A straightforward approach utilizing an exponential model to compensate for turbidity in chemical oxygen demand measurements using UV-vis spectrometry

Recently, ultraviolet-visible (UV-vis) absorption spectrometry has garnered considerable attention because it enables real-time and unpolluted detection of chemical oxygen demand (COD) and plays a crucial role in the early warning of emerging organic contaminants. However, the accuracy of detection is inevitably constrained by the co-absorption of organic pollutants and turbidity at UV wavelengths. To ensure accurate detection of COD, it is necessary to directly subtract the absorbance caused by turbidity from the overlaid spectrum using the principle of superposition. The absorbance of COD is confined to the UV range, whereas that of turbidity extends across the entire UV-vis spectrum. Therefore, based on its visible absorbance, the UV absorbance of turbidity can be predicted. In this way, the compensation for turbidity is achieved by subtracting the predicted absorbance from the overlaid spectrum. Herein, a straightforward yet robust exponential model was employed based on this principle to predict the corresponding absorbance of turbidity at UV wavelengths. The model was used to analyze the overlaid absorption spectra of synthetic water samples containing COD and turbidity. The partial least squares (PLS) method was employed to predict the COD concentrations in synthetic water samples based on the compensated spectra, and the corresponding root mean square error (RMSE) values were recorded. The results indicated that the processed spectra yielded a considerably lower RMSE value (9.51) than the unprocessed spectra (29.9). Furthermore, the exponential model outperformed existing turbidity compensation models, including the Lambert-Beer law-based model (RMSE = 12.53) and multiple-scattering cluster method (RMSE = 79.34). Several wastewater samples were also analyzed to evaluate the applicability of the exponential model to natural water. UV analysis yielded undesirable results owing to filtration procedures. However, the consistency between the compensated spectra and filtered wastewater samples in the visible range demonstrated that the model is applicable to natural water. Therefore, this proposed method is advantageous for improving the accuracy of COD measurement in turbid water.

Morphological Description and Live Weight Prediction from Body Measurements of Socorro Island Merino Lambs

The aim of this study was to describe the morphology and estimate live weight from body measurements of Socorro Island Merino lambs. A group of Socorro Island Merino lambs was recorded from birth to year for live weight, rump width, rump length, withers height, body length, cannon bone perimeter, and chest girth, width, and depth. The effect of the lamb type on body measurements and live weight was analyzed using ANOVA, Pearson's correlation analysis was performed to estimate the relationship between body measurements and live weight, multiple linear regressions were fitted to obtain prediction equations of live weight from the body measurements and finally, chest girth was used to generate prediction equations using linear and exponential models. At birth and at year, differences were observed in body measurements, especially those related to the thoracic region, with crossbred males showing the highest values. Live weight was correlated with almost all the body measurements, with the highest coefficients observed with chest girth, chest width, and chest depth. Live weight can be accurately predicted from multiple regression equations using several body measurements, but using only chest girth (CG) as a predictor, the exponential equation W_0-365 = 0.9142 exp^{(0.0462 CG)} showed the best accuracy.

In Search of the Preference Reversal Zone

A preference reversal is observed when a preference for a larger-later (LL) reward over a smaller-sooner (SS) reward reverses as both rewards come closer in time. Preference reversals are common in everyday life and in the laboratory and are often claimed to support hyperbolic delay-discounting models which, in their simplest form, can model reversals with only one free parameter. However, it is not clear if the temporal location of preference reversals can be predicted a priori. Studies testing model predictions have not found support for them, but they overlooked the well-documented effect of reinforcer magnitude on discounting rate. Therefore, we directly tested hyperbolic and exponential model predictions in a pre-registered study by assessing individual discount rates for two reinforcer magnitudes. We then made individualized predictions about pairs of choices between which preference reversals should occur. With 107 participants, we found (1) little evidence that hyperbolic and exponential models could predict the temporal location of preference reversals, (2) some evidence that hyperbolic models had better predictive performance than exponential models, and (3) in contrast to many previous studies, that exponential models generally produced superior fits to the observed data than hyperbolic models.

Assessment of digestible lysine requirements in lipopolysaccharide-challenged pigs

To evaluate the effect of an E. coli lipopolysaccharide (LPS) challenge on the digestible lysine (Lys) requirement for growing pigs, a nitrogen (N) balance assay was performed. Seventy-two castrated male pigs [19 ± 1.49 kg body weight (BW)] were allocated in a 2 x 6 factorial design composed of two immune activation states (control and LPS-challenged) and 6 dietary treatments with N levels of 0.94, 1.69, 2.09, 3.04, 3.23 and 3.97% N, as fed, where Lys was limiting, with six replicates and one pig per unit. The challenge consisted of an initial LPS dose of 30 μg/kg BW via intramuscular (IM) injection and a subsequent dose of 33.6 μg/kg BW after 48 h. The experimental period lasted 11 days and was composed of a 7-day adaptation and a subsequent 4-day sampling period in which N intake (NI), N excretion (NEX) and N deposition (ND) were evaluated. Inflammatory mediators and rectal temperature were assessed during the 4-day collection period. A 3-way interaction (N levels × LPS challenge × time, P < 0.05) for IgG was observed. Additionally, 2-way interactions (challenge × time, P < 0.05) were verified for IgA, ceruloplasmin, transferrin, haptoglobin, α-1-acid glycoprotein, total protein, and rectal temperature; and (N levels × time, P < 0.05) for transferrin, albumin, haptoglobin, total protein and rectal temperature. LPS-challenged pigs showed lower (P < 0.05) feed intake. A 2-way interaction (N levels × LPS challenge, P < 0.05) was observed for NI, NEX and ND, with a clear dose-response (P < 0.05). LPS-challenged pigs showed lower NI and ND at 2.09% N and 1.69 to 3.97% N (P < 0.05), respectively, and higher NEX at 3.23% N (P < 0.05). The parameters obtained by a nonlinear model (N maintenance requirement, NMR and theoretical maximum N deposition, NDmaxT) were 152.9 and 197.1 mg/BWkg  0.75/d for NMR, and 3,524.7 and 2,077.8 mg/BWkg  0.75/d for NDmaxT, for control and LPS-challenged pigs, respectively. The estimated digestible Lys requirements were 1,994.83 and 949.16 mg/BWkg  0.75/d for control and LPS-challenged pigs, respectively. The daily digestible Lys intakes required to achieve 0.68 and 0.54 times the NRmaxT value were 18.12 and 8.62 g/d, respectively, and the optimal dietary digestible Lys concentration may change depending on the feed intake levels. Based on the derived model parameters obtained in the N balance trial with lower cost and time, it was possible to differentiate the digestible Lys requirement for swine under challenging conditions.

Analysis of Reproduction Number R0 of COVID-19 Using Current Health Expenditure as Gross Domestic Product Percentage (CHE/GDP) across Countries

(1) Background: Impact and severity of coronavirus pandemic on health infrastructure vary across countries. We examine the role percentage health expenditure plays in various countries in terms of their preparedness and see how countries improved their public health policy in the first and second wave of the coronavirus pandemic; (2) Methods: We considered the infectious period during the first and second wave of 195 countries with their current health expenditure as gross domestic product percentage (CHE/GDP). An exponential model was used to calculate the slope of the regression line while the ARIMA model was used to calculate the initial autocorrelation slope and also to forecast new cases for both waves. The relationship between epidemiologic and CHE/GDP data was used for processing ordinary least square multivariate modeling and classifying countries into different groups using PC analysis, K-means and hierarchical clustering; (3) Results: Results show that some countries with high CHE/GDP improved their public health strategy against virus during the second wave of the pandemic; (4) Conclusions: Results revealed that countries who spend more on health infrastructure improved in the tackling of the pandemic in the second wave as they were worst hit in the first wave. This research will help countries to decide on how to increase their CHE/GDP in order to properly tackle other pandemic waves of the present COVID-19 outbreak and future diseases that may occur. We are also opening up a debate on the crucial role socio-economic determinants play during the exponential phase of the pandemic modelling.

Oxyhemoglobin Concentration and Oxygen Uptake Signal During Recovery From Exhaustive Exercise in Healthy Subjects-Relationship With Aerobic Capacity

This proof of concept study is dedicated to the quantification of the short-term recovery phase of the muscle oxygenation and whole-body oxygen uptake kinetics following an exhaustive cycling protocol. Data of 15 healthy young participants (age 26.1 ± 2.8 years, peak oxygen uptake 54.1 ± 5.1 mL^∗min-1^∗kg-1) were recorded during 5 min cool down-cycling with a power output of 50 W on an electro-magnetically braked cycle ergometer. The oxygen uptake (VO₂) signal during recovery was modeled by exponential function. Using the model parameters, the time (T_1/2) needed to return VO₂ to 50% of VO_2peak was determined. The Hill’s model was used to analyze the kinetics of oxyhemoglobin concentration (Sm, %), non-invasively recorded by near-infrared spectroscopy (NIRS) over the M. vastus lateralis. Analysis of the Pearson correlation results in statistically significant negative relationships between T_1/2 and relative VO_2peak (r = −0.7). Relevant significant correlations were determined between constant defining the slope of VO₂ decrease (parameter B) and the duration of the anaerobic phase (r = −0.59), as well as between Hill’s coefficient and average median Sm_max for the final 2 min of recovery. The high correlation between traditional variables commonly used to represent the cardio-metabolic capacity and the parameters of fits from exponential and Hill models attests the validity of our approach. Thus, proposed descriptors, derived from non-invasive NIRS monitoring during recovery, seem to reflect aerobic capacity. However, the practical usefulness of such modeling for clinical or other vulnerable populations has to be explored in studies using alternative testing protocols.

Effect of Mathematical Modeling and Fitting Procedures on the Assessment of Critical Speed and Its Relationship With Aerobic Fitness Parameters

An accurate estimation of critical speed (CS) is important to accurately define the boundary between heavy and severe intensity domains when prescribing exercise. Hence, our aim was to compare CS estimates obtained by statistically appropriate fitting procedures, i.e., regression analyses that correctly consider the dependent variables of the underlying models. A second aim was to determine the correlations between estimated CS and aerobic fitness parameters, i.e., ventilatory threshold, respiratory compensation point, and maximal rate of oxygen uptake. Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of the peak speed of the incremental test on a treadmill. Then, two mathematically equivalent formulations (time as function of running speed and distance as function of running speed) of three different mathematical models (two-parameter, three-parameter, and three-parameter exponential) were employed to estimate CS, the distance that can be run above CS (d'), and if applicable, the maximal instantaneous running speed (s max ). A significant effect of the mathematical model was observed when estimating CS, d', and s max (P < 0.001), but there was no effect of the fitting procedure (P > 0.77). The three-parameter model had the best fit quality (smallest Akaike information criterion) of the CS estimates but the highest 90% confidence intervals and combined standard error of estimates (%SEE). The 90% CI and %SEE were similar when comparing the two fitting procedures for a given model. High and very high correlations were obtained between CS and aerobic fitness parameters for the three different models (r ≥ 0.77) as well as reasonably small SEE (SEE ≤ 6.8%). However, our results showed no further support for selecting the best mathematical model to estimate critical speed. Nonetheless, we suggest coaches choosing a mathematical model beforehand to define intensity domains and maintaining it over the running seasons.

[Application of the log-Logistic Model to Dose Response Relation in Microbial Risk Assessment]

Microbial risk assessment in food safety is a valuable tool to reduce the risks of infection by pathogens. The dose-response relation is aimed to establish the relationship between the dose of a pathogen that populations are exposed to and the probability of the adverse health effect by the pathogen. Among many dose-response models ever proposed, the exponential and beta-Poisson models have been internationally applied, but the decision on which model is selected between them solely depends on the goodness of fit to specific data sets. On the other hands, the log-logistic model, one of the alternative models, has been little studied on the dose-response relation. In the present study, thus, the application of the log-logistic model to dose-response relation was studied with hypothetical and experimental data sets of infection (or death), comparing to the above two models. Here the experimental data sets were for pathogenic organisms such as pathogenic Escherichia coli, Listeria monocytogenes, and Cryptosporidium pavrum. Consequently, this model successfully fit to those data sets in comparison to the two models. These results suggested that log-logistic model would have the potential to apply to the dose-response relation, similar to the exponential and beta-Poisson models.

Modeling the Dose Response Relationship of Waterborne Acanthamoeba

This study developed dose response models for determining the probability of eye or central nervous system infections from previously conducted studies using different strains of Acanthamoeba spp. The data were a result of animal experiments using mice and rats exposed corneally and intranasally to the pathogens. The corneal inoculations of Acanthamoeba isolate Ac 118 included varied amounts of Corynebacterium xerosis and were best fit by the exponential model. Virulence increased with higher levels of C. xerosis. The Acanthamoeba culbertsoni intranasal study with death as an endpoint of response was best fit by the beta-Poisson model. The HN-3 strain of A. castellanii was studied with an intranasal exposure and three different endpoints of response. For all three studies, the exponential model was the best fit. A model based on pooling data sets of the intranasal exposure and death endpoint resulted in an LD₅₀ of 19,357 amebae. The dose response models developed in this study are an important step towards characterizing the risk associated with free-living amoeba like Acanthamoeba in drinking water distribution systems. Understanding the human health risk posed by free-living amoeba will allow for quantitative microbial risk assessments that support building design decisions to minimize opportunities for pathogen growth and survival.

An Overview of the World Current and Future Assessment of Novel COVID-19 Trajectory, Impact, and Potential Preventive Strategies at Healthcare Settings

This study is an overview of the current and future trajectory, as well as the impact of the novel Coronavirus (COVID-19) in the world and selected countries including the state of Kuwait. The selected countries were divided into two groups: Group A (China, Switzerland, and Ireland) and Group B (USA, Brazil, and India) based on their outbreak containment of this virus. Then, the actual data for each country were fitted to a regression model utilizing the excel solver software to assess the current and future trajectory of novel COVID-19 and its impact. In addition, the data were fitted using the Susceptible-Infected-Recovered (SIR) Model. The Group A trajectory showed an "S" shape trend that suited a logistic function with r² > 0.97, which is an indication of the outbreak control. The SIR models for the countries in this group showed that they passed the expected 99% end of pandemic dates. Group B, however, exhibited a continuous increase of the total COVID-19 new cases, that best suited an exponential growth model with r² > 0.97, which meant that the outbreak is still uncontrolled. The SIR models for the countries in this group showed that they are still relatively far away from reaching the expected 97% end of pandemic dates. The maximum death percentage varied from 3.3% (India) to 7.2% with USA recording the highest death percentage, which is virtually equal to the maximum death percentage of the world (7.3%). The power of the exponential model determines the severity of the country's trajectory that ranged from 11 to 19 with the USA and Brazil having the highest values. The maximum impact of this COVID-19 pandemic occurred during the uncontrolled stage (2), which mainly depended on the deceptive stage (1). Further, some novel potential containment strategies are discussed. Results from both models showed that the Group A countries contained the outbreak, whereas the Group B countries still have not reached this stage yet. Early measures and containment strategies are imperative in suppressing the spread of COVID-19.

COVID-19 in India: Statewise Analysis and Prediction

BACKGROUND

The highly infectious coronavirus disease (COVID-19) was first detected in Wuhan, China in December 2019 and subsequently spread to 212 countries and territories around the world, infecting millions of people. In India, a large country of about 1.3 billion people, the disease was first detected on January 30, 2020, in a student returning from Wuhan. The total number of confirmed infections in India as of May 3, 2020, is more than 37,000 and is currently growing fast.

OBJECTIVE

Most of the prior research and media coverage focused on the number of infections in the entire country. However, given the size and diversity of India, it is important to look at the spread of the disease in each state separately, wherein the situations are quite different. In this paper, we aim to analyze data on the number of infected people in each Indian state (restricted to only those states with enough data for prediction) and predict the number of infections for that state in the next 30 days. We hope that such statewise predictions would help the state governments better channelize their limited health care resources.

METHODS

Since predictions from any one model can potentially be misleading, we considered three growth models, namely, the logistic, the exponential, and the susceptible-infectious-susceptible models, and finally developed a data-driven ensemble of predictions from the logistic and the exponential models using functions of the model-free maximum daily infection rate (DIR) over the last 2 weeks (a measure of recent trend) as weights. The DIR is used to measure the success of the nationwide lockdown. We jointly interpreted the results from all models along with the recent DIR values for each state and categorized the states as severe, moderate, or controlled.

RESULTS

We found that 7 states, namely, Maharashtra, Delhi, Gujarat, Madhya Pradesh, Andhra Pradesh, Uttar Pradesh, and West Bengal are in the severe category. Among the remaining states, Tamil Nadu, Rajasthan, Punjab, and Bihar are in the moderate category, whereas Kerala, Haryana, Jammu and Kashmir, Karnataka, and Telangana are in the controlled category. We also tabulated actual predicted numbers from various models for each state. All the R2 values corresponding to the logistic and the exponential models are above 0.90, indicating a reasonable goodness of fit. We also provide a web application to see the forecast based on recent data that is updated regularly.

CONCLUSIONS

States with nondecreasing DIR values need to immediately ramp up the preventive measures to combat the COVID-19 pandemic. On the other hand, the states with decreasing DIR can maintain the same status to see the DIR slowly become zero or negative for a consecutive 14 days to be able to declare the end of the pandemic.

Assessment of different mathematical models for diffusion-weighted imaging as quantitative biomarkers for differentiating benign from malignant solid hepatic lesions

To quantitatively compare the monoexponential, biexponential, and stretched‐exponential diffusion‐weighted imaging (DWI) models in differentiating benign from malignant solid hepatic lesions. The institutional review board approved this retrospective study and waived the informed consent requirement. A total of 188 patients with 288 hepatic lesions included 202 malignant lesions and 86 benign lesions were assessed (confirmed by pathology or clinical follow‐up for 6 months). All patients underwent hepatic 3.0‐T MRI, including multi‐b DWI that used 12 b values. The ADC, D_p, D_t, perfusion fraction (f_p), α, and DDC values for normal liver, benign liver lesions, and malignant liver lesions were calculated. Independent sample t tests were used for comparisons. The diagnostic performance of the parameters was evaluated using ROC analysis. The AUC value for each model was also calculated. The value of D_p was significantly lower in benign lesions than in normal hepatic parenchyma while others were significantly higher (P < .001). Whereas Values of D_t and α in malignant hepatic lesions were significantly higher than in normal hepatic parenchyma (P < .001), and the D_p value was significantly lower (P < .001). Values of ADC, f_p, DDC, and α for malignant hepatic lesions were significantly lower than those for benign hepatic lesions (P < .001). ROC analysis showed that the diagnostic value of the biexponential model of normal hepatic parenchyma vs benign hepatic lesions and normal hepatic parenchyma vs malignant hepatic lesions was high (0.946 and 0.876, respectively). In the differential diagnosis of benign and malignant hepatic lesions, DDC had the highest AUC value (0.819). The biexponential and stretched‐exponential DWI may provide additional information and improve the differential diagnosis of benign and malignant hepatic lesions compared with the monoexponential DWI.

An Exponential Regression Model Reveals the Continuous Development of B Cell Subpopulations Used as Reference Values in Children

B lymphocytes are key players in humoral immunity, expressing diverse surface immunoglobulin receptors directed against specific antigenic epitopes. The development and profile of distinct subpopulations have gained awareness in the setting of primary immunodeficiency disorders, primary or secondary autoimmunity and as therapeutic targets of specific antibodies in various diseases. The major B cell subpopulations in peripheral blood include naïve (CD19⁺ or CD20⁺IgD⁺CD27^-), non-switched memory (CD19⁺ or CD20⁺IgD⁺CD27⁺) and switched memory B cells (CD19⁺ or CD20⁺IgD^-CD27⁺). Furthermore, less common B cell subpopulations have also been described as having a role in the suppressive capacity of B cells to maintain self-tolerance. Data on reference values for B cell subpopulations are limited and only available for older age groups, neglecting the continuous process of human B cell development in children and adolescents. This study was designed to establish an exponential regression model to produce continuous reference values for main B cell subpopulations to reflect the dynamic maturation of the human immune system in healthy children.

A combined gamma frailty and normal random-effects model for repeated, overdispersed time-to-event data

This paper presents, extends, and studies a model for repeated, overdispersed time-to-event outcomes, subject to censoring. Building upon work by Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs et al. (2010), gamma and normal random effects are included in a Weibull model, to account for overdispersion and between-subject effects, respectively. Unlike these authors, censoring is allowed for, and two estimation methods are presented. The partial marginalization approach to full maximum likelihood of Molenberghs et al. (2010) is contrasted with pseudo-likelihood estimation. A limited simulation study is conducted to examine the relative merits of these estimation methods. The modeling framework is employed to analyze data on recurrent asthma attacks in children on the one hand and on survival in cancer patients on the other.

Reinvestigation of the relationship between the amplitude of the first heart sound to cardiac dynamics

The relationships between the amplitude of the first heart sound (S1) and the rising rate of left ventricular pressure (LVP) concluded in previous studies were not consistent. Some researchers believed the relationship was positively linear; others stated the relationship was only positively correlated. To further investigate this relationship, this study simultaneously sampled the external phonocardiogram, electrocardiogram, and intracardiac pressure in the left ventricle in three anesthetized dogs, while invoking wide hemodynamic changes using various doses of epinephrine. The relationship between the maximum amplitude of S1 and the maximum rising rate of LVP and the relationship between the amplitude of dominant peaks/valleys and the corresponding rising rate of LVP were examined by linear, quadratic, cubic, and exponential models. The results showed that the relationships are best fit by nonlinear exponential models.