The New Deal for Communities experience: a final assessment - The New Deal for Communities evaluation: Final report – Volume 7

We show that for all integers $t\geq 8$ and arbitrarily small $\epsilon>0$, there exists a graph property $\Pi$ (which depends on $\epsilon$) such that $\epsilon$-testing $\Pi$ has non-adaptive query complexity $Q=\~{\Theta}(q^{2-2/t})$, where $q=\~{\Theta}(\epsilon^{-1})$ is the adaptive query complexity. This resolves the question of how beneficial adaptivity is, in the context of proximity-dependent properties (\cite{benefits-of-adaptivity}). This also gives evidence that the canonical transformation of Goldreich and Trevisan (\cite{canonical-testers}) is essentially optimal when converting an adaptive property tester to a non-adaptive property tester. To do so, we provide optimal adaptive and non-adaptive testers for the combined property of having maximum degree $O(\epsilon N)$ and being a \emph{blow-up collection} of an arbitrary base graph $H$.Comment: Keywords: Sublinear-Time Algorithms, Property Testing, Dense-Graph Model, Adaptive vs Nonadaptive Queries, Hierarchy Theore

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 Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

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

Chemical Linkage to Injected Tissues Is a Distinctive Property of Oxidized Avidin

We recently reported that the oxidized avidin, named AvidinOX®, resides for weeks within injected tissues as a consequence of the formation of Schiff's bases between its aldehyde groups and tissue protein amino groups. We also showed, in a mouse pre-clinical model, the usefulness of AvidinOX for the delivery of radiolabeled biotin to inoperable tumors. Taking into account that AvidinOX is the first oxidized glycoprotein known to chemically link to injected tissues, we tested in the mouse a panel of additional oxidized glycoproteins, with the aim of investigating the phenomenon. We produced oxidized ovalbumin and mannosylated streptavidin which share with avidin glycosylation pattern and tetrameric structure, respectively and found that neither of them linked significantly to cells in vitro nor to injected tissues in vivo, despite the presence of functional aldehyde groups. The study, extended to additional oxidized glycoproteins, showed that the in vivo chemical conjugation is a distinctive property of the oxidized avidin. Relevance of the high cationic charge of avidin into the stable linkage of AvidinOX to tissues is demonstrated as the oxidized acetylated avidin lost the property. Plasmon resonance on matrix proteins and cellular impedance analyses showed in vitro that avidin exhibits a peculiar interaction with proteins and cells that allows the formation of highly stable Schiff's bases, after oxidation

Archaeological discoveries in the Jewish Quarter of Jerusalem : Second Temple Period

Jerusalem80 p.; 21 c