MSC-clustering and forward stepwise regression for virtual metrology in highly correlated input spaces

Increasingly semiconductor manufacturers are exploring opportunities for virtual metrology (VM) enabled process monitoring and control as a means of reducing non-value added metrology and achieving ever more demanding wafer fabrication tolerances. However, developing robust, reliable and interpretable VM models can be very challenging due to the highly correlated input space often associated with the underpinning data sets. A particularly pertinent example is etch rate prediction of plasma etch processes from multichannel optical emission spectroscopy data. This paper proposes a novel input-clustering based forward stepwise regression methodology for VM model building in such highly correlated input spaces. Max Separation Clustering (MSC) is employed as a pre-processing step to identify a reduced srt of well-conditioned, representative variables that can then be used as inputs to state-of-the-art model building techniques such as Forward Selection Regression (FSR), Ridge regression, LASSO and Forward Selection Ridge Regression (FCRR). The methodology is validated on a benchmark semiconductor plasma etch dataset and the results obtained are compared with those achieved when the state-of-art approaches are applied directly to the data without the MSC pre-processing step. Significant performance improvements are observed when MSC is combined with FSR (13%) and FSRR (8.5%), but not with Ridge Regression (-1%) or LASSO (-32%). The optimal VM results are obtained using the MSC-FSR and MSC-FSRR generated models. © 2012 IEEE.

Thermometry precision in strongly correlated ultracold lattice gases

The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated
system is a question of both fundamental and technological importance. Here, we address such
question by combining tools from quantum metrology together with the study of the quantum
correlations embedded in the system at finite temperatures. Within this frame we examine the spin-
1 2 XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable
bound on the temperature precision. We then address the estimation of the temperature of the sample
from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method.
Remarkably, our results show that the collective quantum correlations can become optimal
observables to accurately estimate the temperature of our model in a given range of temperatures.

Sparse multi-carrier index keying OFDM with index separation over correlated sub-carriers

In this paper, we propose a sparse multi-carrier index keying (MCIK) method for orthogonal frequency division multiplexing (OFDM) system, which uses the indices of sparse sub-carriers to transmit the data, and improve the performance
of signal detection in highly correlated sub-carriers. Although a receiver is able to exploit a power gain with precoding in OFDM, the sensitivity of the signal detection is usually high as the orthogonality is not retained in highly dispersive
environments. To overcome this, we focus on developing the trade-off between the sparsity of the MCIK, correlation, and performances, analyzing the average probability of the error propagation imposed by incorrect index detection over highly correlated sub-carriers. In asymptotic cases, we are able to see how sparsity of MCIK should be designed in order to perform superior to the classical OFDM system. Based on this feature, sparse MCIK based OFDM is a better choice for low detection errors in highly correlated sub-carriers.

Corneal hysteresis is correlated with reduction in axial length after trabeculectomy.

BACKGROUND: We sought to determine whether corneal biomechanical parameters are predictive of reduction in axial length after anti-metabolite trabeculectomy. METHODS: Chinese subjects undergoing trabeculectomy with mitomycin C by a single experienced surgeon underwent the following measurements: Corneal hysteresis (CH, Ocular Response Analyzer, Reichert Ophthalmic Instruments), Goldmann intra-ocular pressure (IOP), central corneal thickness (CCT) and axial length (AL, IOLMaster, Carl Zeiss Meditec, Dublin, CA) were measured pre-operatively, and AL, CH and IOP were measured 1 day and 1 week post-operatively. RESULTS: Mean age of 31 subjects was 52.0 ± 15.2 years, and 15 (48.4%) were female. The mean pre-operative IOP of 21.4 ± 9.3 mmHg was reduced to 8.2 ± 4.6 mmHg 1 day and 11.0 ± 4.4 mmHg 1 week post-operatively (p < 0.001). AL declined from 22.99 ± 0.90 to 22.76 ± 0.87 mm at 1 day and 22.74 ± 0.9 mm at 1 week; 30/31 (%) eyes had a decline in AL (p < 0.001, sign test). In multivariate linear regression models including post-operative data from 1 day and 1 week, greater decline in Goldmann IOP (p < 0.0001, greater pre-op axial length (p < 0.001) and lower pre-operative CH (p = 0.03), were all associated with greater decline in post-operative axial length. CONCLUSIONS: Eyes with lesser ability of the ocular coat to absorb energy (lower CH) had significantly greater decrease in axial length after trabeculectomy-induced IOP-lowering.