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Consider the estimation of a signal \({\mathbf {x}}\in \mathbb {R}^{N}\) from noisy observations \({{\mathbf {r}}={\mathbf {x}}+{\mathbf {z}}}\) , where the input \({{\mathbf x}}\) is generated by an independent and identically distributed (i.i.d.) Gaussian mixture source, and \({{\mathbf z}}\) is additive white Gaussian noise in parallel Gaussian channels. Typically, the \(\ell _{2}\) -norm error (squared error) is used to quantify the performance of the estimation process. In contrast, we consider the \(\ell _\infty \) -norm error (worst case error). For this error metric, we prove that, in an asymptotic setting where the signal dimension \(N\to \infty \) , the \(\ell _\infty \) -norm error always comes from the Gaussian component that has the largest variance, and the Wiener filter asymptotically achieves the optimal expected \(\ell _\infty \) -norm error. The i.i.d. Gaussian mixture case can be extended to i.i.d. Bernoulli-Gaussian distributions, which are often used to model sparse signals. Finally, our results can be extended to linear mixing systems with i.i.d. Gaussian mixture inputs, in settings where a linear mixing system can be decoupled to parallel Gaussian channels. [ABSTRACT FROM AUTHOR]

The performance of heuristic algorithms for combinatorial optimization is often sensitive to problem instances. In extreme cases, a specialized heuristic algorithm may perform exceptionally well on a particular set of instances while fail to produce acceptable solutions on others. Such a problem-sensitive nature is most evident in algorithms for combinatorial optimization problems such as job shop scheduling, vehicle routing, and cluster analysis. This paper proposes a formal method for comparing and selecting heuristic algorithms (or equivalently, different settings of a same algorithm) given a desired confidence level and a particular set of problem instances. We formulate this algorithm comparison problem as a stochastic optimization problem. Two approaches for stochastic optimization, Ordinal Optimization and Optimal Computing Budget Allocation are applied to solve this algorithm selection problem. Computational testing on a set of statistical clustering algorithms in the IMSL library is conducted. The results demonstrate that our method can determine the relative performance of heuristic algorithms with high confidence probability while using a small fraction of computer times that conventional methods require. Index Terms - Algorithm comparison, cluster analysis, computing budget allocation, manufacturing scheduling problems, ordinal optimization, stochastic optimization.

An efficient and environmentally benign procedure for the reactions of three components condensation of salicylaldehyde and two different CH acids to give 2-amino-4 H-chromenes catalyzed by a series of basic-functionalized ionic liquids was reported. The most possible reaction pathway was proposed for the first time by performing density functional theory (DFT) calculations. Both cation and anion of [Bmim]OH have a cooperative effect on the reaction. [Bmim]+ increases the electrophilicity of salicylaldehyde via intermolecular hydrogen bonds, while OH− deprives proton of two CH acids to strengthen their nucleophilic ability. [ABSTRACT FROM AUTHOR]

Meyer-Schuster rearrangements of 2-phenyl-3-butyn-2-ol with H3O+ and (H2O)6 model in high-temperature water (HTW) have been investigated by the use of density functional theory calculations. In the substrate 2-phenyl-3-butyn-2-ol catalyzed by H3O+ and (H2O)6, the Meyer-Schuster rearrangements were predicted by the frontier molecular orbital theory. The results show that the rearrangement does not involve the carbonium ion intermediates, but the first transition state is carboniumion like. Dehydration and hydration may occur via the intermolecular proton relay along the hydrogen-bond chains and the second step of reaction path is a total acid-base catalytic process. Based on the results, a model considered both HTW ambient and water molecules are proposed to represent mechanisms of other reactions in HTW. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 [ABSTRACT FROM AUTHOR]

Abstract: N-methylacetamide (NMA) served as a model to investigate the hydrolysis kinetics and mechanism of N-substituted amides in high-temperature water. The major products are acetic acid and methylamine, and the reaction is reversible. The hydrolysis reaction is first order in water and first order in NMA at both subcritical and supercritical conditions. The hydrolysis rate is also pH dependent, and three distinct regions of pH dependence exist. At low and high pH, the conversion increased rapidly with added acid and base, respectively. At near-neutral pH, however, the rate was essentially insensitive to changes in pH. Further investigation revealed that the hydrolysis rate constant was very sensitive to the size of the substituent on the carbonyl carbon atom. An SN2 mechanism with water as the nucleophile appears to be a likely candidate for the hydrolysis mechanism in high-temperature water at near-neutral conditions. [Copyright &y& Elsevier]

Simulation plays a vital role in analyzing discrete-event systems, particularly in comparing alternative system designs with a view to optimizing system performance. Using simulation to analyze complex systems, however, can be both prohibitively expensive and time-consuming. Effective algorithms to allocate intelligently a computing budget for discrete-event simulation experiments are presented in this paper. These algorithms dynamically determine the simulation lengths for all simulation experiments and thus significantly improve simulation efficiency under the constraint of a given computing budget. Numerical illustrations are provided and the algorithms are compared with traditional two-stage ranking-and-selection procedures through numerical experiments. Although the proposed approach is based on heuristics, the numerical results indicate that it is much more efficient than the compared procedures. [ABSTRACT FROM AUTHOR]

Growing populations and industrialization have led to increased nitrogen (N) loads in wetland ecosystems. A micro-constructed wetland planted with Lythrum salicaria L. to treat artificial wastewater was used to investigate the short-term variations in the plant biomass and dynamics of total nitrogen (TN) content. Our results showed that the biomass of Lythrum salicaria L. rapidly increased during the experiment due to their extensive root system and vigorous spread, and waterlogged conditions had little effect on the relationship between biomass and the TN content in soil and effluent. Under different waterlogged conditions, the TN removal rates in the water were all greater than 60%, providing a reference for the waterlogged conditions used in wetland eutrophication restoration. [ABSTRACT FROM AUTHOR]