Existence of Least-perimeter Partitions

We prove the existence of a perimeter-minimizing partition of R^n into regions of unit volume. We conclude with a short tribute to the late Manuel A. Fortes.Comment: 5 pages; for submission to Fortes memorial isue of Philosphical Magazine Letter

Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex notions are those of boundary and separating edges. When performing proofs about this algorithm, questions of symmetry appear and this exposition attempts to give an account of how these symmetries can be handled. All this work relies on formal developments made with Coq and the mathematical components library

Supporting the game construction process: development of artefacts in the context of a Toolkit to Game Design

The Gamers4Nature project aims to deliver a set of strategies to empower and en-courage youngsters (upper-secondary and undergraduate students) to actively participate in games creation while raising knowledge about environmental preservation and biodiversity conservation. To accomplish these goals, a Toolkit to Game Design is being created, containing a set of resources and tools aiming to help in the creation of mobile digital games, namely a Game Construction Cards Set. This paper presents the creation process of the project’s general identi-ty and its concept adaptation to the Game Construction Cards Set, which required a deep understanding of the target audience and the development of a strategy to engage the participants in its activities. A general identity was defined, where a specific “language” to reach this audience was designed and a brand to support it was created. This “language” was applied in all graphic materials developed since day one, namely to the Game Construction Cards Set – focus of this paper. The validation of the prototypes was made through focus groups, using an iterative design approach. The focus groups participants’ inputs were integrated in the de-sign and helped with the graphic elements’ evolution, allowing the project to maintain a coherent strategy in all its representations that exceeds its graphic lan-guage and a deeper identification with the developed artefacts.publishe

Explicit Logic Circuits Predict Local Properties of the Neocortex's Physiology and Anatomy

Background: Two previous articles proposed an explicit model of how the brain processes information by its organization of synaptic connections. The family of logic circuits was shown to generate neural correlates of complex psychophysical phenomena in different sensory systems. Methodology/Principal Findings: Here it is shown that the most cost-effective architectures for these networks produce correlates of electrophysiological brain phenomena and predict major aspects of the anatomical structure and physiological organization of the neocortex. The logic circuits are markedly efficient in several respects and provide the foundation for all of the brain’s combinational processing of information. Conclusions/Significance: At the local level, these networks account for much of the physical structure of the neocortex as well its organization of synaptic connections. Electronic implementations of the logic circuits may be more efficient than current electronic logic arrays in generating both Boolean and fuzzy logic

From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Hepatopulmonary syndrome in patients with chronic liver disease: role of pulse oximetry

BACKGROUND: Hepatopulmonary syndrome (HPS) is a rare complication of liver diseases of different etiologies and may indicate a poor prognosis. Therefore, a simple non-invasive screening method to detect HPS would be highly desirable. In this study pulse oximetry was evaluated to identify patients with HPS. METHODS: In 316 consecutive patients with liver cirrhosis (n = 245), chronic hepatitis (n = 69) or non-cirrhotic portal hypertension (n = 2) arterial oxygen saturation (SaO(2)) was determined using a pulse oximeter. In patients with SaO(2 )≤92% in supine position and/or a decrease of ≥4% after change from supine to upright position further diagnostic procedures were performed, including contrast-enhanced echocardiography and perfusion lung scan. RESULTS: Seventeen patients (5.4%) had a pathological SaO(2). Four patients (1.3%) had HPS. HPS patients had a significant lower mean SaO(2 )in supine (89.7%, SD 5.4 vs. 96.0%, SD 2.3; p = 0.003) and upright position (84.3%, SD 5.0 vs. 96.0%, SD 2.4; p = 0.001) and had a lower mean PaO(2 )(56.2 mm Hg, SD 15.2 vs. 71.2 mm Hg, SD 20.2; p = 0.02) as compared to patients without HPS. The mean ΔSaO(2 )(difference between supine and upright position) was 5.50 (SD 7) in HPS patients compared to non-HPS patients who showed no change (p = 0.001). There was a strong correlation between shunt volume and the SaO(2 )values (R = -0.94). CONCLUSION: Arterial SaO(2 )determination in supine and upright position is a useful non-invasive screening test for HPS and correlates well with the intrapulmonary shunt volume

Effect of root age on the biomechanics of seminal and nodal roots of barley (<i>Hordeum vulgare L.</i>) in contrasting soil environments

Acknowledgments The James Hutton Institute receives funding from the Scottish Government. The authors would also like to thank Jim McNicol from Biomathematics and Statistics Scotland for his advice on statistical analysis.Peer reviewedPostprin