Two-stage Robust Network Design with Exponential Scenarios

We study two-stage robust variants of combinatorial optimization problems on undirected graphs, like Steiner tree, Steiner forest, and uncapacitated facility location. Robust optimization problems, previously studied by Dhamdhere et al. (Proc. of 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05), pp. 367–378, 2005), Golovin et al. (Proc. of the 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), 2006), and Feige et al. (Proc. of the 12th International Integer Programming and Combinatorial Optimization Conference, pp. 439–453, 2007), are two-stage planning problems in which the requirements are revealed after some decisions are taken in Stage 1. One has to then complete the solution, at a higher cost, to meet the given requirements. In the robust k-Steiner tree problem, for example, one buys some edges in Stage 1. Then k terminals are revealed in Stage 2 and one has to buy more edges, at a higher cost, to complete the Stage 1 solution to build a Steiner tree on these terminals. The objective is to minimize the total cost under the worst-case scenario. In this paper, we focus on the case of exponentially many scenarios given implicitly. A scenario consists of any subset of k terminals (for k-Steiner tree), or any subset of k terminal-pairs (for k-Steiner forest), or any subset of k clients (for facility location). Feige et al. (Proc. of the 12th International Integer Programming and Combinatorial Optimization Conference, pp. 439–453, 2007) give an LP-based general framework for approximation algorithms for a class of two stage robust problems. Their framework cannot be used for network design problems like k-Steiner tree (see later elaboration). Their framework can be used for the robust facility location problem, but gives only a logarithmic approximation. We present the first constant-factor approximation algorithms for the robust k-Steiner tree (with exponential number of scenarios) and robust uncapacitated facility location problems. Our algorithms are combinatorial and are based on guessing the optimum cost and clustering to aggregate nearby vertices. For the robust k-Steiner forest problem on trees and with uniform multiplicative increase factor for Stage 2 (also known as inflation), we present a constant approximation. We show APX-hardness of the robust min-cut problem (even with singleton-set scenarios), resolving an open question of (Dhamdhere et al. in Proc. of 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05), pp. 367–378, 2005) and (Golovin et al. in Proc. of the 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), 2006).     

The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long-memory time series

We establish some asymptotic properties of a log-periodogram regression estimator for the memory parameter of a long-memory time series. We consider the estimator originally proposed by Geweke and Porter-Hudak (The estimation and application of long memory time series models. Journal of Time Ser. Anal. 4 (1983), 221–37). In particular, we do not omit any of the low frequency periodogram ordinates from the regression. We derive expressions for the estimator's asymptotic bias, variance and mean squared error as functions of the number of periodogram ordinates, m , used in the regression. Consistency of the estimator is obtained as long as m ←∞ and n ←∞ with ( m log m )/ n ← 0, where n is the sample size. Under these and the additional conditions assumed in this paper, the optimal m , minimizing the mean squared error, is of order O( n ^4/5). We also establish the asymptotic normality of the estimator. In a simulation study, we assess the accuracy of our asymptotic theory on mean squared error for finite sample sizes. One finding is that the choice m = n ^1/2, originally suggested by Geweke and Porter-Hudak (1983), can lead to performance which is markedly inferior to that of the optimal choice, even in reasonably small samples.     

Metal oxide nanoparticles for advanced energy applications

Hot-wire chemical vapor deposition (HWCVD) has been employed as an economically scalable method for the deposition of crystalline molybdenum oxide nanoparticles at high density. Under optimal synthesis conditions, only crystalline nanostructures with a smallest dimension of ~ 3-50 nm are observed with extensive transmission electron microscopy analyses. The incorporation of crystalline molybdenum oxide nanoparticles into battery electrodes has led to profound advancements in state-of-the-art negative electrodes (anodes) in lithium-ion batteries. The nanoparticle materials exhibit a high rate capability as anticipated for the reduced solid-state Li-ion diffusion length.     

Plug-in Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long-memory Time Series

We consider the problem of selecting the number of frequencies, m , in a log-periodogram regression estimator of the memory parameter d of a Gaussian long-memory time series. It is known that under certain conditions the optimal m , minimizing the mean squared error of the corresponding estimator of d , is given by m ^(opt)= Cn ^4/5, where n is the sample size and C is a constant. In practice, C would be unknown since it depends on the properties of the spectral density near zero frequency. In this paper, we propose an estimator of C based again on a log-periodogram regression and derive its consistency. We also derive an asymptotically valid confidence interval for d when the number of frequencies used in the regression is deterministic and proportional to n ^4/5. In this case, squared bias cannot be neglected since it is of the same order as the variance. In a Monte Carlo study, we examine the performance of the plug-in estimator of d , in which m is obtained by using the estimator of C in the formula for m ^(opt) above. We also study the performance of a bias-corrected version of the plug-in estimator of d . Comparisons with the choice m = n ^1/2 frequencies, as originally suggested by Geweke and Porter-Hudak (The estimation and application of long memory time series models. Journal of Time Ser. Anal. 4 (1983), 221–37), are provided.     

Growth of low dislocation density single crystals of nickel

Low dislocation density single crystals of nickel have been grown at high ambient pressure by the Czochralski method. X-ray Laue picture shows that the crystals are strain-free. The dislocation density was determined to be <10³/cm² by the etching procedure. It was found that the necking and cone regions are very critical in the dislocation introduction in the crystals. An increase in the ambient pressure used during the growth seems to aid the crystal quality.     

Novel technique for investigating high-power microwave pulses using Kerr effect

A novel method for the measurement of peak power of microwave pulses up to the few hundred kilowatts level based on the microwave-induced electro-optical Kerr effect in nonlossy dielectric liquids is described. This method provides additional information about the shape of the pulse, which is not usually given by the conventional methods.<>     

Effective parameter estimation within a multi-dimensional population balance model framework

This study considers optimization problems with multi-dimensional population balance models embedded. The objective function is formulated as a least-squares problem, minimizing the difference between target data and simulated model output and the goal is to find model parameter values that best fit the data. Results show that derivative-free methods, such as the Nelder–Mead simplex method, fail to converge to an optimal solution. A similar result was obtained with gradient-based methods such as BFGS, quasi-Newton, Newton, Gauss–Newton, Levenberg–Marquardt and SQP, and with a stochastic genetic algorithm. It was hypothesized that three main issues could contribute to these convergence failures: (1) gradients were calculated based on finite differences, and as a result of improper step size determination, the numerical error could be prohibitive resulting in inaccurate derivative information, (2) the parameters may not be identifiable and (3) numerical instability could occur during the course of optimization. To circumvent these issues, this work addresses the calculation of derivative information based on automatic differentiation and sensitivity analysis to ensure increased accuracy. Issues such as parameter identifiability are also dealt with by analyzing an accurate Fisher information matrix. Given the computational burden in calculating accurate Jacobians and Hessians, compounded by the potential nonsmoothness introduced into the objective function as a result of granule nucleation, other optimization strategies may be warranted and this work addresses those accordingly. Overall, by systematically assessing the problem formulation and mechanisms, the results show that substantial improvements in convergence can be achieved by utilizing appropriate optimization techniques, thus leading to more successful and optimal parameter estimation.     

A Novel FRFT Beamformer for Rayleigh Faded Channels

A method of optimal beamforming for flat Rayleigh faded channels using the Fractional Fourier Transform (FRFT) is considered in this paper. It has been demonstrated through simulations that optimal beamforming with FRFT allows smaller mean-square errors in restoring signals degraded with linear time-or frequency variant distortions and Additive White Gaussian Noise. This is made possible by the additional flexibility that comes with free parameter ‘a’ of the fractional Fourier transform as oppose to the classical Fourier transform (FT). The method is especially useful in moving source problems, where Doppler Effect produces frequency shift when the source is moving, as in mobile and wireless communication where user produces the frequency shift while moving. In this paper it is shown through simulations that beamforming in fractional domain reduces BER as compared to time or frequency domain.     

Ultrafine particles from diesel vehicle emissions at different driving cycles induce differential vascular pro-inflammatory responses: Implication of chemical components and NF-κB signaling

Background

Nanometer silicon dioxide (nano-SiO₂) has a wide variety of applications in material sciences, engineering and medicine; however, the potential cell biological and proteomic effects of nano-SiO₂ exposure and the toxic mechanisms remain far from clear.

Results

Here, we evaluated the effects of amorphous nano-SiO₂ (15-nm, 30-nm SiO₂). on cellular viability, cell cycle, apoptosis and protein expression in HaCaT cells by using biochemical and morphological analysis, two-dimensional differential gel electrophoresis (2D-DIGE) as well as mass spectrometry (MS). We found that the cellular viability of HaCaT cells was significantly decreased in a dose-dependent manner after the treatment of nano-SiO₂ and micro-sized SiO₂ particles. The IC₅₀ value (50% concentration of inhibition) was associated with the size of SiO₂ particles. Exposure to nano-SiO₂ and micro-sized SiO₂ particles also induced apoptosis in HaCaT cells in a dose-dependent manner. Furthermore, the smaller SiO₂ particle size was, the higher apoptotic rate the cells underwent. The proteomic analysis revealed that 16 differentially expressed proteins were induced by SiO₂ exposure, and that the expression levels of the differentially expressed proteins were associated with the particle size. The 16 proteins were identified by MALDI-TOF-TOF-MS analysis and could be classified into 5 categories according to their functions. They include oxidative stress-associated proteins; cytoskeleton-associated proteins; molecular chaperones; energy metabolism-associated proteins; apoptosis and tumor-associated proteins.

Conclusions

These results showed that nano-SiO₂ exposure exerted toxic effects and altered protein expression in HaCaT cells. The data indicated the alterations of the proteins, such as the proteins associated with oxidative stress and apoptosis, could be involved in the toxic mechanisms of nano-SiO₂ exposure.