An Input Normal Form Homotopy for the L2 Optimal Model Order Reduction Problem

In control system analysis and design, finding a reduced order model, optimal in the L-squared sense, to a given system model is a fundamental problem. The problem is very difficult without the global convergence of homotopy methods, and a homotopy based approach has been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. A homotopy algorithm based on the input normal form characterization of the reduced order model is developed here and is compared with the homotopy algorithms based on Hyland and Bernstein's optimal projection equations. The main conclusions are that the input normal form algorithm can be very efficient, but can also be very ill conditioned or even fail

A Homotopy Algorithm for the Combined H-squared/H-to Infinity Model Reduction Problem

The problem of finding a reduced order model, optimal in the H-squared sense, to a given system model is a fundamental one in control system analysis and design. The addition of a H-to infinity constraint to the H-squared optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probability-one homotopy methods the combined H-squared/H-to infinity model reduction problem is difficult to solve. Several approaches based on homotoppy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on two formulations - input normal form; Ly, Bryson, and Cannon's 2 x 2 block parametrization - are developed and compared here

High-Throughput Screening Platform for Engineered Nanoparticle-Mediated Genotoxicity Using CometChip Technology

The likelihood of intentional and unintentional engineered nanoparticle (ENP) exposure has dramatically increased due to the use of nanoenabled products. Indeed, ENPs have been incorporated in many useful products and have enhanced our way of life. However, there are many unanswered questions about the consequences of nanoparticle exposures, in particular, with regard to their potential to damage the genome and thus potentially promote cancer. In this study, we present a high-throughput screening assay based upon the recently developed CometChip technology, which enables evaluation of single-stranded DNA breaks, abasic sites, and alkali-sensitive sites in cells exposed to ENPs. The strategic microfabricated, 96-well design and automated processing improves efficiency, reduces processing time, and suppresses user bias in comparison to the standard comet assay. We evaluated the versatility of this assay by screening five industrially relevant ENP exposures (SiO[subscript 2], ZnO, Fe[subscript 2]O[subscript 3], Ag, and CeO[subscript 2]) on both suspension human lymphoblastoid (TK6) and adherent Chinese hamster ovary (H9T3) cell lines. MTT and CyQuant NF assays were employed to assess cellular viability and proliferation after ENP exposure. Exposure to ENPs at a dose range of 5, 10, and 20 μg/mL induced dose-dependent increases in DNA damage and cytotoxicity. Genotoxicity profiles of ZnO > Ag > Fe[subscript 2]O[subscript 3] > CeO[subscript 2] > SiO[subscript 2] in TK6 cells at 4 h and Ag > Fe[subscript 2]O[subscript 3] > ZnO > CeO[subscript 2] > SiO[subscript 2] in H9T3 cells at 24 h were observed. The presented CometChip platform enabled efficient and reliable measurement of ENP-mediated DNA damage, therefore demonstrating the efficacy of this powerful tool in nanogenotoxicity studies.National Science Foundation (U.S.) (Grant 1235806)National Institutes of Health (U.S.) (Grant P30ES000002

Generating EQ-5D-3L health utility scores from the Edinburgh Postnatal Depression Scale: a perinatal mapping study

Background: Perinatal depression (PND) describes depression experienced by parents during pregnancy or in the first year after a baby is born. The EQ-5D instrument (a generic measure of health status) is not often collected in perinatal research, however disease-specific measures, such as the Edinburgh Postnatal Depression Scale (EPDS) are widely used. Mapping can be used to estimate generic health utility index values from disease-specific measures like the EPDS. Objective: To develop a mapping algorithm to estimate EQ-5D utility index values from the EPDS. Methods: Patient-level data from the BaBY PaNDA study (English observational cohort study) provided 1068 observations with paired EPDS and EQ-5D (3-level version; EQ-5D-3L) responses. We compared the performance of six alternative regression model types, each with four specifications of covariates (EPDS score and age: base, squared, and cubed). Model performance (ability to predict utility values) was assessed by ranking mean error, mean absolute error, and root mean square error. Algorithm performance in 3 external datasets was also evaluated. Results: There was moderate correlation between EPDS score and utility values (coefficient: – 0.42). The best performing model type was a two-part model, followed by ordinary least squared. Inclusion of squared and cubed covariates improved model performance. Based on graphs of observed and predicted utility values, the algorithm performed better when utility was above 0.6. Conclusions: This direct mapping algorithm allows the estimation of health utility values from EPDS scores. The algorithm has good external validity but is likely to perform better in samples with higher health status

Identification of dynamic displacements and modal frequencies of amedium-span suspension bridge using multimode GNSS processing

Global Navigation Satellite System (GNSS) positioning technology has been employed in the dynamic monitoring of long-span bridges in the recent years. However, it has difficulties to meet the higher accuracy requirements of the dynamic monitoring of small or medium span bridges, due to the presence of measurement noise from multipath, cycle slips, ionosphere delay, orbital errors, etc. To verify the feasibility of using current GNSS technology to monitor these bridges, a series of monitoring experiments have been carried out on the Wilford suspension bridge in Nottingham (UK) with GNSS and a triaxial accelerometer. Three GNSS data processing modes, i.e. Real-Time Kinematic (RTK), network RTK and Post-Processing Kinematic (PPK), were considered. An innovative multimode adaptive filtering (MAF) that combining adaptive filter with Chebyshev highpass filter was used to identify the dynamic displacements of the bridge from the multimode GNSS data. To validate the GNSS results, the dynamic displacements were also computed from double integration of the accelerometer-measured accelerations. The differences of the displacements between the GNSS and accelerometer results were obtained. The standard deviation and the mean deviation of these differences are less than 1 mm, which is good enough for the monitoring purposes. The modal frequencies of the bridge can be accurately identified from GNSS measurements, and successfully validated by those from the accelerometer data. Using the multimode GNSS data and the proposed the MAF algorithm, with sub-millimeter level accuracy GNSS can be used to monitor the vibration response of small or medium span bridges as well as long-span bridges

A Homotopy Algorithm for the Combined H2/H&infin Model Reduction Problem

The problem of finding a reduced order model, optimal in the H2 sense, to a given system model is a fundamental one in control system analysis and design. The addition of an H∞ constraint to the H2 optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probability-one homotopy methods the combined H2 /H∞ model reduction problem is difficult to solve. Several approaches based on homotopy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on two formulations---input normal form; Ly, Bryson, and Cannon's 2x2 block parametrization are developed and compared

Minimal Parameter Homotopies for the L2 Optimal Model Order Reduction Problem

The problem of finding a reduced order model, optimal in the L2 sense, to a given system model is a fundamental one in control system analysis and design. The problem is very difficult without the global convergence of homotopy methods, and a number of homotopy based approaches have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations are developed and compared here. The main conclusions are that dimensionality is inversely related to numerical well conditioning and algorithmic efficiency is inversely related to robustness of the algorithm

Interpolated sequences and critical LL-values of modular forms

Recently, Zagier expressed an interpolated version of the Ap\'ery numbers for $\zeta(3)$ in terms of a critical $L$-value of a modular form of weight 4. We extend this evaluation in two directions. We first prove that interpolations of Zagier's six sporadic sequences are essentially critical $L$-values of modular forms of weight 3. We then establish an infinite family of evaluations between interpolations of leading coefficients of Brown's cellular integrals and critical $L$-values of modular forms of odd weight.Comment: 23 pages, to appear in Proceedings for the KMPB conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theor

Globally Convergent Homotopy Algorithms for the Combined H-squared/ H-to Infinity Model Reduction Problem

The problem of finding a reduced order model, optimal in the H-squared sense, to a given system model is a fundamental one in control system analysis and design. The addition of a H-to infinity constraint to the H-squared optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probablity-one homotopy methods the combined H-squared/H-to infinity model reduction problem is difficult to solve. Several approaches based on homotopy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations -- input normal, Ly, Bryson, and Cannon's 2 x 2 block parametrization -- are developed and compared here