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

Short topotecan-based induction regimen in newly diagnosed high-risk neuroblastoma

Purpose: Topotecan is an active drug in relapsed neuroblastoma. We investigated the efficacy and toxicity of a topotecan-based induction regimen in newly diagnosed neuroblastoma. Methods: Patients older than 1 year with either metastatic or localised stage 2-3 MYCN-amplified neuroblastoma received 2 courses of high-dose topotecan (HD-TPT) 6 mg/m2 and high-dose cyclophosphamide (HD-CPM) 140 mg/kg, followed by 2 courses of ifosfamide, carboplatin and etoposide (ICE) every 28 days. After surgery on primary tumour, a fifth course with vincristine, doxorubicin and CPM was given, followed by high-dose chemotherapy with stem cell support. Response was assessed in accordance with the International Neuroblastoma Response Criteria. Results: Of 35 consecutive patients, 33 had metastatic disease. The median length of induction phase was 133 days (range 91-207) and time to high-dose chemotherapy was 208 days (range 156-285). The median tumour volume reduction was 55% after two HD-TPT/HD-CPM courses and 80% after four courses. Radical surgery was performed in 16/27 patients after chemotherapy. After the fifth course, 29/34 patients (85%) had achieved a partial remission (12) or a CR/very good partial remission (17). CR of metastases was achieved in 13/32 (41%) and bone marrow was in complete remission in 16/24 patients (67%). Grade 4 neutropenia and/or thrombocytopenia occurred in 100% of HD-TPT/HD-CPM and in 95% of ICE courses, while non-haematological toxicities were manageable. Conclusions: These data indicate that our induction regimen is feasible and well tolerated. A major response rate of 85% with 41% complete metastatic response confirms this regimen as effective induction in high-risk neuroblastoma. © 2011 Published by Elsevier Ltd

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

How to think about informal proofs

This document is the Accepted Manuscript version of the following article: Brendan Larvor, ‘How to think about informal proofs’, Synthese, Vol. 187(2): 715-730, first published online 9 September 2011. The final publication is available at Springer via doi:10.1007/s11229-011-0007-5It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the fieldPeer reviewedFinal Accepted Versio

Combining machine learning and metaheuristics algorithms for classification method PROAFTN

© Crown 2019. The supervised learning classification algorithms are one of the most well known successful techniques for ambient assisted living environments. However the usual supervised learning classification approaches face issues that limit their application especially in dealing with the knowledge interpretation and with very large unbalanced labeled data set. To address these issues fuzzy classification method PROAFTN was proposed. PROAFTN is part of learning algorithms and enables to determine the fuzzy resemblance measures by generalizing the concordance and discordance indexes used in outranking methods. The main goal of this chapter is to show how the combined meta-heuristics with inductive learning techniques can improve performances of the PROAFTN classifier. The improved PROAFTN classifier is described and compared to well known classifiers, in terms of their learning methodology and classification accuracy. Through this chapter we have shown the ability of the metaheuristics when embedded to PROAFTN method to solve efficiency the classification problems

Humic Substances Enhance Chlorothalonil Phototransformation via Photoreduction and Energy Transfer

ABSTRACT: The photodegradation of chlorothalonil, a polychlorinated aromatic fungicide widely used in agriculture, was investigated under ultraviolet–visible irradiation in the presence and absence of different humic substances that significantly enhance the chlorothalonil phototransformation. On the basis of a kinetic model, an analytical study, the effect of scavengers, the chlorothalonil phosphorescence measurement, and varying irradiation conditions, it was possible to demonstrate that this accelerating effect is due to their capacity to reduce the chlorothalonil triplet state via H-donor reaction and to energy transfer from the triplet humic to ground state chlorothalonil. Energy transfer occurs at wavelengths below 450 nm and accounts for up to 30% of the reaction in deoxygenated medium upon irradiation with polychromatic light (300–450 nm). This process is more important with Elliott humic and fulvic acids and with humic acids extracted from natural carbonaceous material than with Nordic NOM and Pahokee peat humic acids. The obtained results are of high relevance to understanding the processes involved in chlorothalonil phototransformation and the photoreactivity of humic substances. Chlorothalonil is one of the rare molecules shown to react by energy transfer from excited humic substances

Short Term Synaptic Depression Imposes a Frequency Dependent Filter on Synaptic Information Transfer

Depletion of synaptic neurotransmitter vesicles induces a form of short term depression in synapses throughout the nervous system. This plasticity affects how synapses filter presynaptic spike trains. The filtering properties of short term depression are often studied using a deterministic synapse model that predicts the mean synaptic response to a presynaptic spike train, but ignores variability introduced by the probabilistic nature of vesicle release and stochasticity in synaptic recovery time. We show that this additional variability has important consequences for the synaptic filtering of presynaptic information. In particular, a synapse model with stochastic vesicle dynamics suppresses information encoded at lower frequencies more than information encoded at higher frequencies, while a model that ignores this stochasticity transfers information encoded at any frequency equally well. This distinction between the two models persists even when large numbers of synaptic contacts are considered. Our study provides strong evidence that the stochastic nature neurotransmitter vesicle dynamics must be considered when analyzing the information flow across a synapse