Dr. Doodle: A diagrammatic theorem prover

This paper presents the Dr.Doodle system, an interactive theorem prover that uses diagrammatic representations. The assumption underlying this project is that, for some domains (principally geometry) , diagrammatic reasoning is easier to understand than conventional algebraic approaches -- at least for a significant number of people. The Dr.Doodle system was developed for the domain of metric-space analysis (a geometric domain, but traditionally taught using a dry algebraic formalism). Pilot experiments were conducted to evaluate its potential as the basis of an educational tool, with encouraging results

The importance of being zero

2018 International Symposium on Symbolic and Algebraic Computation (ISSAC), July 2018, New York, NY, United StatesWe present a deterministic algorithm for deciding if a polynomial ideal, with coefficients in an algebraically closed field K of characteristic zero, of which we know just some very limited data, namely:the number n of variables, and some upper bound for the geometric degree of its zero set in Kn, is or not the zero ideal. The algorithm performs just a finite number of decisions to check whether a point is or not in the zero set of the ideal. Moreover, we extend this technique to test, in the same fashion, if the elimination of some variables in the given ideal yields or not the zero ideal. Finally, the role of this technique in the context of automated theorem proving of elementary geometry statements, is presented, with references to recent documents describing the excellent performance of the already existing prototype version, implemented in GeoGebra.Ministerio de Economía y CompetitividadEuropean Regional Development Fun

Supporting the organisation of a workshop on thyroid disruption – final report

Written by Brunel University London, Institute of Environment, Health and Societies National Food Institute, Technical University of Denmark, September– 2017. Framework Contract ENV.A.3/FRA/2014/0029 on implementation of the Community strategy on Endocrine Disrupters. This document has been prepared for the European Commission however it reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.This report describes the outcomes of a project that culminated in a workshop on thyroid disruption, held on 29th – 31st March 2017 in Maison-Alfort near Paris, France, on the premises of ANSES. The workshop objectives were: To address and discuss interpretations of experimental laboratory studies, wildlife field data as well as human epidemiological data in relation to the identification of thyroid disrupting substances; and to identify ways forward in addressing potential gaps in the test methods in relation to identification of thyroid disrupting substances.European Commission ENV.A.3/FRA/2014/002

Intrauterine exposure to mild analgesics during pregnancy and the occurrence of cryptorchidism and hypospadia in the offspring: The Generation R Study

This article is available open access through the publisher’s website. Copyright @ 2012 The Authors.BACKGROUND - Recently, over-the-counter mild analgesic use during pregnancy has been suggested to influence the risk of reproductive disorders in the offspring. We examined the influence of maternal exposure to mild analgesics during pregnancy on the occurrence of cryptorchidism and hypospadia in their offspring. METHODS - Associations between maternal exposure to mild analgesics during pregnancy and cryptorchidism or hypospadia in the offspring were studied in 3184 women participating in a large population-based prospective birth cohort study from early pregnancy onwards in the Netherlands (2002–2006), the Generation R Study. Cryptorchidism and hypospadia were identified during routine screening assessments performed in child health care centres by trained physicians. The use of mild analgesics was assessed in three prenatal questionnaires in pregnancy, resulting in four periods of use, namely, periconception period, first 14 weeks of gestation, 14–22 weeks of gestation and 20–32 weeks of gestation. Logistic regression analyses were used to study the associations between maternal exposure to mild analgesics and cryptorchidism and hypospadia. RESULTS - The cumulative prevalence over 30 months of follow up was 2.1% for cryptorchidism and 0.7% for hypospadia. Use of mild analgesics in the second period of pregnancy (14–22 weeks) increased the risk of congenital cryptorchidism [adjusted odds ratio (OR) 2.12; 95% confidence interval (CI) 1.17–3.83], primarily due to the use of acetaminophen (paracetamol) (adjusted OR 1.89; 95% CI 1.01–3.51). Among mothers of cryptorchid sons, 33.8% reported (23 of 68) the use of mild analgesics during pregnancy, compared with 31.8% (7 of 22) of mothers with a boy with hypospadia and 29.9% (926 of 3094) of mothers with healthy boys. CONCLUSIONS - Our results suggest that intrauterine exposure to mild analgesics, primarily paracetamol, during the period in pregnancy when male sexual differentiation takes place, increases the risk of cryptorchidism.Erasmus University Rotterdam, School of Law and Faculty of Social Sciences, the Municipal Health Service Rotterdam area, Rotterdam, the Rotterdam Homecare Foundation, Rotterdam and the Stichting Trombosedienst & Artsenlaboratorium Rijnmond (STAR), Rotterdam

A case study of neurodevelopmental risks from combined exposures to lead, methyl-mercury, inorganic arsenic, polychlorinated biphenyls, polybrominated diphenyl ethers and fluoride

We performed a mixture risk assessment (MRA) case study of dietary exposure to the food contaminants lead, methylmercury, inorganic arsenic (iAs), fluoride, non-dioxin-like polychlorinated biphenyls (NDL-PCBs) and polybrominated diphenyl ethers (PBDEs), all substances associated with declines in cognitive abilities measured as IQ loss. Most of these chemicals are frequently measured in human biomonitoring studies. A component-based, personalised modified reference point index (mRPI) approach, in which we expressed the exposures and potencies of our chosen substances as lead equivalent values, was applied to perform a MRA for dietary exposures. We conducted the assessment for four different age groups (toddlers, children, adolescents, and women aged 18–45 years) in nine European countries. Populations in all countries considered exceeded combined tolerable levels at median exposure levels. NDL-PCBs in fish, other seafood and dairy, lead in grains and fruits, methylmercury in fish and other seafoods, and fluoride in water contributed most to the combined exposure. We identified uncertainties for the likelihood of co-exposure, assessment group membership, endpoint-specific reference values (ESRVs) based on epidemiological (lead, methylmercury, iAs, fluoride and NDL-PCBs) and animal data (PBDE), and exposure data. Those uncertainties lead to a complex pattern of under- and overestimations, which would require probabilistic modelling based on expert knowledge elicitation for integration of the identified uncertainties into an overall uncertainty estimate. In addition, the identified uncertainties could be used to refine future MRA for cognitive decline.European Union’s Horizon 2020 research and innovation programme under grant agreement number 874583—the Advancing Tools for Human Early Lifecourse Exposome Research and Translation (ATHLETE) project. The author Mousumi Chatterjee is grateful for a Daphne Jackson Trust (UK) fellowship. The authors would like to thank EFSA providing the food consumption databases, data owners for giving permission to use the data, and Gerda van Donkersgoed and Matthijs Sam (RIVM) for organising the food consumption data and chemical concentration data

Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity

We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in 3-dimensional Riemannian space, and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid. Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of [4-5], and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3, and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin \jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large \jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.Comment: 43 pages, 26 figures, LaTeX. Version published in CQG. Typos corrected, presentation slightly extende

Spatial representation for navigation in animats

This article considers the problem of spatial representation for animat navigation systems. It is proposed that the global navigation task, or "wayfinding, " is best supported by multiple interacting subsystems, each of which builds its own partial representation of relevant world knowledge. Evidence from the study of animal navigation is reviewed to demonstrate that similar principles underlie the wayfinding behavior of animals, including humans. A simulated wayfinding system is described that embodies and illustrates several of the themes identified with animat navigation. This system constructs a network of partial models of the quantitative spatial relations between groups of salient landmarks. Navigation tasks are solved by propagating egocentric view information through this network, using a simple but effective heuristic to arbitrate between multiple solutions