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Although the impacts of climate change are long-term in nature, the transformation in climate regime can lead to an ecosystem change from one stable to another stable state through intermediate bistable or metastable states. Such state transition or resilience to change in ecosystems is seldom sharp and therefore difficult to quantify with a single tipping point. Rather, the change can be understood through a tipping point range (tipping zone) across hysteresis loop(s). This study uses a satellite data-derived actual vegetation cover map of India and categorizes it into different vegetation types: forest, scrubland, grassland, and vegetation-less. We used high-resolution long-term average precipitation data to develop moisture-driven hysteresis curves and predict various tipping point ranges for vegetation-type regime shifts. Our results reveal that the forest and vegetation-less states could have one-way, while scrubland and grassland have two-way transition probabilities with a probable shift in precipitation regime. In the dry conditions, the precipitation tipping zone predicted between 154 and 452 mm for the forest to scrubland transitions, while the reverse transition (from scrubland to forest) could occur in wet conditions between 1080 and 1400 mm. Similarly, the transition between scrubland and grassland, between grassland and vegetation-less state, may occur in contrasting dry and wet conditions, creating a hysteresis loop. The results indicate that the reversal of state change requires differential energy spent during the onward and reverse transitions. The study proposes a novel characteristic curve demonstrating the varied precipitation tipping points/zones, precipitation overlaps and distribution of the various vegetation types, and co-existence zones, which has huge implications for understanding the climate change impacts. [ABSTRACT FROM AUTHOR]

Estimates of EC50 from dose–response data play an important role in comparing drug potencies. When the sampling data of dose–response studies fail to follow a sigmoidal shaped curve, and the data display a biphasic property at higher dose levels where the response profile concaves and takes an inverted U-shape, this is known as the hook or prozone effect. To address this concern, some research investigators may pursue data removal. Others may choose to ignore the data shape and fit a model blindly. Unfortunately for both practices, the estimates of the fitting parameters, such as the EC50, will be of poor quality and result in misleading inference. The authors propose the use of an empirical and novel extension of a sigmoid model to properly and effectively capture the information from all of the dose–response data, including that of the inverted U-shaped tail. Methods for using 3- and 4-parameter logistic models with examples, are discussed. [ABSTRACT FROM AUTHOR]

The concomitant vibration and deformation produced by propeller blades in single-sided machining seriously affect the surface machining precision. Double-sided symmetrical machining can improve system rigidity through mutual shoring on both sides which abates the concomitant vibration and deformation. However, the actual double-sided symmetrical machining cannot be applied to blade machining due to its shape complexity. The double-sided collaborative machining method combining symmetrical machining and staggered machining is devised in this paper, and its tool path planning algorithm is investigated. Firstly, the algorithm achieves smooth fitting and correspondence of bilateral cutter position points through double-curve interpolation and position data alignment. Secondly, the blade surface is divided into four regions by two partition parameters: tip region, internal region, variable region, and edge region. Then, the conversion between symmetrical machining and staggered machining is completed through the Sigmoid deformation curve in the variable region. Finally, the feasibility and superiority of double-sided collaborative machining are verified through machining experiments. [ABSTRACT FROM AUTHOR]

Ridge gourd (Luffa acutangula) is a climbing vegetable that produces edible fruits. Young fruits are harvested when the cotyledons have not yet formed. This study covered morphological characteristics, growth behavior, and cultivation practices suitable for increasing the production of the ridge gourd in the urban ecosystem. Results of observation revealed the heart-shape leaf of the ridge gourd was very uniform and the leaf surface was flat so that their leaf area could be accurately estimated using leaf length and/or width (R2 > 0.97), yet leaf thickness was not a reliable predictor for the leaf area (R2 < 0.34). The length of the petioles was not correlated with the leaf blade area. Single leaves, multiple tendrils, bunches of male flowers and/or single female flowers, and one branch could be formed at each stem node. Water content in leaf blade was lower than in the petiole. This phenomenon is related to water favor loss due to transpiration activity. Nevertheless, the total conserved water within the leaf blade was 6.26 times more than that within the petiole. The process of fruit enlargement followed the Sigmoid curve. The upper-end curve flattened 10 days after the female flower bloomed. Moreover, at 10 days, cotyledon has not yet formed. Based on the leaf SPAD value, by time the fruit began to enlarge, 4-5 leaves at the stem base were instigated to show symptoms of senescence. Ridge gourd fruit fresh weight can be best estimated using the length x diameter as the predictor.

Drastic and continuous decline in cane yields has become a major threat to sustainable sugarcane production in Ethiopia. Among the causes for the decline are the inefficient and ineffective system of monitoring sugarcane plantations. Adopting satellite-based crop monitoring through the Landviewer platform may circumvent this problem. However, the reliability of vegetation indexes calculated by the platform is unknown and thus requires evaluation. Accordingly, we tested the accuracy of selected Landviewer Calculated Vegetation Indexes (LCVIs) on three major sugarcane varieties and two cropping types. The goodness-of-fit of the sigmoid curve to the LCVIs profile of sugarcane was evaluated. The correlations between LCVIs and yield components, LCVIs and fractional green canopy cover (FGCC), as well as the time-serious Normalized Difference Vegetation Index (NDVI) and yields, were also analysed. We found that the goodness-of-fit of the sigmoid curve was significant (p

Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree‐rings, and three growth‐rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth‐rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra‐ or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world. [ABSTRACT FROM AUTHOR]

Ridge gourd (Luffa acutangula) is a climbing vegetable that produces edible fruits. Young fruits are harvested at a time when the seed coats have been established, but cotyledons have not yet formed. This study covered morphological characteristics, growth behavior, and cultivation practices suitable for increasing the production of the ridge gourd in urban ecosystems. Results of observation revealed the heart-shaped leaf of the ridge gourd was very uniform, and the leaf surface was flat so that their leaf area could be accurately estimated using leaf length and/or width (R² > 0.97). Yet, leaf thickness was not a reliable predictor for the leaf area (R² < 0.34). The length of petioles was not correlated with the leaf blade area. All single leaves, multiple tendrils, an inflorescence of male flowers and/or a single female flower, and a branch could be formed at each stem node. Water content in the leaf blade was lower than in the petiole. This phenomenon is related to water favor loss due to transpiration activity. Nevertheless, the total conserved water within the leaf blade was 6.26 times more than those within the petiole. The process of fruit enlargement followed the Sigmoid curve. The upper end of the curve started to flatten 10 days after the female flower bloomed. Moreover, at the age of 10 days, cotyledon has not yet formed, so it can be used as a guide to determine the harvest time of the gourd ridge fruit. Based on the leaf SPAD value, by the time the fruit began to enlarge, 4-5 leaves at the stem base were instigated to show symptoms of senescence. Ridge gourd fruit fresh weight can be best estimated using the length x diameter of the plants as a predictor. [ABSTRACT FROM AUTHOR]

The Brière equation (BE) is widely used to describe the effect of temperature on the development rate of insects, and it can produce both symmetrical and asymmetrical bell-shaped curves. Because of its elasticity in curve fitting, the integrated form of BE has been recommended for use as a sigmoid growth equation to describe the increase in plant biomass with time. However, the start time of growth predicted by the sigmoid growth equation based on the BE is not completely comparable to empirical crop growth data. In the present study, we modified the BE by adding an additional parameter to further increase its elasticity for data fitting. We termed this new equation the modified Brière equation (MBE). Data for the actual height and biomass of 15 species of plants (with two cultivars for one species) were fit with the sigmoid growth equations based on both the BE and MBE assuming that the growth start time was zero for both. The goodness of fit of the BE and MBE sigmoid growth equations were compared based on their root-mean-square errors and the corresponding absolute percentage error between them when fit to these data. For most species, we found that the MBE sigmoid growth equation achieved a better goodness of fit than the BE sigmoid growth equation. This work provides a useful tool for quantifying the ontogenetic or population growth of plants. [ABSTRACT FROM AUTHOR]

Strain rate sensitivity of stress-strain curves family generated by the Boltzmann–Volterra linear viscoelasticity constitutive equation (with an arbitrary relaxation modulus) under uni-axial loadings at constant strain rates is studied analytically as the function of strain and strain rate. The general expression for strain rate sensitivity index is derived and analyzed assuming relaxation modulus being arbitrary. Dependence of the strain rate sensitivity index on strain and strain rate and on relaxation modulus qualitative characteristics is examined, conditions for its monotonicity and for existence of extrema, the lower and the upper bounds and the limit values of the strain rate sensitivity as strain rate tends to zero or to infinity are studied. It is found out that (within the framework of the linear viscoelasticity) the strain rate sensitivity index which is, generally speaking, the function of two independent variables (namely strain and strain rate), depends on the single argument only that is the ratio of strain to strain rate. So defined function of one real variable is termed the strain rate sensitivity function and it may be regarded as a material function. The explicit integral expression (and the two-sided bound) for relaxation modulus in terms of strain rate sensitivity function is derived which enables one to restore relaxation modulus assuming a strain rate sensitivity function is given. The strain rate sensitivity function is represented as a linear function of ratio of tangent modulus to secant modulus of a stress-strain curve at any fixed constant strain rate and can be evaluated in such a way using experimental data. It is proved that the strain rate sensitivity value is confined in the interval from zero to unity (the upper bound of strain rate sensitivity index for pseudoplastic media) whatever strain and strain rate magnitudes. It is found out that the linear theory can reproduce increasing or decreasing or non-monotone dependences of strain rate sensitivity on strain rate (for any fixed strain) and it can provide existence of local maximum or minimum or several extrema as well without any complex restrictions on the relaxation modulus. General properties and peculiarities of the theoretic strain rate sensitivity function are illustrated by the examination of the classical regular and singular rheological models (consisting of two, three or four spring and dashpot elements) and fractional models. Namely, the Maxwell, Kelvin–Voigt, standard linear solid, Zener, anti-Zener, Burgers, anti-Burgers, Scott–Blair, fractional Kelvin–Voigt models and their parallel connections are considered. The carried out analysis let us to conclude that the linear viscoelasticity theory (supplied with common relaxation function which are non-exotic from any point of view) is able to produce high values of strain rate sensitivity index close to unity (the upper bound of strain rate sensitivity index for pseudoplastic media) and to provide existence of the strain rate sensitivity index maximum with respect to strain rate. Thus, it is able to simulate qualitatively existence of a flexure point on log-log graph of stress dependence on strain rate and its sigmoid shape which is one of the most distinctive features of superplastic deformation regime observed in numerous materials tests.

The concomitant vibration and deformation produced by propeller blades in single-sided machining seriously affect the surface machining precision. Double-sided symmetrical machining can improve system rigidity through mutual shoring on both sides which abates the concomitant vibration and deformation. However, the actual double-sided symmetrical machining cannot be applied to blade machining due to its shape complexity. The double-sided collaborative machining method combining symmetrical machining and staggered machining is devised in this paper, and its tool path planning algorithm is investigated. Firstly, the algorithm achieves smooth fitting and correspondence of bilateral cutter position points through double-curve interpolation and position data alignment. Secondly, the blade surface is divided into four regions by two partition parameters: tip region, internal region, variable region, and edge region. Then, the conversion between symmetrical machining and staggered machining is completed through the Sigmoid deformation curve in the variable region. Finally, the feasibility and superiority of double-sided collaborative machining are verified through machining experiments.

Several theoretical and empirical models are available to correlate experimental breakthrough curves of water pollutants, one of which is the two-parameter Belter model. Although not as well known as the century-old Bohart–Adams model, the Belter model is being used with sufficient frequency to merit wider awareness of its strengths and weaknesses. Through a systematic analysis, it is shown that the two adjustable parameters of the Belter model are analogous to the equilibrium capacity and rate parameters of the Bohart–Adams model. Breakthrough curves predicted by the Belter model are perfectly symmetric because their inflection points are invariant and always correspond to the midpoint of the curves. As a consequence, the Belter model provides poor fits to asymmetric breakthrough curves. In this work, an improved version of the Belter model is introduced. The new model with a floating inflection point manifests excellent conformity with mildly and, more importantly, severely asymmetric breakthrough curves. [ABSTRACT FROM AUTHOR]

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Analysis of fluorescence-based Real-Time Polymerize Chain Reaction (RT-PCR) amplification data is increasingly used to detect multiple pathogens and variants of those rapidly and simultaneously through gene expression. If the gene of interest for the pathogen exists in the sample, then the PCR amplification data forms a type of logistic curve (sigmoid) with an exponential phase. If the pathogen does not exist in the sample, then the amplification signal produces just a noise. The traditional approach for RT-PCR data analysis focuses on the value of the point where the cutoff-threshold (CT) line crosses the exponential phase of the curve if it exists. Focusing on the determination of the CT value too often causes mislabeling of pathogens as either false positives or false negatives. Therefore, this research demonstrates the possibility of improving the accuracy of RT-PCR pathogen identification performance. • Robust CT Determination with Deep Neural Network with your own data. • Fine tunung the Deep Neural Network to minimize the total number of parameters. • Compare State of the Art Approaches for CT Prediction in diagnostics applications. [ABSTRACT FROM AUTHOR]

The Brière equation (BE) is widely used to describe the effect of temperature on the development rate of insects, and it can produce both symmetrical and asymmetrical bell-shaped curves. Because of its elasticity in curve fitting, the integrated form of BE has been recommended for use as a sigmoid growth equation to describe the increase in plant biomass with time. However, the start time of growth predicted by the sigmoid growth equation based on the BE is not completely comparable to empirical crop growth data. In the present study, we modified the BE by adding an additional parameter to further increase its elasticity for data fitting. We termed this new equation the modified Brière equation (MBE). Data for the actual height and biomass of 15 species of plants (with two cultivars for one species) were fit with the sigmoid growth equations based on both the BE and MBE assuming that the growth start time was zero for both. The goodness of fit of the BE and MBE sigmoid growth equations were compared based on their root-mean-square errors and the corresponding absolute percentage error between them when fit to these data. For most species, we found that the MBE sigmoid growth equation achieved a better goodness of fit than the BE sigmoid growth equation. This work provides a useful tool for quantifying the ontogenetic or population growth of plants.

The process related to the changes in dimensions and mass of grape berry passes through two growth phases separated by a lag phase, and can be described by a double sigmoid curve. The onset of the growth phases and their duration are important factors for understanding the growth processes in grape berries. A new method for their quantitative determination was developed in the present study. In this method, the phase transition dates correspond to the times at which the rate of change of the curvature of the logistic (sigmoid) curve reaches an extreme value. The method was tested on three seedless grape varieties, Sultanina, Ruby Seedless and Rusalka 3, and the changes in grape berry dimensions and mass were tracked from anthesis to harvest. For each of the varieties, a double logistic model of change in berry length, width and mass from anthesis to harvest was developed and the metrics of growth - beginning, stabilisation and end of growth - for each of the two phases were determined. It was found that the metrics in mass and berry dimensions do not match and shift relative to each other over time. A comparison of growth metrics with phenological metrics, such as anthesis, veraison and ripening, showed that phenophases cannot be used as a time scale to record the acceleration of growth processes, as they shifted in time with growth metrics. An exception was veraison, which coincided with the beginning of the accelerated growth of grapes during the second growth phase, following the lag phase. The time scale presented in the current research is a new tool for monitoring growth processes and could help clarify the links between visible changes in the grape berries and the ongoing processes within them. The developed method can also be used for the analysis of various growth processes that follow the logistic law.

The subthalamic nucleus (STN) is an important target during deep brain stimulation (DBS). Accurate lead placement is integral to achieving satisfactory clinical outcomes; however, the STN remains a structure whose visualization is highly variable with borders often difficult to define. We aimed to develop an objective method of evaluating the visibility of the STN on preoperative magnetic resonance imaging (MRI) to standardize future comparative assessments between imaging protocols and patient-specific parameters. An imaging study of 64 prospectively collected patients undergoing bilateral DBS of the STN for various movement disorders was performed with institutional approval. MRI scans were acquired using a uniform protocol involving general anesthesia, cranial fixation in a Leksell stereotactic frame, and long acquisition times using a 3T MRI scanner. The images were analyzed using the iPlan Stereotaxy, version 2.6, workstation. High-resolution T2-weighted axial sections were evaluated, and the voxel values in the region of the presumed posterior border of the STN (as defined by the operating neurosurgeon) were obtained. A 4-parameter logistic symmetrical sigmoid curve was used to map the voxel values as they progressed from within to outside the region of the STN border. The inflection point and Hill coefficient of this symmetrical curve was calculated to provide objective information on the location and clarity of the STN border, respectively. These findings were compared with the surgeon's judgment of the STN border. To demonstrate the use of the sigmoid curve, the patients' head volumes were also calculated and evaluated to assess whether larger head volumes adversely affected STN visibility. The symmetrical sigmoid curve model provided objective information on the visibility of the STN on T2-weighted MRI scans and could be generated in 86% of the patients. The other 14% of patients had MRI scans that generated linear graphs, indicating the poorest scoring for STN image quality. No correlation between head volume and STN visibility was identified. Our proposed statistical model allows for standardized examination of the visibility of the STN border for DBS and has potential for both clinical and academic applications. [ABSTRACT FROM AUTHOR]

The objective of the present review is twofold. First, it aims at highlighting some sigmoid and reverse-sigmoid response patterns observed recently in the course of simulations of the high-strain-rate loading of (mostly, quasibrittle) solids. Second, it aims at reviewing various properties of two models used frequently as curve fitting tools for nonlinear and saturable phenomena. These two models-inspired by the Hill and the Weibull cumulative distribution functions-are bounded by two horizontal asymptotes with a smooth transition between the baseline and the final saturation state, characterized by a non-negative (a non-positive) derivative at each point for the sigmoid (the reverse-sigmoid) shape. Although they were used primarily for data fitting because of their flexibility and effectiveness, these nonlinear models possess other properties useful for the analysis of the irreversible, nonlinear and far-from-equilibrium phenomena. The main features of these two models are systematically examined in this review. In spite of the fact that satisfactory curve-fitting of data could not be considered a proof of causality it could underline a pattern of behavior and, perhaps, provide an investigation guidance.

The traditional potential field-based path planning is likely to generate unexpected path by strictly following the minimum potential field, especially in the driving scenarios with multiple obstacles closely distributed. A hybrid path planning is proposed to avoid the unsatisfying path generation and to improve the performance of autonomous driving by combining the potential field with the sigmoid curve. The repulsive and attractive potential fields are redesigned by considering the safety and the feasibility. Based on the objective of the shortest path generation, the optimized trajectory is obtained to improve the vehicle stability and driving safety by considering the constraints of collision avoidance and vehicle dynamics. The effectiveness is examined by simulations in multiobstacle dynamic and static scenarios. The simulation results indicate that the proposed method shows better performance on vehicle stability and ride comfortability than that of the traditional potential field-based method in all the examined scenarios during the autonomous driving.

Carrot, a highly profitable crop in Israel, is severely damaged by Phelipanche aegyptiaca ‎parasitism. Herbicides can effectively control the parasite and prevent damage, but for ‎optimal results, knowledge about the soil-subsurface phenological stage of the parasite is ‎essential. Parasitism dynamics models have been successfully developed for the parasites P. ‎aegyptiaca, Orobanche cumana and O. minor in the summer crops, tomato, sunflower and ‎red clover, respectively. However, these models, which are based on a linear relationship ‎between thermal time and the parasitism dynamics, may not necessarily be directly ‎applicable to the P. aegyptiaca-carrot system. The objective of the current study was to ‎develop a thermal time model to predict the effect of P. aegyptiaca parasitism dynamics on ‎carrot growth. For development and validation of the models, data was collected from a ‎temperature-controlled growth experiment and from 13 plots naturally infested with P. ‎aegyptiaca in commercial carrot fields. Our results revealed that P. aegyptiaca development ‎is related to soil temperature. Moreover, unlike P. aegyptiaca parasitism in sunflower and ‎tomato, which could be predicted both a linear model, P. aegyptiaca parasitism dynamics ‎on carrot roots required a nonlinear model, due to the wider range of growth temperatures of ‎both the carrot and the parasite. Hence, two different nonlinear models were developed for ‎optimizing the prediction of P. aegyptiaca parasitism dynamics. Both models, a beta ‎function model and combined model composed of a beta function and a sigmoid curve, were ‎able to predict first P. aegyptiaca attachment. However, overall P. aegyptiaca dynamics was ‎described more accurately by the combined model (RMSE =14.58 and 10.79, respectively). ‎The results of this study will complement previous studies on P. aegyptiaca management by ‎herbicides to facilitate optimal carrot growth and handling in fields infested with P. ‎aegyptiaca. ‎

Predicting the grain yield during early to mid-growth stages is important for initial diagnosis of rice and quantitative regulation of topdressing. In this study, we conducted four experiments using different nitrogen (N) application rates (0⁻400 kg N∙ha−1) in three Japonica rice cultivars (Wuyunjing24, Ningjing4, and Lianjing7) grown in Jiangsu province, Eastern China, from 2015⁻2016. Spectral reflectance data were collected multiple times during early to mid-growth stages using an active mounted sensor (RapidScan CS-45, Holland Scientific Inc., Lincoln, NE, USA). Data were then used to calculate optimal vegetation indexes (normalized difference red edge, NDRE; normalized difference vegetation index, NDVI; ratio vegetation index, RVI; red-edge ratio vegetation index, RERVI), which were used to develop a dynamic change model and in-season grain yield prediction model. The NDRE index was more stable than other indexes (NDVI, RVI, RERVI), showing less standard deviation at the same N fertilizer rate. The R2 of the relationships between leaf area index (LAI), plant nitrogen accumulation (PNA), and NDRE also increased compared to other indexes. These findings suggest that NDRE is suitable for analysis of paddy rice N nutrition. According to real-time series changes in NDRE, the resulting dynamic model followed a sigmoid curve, with a coefficient of determination (R2) >0.9 and relative root-mean-square error R2 values of the relationship between SV and yield were >0.7. For every 0.1 increase in SV, grain yield increased by 3608.1 kg·ha−1. Overall, our new dynamic model effectively predicted grain yield at stem elongation and booting stages, providing real-time crop N nutrition data for management of N fertilizer topdressing in rice production.

Carrot, a highly profitable crop in Israel, is severely damaged by Phelipanche aegyptiaca parasitism. Herbicides can effectively control the parasite and prevent damage, but for optimal results, knowledge about the soil-subsurface phenological stage of the parasite is essential. Parasitism dynamics models have been successfully developed for the parasites P. aegyptiaca, Orobanche cumana, and Orobanche minor in the summer crops, tomato, sunflower, and red clover, respectively. However, these models, which are based on a linear relationship between thermal time and the parasitism dynamics, may not necessarily be directly applicable to the P. aegyptiaca-carrot system. The objective of the current study was to develop a thermal time model to predict the effect of P. aegyptiaca parasitism dynamics on carrot growth. For development and validation of the models, data was collected from a temperature-controlled growth experiment and from 13 plots naturally infested with P. aegyptiaca in commercial carrot fields. Our results revealed that P. aegyptiaca development is related to soil temperature. Moreover, unlike P. aegyptiaca parasitism in sunflower and tomato, which could be predicted both a linear model, P. aegyptiaca parasitism dynamics on carrot roots required a nonlinear model, due to the wider range of growth temperatures of both the carrot and the parasite. Hence, two different nonlinear models were developed for optimizing the prediction of P. aegyptiaca parasitism dynamics. Both models, a beta function model and combined model composed of a beta function and a sigmoid curve, were able to predict first P. aegyptiaca attachment. However, overall P. aegyptiaca dynamics was described more accurately by the combined model (RMSE = 14.58 and 10.79, respectively). The results of this study will complement previous studies on P. aegyptiaca management by herbicides to facilitate optimal carrot growth and handling in fields infested with P. aegyptiaca. [ABSTRACT FROM AUTHOR]

In this paper we conduct the error analysis of two models used to simulate the disease profiles in plant pathogen epidemics. The role of the various model parameters is discussed in relation to accuracy

The analysis of the external environment must not be limited to the identification of the external factors, but must also take into account their importance. The real management capacity consists of finding out their signification, of identifying exactly those factors which may have a special influence upon the organization. As a consequence of the fact that the external environment is dynamic, it is important to understand correctly the direction of the moment and the location of the change.

Presented here is a system to standardize clinical studies of nutrient effects, using nutrient-specific physiological criteria. These guidelines are based mainly on analysis of the typical sigmoid curve of biological response to nutrients and are intended for design, interpretation, and pooling of studies of nutrient effects. Five rules have been articulated for individual studies of nutrients, and six for systematic reviews and/or meta-analyses. [ABSTRACT FROM AUTHOR]

The lag phase (L) of grape berry growth is used to determine the timing of hand sampling for yield estimation. In commercial practice, growers apply scalars to measurements of berry of cluster masses under the assumption that fruit was assessed during L, which is the short period of slowest increase in fruit mass that occurs between the first and second sigmoid curves that describe growth in fleshy fruits. To estimate L, we used an automated remote system that indirectly detects increases in vegetative and fruit mass in grapevines by monitoring the tension (T) in the main load-bearing wire of the trellis. We fitted logistic curves to the change in T (ΔT) such that the parameters could be interpreted biologically, particularly the onset of L: the asymptotic deceleration of growth. Curves fit the data well [root mean square error (RMSE) 4.2 to 14.9] in three disparate years and two vineyards. The onset of L was most sensitive to the inflection point of the first logistic curve but relatively insensitive to its shape parameter. The analytical solution of the second derivative of the first logistic curve for its minimum predicted the apparent onset of L with a range of 3 to 5 days among replicates. The roots of the third derivative allowed analytical solutions for the onset of the first rapid growth phase and L, consistently predicting the onset of L 2 to 15 days earlier than was identified by trained observers who examined ΔT curves. Remote sensing of ΔT could better time field sampling and decrease current reliance on visual and tactile assessment to identify the onset of L, thus improving yield estimation in grapes. [ABSTRACT FROM AUTHOR]

D-optimal designs for nonlinear models are often minimally supported. They have been frequently criticized for their inability to test for lack of fit. We construct alternative designs to address this issue for some commonly used sigmoid curves, including logistic, probit, and Gompertz models with two, three, or four parameters. For each model, we compare five nonminimally supported designs in terms of their efficiency, and propose designs that are both statistically efficient and practically convenient for practitioners. [ABSTRACT FROM AUTHOR]

A simplified version of TOMGRO, a well-known model for tomato growth simulation, was delivered by its authors in 1999, with the aim to adapt the program to operational exigencies. This model version was chosen to integrate the functions of a decision support tool, oriented to support Italian tomato growers in soilless crop fertigation management. During the preliminary evaluation phase, its application on data collected in three greenhouse experiments conducted on tomato cv. Jama in Pisa (central Italy) in 2004 and 2005, showed an insufficient accuracy in the Leaf Area Index (LAI) estimation of tomato crops. Consequently, node number and LAI computational algorithms were modified. This paper discusses model modifications, analysing their effects on tomato growth simulation. In comparison with the observed data, the modified model showed a good enhancement of estimation accuracy of node and LAI, with significantly positive effects also on plant and fruit biomass estimation. [ABSTRACT FROM AUTHOR]

Abstract: The Richards model has a shape parameter m that allows it to fit any sigmoidal curve. This article demonstrates the ability of a modified Richards model to fit a variety of technology diffusion curvilinear data that would otherwise be fit by Bass, Gompertz, Logistic, and other models. The performance of the Richards model in forecasting was examined by analyzing fragments of data computed from the model itself, where the fragments simulated either an entire diffusion curve but with sparse data points, or only the initial trajectory of a diffusion curve but with dense data points. It was determined that accurate parameter estimates could be obtained when the data was sparse but traced out the curve at least up to the third inflection point (concave down), and when the data was dense and traced out the curve up to the first inflection point (concave up). Rogers'' Innovation I, II and III are discussed in the context of the Richards model. Since m is scale independent, the model allows for a typology of diffusion curves and may provide an alternative to Rogers'' typology. [Copyright &y& Elsevier]

The acute ecotoxicity of a set of mixture samples (washing powders, wastes, fuel extracts etc.) was assessed using four acute ecotoxicity assays with aquatic organisms (Daphnia magna, Poecilia reticulata, Artemia salina and Desmodesmus subspicatus). The experimental concentration-response curves were fitted by seven two-parameter sigmoid equations using non-linear regression. The regression performance of the equations was compared in three categories (overall fit, mid-range fit, and low-effect fit) using non-parametric statistics. The best overall fit was achieved by Weibüll, Bolztman (i.e. logistic), modified Gompertz and log- Weibüll equations. The best low-effect fit was achieved by a modified Gompertz curve. Those equations transforming concentrations to log c fitted significantly worse than those not transforming them. The obtained EC50 values calculated by all of the equations were comparable to those calculated by the probit model. The results show that regardless of the knowledge of the susceptibility distribution or the mechanisms of toxic action simple two-parameter equations fit the data from acute ecotoxicity assays well and might be used for their evaluation. Key words: Acute eco [ABSTRACT FROM AUTHOR]

Loquat fruit growth measured by increases of equatorial diameter adjusts to a logistic curve. By means of sequential measurements of tagged fruits of cultivar ‘Algerie’, curves were obtained that fit significantly to a single sigmoid model in unthinned as well as in heavily thinned trees. Equations defining growth pattern of fruits from thinned and from unthinned trees showed different slopes that reflect greater growth rates under thinning. On the contrary, small and large fruits within the same tree showed minor variations in growth rates, and fruit size at harvest was largely due to fruit size at initial fruit set. Differences in size among fruitlets of the same tree at the time of hand fruit thinning never reversed and led to different commercial categories related with initial size; that allows us to recommend fruit thinning on a size basis. A strong significant correlation was also found at harvest between fresh fruit weight and equatorial diameter. Size and number of seeds were the major determinants of final fruit size in loquat whereas number of leaves and leaf area index of the bearing shoots showed a weak correlation with final size of fruits. [Copyright &y& Elsevier]

A new empirical equation for the sigmoid pattern of determinate growth, ‘the beta growth function’, is presented. It calculates weight (w) in dependence of time, using the following three parameters: tm, the time at which the maximum growth rate is obtained; te, the time at the end of growth; and wmax, the maximal value for w, which is achieved at te. The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating wmax. Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process‐based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential. [ABSTRACT FROM PUBLISHER]

Silica accumulation in long‐lived leaves of Sasa veitchii was investigated using the molybdenum blue method. In general, silica accumulation was rapid during spring and summer, and slow during winter. The leaves continuously accumulate silica throughout their life. The significance of these observations is discussed in relation to two hypotheses for silica accumulation in plants: (1) that silica accumulation is a result of water consumption by the plant; and (2) that silica is actively accumulated to protect the plant. The results of the present study support the former hypothesis. [ABSTRACT FROM PUBLISHER]

The kinetics on the growth of T. ferroxidans in the presence of Cu(II) was studied using of series piezoelectric quartz crystal (SPQC). Arsenic ion inhibits the growth of T. ferrooxidans, which is consistent with the previous results by other measuring methods. This further demonstrates that the SPQC can monitor the chemical activity of T. ferrooxidans growth. Cupric ion accelerates the growth of T. ferrooxidans. The mechanism was discussed, i. e., copper promotes the protein enzyme of T. ferrooxidans, rusticyanin, to form over the range of cupric ion concentration studied. The reaction order of cupric ion in accelerating the bacterial growth is 0.067. The growth of T. ferrooxidans is dependent on temperature, the apparent reaction activation energy decreases from 25.56 kJ/mol to 18.32 kJ/mol because of the addition of 10 mg/L Cu(II) to the bacterial growth solution of pH 2.0 at initial inoculum of 10%. [ABSTRACT FROM AUTHOR]