \ell_c$ the inequality saturates $\Delta S=0$. In thermal AdS background, the holographic entanglement entropy leads to $\Delta S=0$ for arbitrary $\ell$. We compute the next-to-leading order contributions to $\Delta S$ in the large central charge CFT at both high and low temperatures. In both cases we show that $\Delta S$ is strictly positive except for $\ell = 0$ or $\ell = L$. This turns out to be true for any 2D CFT. In calculating the single interval entanglement entropy in a thermal state, we develop new techniques to simplify the computation. At a high temperature, we ignore the finite size correction such that the problem is related to the entanglement entropy of double intervals on a complex plane. As a result, we show that the leading contribution from a primary module takes a universal form. At a low temperature, we show that the leading thermal correction to the entanglement entropy from a primary module does not take a universal form, depending on the details of the theory.Comment: 32 pages, 8 figures; V2, typos corrected, published versio

Low-cost and low-topography fabrication of multilayer interconnections for microfluidic devices

Multilayer interconnections are needed for microdevices with a large number of independent electrodes. A multi-level photolithographic process is commonly employed to provide multilayer interconnections in integrated circuit (IC) devices, but it is often too expensive for large-area or disposable devices frequently needed for microfluidics. The printed circuit board (PCB) can provide multilayer interconnection at low cost, but its rough topography poses a challenge for small droplets to slide over. Here we report a low-cost fabrication of low-topography multilayer interconnects by selective and controlled anodization of thin-film metal layers. The process utilizes anodization of metal (tantalum in this paper) or, more specifically, repetitions of a partial anodization to form insulation layers between conductive layers and a full anodization to form isolating regions between electrodes, replacing the usual process of depositing, planarizing, and etching insulation layers. After verifying the electric connections and insulations as intended, the developed method is applied to electrowetting-on-dielectric (EWOD), whose complex microfluidic products are currently built on PCB or thin-film transistor (TFT) substrates. To demonstrate the utility, we fabricated a 3 metal-layer EWOD device with steps (surface topography) less than 1 micrometer (vs. > 10 micrometers of PCB EWOD devices) and confirmed basic digital microfluidic operations

Measuring robustness of community structure in complex networks

The theory of community structure is a powerful tool for real networks, which can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks obtained from complex systems always contain error edges, evaluating the robustness of community structure is an urgent and important task. In this letter, we employ the critical threshold of resolution parameter in Hamiltonian function, $\gamma_C$, to measure the robustness of a network. According to spectral theory, a rigorous proof shows that the index we proposed is inversely proportional to robustness of community structure. Furthermore, by utilizing the co-evolution model, we provides a new efficient method for computing the value of $\gamma_C$. The research can be applied to broad clustering problems in network analysis and data mining due to its solid mathematical basis and experimental effects.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1303.7434 by other author

Semiparametric Trending Panel Data Models with Cross-Sectional Dependence

A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A semiparametric profile likelihood approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the time trend function.cross-sectional dependence, nonlinear time trend, panel data, profile likelihood, semiparametric regression

Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series

Estimation theory in a nonstationary environment has been very popular in recent years. Existing studies focus on nonstationarity in parametric linear, parametric nonlinear and nonparametric nonlinear models. In this paper, we consider a partially linear model and propose to estimate both alpha and g semiparametrically. We then show that the proposed estimator of alpha is still asymptotically normal with the same rate as for the case of stationary time series. We also establish the asymptotic normality for the nonparametric estimator of the function g and the uniform consistency of the nonparametric estimator. The simulated example is given to show that our theory and method work well in practice.asymptotic normality; beta-null recurrent Markov chain; consistency; kernel estimator; partially linear model