What do women undergoing in vitro fertilization (IVF) understand about their chance of IVF success?

STUDY QUESTION: How well informed are Australian women who undergo IVF about their chances of having a baby? SUMMARY ANSWER: Only one in four women estimated their individual chance of success with IVF accurately, with most women overestimating their chance. WHAT IS KNOWN ALREADY: Limited knowledge about infertility and infertility treatment in the general population is well-documented. The few studies that have investigated patients' knowledge about the chance of IVF success suggest that while IVF patients are aware of average success rates, they tend to be unrealistic about their own chance of success. STUDY DESIGN, SIZE, DURATION: We conducted an anonymous online survey of 217 women who had started IVF since 2018 in Australia. The survey was advertised on social media, enabling women from across Australia to participate. Responses were collected in June 2021. PARTICIPANTS/MATERIALS, SETTING, METHODS: The survey included questions on demographic characteristics and IVF history. It asked what participants thought their chance of having a baby from one IVF treatment cycle was, how they rated their knowledge about chance of success, and about their experience of receiving IVF-related information. Participants' estimations of their chance of success were compared with their chance as calculated by the Society for Assisted Reproductive Technology's (SART) online calculator. Responses to a free-text question about what information women wished they had been given when they started treatment were analysed thematically. MAIN RESULTS AND THE ROLE OF CHANCE: Only about a quarter (58/217, 27%) of participants accurately estimated their chance of having a baby within 20% relative to their SART calculated chance, with more than half (118/217, 54%) overestimating their chance. Ninety percent of women indicated that their preferred source of treatment information was a consultation with their doctor, despite less than half (44%) reporting that doctors explained the probability of having a baby with IVF well (mean 5.9/10). In free-text responses, many women also reported that they wished they had been given more realistic information about IVF and their chance of success. LIMITATIONS, REASONS FOR CAUTION: The dissemination method precludes calculation of response rate, and it is not possible to know if participants are representative of all women undergoing IVF. Additionally, we only surveyed women undergoing IVF, while those who decided not to have IVF were not included. Therefore, women who overestimated their chance may have been overrepresented. There is also inherent imprecision in the way understanding of chance of success was estimated. The potential impact of recall bias could neither be quantified nor excluded. It is difficult to determine to what extent women's lack of understanding of what is possible with IVF is due to poor information-provision by clinicians and the clinic, and how much can be explained by optimism bias. WIDER IMPLICATIONS OF THE FINDINGS: The finding of poor understanding of personal chance of success amongst women undergoing IVF in Australia requires further investigation to determine potential reasons for this. The findings can be used by clinics to develop strategies for improvement in the information-provision process to ensure that women can make informed decisions about their fertility treatment. STUDY FUNDING/COMPETING INTEREST(S): This study received no external funding. S.L. is supported by a NHMRC Investigator Grant (APP1195189). R.W. is supported by a NHMRC Investigator Grant (APP2009767). B.W.M. is supported by a NHMRC Investigator Grant (GNT1176437). B.W.M. reports consultancy for Merck and ObsEva and has received research funding and travel funding from Merck. The other authors have no conflicts of interest. TRIAL REGISTRATION NUMBER: N/A.

The need for the GREAT+ score to predict relapse in Graves' disease: a questionnaire among patients and internal medicine specialists.

PURPOSE: Graves' disease (GD) is an auto-immune cause of hyperthyroidism. First-line treatment often consists of a 12-18 month course of antithyroid drugs (ATD). After discontinuation of ATD, GD relapses in approximately 50% of patients. The 'Graves recurrent event after therapy+ ' (GREAT+) score may predict individual relapse chances after ATD discontinuation more accurately based on clinical and laboratory parameters at diagnosis. We investigated the need for the GREAT+ score through an online questionnaire among GD patients and physicians treating GD. METHODS: An anonymous online questionnaire was distributed to patients and physicians between June 2022 and August 2023. RESULTS: The questionnaire was completed by 532 patients and 44 physicians. Results showed that 94% of patients were interested in knowing their GREAT+ score at the start of treatment. 55% would consider definite treatment (radioiodine/thyroidectomy) as first-line treatment in case of a high relapse chance. 98% of the physicians indicated the GREAT + score would support patient counseling. 84% may change their advice for first-line treatment if a patient has a high relapse chance based on the score. CONCLUSION: Patients and physicians considered the GREAT+ score as a valuable addition to the current available information which could change treatment decisions. Therefore, external validation of the GREAT+ score is justified to implement this score in clinical practice.

An integrated simulation-optimization approach for combined allocation of water quantity and quality under multiple uncertainties.

Multiple uncertainties such as water quality processes, streamflow randomness affected by climate change, indicators' interrelation, and socio-economic development have brought significant risks in managing water quantity and quality (WQQ) for river basins. This research developed an integrated simulation-optimization modeling approach (ISMA) to tackle multiple uncertainties simultaneously. This approach combined water quality analysis simulation programming, Markov-Chain, generalized likelihood uncertainty estimation, and interval two-stage left-hand-side chance-constrained joint-probabilistic programming into an integration nonlinear modeling framework. A case study of multiple water intake projects in the Downstream and Delta of Dongjiang River Basin was used to demonstrate the proposed model. Results reveal that ISMA helps predict the trend of water quality changes and quantitatively analyze the interaction between WQQ. As the joint probability level increases, under strict water quality scenario system benefits would increase [3.23, 5.90] × 109 Yuan, comprehensive water scarcity based on quantity and quality would decrease [782.24, 945.82] × 106 m3, with an increase in water allocation and a decrease in pollutant generation. Compared to the deterministic and water quantity model, it allocates water efficiently and quantifies more economic losses and water scarcity. Therefore, this research has significant implications for improving water quality in basins, balancing the benefits and risks of water quality violations, and stabilizing socio-economic development.

Risks and pregnancy outcome after fetal reduction in dichorionic twin pregnancies: a Danish national retrospective cohort study.

BACKGROUND: Twin pregnancies carry a higher risk of congenital and structural malformations, and pregnancy complications including miscarriage, stillbirth, and intrauterine fetal death, compared with singleton pregnancies. Carrying a fetus with severe malformations or abnormal karyotype places the remaining healthy fetus at an even higher risk of adverse outcome and pregnancy complications. Maternal medical conditions or complicated obstetrical history could, in combination with twin pregnancy, cause increased risks for both the woman and the fetuses. To our knowledge, no previous studies have evaluated and compared the outcomes of all dichorionic twin pregnancies and compared the results of reduced twins with those of nonreduced and primary singletons in a national cohort. These data are important for clinicians when counseling couples about fetal reduction and its implications. OBJECTIVE: This study aimed to describe and compare the risks of adverse pregnancy outcomes, including the risk of pregnancy loss, in a national cohort of all dichorionic twins-reduced, nonreduced, and primary singletons. In addition, we examined the implications of gestational age at fetal reduction on gestational age at delivery. STUDY DESIGN: This was a retrospective cohort study of all Danish dichorionic twin pregnancies, including pregnancies undergoing fetal reduction and a large proportion of randomly selected primary singleton pregnancies with due dates between January 2008 and December 2018. The primary outcome measures were adverse pregnancy outcomes (defined as miscarriage before 24 weeks, stillbirth from 24 weeks, or single intrauterine fetal death in nonreduced twin pregnancies), preterm delivery, and obstetrical pregnancy complications. Outcomes after fetal reduction were compared with those of nonreduced dichorionic twins and primary singletons. RESULTS: In total, 9735 dichorionic twin pregnancies were included, of which 172 (1.8%) were reduced. In addition, 16,465 primary singletons were included. Fetal reductions were performed between 11 and 23 weeks by transabdominal needle-guided injection of potassium chloride, and outcome data were complete for all cases. Adverse pregnancy outcome was observed in 4.1% (95% confidence interval, 1.7%-8.2%) of reduced twin pregnancies, and 2.4% (95% confidence interval, 0.7%-6.1%) were delivered before 28 weeks, and 4.2% (95% confidence interval, 1.7%-8.5%) before 32 weeks. However, when fetal reduction was performed before 14 weeks, adverse pregnancy outcomes occurred in only 1.4% (95% confidence interval, 0.0%-7.4%), and delivery before 28 and 32 weeks diminished to 0% (95% confidence interval, 0.0%-5.0%) and 2.8% (95% confidence interval, 0.3%-9.7%), respectively. In contrast, 3.0% (95% confidence interval, 2.7%-3.4%) of nonreduced dichorionic twins had an adverse pregnancy outcome, and 1.9% (95% confidence interval, 1.7%-2.1%) were delivered before 28 weeks, and 7.3% (95% confidence interval, 6.9%-7.7%) before 32 weeks. Adverse pregnancy outcomes occurred in 0.9% (95% confidence interval, 0.7%-1.0%) of primary singletons, and 0.2% (95% confidence interval, 0.1%-0.3%) were delivered before 28 weeks, and 0.7% (95% confidence interval, 0.6%-0.9%) before 32 weeks. For reduced twins, after taking account of maternal factors and medical history, it was demonstrated that the later the fetal reduction was performed, the earlier the delivery occurred (P<.01). The overall risk of pregnancy complications was significantly lower among reduced twin pregnancies than among nonreduced dichorionic twin pregnancies (P=.02). CONCLUSION: In a national 11-year cohort including all dichorionic twin pregnancies, transabdominal fetal reduction by needle guide for fetal or maternal indication was shown to be safe, with good outcomes for the remaining co-twin. Results were best when the procedure was performed before 14 weeks.

Triple trouble: uncovering the risks and benefits of early fetal reduction in trichorionic triplets in a large national Danish cohort study.

BACKGROUND: Triplet pregnancies are high risk for both the mother and the infants. The risks for infants include premature birth, low birthweight, and neonatal complications. Therefore, the management of triplet pregnancies involves close monitoring and may include interventions, such as fetal reduction, to prolong the pregnancy and improve outcomes. However, the evidence of benefits and risks associated with fetal reduction is inconsistent. OBJECTIVE: This study aimed to compare the outcomes of trichorionic triplet pregnancies with and without fetal reduction and with nonreduced dichorionic twin pregnancies and primary singleton pregnancies. STUDY DESIGN: All trichorionic triplet pregnancies in Denmark, including those with fetal reduction, were identified between 2008 and 2018. In Denmark, all couples expecting triplets are informed about and offered fetal reduction. Pregnancies with viable fetuses at the first-trimester ultrasound scan and pregnancies not terminated were included. Adverse pregnancy outcome was defined as a composite of miscarriage before 24 weeks of gestation, stillbirth at 24 weeks of gestation, or intrauterine fetal death of 1 or 2 fetuses. RESULTS: The study cohort was composed of 317 trichorionic triplet pregnancies, of which 70.0% of pregnancies underwent fetal reduction to a twin pregnancy, 2.2% of pregnancies were reduced to singleton pregnancies, and 27.8% of pregnancies were not reduced. Nonreduced triplet pregnancies had high risks of adverse pregnancy outcomes (28.4%), which was significantly lower in triplets reduced to twins (9.0%; difference, 19.4%, 95% confidence interval, 8.5%-30.3%). Severe preterm deliveries were significantly higher in nonreduced triplet pregnancies (27.9%) than triplet pregnancies reduced to twin pregnancies (13.1%; difference, 14.9%, 95% confidence interval, 7.9%-21.9%). However, triplet pregnancies reduced to twin pregnancies had an insignificantly higher risk of miscarriage (6.8%) than nonreduced twin pregnancies (1.1%; difference, 5.6%; 95% confidence interval, 0.9%-10.4%). CONCLUSION: Triplet pregnancies reduced to twin pregnancies had significantly lower risks of adverse pregnancy outcomes, severe preterm deliveries, and low birthweight than nonreduced triplet pregnancies. However, triplet pregnancies reduced to twin pregnancies were potentially associated with a 5.6% increased risk of miscarriage.

Screw fixation without fusion for low lumbar chance fracture accompanied by spinal epidural hematoma in patient with ankylosing spondylitis.

Ankylosing spondylitis (AS) is a chronic inflammatory disease involving the sacroiliac joint and axial spine. AS may render the ankylosed spine prone to trauma and cause an increased frequency of associated epidural hematomas in spine fractures. Herein, we report a rare case of L5 chance fracture and epidural hematoma in a 27-year-old female patient with AS. She was treated surgically but without bone fusion or decompressive laminectomy due to the neurologically intact status despite significant neural compression by the spinal epidural hematoma (SEH). We believe that conservative treatment with close observation of neurological status may be effective in SEH presenting with mild neurological symptoms despite significant neural compression.

How to Distinguish Correlation From Causation in Orthopaedic Research.

Correlations in observational studies are commonly misinterpreted as causation. Although correlation is necessary to establish a causal relationship between two variables, correlations may also arise due to chance, reverse causality, or confounding. There are several methods available to orthopaedic researchers to determine whether the observed correlations are causal. These methods depend on the key components of the study including, but not limited to, study design and data availability on confounders. In this article, we illustrate the main concepts surrounding correlation and causation using intuitive real-world examples from the orthopaedic literature. Please visit the following https://www.youtube.com/watch?v=WW7pFudZbHA&t=52s for a video that explains the highlights of the paper in practical terms.

A novel asymmetric horizontal splitting fracture of the lumbar spine: pediatric case report of a lateral bending, flexion and distraction fracture.

BACKGROUND: There are many lateral bending fracture cases presented in the literature that mostly involve facet dislocations or corpus collapse. In this report, we aim to describe a novel asymmetric lateral bending, flexion and distraction fracture, propose a mechanism, and delineate its clinical importance. CASE DESCRIPTION: A 13-year-old girl arrived at our trauma center 12 hours after a head-on truck collision. She had paraplegia, and her imaging revealed a spinal cord avulsion at the T10 level and a horizontal fracture at the L4 spinous process, left lamina, left pedicle, and left posterior-upper corner of the corpus, extending through the right lamina. Her posterior ligamentous complex, right facet joint, pedicle, and right side of the corpus were spared from the injury. The patient stated that she had been sitting on the right side of the back seat, turned toward her cousin in the middle. Her left leg was externally rotated and flexed on the seat while her right foot was on the floor at the time of the accident. The patient was managed conservatively with an orthosis. At follow-up, the patient was free of back pain and no lumbar kyphosis developed. CONCLUSION: The flexion-distraction injuries mostly require surgical stabilization according to TLICS classification, because of the instability. In this particular case, TLICS classification was not adequate for a treatment decision, and the conservative treatment came out to be a more than sufficient treatment option.

Number 19: Another Victim of the COVID-19 Pandemic?

Conscious selection is the mental process by which lottery players select numbers nonrandomly. In this paper, we show that the number 19, which has been heard, read, seen, and googled countless times since March 2020, has become significantly less popular among Belgian lottery players after the World Health Organization named the disease caused by the coronavirus SARS-CoV-2 "COVID-19". We argue that the reduced popularity of the number 19 is due to its negative association with the COVID-19 pandemic. Our study triangulates evidence from field data from the Belgian National Lottery and survey data from a nationally representative sample of 500 Belgian individuals. The field data indicate that the number 19 has been played significantly less frequently since March 2020. However, a potential limitation of the field data is that an unknown proportion of players selects numbers randomly through the "Quick Pick" computer system. The survey data do not suffer from this limitation and reinforce our previous findings by showing that priming an increase in the salience of COVID-19 prior to the players' selection of lottery numbers reduces their preference for the number 19. The effect of priming is concentrated amongst those with high superstitious beliefs, further supporting our explanation for the reduced popularity of the number 19 during the COVID-19 pandemic.

Normalization of Chance-Based Mechanisms in Mobile Games for Children: A Descriptive Analysis.

Games for mobiles present strategies to monetize not only from selling a title but from financial exchanges that take place in the game. Those microtransactions motivate players to purchase random or surprise items (known as loot boxes) to customize game features or to overcome narrative obstacles necessary to progress to new levels. Researchers associate the practice with gambling if completing the transaction does not mean the acquisition of an item but the chance to receive it. This research quantified gambling-like features in games available for free, classified by Apple's marketplace as suitable for children from 4 to 8 years old, and from the top-downloaded list. The findings reveal normalization traces of chance-based mechanisms in most of the games. According to the research literature, early exposure to such features may result in problem gambling in adult life. This paper concluded that legal changes and more information provided by the marketplaces are needed to raise awareness of gambling-like practices in mobile games.

Cautious Bayesian Optimization: A Line Tracker Case Study.

In this paper, a procedure for experimental optimization under safety constraints, to be denoted as constraint-aware Bayesian Optimization, is presented. The basic ingredients are a performance objective function and a constraint function; both of them will be modeled as Gaussian processes. We incorporate a prior model (transfer learning) used for the mean of the Gaussian processes, a semi-parametric Kernel, and acquisition function optimization under chance-constrained requirements. In this way, experimental fine-tuning of a performance objective under experiment-model mismatch can be safely carried out. The methodology is illustrated in a case study on a line-follower application in a CoppeliaSim environment.

From "below chance" to "a single error is one too many": Evaluating various thresholds for invalid performance on two forced choice recognition tests.

This study was designed to empirically evaluate the classification accuracy of various definitions of invalid performance in two forced-choice recognition performance validity tests (PVTs; FCRCVLT-II and Test of Memory Malingering [TOMM-2]). The proportion of at and below chance level responding defined by the binomial theory and making any errors was computed across two mixed clinical samples from the United States and Canada (N = 470) and two sets of criterion PVTs. There was virtually no overlap between the binomial and empirical distributions. Over 95% of patients who passed all PVTs obtained a perfect score. At chance level responding was limited to patients who failed ≥2 PVTs (91% of them failed 3 PVTs). No one scored below chance level on FCRCVLT-II or TOMM-2. All 40 patients with dementia scored above chance. Although at or below chance level performance provides very strong evidence of non-credible responding, scores above chance level have no negative predictive value. Even at chance level scores on PVTs provide compelling evidence for non-credible presentation. A single error on the FCRCVLT-II or TOMM-2 is highly specific (0.95) to psychometrically defined invalid performance. Defining non-credible responding as below chance level scores is an unnecessarily restrictive threshold that gives most examinees with invalid profiles a Pass.

Joint Aperture and Power Allocation Strategy for a Radar Network Localization System Based on Low Probability of Interception Optimization.

In the process of using the Distributed Radar Network Localization System (DRNLS) further to improve the survivability of a carrier platform, the random characteristics of the system's Aperture Resource Allocation (ARA) and Radar Cross Section (RCS) are often not fully considered. However, the random characteristics of the system's ARA and RCS will affect the power resource allocation of the DRNLS to a certain extent, and the allocation result is an essential factor determining the performance of the DRNLS's Low Probability of Intercept (LPI). Therefore, a DRNLS still has some limitations in practical application. In order to solve this problem, a joint allocation scheme of aperture and power for the DRNLS based on LPI optimization (JA scheme) is proposed. In the JA scheme, the fuzzy random Chance Constrained Programmin model for radar antenna aperture resource management (RAARM-FRCCP model) can minimize the number of elements under the given pattern parameters. The random Chance Constrained Programmin model for minimizing Schleher Intercept Factor (MSIF-RCCP model) built on this basis can be used to achieve DRNLS optimal control of LPI performance on the premise of ensuring system tracking performance requirements. The results show that when RCS has some randomness, its corresponding uniform power distribution result is not necessarily the optimal scheme. Under the condition of meeting the same tracking performance, the required number of elements and power will be reduced to a certain extent compared with the number of elements in the whole array and the power corresponding to the uniform distribution. The lower the confidence level is, the more times the threshold is allowed to pass, and the lower the power is, so that the DRNLS can have better LPI performance.

An integrated chance constraints approach for optimal vaccination strategies under uncertainty for COVID-19.

Despite concerted efforts by health authorities worldwide to contain COVID-19, the SARS-CoV-2 virus has continued to spread and mutate into new variants with uncertain transmission characteristics. Therefore, there is a need for new data-driven models for determining optimal vaccination strategies that adapt to the new variants with their uncertain transmission characteristics. Motivated by this challenge, we derive an integrated chance constraints stochastic programming (ICC-SP) approach for finding vaccination strategies for epidemics that incorporates population demographics for any region of the world, uncertain disease transmission and vaccine efficacy. An optimal vaccination strategy specifies the proportion of individuals in a given household-type to vaccinate to bring the reproduction number to below one. The ICC-SP approach provides a quantitative method that allows to bound the expected excess of the reproduction number above one by an acceptable amount according to the decision-maker's level of risk. This new methodology involves a multi-community household based epidemiology model that uses census demographics data, vaccination status, age-related heterogeneity in disease susceptibility and infectivity, virus variants, and vaccine efficacy. The new methodology was tested on real data for seven neighboring counties in the United States state of Texas. The results are promising and show, among other findings, that vaccination strategies for controlling an outbreak should prioritize vaccinating certain household sizes as well as age groups with relatively high combined susceptibility and infectivity.

A controversy about chance and the origins of life: thermodynamicist Ilya Prigogine replies to molecular biologist Jacques Monod.

The ancient, interlinked questions about the role of chance in the living world and the origins of life, gained new relevance with the development of molecular biology in the twentieth century. In 1970, French molecular biologist Jacques Monod, joint winner of the 1965 Nobel Prize in Physiology or Medicine, devoted a popular book on modern biology and its philosophical implications to these questions, which was quickly translated into English as Chance and Necessity. Nine years later, Belgian thermodynamicist Ilya Prigogine, 1977 winner of the Nobel Prize in Chemistry, published a popular book on the history and philosophy of natural sciences with Belgian philosopher Isabelle Stengers. Translated into English under the title Order out of Chaos and widely discussed, the whole book can be seen as a response to Monod on these biological and philosophical questions. This study will trace this intellectual controversy between two Nobel Prize winners defending two opposing scientific and philosophical visions of the living world, rooted in two different scientific disciplines.

Altered neural responses to missed chance contribute to the risk-taking behaviour in individuals with Internet gaming disorder.

Missed chance is a powerful factor in shaping risk-taking behaviour. The abnormal risk-taking behaviour is an obvious feature of individuals with Internet gaming disorder (IGD). However, the relationship between the neural responses to missed chance and risk-taking behaviour in IGD individuals remains unclear. In the current fMRI study, 28 IGD subjects (12 female, 23.04 ± 2.43 years old) and 26 healthy control (HC) subjects (13 female, 23.58 ± 2.67 years old) participated in fMRI scanning during performance of a sequential risk-taking task. The general linear model and the psycho-physiological interaction analyses were conducted to explore the difference in neural responses between the two groups. The results showed that IGD subjects reported more regret for the large missed chance and took more risk than HC subjects. Moreover, compared with HC subjects, IGD subjects exhibited greater activations in brain regions like ventral striatum (VS) and superior frontal gyrus (SFG), and stronger VS-thalamus functional connectivity for the large missed chance. Additionally, among IGD subjects, the SFG activation for the large missed chance was positively correlated with the risk-taking behaviour. Together, the results revealed the altered neural responses to missed chance contributed to the risk-taking behaviour in IGD individuals. The findings could help to clearly understand why IGD individuals continue playing online games despite the risks of widely known and could provide a new perspective for the intervention of IGD.

Dynamic routing for waste collection and transportation with multi-compartment electric vehicle using smart waste bins.

The municipal solid waste (MSW) collection and transportation issue has been studied by numerous researchers; however, a few studies consider the chance-constrained programming for co-collection of sorted waste with electric vehicles (EVs). Therefore, this article attempts to study on the chance-constrained collection and transportation problem for sorted waste with multiple separated compartments EVs. Considering the uncertainty of the waste generation rate under the scenario of application of smart waste bins, chance-constrained programming is applied to transform the uncertain model into a certain one. A Chance-Constrained Multi-Compartment Electric Vehicle Routing Problem (CCMCEVRP) is introduced and the corresponding mathematical formulation is established. A diversity-enhanced particle swarm optimisation with neighbourhood search and simulated annealing (DNSPSOSA) is proposed to solve this problem, and effectiveness of the proposed algorithms is verified by extensive numerical experiments on the newly generated instances. In addition, the application of the model is tested by comparing different compartment and different type vehicles. It is found that, compared with fuel vehicles, 32.66% of the average cost could be saved with EVs. Furthermore, the rate of cost-saving of EVs increases with the increase in the number of compartments: the improvement rate of cost-saving of two-compartment EVs and three-compartment EVs is 52.77% and 68.13%, respectively.

Competition with abundance-dependent fitness and the dynamics of heterogeneous populations in fluctuating environment.

Species competition takes place in a fluctuating environment, so the selective forces on different populations vary through time. In many realistic situations the mean fitness and the amplitude of its temporal variations are abundance-dependent. Here we present a theory of two-species competition with abundance-dependent stochastic fitness variations and solve for the chance of ultimate fixation, the time to absorption and the time to fixation. We then examine the ability of this two-species system to serve as an effective model for high-diversity assemblages and to account for the presence of an intra-specific differential response to environmental variations. The effective model is shown to capture the main features of competition between composite populations.

Simulation-based interval chance-constrained quadratic programming model for water quality management: A case study of the central Grand River in Ontario, Canada.

Effective river water quality management and planning is a complex issue challenged by various complexities and uncertainties. A simulation-based interval chance-constrained quadratic programming (ICCQP) model is developed for the seasonal planning of water quality management (WQM) under various uncertainties. The proposed model incorporates interval quadratic programming, chance-constrained programming, and a seasonal water quality simulation model within a general framework for WQM. Uncertainties associated with the objective and the coefficients in the left-hand sides of the constraints are tackled as intervals. Meanwhile, parameter uncertainties on the right-hand sides are characterized using probability distributions. Nonlinearities in the cost function are reflected by quadratic programming. A multi-segment water quality model is used to simulate the dynamic interactions between wastewater discharges and river water quality. The proposed ICCQP-WQM model is applied in a real case study for the control of total phosphorus (TP) in the central Grand River in Ontario, Canada. The results demonstrate that the proposed model is able to incorporate uncertainties expressed as intervals and probability information into an optimization framework and provide interval solutions. Thus, different cost-effective schemes for seasonal WQM could be generated. The results show the Kitchener wastewater treatment plant (WWTP) affects the value of the objective function more than the other WWTPs in the study area. It is also found that the Kitchener WWTP's cost accounts for the highest proportion (approximately 35.1-37.9%) of the total annual cost, which implies the control of TP at the Kitchener plant is the most important to the system. Moreover, river water TP standards in spring and autumn are usually difficult to meet, indicating different TP control strategies are needed in these two seasons. The generated results are valuable for local decision makers to generate TP control strategies, and also to identify optimized solutions under various uncertainties. The proposed ICCQP-WQM model can be extended to other watersheds to support effective water quality management and planning.

Inexact left-hand side two-stage chance-constrained programming for booster optimization in water distribution system.

In water distribution system (WDS), chlorine is often injected as disinfectant to control the growth of microorganism in WDS. However, the chlorine reacts with organism to form disinfectant byproduct, which can bring risk to human health. As such, the chlorine at nodes in WDS should be kept between acceptable range, which is simulated based on the response at nodes corresponding to unit injection mass at boosters. To deal with the uncertainty in chlorine decay process and lower and upper chlorine concentration limits, an inexact left-hand-side chance-constrained programming (ILCCP) model was proposed in this paper and applied to two WDSs. The response coefficients matrix was expressed as random variables with normal probability distribution in the constraints of lower and upper limits, which was obtained through Monte Carlo simulation by linking with EPANET software. The intervals of injection mass were obtained by solving the ILCCP model with a two-step algorithm. Moreover, the effects of random bulk decay coefficients and interval of chlorine limits on the injection mass were analyzed and compared. The results indicated that the lower bounds of optimal injection mass increased with the rise of probability lever for lower limits, while the upper bounds decreased with the rise of the probability level for upper limits. The results can help managers determine the chlorine injection mass under uncertain scenarios, and can be applied to more complicated WDS to obtain meaningful results.