Research on the reasoning, teaching and learning of probability and uncertainty

In this editorial, we set out the aims in the call to publish papers on informal statistical inference, randomness, modelling and risk. We discuss how the papers published in this issue have responded to those aims. In particular, we note how the nine papers contribute to some of the major debates in mathematics and statistics education, often taking contrasting positions. Such debates range across: (1) whether knowledge is fractured or takes the form of mental models; (2) heuristic or intuitive thinking versus operational thinking as for example in dual process theory; (3) the role of different epistemic resources, such as perceptions, modelling, imagery, in the development of probabilistic reasoning; (4) how design and situation impact upon probabilistic learning

Polarimetric Multi-View Inverse Rendering

A polarization camera has great potential for 3D reconstruction since the angle of polarization (AoP) of reflected light is related to an object's surface normal. In this paper, we propose a novel 3D reconstruction method called Polarimetric Multi-View Inverse Rendering (Polarimetric MVIR) that effectively exploits geometric, photometric, and polarimetric cues extracted from input multi-view color polarization images. We first estimate camera poses and an initial 3D model by geometric reconstruction with a standard structure-from-motion and multi-view stereo pipeline. We then refine the initial model by optimizing photometric and polarimetric rendering errors using multi-view RGB and AoP images, where we propose a novel polarimetric rendering cost function that enables us to effectively constrain each estimated surface vertex's normal while considering four possible ambiguous azimuth angles revealed from the AoP measurement. Experimental results using both synthetic and real data demonstrate that our Polarimetric MVIR can reconstruct a detailed 3D shape without assuming a specific polarized reflection depending on the material.Comment: Paper accepted in ECCV 202

Mutation increasing β-carotene concentrations does not adversely affect concentrations of essential mineral elements in pepper fruit

<div><p>Vitamin and mineral deficiencies are prevalent in human populations throughout the world. Vitamin A deficiency affects hundreds of millions of pre-school age children in low income countries. Fruits of pepper (<i>Capsicum annuum</i> L.) can be a major dietary source of precursors to Vitamin A biosynthesis, such as β-carotene. Recently, pepper breeding programs have introduced the orange-fruited (<i>of</i>) trait of the mutant variety Oranzheva kapiya, which is associated with high fruit β-carotene concentrations, to the mutant variety Albena. In this manuscript, concentrations of β-carotene and mineral elements (magnesium, phosphorus, sulphur, potassium, zinc, calcium, manganese, iron and copper) were compared in fruit from P31, a red-fruited genotype derived from the variety Albena, and M38, a genotype developed by transferring the orange-fruited mutation (<i>of</i>) into Albena. It was observed that fruit from M38 plants had greater β-carotene concentration at both commercial and botanical maturity (4.9 and 52.7 mg / kg fresh weight, respectively) than fruit from P31 plants (2.3 and 30.1 mg / kg fresh weight, respectively). The mutation producing high β-carotene concentrations in pepper fruits had no detrimental effect on the concentrations of mineral elements required for human nutrition.</p></div

Research on Teaching and Learning Probability

This book summarizes the vast amount of research related to teaching and learning probability that has been conducted for more than 50 years in a variety of disciplines. It begins with a synthesis of the most important probability interpretations throughout history: intuitive, classical, frequentist, subjective, logical propensity and axiomatic views. It discusses their possible applications, philosophical problems, as well as their potential and the level of interest they enjoy at different educational levels. Next, the book describes the main features of probabilistic thinking and reasoning, including the contrast to classical logic, probability language features, the role of intuitions, as well as paradoxes and the relevance of modeling. It presents an analysis of the differences between conditioning and causation, the variability expression in data as a sum of random and causal variations, as well as those of probabilistic versus statistical thinking. This is followed by an analysis of probability’s role and main presence in school curricula and an outline of the central expectations in recent curricular guidelines at the primary, secondary and high school level in several countries. This book classifies and discusses in detail the three different research periods on students’ and people’s intuitions and difficulties concerning probability: early research focused on cognitive development, a period of heuristics and biases programs, and the current period marked by a multitude of foci, approaches and theoretical frameworks

Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Geoeconomic variations in epidemiology, ventilation management, and outcomes in invasively ventilated intensive care unit patients without acute respiratory distress syndrome: a pooled analysis of four observational studies

Background: Geoeconomic variations in epidemiology, the practice of ventilation, and outcome in invasively ventilated intensive care unit (ICU) patients without acute respiratory distress syndrome (ARDS) remain unexplored. In this analysis we aim to address these gaps using individual patient data of four large observational studies. Methods: In this pooled analysis we harmonised individual patient data from the ERICC, LUNG SAFE, PRoVENT, and PRoVENT-iMiC prospective observational studies, which were conducted from June, 2011, to December, 2018, in 534 ICUs in 54 countries. We used the 2016 World Bank classification to define two geoeconomic regions: middle-income countries (MICs) and high-income countries (HICs). ARDS was defined according to the Berlin criteria. Descriptive statistics were used to compare patients in MICs versus HICs. The primary outcome was the use of low tidal volume ventilation (LTVV) for the first 3 days of mechanical ventilation. Secondary outcomes were key ventilation parameters (tidal volume size, positive end-expiratory pressure, fraction of inspired oxygen, peak pressure, plateau pressure, driving pressure, and respiratory rate), patient characteristics, the risk for and actual development of acute respiratory distress syndrome after the first day of ventilation, duration of ventilation, ICU length of stay, and ICU mortality. Findings: Of the 7608 patients included in the original studies, this analysis included 3852 patients without ARDS, of whom 2345 were from MICs and 1507 were from HICs. Patients in MICs were younger, shorter and with a slightly lower body-mass index, more often had diabetes and active cancer, but less often chronic obstructive pulmonary disease and heart failure than patients from HICs. Sequential organ failure assessment scores were similar in MICs and HICs. Use of LTVV in MICs and HICs was comparable (42\ub74% vs 44\ub72%; absolute difference \u20131\ub769 [\u20139\ub758 to 6\ub711] p=0\ub767; data available in 3174 [82%] of 3852 patients). The median applied positive end expiratory pressure was lower in MICs than in HICs (5 [IQR 5\u20138] vs 6 [5\u20138] cm H2O; p=0\ub70011). ICU mortality was higher in MICs than in HICs (30\ub75% vs 19\ub79%; p=0\ub70004; adjusted effect 16\ub741% [95% CI 9\ub752\u201323\ub752]; p&lt;0\ub70001) and was inversely associated with gross domestic product (adjusted odds ratio for a US$10 000 increase per capita 0\ub780 [95% CI 0\ub775\u20130\ub786]; p&lt;0\ub70001). Interpretation: Despite similar disease severity and ventilation management, ICU mortality in patients without ARDS is higher in MICs than in HICs, with a strong association with country-level economic status. Funding: No funding

A 1-Year Prospective French Nationwide Study of Emergency Hospital Admissions in Children and Adults with Primary Immunodeficiency.

PURPOSE: Patients with primary immunodeficiency (PID) are at risk of serious complications. However, data on the incidence and causes of emergency hospital admissions are scarce. The primary objective of the present study was to describe emergency hospital admissions among patients with PID, with a view to identifying "at-risk" patient profiles. METHODS: We performed a prospective observational 12-month multicenter study in France via the CEREDIH network of regional PID reference centers from November 2010 to October 2011. All patients with PIDs requiring emergency hospital admission were included. RESULTS: A total of 200 admissions concerned 137 patients (73 adults and 64 children, 53% of whom had antibody deficiencies). Thirty admissions were reported for 16 hematopoietic stem cell transplantation recipients. When considering the 170 admissions of non-transplant patients, 149 (85%) were related to acute infections (respiratory tract infections and gastrointestinal tract infections in 72 (36%) and 34 (17%) of cases, respectively). Seventy-seven percent of the admissions occurred during winter or spring (December to May). The in-hospital mortality rate was 8.8% (12 patients); death was related to a severe infection in 11 cases (8%) and Epstein-Barr virus-induced lymphoma in 1 case. Patients with a central venous catheter (n = 19, 13.9%) were significantly more hospitalized for an infection (94.7%) than for a non-infectious reason (5.3%) (p = 0.04). CONCLUSION: Our data showed that the annual incidence of emergency hospital admission among patients with PID is 3.4%. The leading cause of emergency hospital admission was an acute infection, and having a central venous catheter was associated with a significantly greater risk of admission for an infectious episode

INFOGEST static in vitro simulation of gastrointestinal food digestion

peer-reviewedSupplementary information is available at http://dx.doi.org/10.1038/s41596-018-0119-1 or https://www.nature.com/articles/s41596-018-0119-1#Sec45.Developing a mechanistic understanding of the impact of food structure and composition on human health has increasingly involved simulating digestion in the upper gastrointestinal tract. These simulations have used a wide range of different conditions that often have very little physiological relevance, and this impedes the meaningful comparison of results. The standardized protocol presented here is based on an international consensus developed by the COST INFOGEST network. The method is designed to be used with standard laboratory equipment and requires limited experience to encourage a wide range of researchers to adopt it. It is a static digestion method that uses constant ratios of meal to digestive fluids and a constant pH for each step of digestion. This makes the method simple to use but not suitable for simulating digestion kinetics. Using this method, food samples are subjected to sequential oral, gastric and intestinal digestion while parameters such as electrolytes, enzymes, bile, dilution, pH and time of digestion are based on available physiological data. This amended and improved digestion method (INFOGEST 2.0) avoids challenges associated with the original method, such as the inclusion of the oral phase and the use of gastric lipase. The method can be used to assess the endpoints resulting from digestion of foods by analyzing the digestion products (e.g., peptides/amino acids, fatty acids, simple sugars) and evaluating the release of micronutrients from the food matrix. The whole protocol can be completed in ~7 d, including ~5 d required for the determination of enzyme activities.COST action FA1005 INFOGEST (http://www.cost-infogest.eu/ ) is acknowledged for providing funding for travel, meetings and conferences (2011-2015). The French National Institute for Agricultural Research (INRA, www.inra.fr) is acknowledged for their continuous support of the INFOGEST network by organising and co-funding the International Conference on Food Digestion and workgroup meeting