On the relationship between plane and solid geometry

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned area

Heinrich Behmann's 1921 lecture on the decision problem and the algebra of logic

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in G\"ottingen in 1921 with a thesis on the decision problem. In his thesis, he solved-independently of L\"owenheim and Skolem's earlier work-the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in G\"ottingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included

Book Review: Logicomix by Apostolos Doxiadis, Christos H. Papadimitriou, Alecos Papadatos, and Annie di Donna

The first two parts of the review provide background on Russell\u27s biography and on developments in the foundations of mathematics in the early part of the twentieth century that will help the reader set Logicomix in context. The third part contains critical remarks on 1) the relationship between Logicomix and reality; 2) the issue of faithfulness of the graphic novel to the development of ideas in philosophy of logic and the foundations of mathematics; 3) logical inaccuracies; 4) the connection to madness and tragedy

Book Review: Prime Suspects: The Anatomy of Integers and Permutations by Andrew Granville and Jennifer Granville

Prime Suspects is a delightful graphic novel that performs what might, prima facie, seem almost like an impossible feat. Apart from the aesthetic pleasure it provides by being a well-illustrated and well thought out graphic novel, I would describe its major conceptual goal to be that of conveying to its reader a taste of the exciting nature of mathematical discovery. This is accomplished by focusing on a set of results connecting the study of prime numbers, the study of cycles of permutations, irreducible polynomials in finite fields and more

The Origin of the Group in Logic and the Methodology of Science

The Group in Logic and the Methodology of Science at UC Berkeley was founded in 1957. It has been a key institutional element in carrying out Tarski’s vision for making UC Berkeley one of the most important centers of logical research in the world. In this brief history, I look at the emergence of the Group in Logic with an eye towards understanding the circumstances that made it possible

Logic and Biology: The Correspondence Between Alfred Tarski and Joseph H. Woodger

This article makes available some early letters chronicling the relationship between the biologist Joseph H. Woodger and the logician Alfred Tarski. Using twenty-five unpublished letters from Tarski to Woodger preserved in the Woodger Papers at University College, London, I reconstruct their relationship for the period 1935-1950. The scientific aspects of the correspondence concern, among other things, Tarski’s reports on the work he is doing, his interests, and his --- sometimes critical but always well-meaning --- reactions to Woodger’s attempts at axiomatizing and formalizing biology using the system of Principia Mathematica. Perhaps the most interesting letter from a philosophical point of view is a very informative letter on nominalism dated November 21, 1948. But just as fascinating are the personal elements, the dramatic period leading to the second world war, their reaction to the war events, Tarski\u27s anguish for his family stranded back in Poland, the financial worries, and his first reports on life in the East Coast and, as of 1942, at the University of California, Berkeley

Ensemble Methods for Multi-Organ Segmentation in CT Series

In the medical images field, semantic segmentation is one of the most important, yet difficult and time-consuming tasks to be performed by physicians. Thanks to the recent advancement in the Deep Learning models regarding Computer Vision, the promise to automate this kind of task is getting more and more realistic. However, many problems are still to be solved, like the scarce availability of data and the difficulty to extend the efficiency of highly specialised models to general scenarios. Organs at risk segmentation for radiotherapy treatment planning falls in this category, as the limited data available negatively affects the possibility to develop general-purpose models; in this work, we focus on the possibility to solve this problem by presenting three types of ensembles of single-organ models able to produce multi-organ masks exploiting the different specialisations of their components. The results obtained are promising and prove that this is a possible solution to finding efficient multi-organ segmentation methods

Haplotype affinities resolve a major component of goat (<i>Capra hircus</i>) MtDNA D-loop diversity and reveal specific features of the Sardinian stock

Goat mtDNA haplogroup A is a poorly resolved lineage absorbing most of the overall diversity and is found in locations as distant as Eastern Asia and Southern Africa. Its phylogenetic dissection would cast light on an important portion of the spread of goat breeding. The aims of this work were 1) to provide an operational definition of meaningful mtDNA units within haplogroup A, 2) to investigate the mechanisms underlying the maintenance of diversity by considering the modes of selection operated by breeders and 3) to identify the peculiarities of Sardinian mtDNA types. We sequenced the mtDNA D-loop in a large sample of animals (1,591) which represents a non-trivial quota of the entire goat population of Sardinia. We found that Sardinia mirrors a large quota of mtDNA diversity of Western Eurasia in the number of variable sites, their mutational pattern and allele frequency. By using Bayesian analysis, a distance-based tree and a network analysis, we recognized demographically coherent groups of sequences identified by particular subsets of the variable positions. The results showed that this assignment system could be reproduced in other studies, capturing the greatest part of haplotype diversity. We identified haplotype groups overrepresented in Sardinian goats as a result of founder effects. We found that breeders maintain diversity of matrilines most likely through equalization of the reproductive potential. Moreover, the relevant amount of inter-farm mtDNA diversity found does not increase proportionally with distance. Our results illustrate the effects of breeding practices on the composition of maternal gene pool and identify mtDNA types that may be considered in projects aimed at retrieving the maternal component of the oldest breeds of Sardinia.</br