Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

Reliability Growth Modeling and Optimal Release Policy Under Fuzzy Environment of an N-version Programming System Incorporating the Effect of Fault Removal Efficiency

Failure of a safety critical system can lead to big losses. Very high software reliability is required for automating the working of systems such as aircraft controller and nuclear reactor controller software systems. Fault-tolerant softwares are used to increase the overall reliability of software systems. Fault tolerance is achieved using the fault-tolerant schemes such as fault recovery （recovery block scheme）, fault masking （N-version programming （NVP）） or a combination of both （Hybrid scheme）. These softwares incorporate the ability of system survival even on a failure. Many researchers in the field of software engineering have done excellent work to study the reliability of fault-tolerant systems. Most of them consider the stable system reliability. Few attempts have been made in reliability modeling to study the reliability growth for an NVP system. Recently, a model was proposed to analyze the reliability growth of an NVP system incorporating the effect of fault removal efficiency. In this model, a proportion of the number of failures is assumed to be a measure of fault generation while an appropriate measure of fault generation should be the proportion of faults removed. In this paper, we first propose a testing efficiency model incorporating the effect of imperfect fault debugging and error generation. Using this model, a software reliability growth model （SRGM） is developed to model the reliability growth of an NVP system. The proposed model is useful for practical applications and can provide the measures of debugging effectiveness and additional workload or skilled professional required. It is very important for a developer to determine the optimal release time of the software to improve its performance in terms of competition and cost. In this paper, we also formulate the optimal software release time problem for a 3VP system under fuzzy environment and discuss a the fuzzy optimization technique for solving the problem with a numerical illustration.

Latent Growth Mixture Modeling to Estimate Differential PTSD Trajectories and Associated Risk Factors in Psychiatric Staff Following Workplace Violence

Background: Workplace violence (WV) towards psychiatric staff has commonly been associated with Posttraumatic Stress Disorder (PTSD). However, prospective studies have shown that not all psychiatric staff who experience workplace violence experience post-traumatic stress. Purpose: We want to examine the longitudinal trajectories of PTSD in this population to identify possible subgroups that might be more at risk. Furthermore, we need to investigate whether certain risk factors of PTSD might identify membership in the subgroups. Method: In a sample of psychiatric staff from 18 psychiatric wards in Denmark who had reported an incident of WV, we used Latent Growth Mixture Modelling (LGMM) and further logistic regression analysis to investigate this. Results: We found three separate PTSD trajectories: a recovering, a delayed-onset, and a moderate-stable trajectory. Higher social support and negative cognitive appraisals about oneself, the world and self-blame predicted membership in the delayed-onset trajectory, while higher social support and lower accept coping predicted membership in the delayed-onset trajectory. Conclusion: Although most psychiatric staff go through a natural recovery, it is important to be aware of and identify staff members who might be struggling long-term. More focus on the factors that might predict these groups should be an important task for psychiatric departments to prevent posttraumatic symptomatology from work.

Shock Initiation Experiments with Modeling on a DNAN Based MeltCast Insensitive Explosive

2,4-dinitroanisole(DNAN)is a good replacement for 2,4,6-trinitrotoluene(TNT)in melt-cast explosives due to its superior insensitivity.With the increasing use of DNAN-based melt-cast explosives,the prediction of reaction violence and hazard assessment of the explosives subjected to shock is of great significance.This study investigated the shock initiation characteristics for a DNAN-based melt-cast explosive,DHFA,using the one-dimensional Lagrangian apparatus.The embedded manganin gauges in the apparatus record the pressure histories at four Lagrangian positions and show that shock-todetonation transition in DHFA needs a high input shock pressure.The experimental data are analyzed to calibrate the Ignition and Growth model.The calibration is performed using an objective function based on both pressure history and the arrival time of shock.Good agreement between experimental and calculated pressure histories indicates the high accuracy of the calibrated parameters with the optimization method.

Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson(EW) and Kardar–Parisi–Zhang(KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation(RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition(BD), etching, and restricted solid on solid(RSOS). The scaling exponents are obtained in both the(1 + 1)-and(2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1-p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Control of GaN inverted pyramids growth on c-plane patterned sapphire substrates

Growth of gallium nitride(GaN)inverted pyramids on c-plane sapphire substrates is benefit for fabricating novel devices as it forms the semipolar facets.In this work,GaN inverted pyramids are directly grown on c-plane patterned sapphire substrates(PSS)by metal organic vapor phase epitaxy(MOVPE).The influences of growth conditions on the surface morphol-ogy are experimentally studied and explained by Wulff constructions.The competition of growth rate among{0001},{1011},and{1122}facets results in the various surface morphologies of GaN.A higher growth temperature of 985 ℃ and a lowerⅤ/Ⅲratio of 25 can expand the area of{}facets in GaN inverted pyramids.On the other hand,GaN inverted pyramids with almost pure{}facets are obtained by using a lower growth temperature of 930℃,a higherⅤ/Ⅲratio of 100,and PSS with pattern arrangement perpendicular to the substrate primary flat.

Examining approaches for modeling individual tree growth response to thinning in Norway spruce

Using periodic measurements from permanent plots in non-thinned and thinned Norway spruce(Picea abies(L.)H.Karst.)stands in Norway,individual-tree growth models were developed to predict annual diameter increment,height increment,and height to crown base increment.Based on long-term data across a range of thinning regimes and stand conditions,alternative approaches for modeling response to treatment were assessed.Dynamic thinning response functions in the form of multiplicative modifiers that predict no effect at the time of thinning,a rapid increase followed by an early maximum before the effect gradually declines to zero could not be fitted to initially derived baseline models without thinning related predictors.However,alternative approaches were used and found to perform well.Specifically,indicator variables representing varying time periods after thinning were statistically significant and behaved in a robust manner as well as consistent with general expectations.In addition,they improved overall prediction accuracy when incorporated as fixed effects into the baseline models for diameter and height to crown base increment.Further,more simply,including exponentially decreasing multiplicative thinning response functions improved prediction accuracy for height increment and height to crown base increment.Irrespective of studied attribute and modelling approach,improvement in performance of these extended models was relatively limited when compared to the corresponding baseline models and more pronounced in trees from thinned stands.We conclude that the largely varying and often multi-year measurement intervals of the periodic data used in this study likely prevented the development of more sophisticated thinning response functions.However,based on the evaluation of the final models’overall performance such complex response functions may not to be necessary to reliably predict individual tree growth after thinning for certain conditions or species,which should be further considered in future analyses of similar nature.

Methods of modeling relative growth rate

Background： Analysing and modelling plant growth is an important interdisciplinary field of plant science. The use of relative growth rates, involving the analysis of plant growth relative to plant size, has more or less independently emerged in different research groups and at different times and has provided powerful tools for assessing the growth performance and growth efficiency of plants and plant populations. In this paper, we explore how these isolated methods can be combined to form a consistent methodology for modelling relative growth rates. Methods： We review and combine existing methods of analysing and modelling relative growth rates and apply a combination of methods to Sitka spruce （Piceo sitchensis （Bong.） Carr.） stem-analysis data from North Wales （UK） and British Douglas fir （Pseudotsugd menziesii （Mirb.） Franco） yield table data. Results： The results indicate that, by combining the approaches of different plant-growth analysis laboratories and using them simultaneously, we can advance and standardise the concept of relative plant growth. Particularly the growth multiplier plays an important role in modelling relative growth rates. Another useful technique has been the recent introduction of size-standardised relative growth rates. Conclusions： Modelling relative growth rates mainly serves two purposes, 1） an improved analysis of growth performance and efficiency and 2） the prediction of future or past growth rates. This makes the concept of relative growth ideally suited to growth reconstruction as required in dendrochronology, climate change and forest decline research and for interdisciplinary research projects beyond the realm of plant science.

Modelling the response of larch growth to age,density,and elevation and the implications for multifunctional management in northwest China

Plantations of Rupprecht's larch(Larix principis-rupprechtii)have been widely established in the drylands of northwest and north China under traditional fastgrowing plantation management strategies.These strategies and the long-term logging ban have led to over-populated stands with lower structural and functional stability,less economic benefit and higher water consumption.To guide the sustainable management of larch plantations,field surveys and historical data compilation were undertaken in the Liupan Mountains of northwest China.The main influencing factors(stand structure and site condition)and their effects on mean tree height,mean DBH and timber volumes were determined based on up-boundary line analysis.Tree growth models coupling the effects of tree age,stand density,and elevation were established.Both height and DBH markedly increased initially and then slowly with tree age,decreased with stand density,and showed unimodal change with elevation.The coupled growth models accounted for72-78%of the variations in tree height,DBH and timber growth.Recommendations for future plantation management are:(1)prolong the rotation to at least 60 years to produce large-diameter,high-quality timber and maintain greater carbon stocks;(2)zone the target functions of stands by elevation;and,(3)reduce stand density for balanced supply of multiple ecosystem services.The growth models developed can predict growth response of larch plantations to density alteration under given ages and elevations,and assist the transformation from traditional management for maximum timber production to site-specific and multifunctional management with longer rotations and moderate tree density.

Monitoring the impact of Movement Control Order (MCO) in flattening the cummulative daily cases curve of Covid-19 in Malaysia: A generalized logistic growth modeling approach

Introduction:COVID-19 has affected almost every country in the world,which causing many negative implications in terms of education,economy and mental health.Worryingly,the trend of second or third wave of the pandemic has been noted in multiple regions despite early success of flattening the curve,such as in the case of Malaysia,post Sabah state election in September 2020.Hence,it is imperative to predict ongoing trend of COVID-19 to assist crucial policymaking in curbing the transmission.Method:Generalized logistic growth modelling(GLM)approach was adopted to make prediction of growth of cases according to each state in Malaysia.The data was obtained from official Ministry of Health Malaysia daily report,starting from 26 September 2020 until 1 January 2021.Result:Sabah,Johor,Selangor and Kuala Lumpur are predicted to exceed 10,000 cumulative cases by 2 February 2021.Nationally,the growth factor has been shown to range between 0.25 to a peak of 3.1 throughout the current Movement Control Order(MCO).The growth factor range for Sabah ranged from 1.00 to 1.25,while Selangor,the state which has the highest case,has a mean growth factor ranging from 1.22 to 1.52.The highest growth rates reported were inWP Labuan for the time periods of 22 Nov-5 Dec 2020 with growth rates of 4.77.States with higher population densities were predicted to have higher cases of COVID-19.Conclusion:GLM is helpful to provide governments and policymakers with accurate and helpful forecasts on magnitude of epidemic and peak time.This forecast could assist government in devising short-and long-term plan to tackle the ongoing pandemic.

Growth phenology adjusts to seasonal changes in water availability in coexisting evergreen and deciduous mediterranean oaks

Different leaf(evergreen vs.deciduous habit)and xylem(diffuse-vs.ring-porous wood)traits represent contrasting strategies to face seasonal changes in water availability and temperature.However,how contrasting leaf and xylem habits of coexisting tree species affect stem wood formation and tree-ring development remains poorly understood.Here,we investigated the spatio-temporal patterns of wood formation in two deciduous oaks(Quercus faginea and Quercus petraea)and two evergreen oaks(Quercus ilex and Quercus suber)coexisting in seasonally dry Mediterranean forests along an aridity gradient in Spain.We hypothesized that growth responses to drought and intra-and inter-annual growth patterns would differ between functional groups.We simulated intra-and interannual growth using a modified version of the Vaganov-Shashkin(VS)process-based,growth model.The VS model simulations were used to estimate growth changes under a high emission scenario(RCP 8.5)for the current distribution of the study oak species and to forecast their future performance under warm(4.8℃)conditions in the Iberian Peninsula.Our simulations indicate that climate warming would induce a shortening of the ringgrowth season and a reduction of radial growth in evergreen and deciduous Mediterranean oaks,particularly in dry sites from southern and eastern Iberia currently occupied by Q.ilex and Q.faginea.Evergreen oaks may better recover after dry periods than deciduous oaks by resuming growth after the summer drought.Low soil water availability in spring would be more detrimental to growth of deciduous oaks.Process-based growth models should be refined and validated to better forecast changes in tree growth as a function of climate.

Effects of site productivity on individual tree maximum basal area growth rates of Eucalyptus pilularis in subtropical Australia

Inventory data were available from 96 plots of even-aged,monoculture,tall-open forests of Eucalyptus pilularis Smith,aged 2-63 years,growing in sub-tropical regions along the east coast of Australia.A model was developed relating the maximum possible stem basal area growth rate of individual trees to their stem basal area.For any tree size,this maximum increased as site productivity increased.However,the size at which this maximum occurred decreased as productivity increased.Much research has shown that,at any stand age,trees of a particular stem basal area are taller on more productive sites than on less productive ones.Taller trees incur greater respiratory costs to ensure maintenance of the photo synthetic capacity of their canopies;this reduces their growth rates.It was concluded that trees with larger basal areas will have the maximum possible growth rate on a less productive site,whilst trees with smaller basal areas will have the maximum possible on a more productive site.The model developed may constitute the first stage of a complete individual tree growth model system to predict wood yields from these forests.

The trajectories of physical growth in 4 months postnatal corrected age among preterm infants discharged from neonatal intensive care units and associated factors: A prospective study

Objectives Growth retardation is a risk for premature infants.In addition to demographic and perinatal factors,preterm infants’physical growth may be affected by neonatal intensive care unit(NICU)stress,maternal postpartum depression,and mother-infant interaction.This study aimed to investigate the trajectories of physical growth in 4 months corrected age among preterm infants discharged from the NICU and the impactors on these trajectories.Methods A prospective study was conducted among 318 preterm infants from September 2019 to April 2021 in Shanghai,China.Latent growth modeling was applied to identify the weight,length,and head circumference growth trajectories in 4 months corrected age and explore the effects of demographic and medical characteristics,infant stress during NICU stay,maternal postpartum depression,and mother-infant interaction on each trajectory.Results Unconditional latent growth models showed curve trajectories with increasingly slower growth in weight,length,and head circumference until 4 months of corrected age.Conditional latent growth models showed that a longer length of stay in the NICU and more skin punctures were negatively associated with weight at 40 weeks corrected gestational age(β=−0.43 and−0.19,respectively,P<0.05).The maternal postpartum depression between 40 weeks corrected gestational age and 1 month corrected postnatal age was associated with a lower growth rate of length(β=−0.17,P=0.040),while between 2 and 3 months corrected postnatal age,there were lower growth rates of weight and head circumference(β=−0.15 and−0.19,respectively,P<0.05).The mother-infant interaction scores between 40 weeks corrected gestational age and 1 month corrected postnatal age negatively predicted the growth rate of weight(β=−0.19,P=0.020).Conclusion The physical growth trajectories of preterm infants discharged from the NICU were influenced by infant stress during the NICU stay,maternal postpartum depression and mother-infant interaction.

Toward a sustainable growth path in Arab economies:an extension of classical growth model

Background/Objectives:Many economies are on the trajectory of alternative growth drivers other than conventional capital and labor.Access to credit facilities is a pertinent indicator of economic growth.In line with the United Nations Sustainable Development Goals(UNSDGs-8)agenda,the national goal for sustainable development for most economies and Arab economies is no exception.Therefore,the current study adopts a traditional growth model by exploring the relationship between gross domestic product(GDP)per capita,credit for private sectors,ratio of exports,real GDP,and per labor force participants for selected Arab economies annually from 2001 to 2020.Research design:This study leverages the Fourier Kwiatkowski–Phillips–Schmidt–Shin(KPSS)unit root test and second-generation panel econometrics as estimation techniques,such as Westerlund and Edgerton panel cointegration test,and the use of two estimators,namely the augmented mean group(AMG)and common correlated error mean group(CCEMG),to obtain robust results.Findings:Empirical findings from Westerlund and Edgerton panel cointegration tests validate the long-run equilibrium relationship among the outlined variables.Further empirical results indicate that the share of exports is negatively significant with economic growth in countries such as Kuwait,Lebanon,Tunisia,and Jordan.Additionally,savings and labor force participation have a positive relationship with economic growth in individual countries such as Algeria and Bahrain.As per the panel,there is no significant relationship between labor force participation and economic growth.This indicates that the skilled labor force enhanced economic growth.Conclusions:These findings come with inherent far-reaching policy suggestions for economies and panels.Further details on country-specific policy actions are presented in the concluding section.

Modeling urban land use dynamics using Markov-chain and cellular automata in Gondar City,Northwest Ethiopia

Modeling urban land-use dynamics is critical for urban experts’and infrastructure managers’planning.This study attempts to explore the land-use/land-cover(LULC)dynamics of Gondar using satellite images from 1984 to 2020.Markov-Chain and Cellular Automata(MC-CA)models have been recognized as performing well in predicting urban land-use change.However,only a few models work in Ethiopia in general,and no study in Gondar has applied this approach to study urban land-use patterns.Therefore,Gondar land-use/land cover changes of Gondar were predicted using the MC-CA model in IDRISI.The built-up area in Gondar city covered 1413 ha(3%of the total area)in 1984 and increased to 2380 ha(5%)in 1994;21153 ha(45.5%)in 2004;22622 ha(48.7%)in 2014;and 23427 ha(50.5%)in 2020.The area has been predicted to reach 57.5%in the 2050s,showing a faster increase that will cause a very vast loss of farmland.This will increase urban sprawl challenges as well as overall environmental disequilibrium in the preceding decade.Thus,innovative and careful structures and systems in urban planning are required to secure a sustainable urban future and to make our cities livable and competitive in the paradigm of sustainable cities.

Evolution of Growth Model and Cultivation of Competitive Advantages Under the Ambidextrous Innovation Strategy: In the Case of China’s High-Tech Enterprises

This study focuses on the evolution of growth model and cultivation of competitive advantages under the ambidextrous innovation strategy.After a brief introduction of the connotation of ambidextrous innovation strategy,the evolution of growth model of high-tech enterprises under the conventional strategy and the ambidextrous innovation strategy is analyzed.Furthermore,a discussion is made on how to cultivate enterprises’competitive advantages under the ambidextrous innovation strategy,thereby enabling enterprises to stand out from competitors under this new strategic model and truly achieve the goal of sustainable development.

The effects of data aggregation on long-term projections of forest stands development

Forest management planning often relies on Airborne Laser Scanning(ALS)-based Forest Management Inventories(FMIs)for sustainable and efficient decision-making.Employing the area-based(ABA)approach,these inventories estimate forest characteristics for grid cell areas(pixels),which are then usually summarized at the stand level.Using the ALS-based high-resolution Norwegian Forest Resource Maps(16 m×16 m pixel resolution)alongside with stand-level growth and yield models,this study explores the impact of three levels of pixel aggregation(standlevel,stand-level with species strata,and pixel-level)on projected stand development.The results indicate significant differences in the projected outputs based on the aggregation level.Notably,the most substantial difference in estimated volume occurred between stand-level and pixel-level aggregation,ranging from-301 to+253 m^(3)·ha^(-1)for single stands.The differences were,on average,higher for broadleaves than for spruce and pine dominated stands,and for mixed stands and stands with higher variability than for pure and homogenous stands.In conclusion,this research underscores the critical role of input data resolution in forest planning and management,emphasizing the need for improved data collection practices to ensure sustainable forest management.

Problems with models assessing influences of tree size and inter-tree competitive processes on individual tree growth:a cautionary tale

In forest growing at any one site, the growth rate of an individual tree is determined principally by its size, which reflects its metabolic capacity, and by competition from neighboring trees. Competitive effects of a tree may be proportional to its size;such competition is termed ‘sym-metric’ and generally involves competition below ground for nutrients and water from the soil. Competition may also be ‘asymmetric’, where its effects are disproportionate to the size of the tree;this generally involves competition above ground for sunlight, when larger trees shade smaller, but the reverse cannot occur. This work examines three model systems often seen as exemplars relating individual tree growth rates to tree size and both competitive processes. Data of tree stem basal area growth rates in plots of even- aged, monoculture forest of blackbutt (Eucalyptus pilularis Smith) growing in sub-tropical eastern Australia were used to test these systems. It was found that none could distin-guish between size and competitive effects at any time in any one stand and, thus, allow quantification of the contribution of each to explaining tree growth rates. They were prevented from doing so both by collinearity between the terms used to describe each of the effects and technical problems involved in the use of nonlinear least-squares regression to fit the models to any one data set. It is concluded that quite new approaches need to be devised if the effects on tree growth of tree size and competitive processes are to be quantified and modelled successfully.

Evaluation of unconstrained and constrained mathematical functions to model girth growth of rubber trees (Hevea brasiliensis) using young agemeasurements

No attempt has been made to date to model growth in girth of rubber tree （Hevea brasiliansis）. We evaluated the few widely used growth functions to identify the most parsimonious and biologically reasonable model for describing the girth growth of young rubber trees based on an incomplete set of young age measurements. Monthly data for girth of immature trees （age 2 to 12 yearsi from two locations were sub- jected to modelling. Re-parameterized, unconstrained and constrained growth functions,of Richards （RM）, Gompertz （GM） and the monomo- lecular ＇model ^（MM） were fitted to data. Duration of growth was the firsf constraint introduced. In the stagel We attempted a population aver- age （PA） model to capture the trend in growth. The best PA model was fitted as a subject specific （SS） model. We used appropriate error vari- ance-covariance structure to account for correlation due to repeated measurements over time. Unconstrainecl functions underestimated the asymptotic maximum that did not reflective carrying capacity of the locations. Underestimafions were attributed to the partial set＇ of meas- urements made during the early growth phase of the trees. MM proved superior to RM and GM. In the randomcoefficient models, both Gf and Go appeared to be influenced by tree level effects. Inclusion of diagonal definite positive matrix removed the correlation between random effects. The results were similar at both locations. In the overall assessment MM appeared as the candidate model for studying the girth-age relationships in Hevea trees. Based on the fitted model we conclude that, in Hevea trees, growth rate is maintained at maximum value at to, then decreases until the final state at dG/dt 〉 0, resulting in yield curve with no period of accelerating growth. One physiological explanation is that photosynthetic activity in Hevea trees decreases as girth increases and constructive metabolism is larger than destructive metabolism.

A derivation of the generalized Korf growth equation and its application

Based on the biological hypothesis of tree growth, the generalized Korf growth equation, was derived theoretically. From a standpoint of applications, the equation can be used in two ways associated with the power exponent ofp, and two types of growth equations: the Korf-A (p>1) and the Korf-B (O<p<1) were developed and between them, there is the Gompertz equation (p=1) to separate each other. All of the three types of equations are independent. It was concluded that the Korf-A equation could be used to describe the growth of trees, of which inflection point is between 0 andA/e, while the Korf-B equation with the inflection point betweenA/e andA could be applied to describe the biological population growth. It was found that the Korf-A equation had a better property in describing the growth process of a tree or a stand and its applications to predicting height growth and stand self-thinning showed general good fitness.