Free Parameter Model Research Articles

Uncertainties in TDCR measurement revisited: Contribution of optical effects

In the Triple to Double Coincidence Ratio method in Liquid Scintillation Counting, the detection efficiency is calculated from the value of a free parameter describing the intrinsic light yield of the counting system. This model is generally based on a Poisson distribution of the number of photoelectrons detected and the detection efficiency is obtained from the complement of the non-detection efficiency. In the classical free parameter model, the mean of the Poisson distribution, m, is a constant but some variability of this mean could be expected from optical effects due to internal reflections inside the LS source or from non-homogeneity of the detection efficiency of the photomultiplier tubes. Then, m becomes a random variable and the distribution of the photoelectrons becomes a compound Poisson distribution, with a random variable as mean value.This paper explores the implications of the variance of m, which were, to our knowledge, never considered previously in the uncertainty budget of TDCR measurements.

Robustness of calibration model for prediction of lignin content in different batches of snow pears based on NIR spectroscopy.

Snow pear is very popular in southwest China thanks to its fruit texture and potential medicinal value. Lignin content (LC) plays a direct and negative role (higher concentration and larger size of stone cells lead to thicker pulp and deterioration of the taste) in determining the fruit texture of snow pears as well as consumer purchasing decisions of fresh pears. In this study, we assessed the robustness of a calibration model for predicting LC in different batches of snow pears using a portable near-infrared (NIR) spectrometer, with the range of 1033-2300 nm. The average NIR spectra at nine different measurement positions of snow pear samples purchased at four different periods (batch A, B, C and D) were collected. We developed a standard normal variate transformation (SNV)-genetic algorithm (GA) -the partial least square regression (PLSR) model (master model A) - to predict LC in batch A of snow pear samples based on 80 selected effective wavelengths, with a higher correlation coefficient of prediction set (Rp) of 0.854 and a lower root mean square error of prediction set (RMSEP) of 0.624, which we used as the prediction model to detect LC in three other batches of snow pear samples. The performance of detecting the LC of batch B, C, and D samples by the master model A directly was poor, with lower Rp and higher RMSEP. The independent semi-supervision free parameter model enhancement (SS-FPME) method and the sequential SS-FPME method were used and compared to update master model A to predict the LC of snow pears. For the batch B samples, the predictive ability of the updated model (Ind-model AB) was improved, with an Rp of 0.837 and an RMSEP of 0.614. For the batch C samples, the performance of the Seq-model ABC was improved greatly, with an Rp of 0.952 and an RMSEP of 0.383. For the batch D samples, the performance of the Seq-model ABCD was also improved, with an Rp of 0.831 and an RMSEP of 0.309. Therefore, the updated model based on supervision and learning of new batch samples by the sequential SS-FPME method could improve the robustness and migration ability of the model used to detect the LC of snow pears and provide technical support for the development and practical application of portable detection device.

A study of the non-uniformity of the PMT photocathode response and its influence on the results obtained in different scintillation counting experiments

This work presents an investigation on the non-uniformity of the response of the photocathode of two photomultiplier tubes (PMTs) and its potential influence on the results of scintillation measurements. An experimental system was developed which allows studies of the non-uniformity of the photocathode response and its influence on the shape of alpha spectra obtained after pulse-shape discrimination. The system is presented together with tests of Hamamatsu R7600U-200 and H11934-203 PMTs. A degradation of the counting efficiency and a shift of the peak position towards smaller values were identified in the measurements near the edges of the photocathode where the energy resolution is significantly worse compared to the central region of the PMT. Such non-uniformity also affects absolute activity measurements based on the free parameter model, i.e., the Triple to Double Coincidence Ratio and the CIEMAT/NIST efficiency tracing methods. A significant non-uniformity of the response of a PMT would interfere with the assumption of the traditional free parameter model of a Poisson distribution of the number of emitted photons. Experimental results are presented in the paper, together with a discussion of their practical influence on scintillation and absolute activity measurements.

A Two‐Parameter Exponential‐Demand Formula with a Behavioral Momentum Normalization: A Novel Method to Characterize the Reinforcing Effectiveness of Drugs

Application of behavioral economic principles to the characterization of drugs of abuse has yielded compelling evidence for a relationship between price (P) and consumption (Q). In turn, a quantitative assessment of this relationship provides a metric for comparing the reinforcing effectiveness (α) of various drugs, and demand analysis may provide a screening mechanism to evaluate candidate medications for the management of substance abuse. However, discordance between the α values for some drugs in nonhuman subjects and their reinforcing effectiveness in humans (e.g., high α avalues and high rates of abuse of nicotine) suggests that previous demand equations may require further refinement. In the present work, demand equations were derived to try to more accurately reflect the contribution of behavioral momentum‐ evident in resistance to vehicle extinction‐ to the calculation of reinforcing effectiveness. Resistance to extinction conceivably may influence demand curve elasticity, especially at higher prices. Here, demand curves were derived from intravenous self‐administration data obtained with four psychomotor stimulant drugs using a logarithmic model modified from the Hursh‐Silberberg (2008) exponential equation with a two‐parameter fitting algorithm for consumption versus price. The new algorithm reduces the three free parameter model to a two free parameter model by interpolating data at the minimum fixed ratio (FR) and at the breakpoint pB (i.e., the FR where Q=0). The augmented model takes the form: urn:x-wiley:08926638:media:fsb2fasebj2019331supplement80512:fsb2fasebj2019331supplement80512-math-0001where QFRLdenotes consumption at the lowest evaluated FR and pB denotes the breakpoint price. A strategy was tested for developing a single parameter classification scheme for fitted models using the parameter α as a measure of elasticity of the demand curves. The strategy normalizes behavioral momentum as measured by data for vehicle self‐administration. More specifically, if Q(P) denotes the demand curve for a particular drug, the discounted demand curve, Qd(P), is defined by: urn:x-wiley:08926638:media:fsb2fasebj2019331supplement80512:fsb2fasebj2019331supplement80512-math-0002where Qs(P) denotes the demand curve generated by vehicle. To test this approach, two doses of cocaine, 3,4‐methylenedioxymethamphetamine (MDMA), methylenedioxypyrovalerone (MDPV), and methcathinone (MCAT) were examined in rhesus monkeys (N=4). Using the Hursh‐Silberberg (2008) exponential formula, a rank‐order of reinforcing effectiveness of cocaine>MDPV>MCAT>>MDMA was established, and reinforcing effectiveness did not vary as a function of dose. However, in the Two‐Parameter Exponential‐Demand formula, a rank‐order of cocaine (large dose)>MDMA=MCAT>MDPV (large dose)>MDPV (small dose)>cocaine (small dose) was established. These results suggest that behavioral momentum may influence demand elasticity in a dose‐dependent manner, and α values derived in the augmented model may differentiate drug effects that contribute to price‐consumption relationships in a pharmacologically sensitive manner.Support or Funding InformationDA002519, DA039306, and HMS‐ Livingston AwardThis abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

The optimal use of non-optimal letter information in foveal and parafoveal word recognition

Letters and words across the visual field can be difficult to identify due to limiting visual factors such as acuity, crowding and position uncertainty. Here, we show that when human readers identify words presented at foveal and para-foveal locations, they act like theoretical observers making optimal use of letter identity and letter position information independently extracted from each letter after an unavoidable and non-optimal letter recognition guess. The novelty of our approach is that we carefully considered foveal and parafoveal letter identity and position uncertainties by measuring crowded letter recognition performance in five subjects without any word context influence. Based on these behavioral measures, lexical access was simulated for each subject by an observer making optimal use of each subject's uncertainties. This free-parameter model was able to predict individual behavioral recognition rates of words presented at different positions across the visual field. Importantly, the model was also able to predict individual mislocation and identity letter errors made during behavioral word recognition. These results reinforce the view that human readers recognize foveal and parafoveal words by parts (the word letters) in a first stage, independently of word context. They also suggest a second step where letter identity and position uncertainties are generated based on letter first guesses and positions. During the third lexical access stage, identity and position uncertainties from each letter look remarkably combined together through an optimal word recognition decision process.

Constraints on Janus Cosmological model from recent observations of supernovae type Ia

From our exact solution of the Janus Cosmological equation we derive the relation of the predicted magnitude of distant sources versus their red shift. The comparison, through this one free parameter model, to the available data from 740 distant supernovae shows an excellent fit.

Breakup of confined drops against a micro-obstacle: an analytical model for the drop size distribution

A confined drop flowing against a rectangular obstacle placed off-center in a microfluidic conduct may break into two daughter droplets of different volumes when the capillary number at play $$\mathcal {C}$$ , the ratio between viscous and capillary effects, exceeds a threshold $$\mathcal {C}_{\scriptstyle b}$$ . We study the influence of the viscosity ratio p between dispersed and continuous phases on that process by discussing the experimental variations of the volume fraction of the daughter droplets with $$\mathcal {C}$$ and p. A single free parameter model that yields an analytical formula for the volume of the daughter droplets as a function of the variables at play is introduced. Using this model that well describes our experiments, we accurately determine $$\mathcal {C}_{\scriptstyle b}$$ for different p. Our findings underline the key role of confinement on drop breakup showing that $$\mathcal {C}_{\scriptstyle b}$$ is three orders of magnitude smaller than the value found in bulk experiments under shear flow and that $$\mathcal {C}_{\scriptstyle b}$$ decreases with p in our study.

Activity determination of 227Ac and 223Ra by means of liquid scintillation counting and determination of nuclear decay data

The activity concentrations of solutions containing 227Ac and 223Ra in equilibrium with their progenies, respectively, were measured by means of liquid scintillation counting. The counting efficiencies were determined with the aid of a free parameter model. The corresponding calculations comprise the computation of several alpha, beta and beta/gamma branches. For short-lived progenies like 215Po the counting efficiency depends on the counter dead time. Measurements were made in custom-built triple-to-double coincidence ratio (TDCR) systems and various dead-time adjustments were used. In addition, two commercial counters were used to apply the CIEMAT/NIST efficiency tracing technique using 3H as a tracer.For the 227Ac solution, the overall relative standard uncertainty of the activity concentration was found to be 0.93%. The dominant uncertainty components are assigned to the efficiency computation of the low-energy beta transitions of 227Ac. We have identified a need for improved 227Ac decay data to achieve a significant reduction in the overall uncertainty.In the case of 223Ra, the activity concentrations were determined with relative standard uncertainties below 0.3%. Hence, PTB is prepared to provide calibration services for 223Ra, which is an isotope of increasing interest in nuclear medicine.The TDCR measurements were also used to determine the half-life of 223Ra. The decay was followed for about 58 days and a half-life T1/2=11.4362(50)d was obtained.

Activity determination of 59Fe

Iron-59 was measured in three commercial and two custom-built liquid scintillation counters. The counting efficiencies were determined using CIEMAT/NIST efficiency tracing and the triple-to-double coincidence ratio (TDCR) method, respectively.The efficiency computation for the TDCR method was realized by means of the MICELLE2 program, applying a stochastic model for the computation of electron emission spectra. The program was extended to make calculations of spectra originating from complex decay schemes possible. In addition, a new parameterization of electron stopping powers for 10 commercial liquid scintillation cocktails was included in the software.The activities determined with the two methods were in very good agreement; the relative standard uncertainty of the combined result was found to be 0.16%. It was used to calibrate a 4π ionization chamber at PTB for future calibrations of this isotope which is used for investigations of iron metabolism.A standardized solution was submitted to the Bureau International des Poids et Mesures (BIPM) to be measured in the ionization chambers of the International Reference System (SIR) for comparison purposes.The liquid scintillation samples were also measured in a new portable TDCR system with three channel photomultipliers. Although this system has a much lower counting efficiency, the activity was in satisfactory agreement with the conventional TDCR system. The usage of the portable TDCR system, thus, provides an important test of the free parameter model.

Improved Čerenkov counting techniques based on a free parameter model

In the past few years, two Čerenkov methods were developed to make activity measurements of high-energy beta emitters in liquid scintillation counters with two or three photomultiplier tubes (PMTs) possible. Both methods are based on a free parameter model and make use of the Frank and Tamm theory for the emission of Čerenkov light. In this article, additional effects are discussed and further improvements are presented. The dependence of the refractive index of water on the wavelength can now be taken into account, which has also an influence on the upper limit of the wavelength region for the production of Čerenkov light. In addition, the dependence of the PMT response on the wavelength is taken into account. Finally, it is possible to take a potential asymmetry of efficiencies in a system with three PMTs into account. To this end, three free parameters are assigned to each individual PMT and then determined by means of a downhill simplex optimization algorithm. The computed counting efficiencies for a triple-to-double coincidence ratio (TDCR) system were compared with experimental data for 32P, 89Sr, and 90Y.

Activity determination of 229Th by means of liquid scintillation counting

Liquid scintillation measurements of 229Th in radioactive equilibrium with its progenies were carried out. The counting efficiency was determined by means of a free parameter model. The measurements were made in a custom-built triple-to-double coincidence ratio (TDCR) system. In addition, a new portable mini-TDCR system with three channel photomultipliers and two commercial counters were tested. The decay of the short-lived 213Po requires great care, since it often occurs during the dead time of the counter systems. Also the rather short-lived 217At may decay during the dead time caused by 221Fr decay events. The overall counting efficiency of the TDCR system of PTB was found to be about 700% (depending on the degree of chemical quenching) and the relative standard uncertainty of the activity concentration was found to be about 0.23%. The determined activity concentration was compared with the outcome of alpha spectrometry under defined solid angle and excellent agreement was found. The TDCR efficiency calculations can be easily adapted to activity determinations of 225Ra or 225Ac in equilibrium with their progenies.

Extension of the TDCR model to compute counting efficiencies for radionuclides with complex decay schemes

The triple-to-double coincidence ratio (TDCR) method is frequently used to measure the activity of radionuclides decaying by pure β emission or electron capture (EC). Some radionuclides with more complex decays have also been studied, but accurate calculations of decay branches which are accompanied by many coincident γ transitions have not yet been investigated.This paper describes recent extensions of the model to make efficiency computations for more complex decay schemes possible. In particular, the MICELLE2 program that applies a stochastic approach of the free parameter model was extended. With an improved code, efficiencies for β−, β+ and EC branches with up to seven coincident γ transitions can be calculated. Moreover, a new parametrization for the computation of electron stopping powers has been implemented to compute the ionization quenching function of 10 commercial scintillation cocktails.In order to demonstrate the capabilities of the TDCR method, the following radionuclides are discussed: 166mHo (complex β−/γ), 59Fe (complex β−/γ), 64Cu (β−, β+, EC and EC/γ) and 229Th in equilibrium with its progenies (decay chain with many α, β and complex β−/γ transitions).

Quantum Hall effect in narrow graphene ribbons

The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a combined experimental and theoretical analysis, that this does not hold for the quantum Hall effect in narrow graphene ribbons. In our graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect up to Landau level index k=2 and show within a zero free-parameter model that the spatial extent of the compressible and incompressible strips is of a similar magnitude as the magnetic length. We conclude that in narrow graphene ribbons the single-particle picture is a more appropriate description of the quantum Hall effect and that electrostatic effects are of minor importance.

Application of a free parameter model to plastic scintillation samples

In liquid scintillation (LS) counting, the CIEMAT/NIST efficiency tracing method and the triple-to-double coincidence ratio (TDCR) method have proved their worth for reliable activity measurements of a number of radionuclides. In this paper, an extended approach to apply a free-parameter model to samples containing a mixture of solid plastic scintillation microspheres and radioactive aqueous solutions is presented.Several beta-emitting radionuclides were measured in a TDCR system at PTB. For the application of the free parameter model, the energy loss in the aqueous phase must be taken into account, since this portion of the particle energy does not contribute to the creation of scintillation light. The energy deposit in the aqueous phase is determined by means of Monte Carlo calculations applying the PENELOPE software package. To this end, great efforts were made to model the geometry of the samples. Finally, a new geometry parameter was defined, which was determined by means of a tracer radionuclide with known activity. This makes the analysis of experimental TDCR data of other radionuclides possible. The deviations between the determined activity concentrations and reference values were found to be lower than 3%.The outcome of this research work is also important for a better understanding of liquid scintillation counting. In particular the influence of (inverse) micelles, i.e. the aqueous spaces embedded in the organic scintillation cocktail, can be investigated. The new approach makes clear that it is important to take the energy loss in the aqueous phase into account. In particular for radionuclides emitting low-energy electrons (e.g. M-Auger electrons from 125I), this effect can be very important.

Beta shape-factor function and activity determination of 241Pu

The Physikalisch-Technische Bundesanstalt (PTB) investigated the low-energy beta emitter (241)Pu within the scope of an international key comparison on the activity concentration of the same solution. The activity concentration was measured by means of liquid scintillation counters with two and three photomultiplier tubes (PMT). The counting efficiencies were determined with two established techniques, which are based on a free parameter model. The free parameter is determined via (3)H-efficiency tracing in systems with two PMTs, or it is derived from the triple-to-double coincidence ratio (TDCR) in a system with three PMTs. Both methods require an accurate computation of the beta emission spectrum of the first-forbidden (non-unique) transition. In this work, the experimental outcome of a recent measurement from Loidl et al. (2010) with cryogenic magnetic calorimeters was used to determine a shape-factor function. The computed beta spectrum is in good agreement with the measured data when the shape-factor function C(W)=1-1.9582W+0.96078 W(2) and an end-point energy E(β,max)=21.6 keV are used. The activity concentrations determined with the two methods agree well when using the new shape-factor function, whereas a considerable discrepancy is found when assuming C(W)=1, as for an allowed beta transition. Consequently, the difference between the efficiency tracing method and the TDCR method, as observed by other researchers, could be resolved.

Application of a stochastic TDCR model based on Geant4 for Cherenkov primary measurements

Cherenkov measurements can be advantageously carried out using a counting instrumentation dedicated to liquid scintillation. In the case of radionuclide measurements, the interest of this technique is largely described in the literature. For instance, it is generally quoted that the possibility to measure directly the activity of aqueous solutions makes the sample preparation easier. Based on a three-photomultipliers apparatus, the Triple to Double Coincidence Ratio (TDCR) method is implemented in National Metrology Institutes for liquid scintillation measurements. Knowing the decay scheme associated with the radionuclide to be standardized, a free parameter model of light emission is constructed to determine the counter detection efficiency using the experimental TDCR value. Contrary to liquid scintillation, Cherenkov emission is characterized by a directional behavior. Instead of using an additional free parameter to take this effect into account, a stochastic modeling based on the Monte Carlo code Geant4 is proposed in order to extend the TDCR method to Cherenkov counting. The purpose of this model is to simulate the different optical processes of Cherenkov photons leading to the production of photoelectrons in the three-photomultipliers counter. The validation of this stochastic approach of the TDCR method for Cherenkov counting is carried out in the case of (90)Y activity measurements.

Activity standardization by means of a new TDCR-Čerenkov counting technique

Samples containing high-energy beta emitters in hydrochloric acid were measured in an in-house built triple-to-double coincidence counter. For the analysis of the results, a new method was developed that is based on a free parameter model. Formulas for the determination of the counting efficiencies were derived assuming a Poisson distribution for the generation of photoelectrons at the photocathodes and applying the Frank and Tamm theory to the production of Cerenkov light. The anisotropy effect for the emission of Cerenkov light was taken into account. The activities determined with the new method were compared with the results from other primary standardization techniques. The following radionuclides were successfully studied: (32)P, (89)Sr, (90)Y, (204)Tl and (106)Rh.

Radionuclide metrology using liquid scintillation counting

Liquid scintillation counting (LSC) techniques can be used for radionuclide standardization when the calculation of detection efficiency is possible. This is done using a model of the physicochemical processes involved in light emission and also of the statistics of photon emission: the free parameter model. This model can then be applied in two ways: by deducing the free parameter from the measurement of a tracer (the CIEMAT/NIST method) or by calculating this free parameter from coincidence ratio in a specific LS counter (the TDCR method). The purpose of this paper is to describe both these models and some practical issues that need to be addressed if LSC is to be effectively used in radionuclide metrology.

Physical mechanism responsible for the stretched exponential decay behavior of aging organic light-emitting diodes

The main process responsible for the luminance degradation in organic light-emitting diodes (OLEDs) driven under constant current has not yet been identified. In this paper, we propose an approach to describe the intrinsic mechanisms involved in the OLED aging. We first show that a stretched exponential decay can be used to fit almost all the luminance versus time curves obtained under different driving conditions. In this way, we are able to prove that they can all be described by employing a single free parameter model. By using an approach based on local relaxation events, we will demonstrate that a single mechanism is responsible for the dominant aging process. Furthermore, we will demonstrate that the main relaxation event is the annihilation of one emissive center. We then use our model to fit all the experimental data measured under different driving condition, and show that by carefully fitting the accelerated luminance lifetime-curves, we can extrapolate the low-luminance lifetime needed for real display applications, with a high degree of accuracy.

Review of John Cochrane's 'Asset Pricing'

John Cochrane's Asset Pricing (2001, Princeton University Press) is targeted at economics and finance Ph.D. students, advanced MBA students, or professionals with similar background. Residing in the third camp, I can say from this point of view that Asset Pricing could have been subtitled, the Practitioner's Portable Ph.D. Academic researchers, students, and practitioners of finance should all value Cochrane's Asset Pricing enough to own a copy. The book is extremely readable, as Cochrane stresses economic intuition over formal proofs. It is structured into four parts: 1) asset pricing theory; 2) asset pricing models; 3) options and interest rates; 4) an empirical survey. Cochrane begins powerfully, introducing us to the notion that the consumption-based asset pricing equation, given by an investor's first-order conditions, is the central formulation in asset pricing; market-based models simply consider the market returns specified in the consumption models to be exogenously determined free parameters. In Part 1, Cochrane covers the field from the Law of One Price, to the mean-variance frontier, to the CCAPM, the CAPM, ICAPM and APT, covering both discrete- and continuous-time, as well as market- and consumption-oriented approaches. Part 2 introduces us to The Generalized Method of Moments (GMM) approach to free parameter selection, distribution estimation, and model evaluation. In Part 3, Cochrane covers option pricing and term structure of interest rate models. Part 4 provides a well-written survey of the empirical work in the field, specifically on time-series predictability, cross-sectional models and equity premium puzzles, and new variations on the consumption-based models. Most chapters include several problems at the end, a nice addition for readers who really want to dig in and explore asset pricing directly. Although solutions are not provided in the book, Cochrane's website offers them via e-mail to teachers using Asset Pricing as a class text. The website also offers a preview of the book through page 50, which encompasses the Contents, Preface, and chapters 1 and 2 in their entirety. The website also contains an important errata page describing more than 160 equation typos and errors, additions and clarifications to the manuscript. Cochrane's experience as editor of the Journal of Political Economy shines through in his clear writing style, and his students at Chicago's GSB, where he is Theodore O. Yntema Professor of Finance, are lucky indeed if this book is any indication of his teaching ability. Asset Pricing is not a book to be missed.