An optimization strategy for charged aerosol detection to linearize the detector response in the multicomponent quantitative analysis of Qishen Yiqi dripping pills.

Charged aerosol detection, increasingly recognized for quantifying pharmaceutical compounds with weak ultraviolet absorption, is a universal detection technique for high-performance liquid chromatography (HPLC). Charged aerosol detection shows a non-linear response with increasing analyte concentration over a wide range, limiting its versatility in various analytical applications. In this work, a co-optimization strategy for power function value (PFV) and power laws was proposed and applied to broaden the linear range of the standard curve of saccharides in Qishen Yiqi dripping pills using the HPLC-charged aerosol detection (HPLC-CAD) method. Power function values for all analytes were optimized based on empirical models. Subsequently, the optimum power laws were investigated based on a preferred PFV. Additionally, various regression equations were evaluated to ensure the accuracy and precision of the results. With the optimized PFV and power law, the ordinary least squares model demonstrated a satisfactory fit. The optimal PFVs and power laws expanded the standard curve's linear range by 2.7 times compared to default settings, reducing model uncertainty. This paper presents a vital method for developing a multi-component quantitative HPLC-CAD approach without external data transformation outside the provided software, especially suitable for analytical applications of traditional Chinese medicine with significant quality differences.

Quantum Obfuscation of Generalized Quantum Power Functions with Coefficient.

Quantum obfuscation is one of the important primitives in quantum cryptography that can be used to enhance the security of various quantum cryptographic schemes. The research on quantum obfuscation focuses mainly on the obfuscatability of quantum functions. As a primary quantum function, the quantum power function has led to the development of quantum obfuscation because it is applicable to construct new obfuscation applications such as quantum encryption schemes. However, the previous definition of quantum power functions is constrained and cannot be beneficial to the further construction of other quantum functions. Thus, it is essential to extend the definition of the basic quantum power function in a more general manner. In this paper, we provide a formal definition of two quantum power functions called generalized quantum power functions with coefficients, each of which is characterized by a leading coefficient and an exponent that corresponds to either a quantum or classical state, indicating the generality. The first is the quantum power function with a leading coefficient, and the second is the quantum n-th power function, which are both fundamental components of quantum polynomial functions. In addition, obfuscation schemes for the functions are constructed by quantum teleportation and quantum superdense coding, and demonstrations of their obfuscatability are also provided in this paper. This work establishes the fundamental basis for constructing more quantum functions that can be utilized for quantum obfuscation, therefore contributing to the theory of quantum obfuscation.

4-Methylcytosine distribution follows the power function in Geobacter sulfurreducens genome.

Single-molecule real-time DNA sequencing revealed that 4-methylcytosine (m4C) commonly exists in bacterial genomes. In this work, samples with different m4C methylation patterns were studied. Results reveal that m4C modification is a biochemical reaction with distance effect, and its distribution follows the power function in the positive, negative, and double strands of genomic DNA sequences of Geobacter sulfurreducens. Furthermore, the value of regression coefficient in the fitting formula for double strands was the sum of those in the fitting formulae for positive and negative strands. Meanwhile, the value of exponent coefficient was the average, implicating an interesting mathematical phenomenon about power function. Considering the potent role of m4C in gene expression and the present results being obtained from the same genomic DNA sequence, this work suggests that the patterns of m4C distribution may be served as a signal for G. sulfurreducens to rapidly identify the genes to respond to environmental stresses or signals. This study opens a new avenue to extend our knowledge about the modification mechanisms and the epigenetic information of m4C modification in prokaryotes.

Regularization Methods Based on the Lq-Likelihood for Linear Models with Heavy-Tailed Errors.

We propose regularization methods for linear models based on the Lq-likelihood, which is a generalization of the log-likelihood using a power function. Regularization methods are popular for the estimation in the normal linear model. However, heavy-tailed errors are also important in statistics and machine learning. We assume q-normal distributions as the errors in linear models. A q-normal distribution is heavy-tailed, which is defined using a power function, not the exponential function. We find that the proposed methods for linear models with q-normal errors coincide with the ordinary regularization methods that are applied to the normal linear model. The proposed methods can be computed using existing packages because they are penalized least squares methods. We examine the proposed methods using numerical experiments, showing that the methods perform well, even when the error is heavy-tailed. The numerical experiments also illustrate that our methods work well in model selection and generalization, especially when the error is slightly heavy-tailed.

[Comparison between charged aerosol detector and evaporative light scattering detector for analysis of sugar in Zhusheyong Yiqi Fumai and study on accuracy of methods].

Evaporative light scattering detector(ELSD) and charged aerosol detector(CAD) methods were established in this study for the content determination of four kinds of sugars in Zhusheyong Yiqi Fumai(YQFM), and the factors affecting the accuracy of CAD methods were discussed. HPLC-ELSD chromatographic separation was performed on a Shodex Asahipak NH2 P-50 column with acetonitrile-water(75∶25)as the mobile phase, with a flow rate of 0.8 mL·min~(-1), drift tube temperature of 80 ℃. The analysis by HPLC-CAD was performed on the same column with acetonitrile-water as mobile phase for gradient elution, with a flow rate of 0.8 mL·min~(-1), a neb temperature of 45 ℃, and power function(PF) of 1.3. The samples of YQFM were detected by ELSD and CAD respectively. It was found that YQFM was composed of fructose, glucose, sucrose and maltose. The linear relationship of the two methods was good, and the recoveries, reproducibility and stability of these four kinds of sugars measured by the two methods satisfied the requirements of methodology. Both CAD and ELSD detectors were accurate and reliable in detecting saccharides components in YQFM. In addition, it was revealed in this study for the first time that the PF parameter of CAD had an important influence on the accuracy of sugar determination and acted as the key parameter of CAD method. It was also found that for CAD, a non-linear detector, there was no significant difference between the results of linear regression and logarithmic regression.

Sensitivity analysis and power for instrumental variable studies.

In observational studies to estimate treatment effects, unmeasured confounding is often a concern. The instrumental variable (IV) method can control for unmeasured confounding when there is a valid IV. To be a valid IV, a variable needs to be independent of unmeasured confounders and only affect the outcome through affecting the treatment. When applying the IV method, there is often concern that a putative IV is invalid to some degree. We present an approach to sensitivity analysis for the IV method which examines the sensitivity of inferences to violations of IV validity. Specifically, we consider sensitivity when the magnitude of association between the putative IV and the unmeasured confounders and the direct effect of the IV on the outcome are limited in magnitude by a sensitivity parameter. Our approach is based on extending the Anderson-Rubin test and is valid regardless of the strength of the instrument. A power formula for this sensitivity analysis is presented. We illustrate its usage via examples about Mendelian randomization studies and its implications via a comparison of using rare versus common genetic variants as instruments.

Satiation meal and the effects of meal and body sizes on gastric evacuation rate in brook trout Salvelinus fontinalis fed commercial pellets.

Gastric evacuation (GE) experiments were performed on brook trout Salvelinus fontinalis fed commercial food pellets. The experiments included small fish (36 g; 15 cm total length, LT ) fed meals of 0·2, 0·4 and 0·8 g and large fish (152 g; 23 cm) fed meals of 0·8, 2·0 and 4·0 g at temperatures ranging from 15·1 to 18·2° C. The stomach contents were thereafter sampled and weighed at 3 h intervals until the first empty stomach was observed. The course of GE was examined by use of a general power function of the data that revealed that the square-root function described the GE rate (GER) by the current stomach content mass independently of original meal size. Using the square-root function, the relationship between GER and fish size was described by a power function of fish length, whereas the effect of temperature was described by a simple exponential function. GER of the commercial pellets fed to S. fontinalis could thus be described by dStdt=-0·000464L1·31e0·052TSt (g h(-1) ), where St is stomach mass (g) at time t (h), L is total fish length (cm) and T is temperature (° C). The result of this study should provide a useful tool for planning of feeding regimes in production of S. fontinalis by optimizing growth and minimizing food waste.

Sugar reduction of skim chocolate milk and viability of alternative sweetening through lactose hydrolysis.

Milk consumption by Americans has not met the standards of the Dietary Guidelines for Americans. Chocolate milk can improve milk consumption, especially by children, due to its color and taste. However, the high sugar content of chocolate milk is a cause for concern about its healthfulness, resulting in its removal from some school lunch programs. It is important to reduce the sugar content of chocolate milk and still maintain acceptability among consumers. It is also important to investigate other natural alternatives to sweetening. The objectives of this study were to identify the different sweetness intensity perceptions of sucrose in water and various dairy matrices, to identify the acceptable reduction in sweet taste for chocolate milk for both young adults (19-35 yr) and children (5-13 yr), and to determine if lactose hydrolysis is a viable alternative. Threshold and power function studies were used to determine the benchmark concentration of sucrose in chocolate milk. The acceptability of sugar reduction from the benchmark concentration for both young adults and children and the acceptability of lactose hydrolyzed chocolate milk (4°C for 24 h) with added lactose for young adults were evaluated. Acceptability results demonstrated that sugar reduction in chocolate milk is possible for both young adults and children as long as it does not exceed a 30% reduction (from 205 mM). Lactose hydrolysis of added lactose was used to achieve the sweetness of sucrose in chocolate milk but required >7.5% (wt/vol) added lactose, which contributed undesirable calories, indicating that lactose hydrolysis may be more suitable for other dairy beverages that require less added sugar. The findings of this study demonstrate consumer acceptance of reduced-sugar chocolate milk and a possible way to use lactose hydrolysis in dairy beverages.

The influence of cooling forearm/hand and gender on estimation of handgrip strength.

Handgrip strength is essential in manual operations and activities of daily life, but the influence of forearm/hand skin temperature on estimation of handgrip strength is not well documented. Therefore, the present study intended to investigate the effect of local cooling of the forearm/hand on estimation of handgrip strength at various target force levels (TFLs, in percentage of MVC) for both genders. A cold pressor test was used to lower and maintain the hand skin temperature at 14°C for comparison with the uncooled condition. A total of 10 male and 10 female participants were recruited. The results indicated that females had greater absolute estimation deviations. In addition, both genders had greater absolute deviations in the middle range of TFLs. Cooling caused an underestimation of grip strength. Furthermore, a power function is recommended for establishing the relationship between actual and estimated handgrip force. Statement of relevance: Manipulation with grip strength is essential in daily life and the workplace, so it is important to understand the influence of lowering the forearm/hand skin temperature on grip-strength estimation. Females and the middle range of TFL had greater deviations. Cooling the forearm/hand tended to cause underestimation, and a power function is recommended for establishing the relationship between actual and estimated handgrip force. Practitioner Summary: It is important to understand the effect of lowering the forearm/hand skin temperature on grip-strength estimation. A cold pressor was used to cool the hand. The cooling caused underestimation, and a power function is recommended for establishing the relationship between actual and estimated handgrip force. STATEMENT OF RELEVANCE: Manipulation with grip strength is essential in daily life and the workplace, so it is important to understand the influence of lowering the forearm/hand skin temperature on grip-strength estimation. Females and the middle range of TFL had greater deviations. Cooling the forearm/hand tended to cause underestimation, and a power function is recommended for establishing the relationship between actual and estimated handgrip force. PRACTITIONER SUMMARY: It is important to understand the effect of lowering the forearm/hand skin temperature on grip-strength estimation. A cold pressor was used to cool the hand. The cooling caused underestimation, and a power function is recommended for establishing the relationship between actual and estimated handgrip force

Magnetic levitation system control based on a novel tracking differentiator.

This study proposes a novel tracking differentiator and applies it to the sliding-mode control (SMC) algorithm to address the unsatisfactory disturbance suppression and low tracking accuracy of magnetic levitation (maglev) systems. First, to assess performance in terms of filtering, tracking, and differentiation, an inverse hyperbolic sine function and a two-phase power function are introduced to improve the tracking differentiator. This can accelerate the global convergence speed, ensure smooth convergence at the equilibrium point, reduce system jitter, and enhance the noise-suppression ability of the system. The differentiator parameter-adjustment rules are derived from a system sweep. A comparison of the simulation results show that the proposed differentiator effectively suppresses noise and performs signal tracking and differentiation. Finally, the new differentiator is applied to the SMC of a maglev system. Simulation and experimental results show that the response speed of the maglev system under the SMC based on the new tracking differentiator is high, the jitter is effectively reduced, and the noise-suppression ability is improved.

A New Approach for Classifying the Permanent Deformation Properties of Granular Materials under Cyclic Loading.

A series of medium-sized cyclic triaxial tests were performed to investigate the permanent deformation properties of granular materials. The strain rate was then plotted against loading cycles to classify the permanent deformation properties of granular materials under different cyclic stress ratios (CSRs). It was found that (1) the permanent strain rate dεp/dN was linearly correlated with loading cycles N using a double-log coordinate on the condition of CSR < 60%; (2) the deformation tendency factor ß, which was extracted from the linear relationship between dεp/dN and N, significantly varied with CSR and, thus, can be adopted to identify the deformation states; (3) ß > 1 implying that permanent strain accumulation ceases in limited cycles and corresponds to the plastic shakedown range, while 0 < ß ≤ 1 indicates the temporary steady state, corresponding to the plastic creep range; (4) sluggish decrease or remarkable increase in dεp/dN appeared as CSR ≥ 60%, leading to soil collapsed in limited loading cycles and resulting in an incremental collapse range. The new approach was validated by the crushed tuff aggregates and subgrade materials reported previously. It is expected that the new approach will have wider applicability than the traditional one and can provide technical guidance for the design and construction of substructures in roadway and railway engineering.

Development and application of a relative soil water content - transpiration efficiency curve for screening high water use efficiency wheat cultivars.

Improving water use efficiency (WUE) has been proven to be a prosperous way to produce more grain in drought-prone areas. Transpiration efficiency (TE) has been proposed as a criterion for screening cultivars with high WUE. This study quantifies the relations of TE to relative soil water content (RSWC) gradients using pot experiments and evaluates the capability of the relations of TE-RSWC on assessing the cultivar performance in field yield and WUE. Twelve winter wheat cultivars were grown at 6 RSWC, 12.1, 24.2, 36.3, 48.4, 60.5, and 72.6% of field capacity (FC = 24.8 g/g) for 33 days in tightly sealed pots preventing soil evaporation. The results showed that TE decreased power functionally following the increase in RSWC for all cultivars. The relationship could be described as TE = TE FC × (RSWC) b , named TE-RSWC curve. This curve could be divided into an orderly area where the rank of cultivars was stable when RSWC ≤ 12.1% or RSWC ≥ 72.6% and a disorderly area where the rank was unstable when 12.1% < RSWC < 72.6%. To assess the consistency of pot TE to field yield and WUE, the same 12 varieties were grown under rainfed and two irrigations (75 mm at the jointing and flowering stages, respectively). TE FC was found to be positively related to field yield and WUE independent of irrigation. TE measured near the wilting point was negatively related to field yield and WUE. These results indicated that TE FC could be used as a surrogate for screening high-yield and high-WUE cultivars. The consistency and inconsistency can be attributed to the orderly area and disorderly area of the TE-RSWC curves.

POWER-ENHANCED MULTIPLE DECISION FUNCTIONS CONTROLLING FAMILY-WISE ERROR AND FALSE DISCOVERY RATES.

Improved procedures, in terms of smaller missed discovery rates (MDR), for performing multiple hypotheses testing with weak and strong control of the family-wise error rate (FWER) or the false discovery rate (FDR) are developed and studied. The improvement over existing procedures such as the Sidák procedure for FWER control and the Benjamini-Hochberg (BH) procedure for FDR control is achieved by exploiting possible differences in the powers of the individual tests. Results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual p-values, as is the case, for example, with the Sidák, Bonferroni, or BH procedures. They also enhance understanding of the role of the powers of individual tests, or more precisely the receiver operating characteristic (ROC) functions of decision processes, in the search for better multiple hypotheses testing procedures. A decision-theoretic framework is utilized, and through auxiliary randomizers the procedures could be used with discrete or mixed-type data or with rank-based nonparametric tests. This is in contrast to existing p-value based procedures whose theoretical validity is contingent on each of these p-value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis. Proposed procedures are relevant in the analysis of high-dimensional "large M, small n" data sets arising in the natural, physical, medical, economic and social sciences, whose generation and creation is accelerated by advances in high-throughput technology, notably, but not limited to, microarray technology.

α-Power transformed transformed power function distribution with applications.

By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey (2004) which we called the Transformed Power Function (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu (2017) we generalized the TPF distribution as the α-Power Transformed Transformed Power Function (αPTTPF) distribution. Some of the properties of the αPTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates. Three real data-sets are used to demonstrate the usefulness of the new model.

Modelling the reproductive power function.

This paper discusses methods of estimating the reproductive power and the accompanying survival function of communicable events, e.g. infectious disease transmission. The early stage of an outbreak can be described by the infectiousness of the outbreak process, but in later stages of the outbreak, this is complicated by factors such as changing contact patterns and the impact of control measures. It is important to take these factors into account in order to get a good, if approximate, model for an outbreak process. This paper proposes a non-homogeneous birth process and regression model for the reproductive power function, similar to models in discrete survival analysis. A baseline reproductive power function gives a description of the outbreak when covariates are at their baseline values. As an illustration these methods are applied to an avian influenza (H5N1) outbreak among poultry in Thailand.

Power function setting in charged aerosol detection for the linearization of detector response - optimization strategies and their application.

Charged aerosol detection (CAD) is an universal technique in liquid chromatography that is increasingly used for the quality control of drugs. Consequently, it has found its way into compendial monographs promoted by its simple and robust application. However, the response of CAD is inherently nonlinear due to its principle of function. Thus, easy and rapid linearization procedures, in particular regarding compendial applications, are highly desirable. One effective approach to linearize the detector's signal makes use of the built-in power function value (PFV) setting of the instrument. The PFV is basically a multiplication factor to the power law exponent of the equation describing the CAD's response, thereby altering the detector's signal output to optimize the quasi-linear range of the response curve. The experimental optimization of the PFV for a series of analytes is a time-consuming process, limiting the practicability of this approach. Here, two independent approaches for the determination of the optimal PFV based on an empirical model and a mathematical transformation in each case, are evaluated. Both approaches can be utilized to predict the optimal PFV for each analyte solely based on the experimental results of a series of calibration standards obtained at a single PFV. The approaches were applied to the HPLC-UV-CAD impurity analysis of the drug gabapentin to improve the observed nonlinear response of the impurities in the range of interest. The predicted optimal PFV of both approaches were in good agreement with the experimentally obtained optimal PFV of the analytes. As a result, the accuracy of the method was significantly improved when using the optimal PFV (90 - 105% versus 81 - 115% recovery rate for quantitation by either single-point calibration or linear regression) for the majority of the analytes. The final method with a PFV adjusted to 1.30 was validated with respect to ICH guideline Q2(R1).

Dynamics of pertussis toxin IgG after symptomatic pertussis in children and adults.

BACKGROUND AND AIM: The knowledge of dynamics of pertussis toxin (PT)-IgG after pertussis and the appropriate diagnostic cut-off value is limited. We aimed to describe the dynamics of PT-IgG in children and adults up to three years after symptomatic pertussis. METHODS: Patients with persistent cough of unknown aetiology were prospectively enrolled 2012-2014. Pertussis was confirmed by culture, PCR and/or serology. The follow-up samples were taken 4-6 weeks, 1, 2 and 3 years after enrolment. PT-IgG kinetics was described by biexponential model. RESULTS: Pertussis was diagnosed in 22 patients [median (IQR) age 17.7 (8.4-38.6) years]. Adults compared with children had higher peak of the PT-IgG 397 (IQR 374-518) vs 292 (200-363), p = 0.007, longer time to reach peak PT-IgG 16.4 (IQR 15.6-16.8) days vs 13.3 (13.2-13.4) days, p=<0.001 and shorter PT-IgG half-life 24 days (IQR 20-40) and 364 days (IQR 359-486) p < 0.001. CONCLUSION: After symptomatic pertussis, adults and children have different dynamics of PT-IgG. Clinical trial registry: Not applicable.

Matching theory and induction explain operant performance.

Matching theory is a general framework for understanding allocation of behavior among activities. It applies to choice in concurrent schedules and was extended to single schedules by assuming that other unrecorded behavior competes with operant behavior. Baum and Davison (2014) found that the competing activities apparently are induced by the "reinforcers" (phylogenetically important events, e.g., food) according to power functions. Combined with power-function induction, matching theory provides new equations with greater explanatory power. Four pigeons were exposed to conditions in which 7 different schedules of food delivery were presented within each experimental session. We replicated earlier results with variable-interval schedules: (a) a negatively accelerated increase of peck rate as food rate increased in the low range of food rates; (b) an upturn in pecking at higher rates; and (c) a downturn in pecking at extremely high food rates. When the contingency between pecking and food was removed, the food continued to induce pecking, even after 20 sessions with no contingency. A ratio schedule inserted in place of 1 variable-interval schedule maintained peck rates comparable to peck rates maintained by short interval schedules. We explained the results by fitting equations that combined matching theory, competition, and induction.

Brain networks construction using Bayes FDR and average power function.

Brain functional connectivity is a widely investigated topic in neuroscience. In recent years, the study of brain connectivity has been largely aided by graph theory. The link between time series recorded at multiple locations in the brain and the construction of a graph is usually an adjacency matrix. The latter converts a measure of the connectivity between two time series, typically a correlation coefficient, into a binary choice on whether the two brain locations are functionally connected or not. As a result, the choice of a threshold τ over the correlation coefficient is key. In the present work, we propose a multiple testing approach to the choice of τ that uses the Bayes false discovery rate and a new estimator of the statistical power called average power function to balance the two types of statistical error. We show that the proposed average power function estimator behaves well both in case of independence and weak dependence of the tests and it is reliable under several simulated dependence conditions. Moreover, we propose a robust method for the choice of τ using the 5% and 95% percentiles of the average power function and False Discovery Rate bootstrap distributions, respectively, to improve stability. We applied our approach to functional magnetic resonance imaging and high density electroencephalogram data.

Response-reinforcer contiguity versus response-rate-reinforcer-rate covariance in rats' lever pressing: Support for a multiscale view.

The multiscale molar view sees behavior as a flow, like a river, extended in time. Matching theory expresses the way activities compete for time. Relative time taken by any activity depends on relative induction. The present experiment tested matching theory applied to concurrent contingent and noncontingent food. As adjunctive activities that compete with operant activity, we recorded hopper head entries and presses on a lever near the food hopper that had no programmed consequences. Eight naïve rats were first exposed to a variable-time 60 s schedule, which across conditions was gradually transformed into a variable-interval 60 s schedule by increasing the proportion of food that was delivered contingent on pressing a lever far from the hopper. Another group of 4 rats that had been trained to press a lever near a food hopper were introduced in the second condition, in which one food delivery was contingent on far-lever pressing. We found induction following a power function to describe pressing on the far lever (operant activity). Matching theory combined with power-function induction also accounted for adjunctive activity. Results with single contingent food deliveries provided little support for the molecular view that behavior consists of discrete responses "strengthened" by immediately following reinforcers.