Many Hard Examples in Exact Phase Transitions with Application to Generating Hard Satisfiable Instances

This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it is proved that almost all instances of Model RB/RD have no tree-like resolution proofs of less than exponential size. Thus, we not only introduce new families of CNF formulas hard for resolution, which is a central task of Proof-Complexity theory, but also propose models with both many hard instances and exact phase transitions. Then, the implications of such models are addressed. It is shown both theoretically and experimentally that an application of Model RB/RD might be in the generation of hard satisfiable instances, which is not only of practical importance but also related to some open problems in cryptography such as generating one-way functions. Subsequently, a further theoretical support for the generation method is shown by establishing exponential lower bounds on the complexity of solving random satisfiable and forced satisfiable instances of RB/RD near the threshold. Finally, conclusions are presented, as well as a detailed comparison of Model RB/RD with the Hamiltonian cycle problem and random 3-SAT, which, respectively, exhibit three different kinds of phase transition behavior in NP-complete problems.Comment: 19 pages, corrected mistakes in Theorems 5 and

Empirical Likelihood for Regression Discontinuity Design

This paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs. We consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric. The proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes, unlike the conventional Wald-type method. These features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils' scholastic achievements. Bandwidth selection methods, higher-order properties, and extensions to incorporate additional covariates and parametric functional forms are also discussed.Empirical likelihood, Nonparametric methods, Regression discontinuity design, Treatment effect

Adaptive Estimation of Autoregressive Models with Time-Varying Variances

Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized least squares (GLS). Comparisons of the efficient procedure and the ordinary least squares (OLS) reveal that least squares can be extremely inefficient in some cases while nearly optimal in others. Simulations show that, when least squares work well, the adaptive estimators perform comparably well, whereas when least squares work poorly, major efficiency gains are achieved by the new estimators.Adaptive estimation, Autoregression, Heterogeneity, Weighted regression

Adaptive Estimation of Autoregressive Models with Time-Varying Variances

Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized least squares (GLS). Comparisons of the efficient procedure and ordinary least squares (OLS) reveal that least squares can be extremely inefficient in some cases while nearly optimal in others. Simulations show that, when least squares work well, the adaptive estimators perform comparably well, whereas when least squares work poorly, major efficiency gains are achieved by the new estimators.Adaptive estimation, Autoregression, Heterogeneity, Weighted regression

Antibacterial Performance of a Cu-bearing Stainless Steel against Microorganisms in Tap Water

This document is the Accepted Manuscript of the following article: Mingjun Li, Li Nan, Dake xu, Guogang Ren, Ke Yang, ‘Antibacterial Performance of a Cu-bearing Stainless Steel against Microorganisms in Tap Water’, Journal of Materials Science & Technology, Vol. 31 (3): 243-251, March 2015, DOI: https://doi.org/10.1016/j.jmst.2014.11.016, made available under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License CC BY NC-ND 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/).Tap water is one of the most commonly used water resources in our daily life. However, the increasing water contamination and the health risk caused by pathogenic bacteria, such as Staphylococcus aureus and Escherichia coli have attracted more attention. The mutualism of different pathogenic bacteria may diminish antibacterial effect of antibacterial agents. It was found that materials used for making pipe and tap played one of the most important roles in promoting bacterial growth. This paper is to report the performance of an innovative type 304 Cu-bearing stainless steel (304CuSS) against microbes in tap water. The investigation methodologies involved were means of heterotrophic plate count, contact angle measurements, scanning electron microscopy for observing the cell and subtract surface morphology, atomic absorption spectrometry for copper ions release study, and confocal laser scanning microscopy used for examining live/dead bacteria on normal 304 stainless steel and 304CuSS. It was found that the surface free energy varied after being immersed in tap water with polar component and Cu ions release. The results showed 304CuSS could effectively kill most of the planktonic bacteria (max 95.9% antibacterial rate), and consequently inhibit bacterial biofilms formation on the surface, contributing to the reduction of pathogenic risk to the surrounding environments.Peer reviewe