Richards Model Research Articles

Kazlarda Çevresel Zenginleştirmenin Büyüme Üzerine Etkilerinin Bazı Modellerle Karşılaştırılması

The aim ofthe present study is to determine the time-dependent changes in the live weights of the geese, for which environmental enrichment was applied (Turkish local goose genotype), between the days 7 and 98. For this purpose, nonlinear Brody, Gompertz, Logistic, von Bertalanffy, and Richards growth models, which are used commonly, were used to determine the growth and development of poultry. Geese were divided into 3 groups (control group (C), broom group (B), mirror group (M)) based on their enrichment characteristics. The success status of the models applied in the present study was assessed based on error mean square (EMS) and coefficient of determination (R2) values. It was found thatR2 value was be 96.86 in the Logistic model, 96.82 in Brody model, 96.16 in vonBertalanffy model,95.04 in Gompertz model and 93.85 in Richards model, respectively, and EMS value was 0.2368 in Logistic model, 0.2004in Brody model, 0.1992 in von Bertalanffy model, 0.3567 in Gompertz model and 0.3711 in Richards model, respectively. As a result, it was concluded that the most suitable models with high coefficient of determination but low error mean square were Brody,Gompertz, and von Bertalanffy models, respectively, in determining the time-dependent live weight change in the geese (Turkish local goose genotype), for which environmental enrichment was applied, and it was suitable to use these three models in determining the effect of environmental enrichment on live weight.

Growth Parameters and Spawning Season Estimation of Four Important Flyingfishes in the Kuroshio Current Off Taiwan and Implications From Comparisons With Global Studies

Growth shapes the life history of fishes. Establishing appropriate aging procedures and selecting representative growth models are important steps in developing stock assessments. Flyingfishes (Exocoetidae) have ecological, economic, and cultural importance to many coastal countries including Taiwan. There are 29 species of flyingfishes found in the Kuroshio Current off Taiwan and adjacent waters, comprising 56% of the flyingfishes taxa recorded worldwide. Among the six dominant species in Taiwan, four are of special importance. This study reviews aging data of these four species, documents major points of the aging methods to address three aging issues identified in the literature, and applies multi-model inference to estimate sex-combined and sex-specific growth parameters for each species. The candidate growth models examined included von Bertalanffy, Gompertz, Logistic, and Richards models, and the resulting optimal model tended to be the von Bertalanffy model for sex-combined data and Gompertz and von Bertalanffy models for sex-specific cases. The study also estimates hatch dates from size data collected from 2008 to 2017; the results suggest that the four flyingfishes have two spawning seasons per year. Length-weight relationships are also estimated for each species. Finally, the study combines the optimal growth estimates from this study with estimates for all flyingfishes published globally, and statistically classifies the estimates into clusters by hierarchical clustering analysis of logged growth parameters. The results demonstrate that aging materials substantially affect growth parameter estimates. This is the first study to estimate growth parameters of flyingfishes with multiple model consideration. This study provides advice for aging flyingfishes based on the three aging issues and the classification analysis, including a recommendation of using the asterisci for aging flyingfishes to avoid complex otolith processing procedures, which could help researchers from coastal countries to obtain accurate growth parameters for many flyingfishes.

The doubling time analysis for modified infectious disease Richards model with applications to COVID-19 pandemic.

In the absence of reliable information about transmission mechanisms for emerging infectious diseases, simple phenomenological models could provide a starting point to assess the potential outcomes of unfolding public health emergencies, particularly when the epidemiological characteristics of the disease are poorly understood or subject to substantial uncertainty. In this study, we employ the modified Richards model to analyze the growth of an epidemic in terms of 1) the number of times cumulative cases double until the epidemic peaks and 2) the rate at which the intervals between consecutive doubling times increase during the early ascending stage of the outbreak. Our theoretical analysis of doubling times is combined with rigorous numerical simulations and uncertainty quantification using synthetic and real data for COVID-19 pandemic. The doubling-time approach allows to employ early epidemic data to differentiate between the most dangerous threats, which double in size many times over the intervals that are nearly invariant, and the least transmissible diseases, which double in size only a few times with doubling periods rapidly growing.

Pedestrian Traffic Characterization Based on Pedestrian Response

Pedestrian behavior is studied during normal and emergency evacuation of two groups of students. One group consists of grade nine high school students while the other group includes diploma (college) students. The evacuation time, number of steps, step frequency, and velocity are observed. It is found that the number of steps, step frequency, and velocity are larger during an emergency evacuation. These results are used to develop a macroscopic pedestrian response model. This model is compared with the Lighthill, Whitham, and Richards (LWR) model for pedestrian traffic using the First Order Centered (FORCE) scheme. Pedestrian parameters from the experiments are used for model evaluation. The direction of pedestrian movement is changed multiple times to observe pedestrian alignment behavior. It has been found that the proposed model performs more realistically than the LWR model.

Growth and Productivity Modeling of Seven Eucalyptus Species in Souiniet’s Arboretum in the Northwestern of Tunisia

This study consists of the development of tree growth models to deduce stands productivity and determine the highest productive species in the conditions of the concerned plantation. Seven Eucalyptus, introduced in the arboretum of Souiniet (north-west of Tunisia, wet Mediterranean bioclimate) in a Cork Oak natural forest, were studied. Stem analysis and non-linear growth modeling regression equations were used to predict wood productivities. Gompertz and Chapman–Richards growth function appeared as being great numerical models to estimate the Eucalyptus tree diameter and height evolutions, respectively. Moreover, an adapted Chapman–Richards model allowed predicting the volume of trees in an efficient manner. The values of mean annual volume productivity of the Eucalyptus spp.studied, allow us to classify them in order of increasing annual productivity, as follows: E. sideroxylon, E. cinerea, E. maidenii, E. macrorhyncha, E. tereticornis, E. viminalis and E. bicostata. The first three Eucalyptus spp. appeared as the best-adapted and most suitable Eucalyptus trees for new plantations in this area. These species had the highest mean annual increments, ranged from 5 to 10 m3.ha−1.year−1 with 15 to 20 years of rotation. E. bicostata is the most promising, with annual average production exceeding 10 m3.ha−1.year−1 after 25 years, and reaching 20 m3.ha−1.year−1 at 40 years old. These modeling approaches provide additional knowledge on the productivity of the different Eucalyptus species, thus enabling forestry operators to simulate the development of forest stands in order to optimize timber production and harvesting.

Transmission Dynamics and Short-Term Forecasts of COVID-19: Nepal 2020/2021.

Nepal was hard hit by a second wave of COVID-19 from April-May 2021. We investigated the transmission dynamics of COVID-19 at the national and provincial levels by using data on laboratory-confirmed RT-PCR positive cases from the official national situation reports. We performed 8 week-to-week sequential forecasts of 10-days and 20-days at national level using three dynamic phenomenological growth models from 5 March 2021-22 May 2021. We also estimated effective and instantaneous reproduction numbers at national and provincial levels using established methods and evaluated the mobility trends using Google's mobility data. Our forecast estimates indicated a declining trend of COVID-19 cases in Nepal as of June 2021. Sub-epidemic and Richards models provided reasonable short-term projections of COVID-19 cases based on standard performance metrics. There was a linear pattern in the trajectory of COVID-19 incidence during the first wave (deceleration of growth parameter (p) = 0.41-0.43, reproduction number (Rt) at 1.1 (95% CI: 1.1, 1.2)), and a sub-exponential growth pattern in the second wave (p = 0.61 (95% CI: 0.58, 0.64)) and Rt at 1.3 (95% CI: 1.3, 1.3)). Across provinces, Rt ranged from 1.2 to 1.5 during the early growth phase of the second wave. The instantaneous Rt fluctuated around 1.0 since January 2021 indicating well sustained transmission. The peak in mobility across different areas coincided with an increasing incidence trend of COVID-19. In conclusion, we found that the sub-epidemic and Richards models yielded reasonable short-terms projections of the COVID-19 trajectory in Nepal, which are useful for healthcare utilization planning.

Kinetics of In Vitro Gas Production and Fitting Mathematical Models of Corn Silage

This study aimed at examining the effects of rumen inoculum of steers receiving different combinations of ionophore and probiotics in their diets on in vitro gas production of corn silage. The fitting of gas production was performed with five mathematical models and its kinetics was evaluated. Four crossbred steers (403.0 ± 75.5 kg body weight) with ruminal cannula were assigned to a 4 × 4 Latin square design. The additives used were Monensin sodium (Rumensin® 100, 3 g/day), Bacillus toyonensis (Micro-Cell Platinum® 109, 1 g/day) and Saccharomyces cerevisiae boulardii (ProTernative®20, 0.5 g/day). Additives were arranged into the following treatments, supplied daily into total mixed diet: (1) Monensin; (2) Monensin + B. toyonensis; (3) Monensin + S. boulardii; and (4) B. toyonensis + S. boulardii. The gas production data were fitted into the models of Gompertz, Groot, Ørskov, Brody, Richards, and Dual-pool Logistic. A perfect agreement between observed and predicted values in curves of accumulated in vitro gas production was observed in the Groot and Richards models, with higher coefficient of determination (R2 = 0.770 and 0.771, respectively), concordance correlation coefficient (CCC = 0.871 and 0.870, respectively), and root mean square error of prediction (RMSEP = 1.14 and 1.15, respectively). Evaluating the feed additives throughout the Groot model, the B. toyonensis + S. boulardii treatment presented higher VF (12.08 mL/100 mg of DM; p = 0.0022) than Monensin and Monensin + S. boulardii (9.16 and 9.22 mL/100 mg of DM, respectively). In addition, the fractional rate of gas production (k) was higher (p = 0.0193) in B. toyonensis + S. boulardii than in Monensin, not presenting a statistical difference (p > 0.05) from the other two treatments. Additionally, with the time of beginning to gas production, the lag time (λ), was greater (p < 0.001) with Monensin and Monensin + B. toyonensis than with Monensin + S. boulardii and B. toyonensis + S. boulardii. The combination of Monensin and probiotics (B. toyonensis + S. boulardii) resulted in better kinetics of degradation of corn silage, being that the Groot and Richards models had the best fit for estimates of the in vitro gas production data of corn silage tested with different feed additive combinations.

Effects of drip irrigation nitrogen coupling on dry matter accumulation and yield of Summer Maize in arid areas of China

To explore the effects of irrigation and nitrogen on dry matter accumulation (DMA) and yield of summer maize in arid regions, field experiments were conducted in experimental plot in 2017 and 2018. There were three drip irrigation quotas (3000 m3/hm2, 3750 m3/hm2, and 4500 m3/hm2) and four nitrogen levels (no nitrogen applied, 168 kg/hm2, 306.5 kg/hm2, and 444.5 kg/hm2) set in the experiment. The Richards model was used to fit the relationship of DMA and irrigation quantity or nitrogen level, and then the dynamics of DMA of maize were investigated. Furthermore, the effects of irrigation and nitrogen on maize grain yield were analyzed. Results showed that the maximum and average DMA rates in maize plants increased as irrigation quota increased from 3000 to 3750 m3/hm2 and as the applied nitrogen increased from 0 to 306.5 kg/hm2. Maize plants under the condition of irrigation 3750 m3/hm2 together with nitrogen 306.5 kg/hm2 showed the maximum dry matter growth rate (GRmax), the maximum average dry matter growth rate (GRavg), the maximum duration of dry matter fast growth period, and the maximum DMA and grain yield. The maximum grain yield was up to 1.340 × 104 kg/hm2 and 1.291 × 104 kg/hm2 in 2017 and 2018, respectively. However, when the irrigation quota was increased to 4500 m3/hm2 and the nitrogen application rate was up to 444.5 kg/ hm2, GRmax, GRavg, and yield of maize were all decreased with the increase of irrigation quantity, this law is reproducible between years. So the management practice of irrigation 3750 m3/hm2 along with nitrogen 306.5 kg/hm2 is optimal for maize production in the experimental region. Furthermore, a stepwise regression model was established to predict grain yield (Y1) on the basis of the characteristic parameters of the Richards model, and the regression model was: Y1 = 0.499YGRmax+0.074GRavg-6.399x2+2.25, R2 = 0.803. The contribution rate of each characteristic parameter to yield prediction model from high to low was: YGRmax>GRavg>x2. GRavg was extremely positive correlated with the final DMA and yield of maize, the study would provide technical basis for the efficient utilization of water and nitrogen in arid regions.

APPROXIMATION OF GROWTH INDICATORS AND ANALYSIS OF INDIVIDUAL GROWTH CURVES BY LINEAR DIMENSIONS OF TUBULAR BONES IN CHICKENS OF MEAT PRODUCTION DIRECTION DURING POSTNATAL PERIOD OF ONTOGENESIS

Medical and biological sciences, including morphology, now require the introduction of the latest information technologies and mathematical methods to process the obtained and accumulated research results. To study the growth dynamics of body weight in domestic birds, classical growth models, Gompertz, were used for the purpose of quantitative description of the growth processes in biological objects, in particular for the growth and development of birds – Von Bertalanffy, Richards, and hyperbolastic models. The research material was tubular bones of the thoracic (humerus, ulna, and radius) and pelvic (femur, tibia, and tarsometatarsus) limbs in birds of meat production (broiler chickens and laying hens from the parent broiler flock of Cobb-500 strain) of different age groups during the postnatal period of ontogenesis. An appropriate regression analysis of experimental data based on known growth models was performed to solve the goal of obtaining growth curves and identifying special points (extremes, inflections, etc.), to build a picture of the overall development of the body as a whole and individual bones of the extremities. The most biologically suitable growth models for describing the growth dynamics of the body as a whole and individual studied bones were determined. The absence of a unified growth model of linear parameters of different tubular bones in meat producing chickens during the postnatal period of ontogenesis was established. This implies the need for a clear selection of growth models taking into account age, species, breed, keeping and feeding conditions of domestic birds. The growth model that best describes the body weight dynamics of broiler chickens is the hyperbolastic growth model of the H3 type, and in laying hens from the parent broiler flock – the Brody growth model.

Nodal charging demand forecast of EVs considering drivers’ psychological bearing ability based on NMC‐MCS

Widespread adoption of electric vehicles (EVs) would significantly increase the electrical load demand in power distribution networks. Most previous studies investigated EV charging demand based on drivers’ trip habits, but the impact of psychological bearing ability (PBA) about the range anxiety on EV drivers’ charging decision are ignored. Here a novel forecast method considering drivers’ PBA for predicting nodal charging demand of EVs is proposed. The charging decision model considering PBA is established based on an improved Richards model, and the spatial-temporal dynamics model is established based on the non-homogeneous Markov chain (NMC) and random trip chain. Meanwhile, the Monte Carlo simulation (MCS) is adopted to avoid the disaster of dimensionality in large scale EVs charging problem. The proposed method is illustrated by an actual system integrated traffic network and power grid. The simulation results demonstrate that drivers’ PBA will significantly affect the charging decision, then changes the spatial-temporal distribution of charging power demand. The conclusion is that the drivers with lower PBA have a higher charging demand, and the impact of drivers’ PBA on charging power has a close relation with the initial battery level (IBL) of EVs.

A statistical mechanics approach to macroscopic limits of car-following traffic dynamics

We study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw–Rascle–Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill–Whitham–Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations.

Dynamic Top Height Growth Models for Eight Native Tree Species in a Cool-Temperate Region in Northeast China

In this study, we developed dynamic top height growth models for the eight important Chinese tree species Larix gmelinii var. principis-rupprechtii, Pinus tabuliformis Carr., Pinus sylvestris var. mongolica Litv., Picea asperata Mast., Quercus mongolica Fisch. ex Ledeb, Betula platyphylla Suk., Betula dahurica Pall. and Populus davidiana Dode based on age-height relationships. For this purpose, commonly growth data from long-term observations of permanent experimental plots are used, which ideally cover all development stages from stand establishment to final harvest. As such data were not available in the research area of Hebei Province in Northeast China, we used stem analysis data as well as tree height and annual shoot length measurements. The dataset consisted of 72 stands, 233 dominant trees and 10,195 observations of stem discs and annual shoot length measurements. Five dynamic base-age invariant top height growth models were derived from four base models with the generalized algebraic difference approach and fitted to our age-height data using nested regression techniques. According to biological plausibility and model accuracy the Chapman–Richards model showed the best performance for Picea asperata. This selected model accounted for 99% of the total variance in age-height relationship with average absolute bias of 0.2322 m, root mean square error of 0.3337 m and Radj2 of 0.9979, respectively. The distribution of the residuals was scattered around 0 and without visible trends, indicating that the fitness of the models was good. All developed models are able to generate top height growth curves representing the analyzed height growth data and can be utilized for predicting height growth on the base of current height and age of dominant trees. Additionally, they are the base for calculating the development of other relevant stand attributes such as basal area and volume growth. The determination of potential site productivity by the use of top height growth curves is a practical and convenient method for a simplified presentation of complex growth processes in stands and helps to create growth models, which facilitate implementing sustainable forest management practices in Mulan Forest.

Transmission dynamics and forecasts of the COVID-19 pandemic in Mexico, March-December 2020.

Mexico has experienced one of the highest COVID-19 mortality rates in the world. A delayed implementation of social distancing interventions in late March 2020 and a phased reopening of the country in June 2020 has facilitated sustained disease transmission in the region. In this study we systematically generate and compare 30-day ahead forecasts using previously validated growth models based on mortality trends from the Institute for Health Metrics and Evaluation for Mexico and Mexico City in near real-time. Moreover, we estimate reproduction numbers for SARS-CoV-2 based on the methods that rely on genomic data as well as case incidence data. Subsequently, functional data analysis techniques are utilized to analyze the shapes of COVID-19 growth rate curves at the state level to characterize the spatiotemporal transmission patterns of SARS-CoV-2. The early estimates of the reproduction number for Mexico were estimated between Rt ~1.1–1.3 from the genomic and case incidence data. Moreover, the mean estimate of Rt has fluctuated around ~1.0 from late July till end of September 2020. The spatial analysis characterizes the state-level dynamics of COVID-19 into four groups with distinct epidemic trajectories based on epidemic growth rates. Our results show that the sequential mortality forecasts from the GLM and Richards model predict a downward trend in the number of deaths for all thirteen forecast periods for Mexico and Mexico City. However, the sub-epidemic and IHME models perform better predicting a more realistic stable trajectory of COVID-19 mortality trends for the last three forecast periods (09/21-10/21, 09/28-10/27, 09/28-10/27) for Mexico and Mexico City. Our findings indicate that phenomenological models are useful tools for short-term epidemic forecasting albeit forecasts need to be interpreted with caution given the dynamic implementation and lifting of social distancing measures.

Quantitative trait loci for growth-related traits in Japanese quail (Coturnix japonica) using restriction-site associated DNA sequencing.

This study aimed to identify quantitative trait loci (QTLs) for growth-related traits by constructing a genetic linkage map based on single nucleotide polymorphism (SNP) markers in Japanese quail. A QTL mapping population of 277 F2 birds was obtained from an intercross between a male of a large-sized strain and three females of a normal-sized strain. Body weight (BW) was measured weekly from hatching to 16weeks of age. Non-linear regression growth models of Weibull, Logistic, Gompertz, Richards, and Brody were analyzed, and growth curve parameters of Richards was selected as the best model to describe the quail growth curve of the F2 birds. Restriction-site associated DNA sequencing developed 125 SNP markers that were informative between their parental strains. The SNP markers were distributed on 16 linkage groups that spanned 795.9 centiMorgan (cM) with an average marker interval of 7.3cM. QTL analysis of phenotypic traits revealed four main-effect QTLs. Detected QTLs were located on chromosomes 1 and 3 and were associated with BW from 4 to 16weeks of age and asymptotic weight of Richards model at genome-wide significant at 1% or 5% level. No QTL was detected for BW from 0 to 3weeks of age. This is the first report identified QTLs for asymptotic weight of the Richards parameter in Japanese quail. These results highlight that the combination of QTL studies and the RAD-seq method will aid future breeding programs identify genes underlying the QTL and the application of marker-assisted selection in the poultry industry, particularly the Japanese quail.

Age and Growth of Yellowfin Tuna in the U.S. Gulf of Mexico and Western Atlantic

AbstractAge, growth, and mortality were estimated for Yellowfin Tuna Thunnus albacares from the U.S. Gulf of Mexico and western Atlantic Ocean. During 2004–2017, 3,443 Yellowfin Tuna were sampled, primarily from recreational landings off the coast of Louisiana (90%). Based on reading otoliths, ages ranged from 1 to 18 years, with younger fish (<4 years) representing the majority (78%) of the age‐classes. Otolith weight was allometrically related to fish age (r2 = 0.91), which suggests that it may be a useful tool in indirectly estimating age given the challenges associated with directly aging tropical tunas. Based on Akaike’s information criterion (AIC), the Richards growth model had the most parsimonious fit to the length‐at‐age data (average maximum length L∞ = 1,658 mm, growth coefficient k = 0.23 year−1, a = 1.04, b = 0.45) compared to the von Bertalanffy growth model (L∞ = 1,589 mm, k = 0.36 year−1, theoretical age at zero length t0 = −0.8 year; AIC difference = 26.21), which had a relatively poor fit. The size‐modified Richards model, which assumed a truncated error structure at the minimum size limit (686 mm curved fork length [CFL]) in fishery‐dependent collections, improved the fit in the smallest individuals and was therefore the preferred model. Males and females had similar maximum ages (18 and 17 years, respectively) but showed significant differences in growth, with males reaching a larger L∞ than females (size‐modified Richards: 1,706 versus 1,568 mm CFL, respectively). Baseline natural mortality (M) using a maximum age of 18 years was 0.346 and was then scaled across age‐classes. These growth and mortality estimates and the individual age data have been used in improving stock assessments for Yellowfin Tuna to support scientific management.

Improved hydrological modeling with APEX and EPIC: Model description, testing, and assessment of bioenergy producing landscape scenarios

A Richards-based soil water model was implemented in the APEX and EPIC terrestrial ecosystem models to improve their hydrologic modeling capabilities. The Richards model together with two existing soil water models were calibrated and evaluated to assess their performance for simulating watershed-level hydrology under scenarios of landscape conversion to bioenergy crop production. The Richards model was shown to better reflect observed soil-water dynamics in grain (corn) and cellulosic (switchgrass) bioenergy agroecosystems, whereas all three models simulated historic streamflows comparably. Application of the models to understand the impacts of widespread landscape conversion from traditional agriculture to bioenergy producing landscapes indicated disparate conclusions, with the Richards-based simulations indicating a modest 1.0% reduction in streamflow whereas the existing models simulated sizable reductions of 10.6–16.1%. This study clearly demonstrates the impact of model methodology on system understanding and contextualizes the wide range of simulated streamflow impacts from bioenergy conversions reported in the literature.

A Macroscopic Traffic Model Based on the Safe Velocity at Transitions

The increasing volume of vehicles on the road has had a significant impact on traffic flow. Congestion in urban areas is now a major concern. To mitigate congestion, an accurate model is required which is based on realistic traffic dynamics. A new traffic model is proposed based on the conservation law of vehicles which considers traffic dynamics at transitions. Traffic alignment to forward conditions is affected by the time and distance between vehicles. Thus, the well-known Lighthill, Whitham, and Richards (LWR) model is modified to account for traffic behavior during alignment. A model for inhomogeneous traffic flow during transitions is proposed which can be used to characterize traffic evolution. The performance of the proposed model is compared with the LWR model using the Greenshields and Underwood target velocity distributions. These models are evaluated using the Godunov technique and numerical stability is guaranteed by considering the Courant, Friedrich, and Lewy (CFL) condition. The results obtained show that the proposed model characterizes the flow more realistically, and thus can provide better insight into traffic behavior for use in controlling congestion and pollution levels, and improving public safety. Doi: 10.28991/cej-2021-03091710 Full Text: PDF

A linear Lagrangian model predictive controller of macro- and micro- variable speed limits to eliminate freeway jam waves

Variable speed limits (VSLs) are a common traffic control measure to resolve freeway jam waves. State-of-the-art model predictive control (MPC) approaches of VSLs are developed based on Eulerian Lighthill-Whitham and Richards (LWR) models, where the decision variables are flows between road segments. It is difficult to implement constraints on speeds that are necessary in typical real-world speed limit systems, because converting flow to speed results in nonlinear and non-convex optimization formulations. In this paper, we develop a new MPC of VSLs based on a discrete Lagrangian LWR model, in which the decision variables are average speeds of vehicle groups. This allows formulating speed constraints as control constraints rather than state constraints in the MPC problem. The optimization of vehicle groups speeds is formulated as a linear programming problem which can be solved efficiently. We further integrate the presented MPC to a hierarchical VSL control framework leveraging connected vehicles. The presented MPC decides the optimal target speed of each vehicle group led by a connected automated vehicle (CAV) at the upper macroscopic level with a prediction horizon of 20 min. At the lower microscopic level, CAVs randomly distributed in mixed traffic are regarded as actuators of the upper layer. Microscopic CAV accelerations are optimized in a short horizon of the order 5–10 s so that the human-driven vehicles following them reach the target speed from the upper layer in an efficient and smooth manner. The presented MPC and the hierarchical control approach are tested in microscopic simulation environments. Simulation results show that (i) the presented MPC resolves freeway jam waves efficiently with reasonable safety constraints implemented, and (ii) the presented hierarchical control approach can effectively resolve jam waves in a single-lane freeway, even though the penetration rate of CAVs is as low as 5%.

Alkaline pretreatment of tannery wastewater impact on biochemical methane potential tests: experimental study and kinetic modeling

Studies were carried out on anaerobic digestion of tannery wastewater obtained from leather processing. Degassed activated sludge biomass collected from a wastewater treatment plant was used as source of microorganisms. The study was carried out to examine the impact of alkaline pretreatment on a real tannery wastewater prior anaerobic digestion process. Bio-methane potential tests were conducted at 35±2°C on tannery wastewater pretreated by adding different volumes of 2N NaOH solution up to set pH values at 9, 10, 11, and 12, respectively. NaOH solution addition resulted in a partial removal of total Cr showing efficiency from 16.84 to 95.72% as well as in an increase of the soluble chemical oxygen demand concentration from 8.53 to 29.02%. The effects of this pretreatment affected significantly the results obtained with bio-methane potential tests that showed methane production from all the pretreated tannery wastewater samples much higher than from that unpretreated. Finally, the lag phase duration and the maximum specific methane production rate of the anaerobic digestion process were evaluated by fitting the experimental results from bio-methane potential tests with the following three models: (i) the modified Gompertz model, (ii) the Logistic function, and (iii) the Richards model. All the previous models showed a high level of accordance with the experimental data, even though Richards model resulted in being the most accurate.

Forecasting COVID-19 Epidemic in Spain and Italy Using A Generalized Richards Model with Quantified Uncertainty

The Richards model and its generalized version are deterministic models that are often implemented to fit and forecast the cumulative number of infective cases in an epidemic outbreak. In this paper we employ a generalized Richards model to predict the cumulative number of COVID-19 cases in Spain and Italy, based on available epidemiological data. To quantify uncertainty in the parameter estimation, we use a parametric bootstrapping approach to construct a 95% confidence interval estimation for the parameter model. Here we assume that the time series data follow a Poisson distribution. It is found that the 95% confidence interval of each parameter becomes narrow with the increasing number of data. All in all, the model predicts daily new cases of COVID-19 reasonably well during calibration periods. However, the model fails to produce good forecasts when the amount of data used for parameter estimations is not sufficient. Based on our parameter estimates, it is found that the early stages of COVID-19 epidemic, both in Spain and in Italy, followed an almost exponentially growth. The epidemic peak in Spain and Italy is respectively on 2 April 2020 and 28 March 2020. The final sizes of cumulative number of COVID-19 cases in Spain and Italy are forecasted to be at 293220 and 237010, respectively.