Black Hole Quasinormal Modes and Seiberg–Witten Theory

We present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $${\mathcal {N}}=2$$ N = 2 supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the $$\Omega $$ Ω -background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.

Double reading in breast cancer screening: considerations for policy-making

In this article, we explore the evidence around the relative benefits and harms of breast cancer screening using a single radiologist to examine each female’s mammograms for signs of cancer (single reading), or two radiologists (double reading). First, we briefly explore the historical evidence using film-screen mammography, before providing an in-depth description of evidence using digital mammography. We classify studies according to which exact version of double reading they use, because the evidence suggests that effectiveness of double reading is contingent on whether the two radiologists are blinded to one another’s decisions, and how the decisions of the two radiologists are integrated. Finally, we explore the implications for future mammography, including using artificial intelligence as the second reader, and applications to more complex three-dimensional imaging techniques such as tomosynthesis.

Exact Algorithms for the Graph Coloring Problem

The graph coloring problem is the problem of partitioning the vertices of a graph into the smallest possible set of independent sets. Since it is a well-known NP-Hard problem, it is of great interest of the computer science finding results over exact algorithms that solve it. The main algorithms of this kind, though, are scattered through the literature. In this paper, we group and contextualize some of these algorithms, which are based in Dynamic Programming, Branch-and-Bound and Integer Linear Programming. The algorithms for the first group are based in the work of Lawler, which searches maximal independent sets on each subset of vertices of a graph as the base of his algorithm. In the second group, the algorithms are based in the work of Brelaz, which adapted the DSATUR procedure to an exact version, and in the work of Zykov, which introduced the definition of Zykov trees. The third group contains the algorithms based in the work of Mehrotra and Trick, which uses the Column Generation method.

The World of Truth-Making

This chapter considers a number of different ways to develop a semantics in which statements are evaluated at partial possibilities rather than possible worlds. These include the exact version of truth-maker semantics in which truth-makers are wholly relevant to the statements they make true, the inexact version in which they are relevant, but not necessarily wholly relevant, to the statements they make true, and the loose version, in which they need only necessitate the statements they make true, regardless of relevance. The chapter explores the question of how these different semantical schemes are related; and it argues for the surprising conclusion that classical logic can only be properly accommodated within the ‘relevantist’ version of these approaches by allowing possible worlds to be among the partial possibilities. Thus, whatever reasons there might be for adopting such a semantics, they should not include a distaste for possible worlds.

Exact Minimum Codegree Threshold for K−4-Factors

Given hypergraphs F and H, an F-factor in H is a set of vertex-disjoint copies of F which cover all the vertices in H. Let K−4 denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large n ∈ 4ℕ, every 3-uniform hypergraph H on n vertices with minimum codegree at least n/2−1 contains a K−4-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markström [15] for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft [11] concerning almost perfect matchings in hypergraphs.

The causal meaning of Hamilton’s rule

Hamilton’s original derivation of his rule for the spread of an altruistic gene ( rb > c ) assumed additivity of costs and benefits. Recently, it has been argued that an exact version of the rule holds under non-additive pay-offs, so long as the cost and benefit terms are suitably defined, as partial regression coefficients. However, critics have questioned both the biological significance and the causal meaning of the resulting rule. This paper examines the causal meaning of the generalized Hamilton’s rule in a simple model, by computing the effect of a hypothetical experiment to assess the cost of a social action and comparing it to the partial regression definition. The two do not agree. A possible way of salvaging the causal meaning of Hamilton’s rule is explored, by appeal to R. A. Fisher’s ‘average effect of a gene substitution’.

Exact Geometrical Predicate: Point in circle

This document describes the implementation in ITK of the “point in circle” geometrical predicate. Based on Jonathan Shewchuk’s work which implements an exact version of the predicate using standard floating point types and arithmetic, the implementation consist of an ITK wrapper around the public domain C routines made available by the author of the precedent paper. Wrapper using itk::PointSet, itk:CellInterface and itk:Mesh / itk:QuadEdgeMesh APIs are provided along with corresponding examples which should provide enough details for users to directly copy paste code in their application.The application in mind for us is an exact and robust implementation of a delaunay triangulation / voronoi tesselation in ITK, and will be presented in a separate paper.

Alexandre d'AphrodisevsJean Philopon: Notes sur quelques traités d'Alexandre “perdus” en grec, conservés en arabe

In this paper, are included new data about three treatises ascribed in Arabic to Alexander of Aphrodisias. These treatises were thought to have no Greek correspondent. The author shows that one of them, (D.8a), is an adapted version – following the norms of “al-Kindi circle” – ofQuaestioI 21, along with the later and more exact version of thisQuaestioby Abū ‘Uṭmān al-Dimašqi (d. 900). He shows also that the two other treatises (D.9 and D.16) are, in contradistinction to the first, adapted versions of passages belonging in theDe Aeternitate mundi contra Proclumof John Philoponus: respectively IV, 4–6 and IX, 11. Philoponus’ book was known to have been translated, into Arabic. But, except for some short fragments in al-Bīrūnī (d. 1048), it seems that it is the first time that important adapted extracts of it are put in light. Some points are made about the historical position of the epitomator of these passages. In Appendix II, another treatise ascribed to Alexander (D.27g) appears – provisionally – as a composite text, mixing elements coming from Philoponus and others from neoplatonic texts in Arabic. In Appendix III is analysed the use of D.16 by Miskawayh (d. 1030), and the use of D.27g by ‘Abdallaṭīf al-Baġdādī (d. 1231).