A Simple Technique for the Rapid Estimation of the Optimal Support Locations for a Vibrating Plate

1992 ◽  
Vol 114 (1) ◽  
pp. 112-118 ◽  
Author(s):  
J. M. Pitarresi ◽  
R. J. Kunz
Keyword(s):  
Simple Technique ◽  
Optimization Theory ◽  
Nonlinear Least Squares ◽  
Response Surfaces ◽  
Accurate Estimation ◽  
Optimal Point ◽  
Spreadsheet Program ◽  
Rapid Estimation ◽  
Least Squares Fit ◽  
Vibrating Plates

This paper is aimed at presenting a simple technique for the rapid estimation of the optimal point support locations of vibrating plates. Using a two-dimensional nonlinear least-squares fit of natural frequency versus support location data, along with the concept of response surfaces, a difficult design optimization problem involving changing boundary conditions is transformed to a much simpler, approximate form. By using classical optimization theory, the estimated optimal location of the support can then be readily found. The computations for the formation of the response function and its optimum can be readily carried out on a personal computer using a spreadsheet program. The validity of this approach is demonstrated through a number of examples using analytical, computational, and experimental data. The technique is well suited to preliminary design investigations where a rapid but accurate estimation of the support location is required. Finally, a key advantage of the proposed method is that it can be used with data from any analytical, computational, or experimental effort, including any combination of the above.

Comparison of turbidimetric and light-scattering measurements of immunoglobulins by use of a centrifugal analyzer with absorbance and fluorescence/light-scattering optics.

1980 ◽  
Vol 26 (10) ◽  
pp. 1459-1466 ◽  
Author(s):  
L P Hills ◽  
T O Tiffany
Keyword(s):  
Light Scattering ◽  
Kinetic Curve ◽  
Nonlinear Least Squares ◽  
Light Scatter ◽  
Assay Sensitivity ◽  
Human Immunoglobulins ◽  
Least Squares Fit ◽  
Scattering Measurements ◽  
Fluorescence Light ◽  
Antigen Antibody

Abstract We have developed a centrifugal analyzer with both fluorescence/light-scatter and conventional absorbance optics. The instrument is used in this investigation to study the formation of antigen-antibody complexes by light scattering and turbidimetric measurements, and to develop assays for human immunoglobulins G, A, and M. Concentrations are calculated from a nonlinear least-squares fit of calibrators, and antigen excess is automatically detected from kinetic curve characteristics. Precisions and patients’ results are presented, and assay sensitivity and reliability in the detection of antigen excess are compared. We also investigated the effects of centrifugal force on complex formation. Both nephelometry and turbidimetry can be very satisfactorily adapted to centrifugal analyzers. We present a model to describe the observed differences between the light-scatter and the turbidity data.

scholarly journals Quantification of uncertainty in rapid estimation of earthquake fatalities based on scenario analysis

2018 ◽  
Author(s):  
Xiaoxue Zhang ◽  
Hanping Zhao ◽  
Fangping Wang ◽  
Zezheng Yan ◽  
Sida Cai ◽  
...  
Keyword(s):  
Emergency Response ◽  
Preliminary Analysis ◽  
Accurate Estimation ◽  
Earthquake Parameters ◽  
Rapid Estimation ◽  
Factors Affecting ◽  
The Core ◽  
Comparison Results ◽  
Emergency Scenarios ◽  
Earthquake Fatalities

Abstract. The rapid estimation of earthquake fatalities using earthquake parameters is the core basis for emergency response. However, there are numerous factors affecting earthquake fatalities, and it is impossible to obtain an accurate estimation result. The key to solve this problem is quantifying the uncertainty. In this paper, we proposed a new method to estimate earthquake fatalities and quantify the uncertainty based on basic earthquake emergency scenarios. The accuracy of the model is verified by earthquake that occurred during recent year. The preliminary analysis and comparison results show that the model is more effective and reasonable and can also provide a theoretical basis for post-earthquake emergency response.

scholarly journals Near infrared nadir sounding of vertical column densities: methodology and application to SCIAMACHY

2011 ◽  
Vol 4 (3) ◽  
pp. 3685-3737
Author(s):  
S. Gimeno García ◽  
F. Schreier ◽  
G. Lichtenberg ◽  
S. Slijkhuis
Keyword(s):  
Least Squares ◽  
Near Infrared ◽  
Nonlinear Least Squares ◽  
Retrieval Algorithm ◽  
Atmospheric Gases ◽  
Vertical Column ◽  
Least Squares Fit ◽  
Least Squares Optimization ◽  
Shortwave Infrared ◽  
And Inversion

Abstract. Nadir observations with the shortwave infrared channels of SCIAMACHY onboard the ENVISAT satellite can be used to derive information on atmospheric gases such as CO, CH4, N2O, CO2, and H2O. For the operational level 1b–2 processing of SCIAMACHY data a new retrieval code BIRRA (Beer InfraRed Retrieval Algorithm) has been developed: BIRRA performs a nonlinear least squares fit of the measured radiance, where molecular concentration vertical profiles are scaled to fit the observed data. Here we present the forward modeling (radiative transfer) and inversion (least squares optimization) fundamentals of the code along with the further processing steps required to generate higher level products such as global distributions and time series. Moreover, various aspects of level 1 (observed spectra) and auxiliary input data relevant for successful retrievals are discussed. BIRRA is currently used for operational analysis of carbon monoxide vertical column densities from SCIAMACHY channel 8 observations, and is being prepared for methane retrievals using channel 6 spectra. A set of representative CO retrievals and first CH4 results are presented to demonstrate BIRRA's capabilities.

Automatic calibration of powder diffraction experiments using two-dimensional detectors

2007 ◽  
Vol 22 (1) ◽  
pp. 3-19 ◽  
Author(s):  
P. Rajiv ◽  
B. Hinrichsen ◽  
R. Dinnebier ◽  
M. Jansen ◽  
M. Joswig
Keyword(s):  
Powder Diffraction ◽  
Computational Cost ◽  
Nonlinear Least Squares ◽  
Calibration Method ◽  
High Signal ◽  
Automatic Calibration ◽  
Experimental Calibration ◽  
One Dimensional ◽  
Least Squares Fit ◽  
Image Artefacts

Calibration of powder diffraction experiments using area detectors is essential to extract high quality one-dimensional powder diffraction pattern. Precise calibration necessitates a sensible characterization of the Debye-Scherrer rings formed on the detector plane. An algorithm, designed and developed to automate this process, is described in this paper. All the parameters required for an experimental calibration are extracted using robust pattern recognition techniques. Several image preprocessing methods are employed, reducing the computational cost but retaining high signal quality. A modified version of a one-dimensional Hough transformation is used to determine the final parameters of the ellipses. After extraction, the parameters are optimized using nonlinear least squares fit. The presented algorithm is insensitive to image artefacts and was successfully applied to a large number of calibration images. The performance of the algorithm is demonstrated by the comparison of results obtained from the presented automatic calibration method and an existing manual method.

Molecular Parameters for the a3Πu and b3Σg− States in C2

1975 ◽  
Vol 53 (3) ◽  
pp. 299-302 ◽  
Author(s):  
L. Veseth
Keyword(s):  
Least Squares ◽  
Electronic Spectra ◽  
Nonlinear Least Squares ◽  
Experimental Information ◽  
Present Approach ◽  
Energy Separation ◽  
Molecular Parameters ◽  
Triplet Splitting ◽  
Least Squares Fit

Molecular parameters for the a3Πu and b3Σg− states in C2 (Ballik–Ramsay system) are determined by a nonlinear least squares fit directly to the observed wavelengths. No satellite lines are observed in the electronic spectra of C2, and the influence of nuclear statistics yields further restrictions with regard to observable lines. The present approach, however, yields accurate values of the various triplet splitting and Λ-doubling parameters in spite of this lack of experimental information. Finally a refined value of the triplet–singlet energy separation is obtained.

scholarly journals Polarization-Sensitive CARS of Excited-State Rhodamine 6G: Induced Anisotropy Effects on Depolarization Ratios

1993 ◽  
Vol 47 (12) ◽  
pp. 1975-1988 ◽  
Author(s):  
Gerald W. Lucassen ◽  
Wim P. De Boeij ◽  
Jan Greve
Keyword(s):  
Excited State ◽  
Ground State ◽  
Rhodamine 6G ◽  
Dipole Moments ◽  
Nonlinear Least Squares ◽  
Isotropic Case ◽  
Induced Anisotropy ◽  
Least Squares Fit ◽  
Nanosecond Time Resolution ◽  
Depolarization Ratios

Resonance polarization-sensitive coherent anti-Stokes Raman scattering (PS CARS) spectra of the electronic ground state and excited singlet S1 state of rhodamine 6G in ethanol were obtained with the use of the pump-probe technique with nanosecond time resolution. Variation of the polarization orientation of the pump laser beam showed differences in the excited-state spectra due to optically induced anisotropy. The pure electronic susceptibility of ground-state rhodamine 6G was shown to be small in comparison with nonresonant susceptibility of the solvent, and was neglected in further analyses. The pure electronic susceptibility of excited rhodamine 6G was examined by coherent ellipsometry. The complex third-order susceptibility was analyzed by means of a nonlinear least-squares fit program that provides detailed information on the Raman vibration parameters, including depolarization ratios and phases. In the isotropic case the measured depolarization ratios are close to 1/3, whereas in the anisotropic case, ground-state depolarization ratios are 0.5–0.65 and in the excited state 0.17–0.22. Estimated depolarization ratio changes in ground-state and excited-state rhodamine 6G are in agreement with theoretically predicted values in the case of induced anisotropy under the assumption of parallel dipole moments of the CARS process. The effects of possible changed molecular structure or symmetry and changed enhancement of different electronic transitions cannot be determined without making some assumptions about one of these effects. The obtained phase differences reflect different enhancements and vibronic coupling for ground-state and excited-state vibrations. The ground-state and excited-state hyperpolarizabilities, [Formula: see text], of rhodamine 6G were estimated to be 3.8·10−35 esu and 27.4·10−35 esu, respectively.

Dynamical Mechanism of Sampling-Based Probabilistic Inference under Probabilistic Population Codes

2022 ◽  
pp. 1-24
Author(s):  
Kohei Ichikawa ◽  
Asaki Kataoka
Keyword(s):  
Dynamical Systems ◽  
Probability Distributions ◽  
Probabilistic Inference ◽  
Point Estimation ◽  
Accurate Estimation ◽  
Neural Basis ◽  
Optimal Point ◽  
Dynamical Mechanism ◽  
Noisy Information ◽  
Population Codes

Abstract Animals make efficient probabilistic inferences based on uncertain and noisy information from the outside environment. It is known that probabilistic population codes, which have been proposed as a neural basis for encoding probability distributions, allow general neural networks (NNs) to perform near-optimal point estimation. However, the mechanism of sampling-based probabilistic inference has not been clarified. In this study, we trained two types of artificial NNs, feedforward NN (FFNN) and recurrent NN (RNN), to perform sampling-based probabilistic inference. Then we analyzed and compared their mechanisms of sampling. We found that sampling in RNN was performed by a mechanism that efficiently uses the properties of dynamical systems, unlike FFNN. In addition, we found that sampling in RNNs acted as an inductive bias, enabling a more accurate estimation than in maximum a posteriori estimation. These results provide important arguments for discussing the relationship between dynamical systems and information processing in NNs.

Temporal relation between energy metabolism and myocardial function during ischemia and reperfusion

1987 ◽  
Vol 253 (2) ◽  
pp. H412-H421 ◽  
Author(s):  
K. Clarke ◽  
A. J. O'Connor ◽  
R. J. Willis
Keyword(s):  
Energy Metabolism ◽  
Contractile Function ◽  
Rapid Change ◽  
Nonlinear Least Squares ◽  
Creatine Phosphate ◽  
Resonance Spectroscopy ◽  
Metabolic Parameter ◽  
Guinea Pig Heart ◽  
Phosphorylation Potential ◽  
Least Squares Fit

The purpose of the present investigation was to study the relation between energy metabolism and contractile function in the isovolumic guinea pig heart. 31P nuclear magnetic resonance spectroscopy was used to measure changes in the intracellular levels of creatine phosphate, ATP, inorganic phosphate, and pH during 2.43 min total global ischemia and 2.43 min reperfusion, with a time resolution of 9.7 s. From these data, cytosolic changes in the phosphorylation potential, [ATP]-to-[ADP] ratio, free-energy change of ATP hydrolysis, and concentration of free ADP were estimated. The simultaneous monitoring of functional and biochemical parameters allowed them to be directly correlated with respect to time and with respect to each other. No significant changes in ATP were detected at any time, but changes in all other biochemical data were highly correlated with changes in contractile function. Kinetic analysis, using a nonlinear least-squares fit of the experimental points, revealed that the changes in most parameters fitted monoexponential functions. Each parameter was ranked according to its half time, which revealed that the phosphorylation potential was the only metabolic parameter to change at a rate faster than loss of contractile function during ischemia, and all metabolic changes, with the exception of pH, led the recovery of contractile function during reperfusion, the most rapid change occurring in the free ADP concentration. It is concluded that the cytosolic phosphorylation potential controls the contractile function of the heart and that cytosolic free ADP is important in the control of mitochondrial oxidative phosphorylation.

A Model of Load Sharing Between Muscles and Soft Tissues at the Human Knee During Static Tasks

1996 ◽  
Vol 118 (3) ◽  
pp. 367-376 ◽  
Author(s):  
D. G. Lloyd ◽  
T. S. Buchanan
Keyword(s):  
Soft Tissue ◽  
External Load ◽  
Muscle Activation ◽  
Soft Tissues ◽  
Nonlinear Least Squares ◽  
Joint Moment ◽  
Muscle Forces ◽  
Least Squares Fit ◽  
Average Maximum ◽  
Flexion And Extension

In this study, we had subjects voluntarily generate various forces in a transverse plane just above their ankles. The contributions of their muscles and soft tissues to the support of the total external knee joint moment were determined by analyzing the experimental data using a biomechanical model of the knee. In this model, muscle forces were estimated using the recorded EMGs. To account for subject variability, various muscle parameters were adjusted using a nonlinear least-squares fit of the model’s estimated flexion and extension joint moments to those recorded externally. Using the estimated muscle forces, the contributions from the muscles and other soft tissues to the total joint moment were obtained. The results showed that muscles were primarily used to support flexion and extension loads at the knee, but in so doing, were able to support some part of the varus or valgus loads. However, soft tissue loading was still required. Soft tissues supported up to an average maximum of 83 percent of the external load in pure varus and valgus. Soft tissue loading in pure varus and valgus was less than 100 percent of the external load as the muscles, on average, were able to support 17 percent of the external load. This muscle support was by virtue of muscle cocontraction and/or specific muscle activation.

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