On non-rigid del Pezzo fibrations of low degree

We consider $\mathbb{P}(1,1,1,2)$ bundles over $\mathbb{P}^1$ and construct hypersurfaces of these bundles which form a degree 2 del Pezzo fibration over $\mathbb{P}^1$ as a Mori fibre space. We classify all such hypersurfaces whose type \III or \IV Sarkisov links pass to a different Mori fibre space. A similar result for cubic surface fibrations over $\mathbb{P}^2$ is also presented.Comment: 34 page

Domesticating Descartes, Renovating Scholasticism: Johann Clauberg And The German Reception Of Cartesianism

This article studies the academic context in which Cartesianism was absorbed in Germany in the mid-seventeenth century. It focuses on the role of Johann Clauberg (1622-1665), first rector of the new University of Duisburg, in adjusting scholastic tradition to accommodate Descartes’ philosophy, thereby making the latter suitable for teaching in universities. It highlights contextual motivations behind Clauberg’s synthesis of Cartesianism with the existing framework such as a pedagogical interest in Descartes as offering a simpler method, and a systematic concern to disentangle philosophy from theological disputes. These motivations are brought into view by situating Clauberg in the closely-linked contexts of Protestant educational reforms in the seventeenth century, and debates around the proper relation between philosophy and theology. In this background, it argues that Clauberg nevertheless retains an Aristotelian conception of ontology for purely philosophical reasons, specifically, to give objective foundations to Descartes’s metaphysics of substance. In conclusion, Clauberg should not be assimilated either to Aristotelianism or to Cartesianism or, indeed, to syncretic labels such as ‘Cartesian Scholastic’. Instead, he should be read as transforming both schools by drawing on a variety of elements in order to address issues local to the academic milieu of his time

Some Problems With Steadfast Strategies for Rational Disagreement

Current responses to the question of how one should adjust one’s beliefs in response to peer disagreement have, in general, formed a spectrum at one end of which sit the so-called ‘conciliatory’ views and whose other end is occupied by the ‘steadfast’ views. While the conciliatory views of disagreement maintain that one is required to make doxastic conciliation when faced with an epistemic peer who holds a different stance on a particular subject, the steadfast views allow us to maintain our confidence in our relevant beliefs. My aim in this paper is not to adjudicate between these views. Rather, I shall focus on a particular strategy, namely, denying the appearance of epistemic symmetry between peers, that the steadfast views standardly invoke in support of their position. Having closely examined certain representative examples of the steadfast approach, I will argue that this strategy is fundamentally flawed

Non-adaptive Group Testing on Graphs

Grebinski and Kucherov (1998) and Alon et al. (2004-2005) study the problem of learning a hidden graph for some especial cases, such as hamiltonian cycle, cliques, stars, and matchings. This problem is motivated by problems in chemical reactions, molecular biology and genome sequencing. In this paper, we present a generalization of this problem. Precisely, we consider a graph G and a subgraph H of G and we assume that G contains exactly one defective subgraph isomorphic to H. The goal is to find the defective subgraph by testing whether an induced subgraph contains an edge of the defective subgraph, with the minimum number of tests. We present an upper bound for the number of tests to find the defective subgraph by using the symmetric and high probability variation of Lov\'asz Local Lemma