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Abundance for slc surfaces over arbitrary fields
No full textWe prove the abundance conjecture for projective slc surfaces over arbitraryfields of positive characteristic. The proof relies on abundance for lcsurfaces over abritrary fields, proved by Tanaka, and on the technique of Haconand Xu to descend semi-ampleness from the normalization. We also presentapplications to dlt threefold pairs, and to mixed characteristic families ofsurfaces.Comment: 22 pages. Comments welcome anytime. v2: some proofs in Sections 3.1 and 3.2 have been clarified. v4: Final version, to appear in Epijournal de Geometrie algebriqu
From exemplar to copy: the scribal appropriation of a Hadewijch manuscript computationally explored
No full textThis study is devoted to two of the oldest known manuscripts in which theoeuvre of the medieval mystical author Hadewijch has been preserved: Brussels,KBR, 2879-2880 (ms. A) and Brussels, KBR, 2877-2878 (ms. B). On the basis ofcodicological and contextual arguments, it is assumed that the scribe whoproduced B used A as an exemplar. While the similarities in both layout andcontent between the two manuscripts are striking, the present article seeks toidentify the differences. After all, regardless of the intention to produce acopy that closely follows the exemplar, subtle linguistic variation isapparent. Divergences relate to spelling conventions, but also to the way inwhich words are abbreviated (and the extent to which abbreviations occur). Thepresent study investigates the spelling profiles of the scribes who producedmss. A and B in a computational way. In the first part of this study, we willpresent both manuscripts in more detail, after which we will consider priorresearch carried out on scribal profiling. The current study both builds andexpands on Kestemont (2015). Next, we outline the methodology used to analyseand measure the degree of scribal appropriation that took place when ms. B wascopied off the exemplar ms. A. After this, we will discuss the resultsobtained, focusing on the scribal variation that can be found both at the levelof individual words and n-grams. To this end, we use machine learning toidentify the most distinctive features that separate manuscript A from B.Finally, we look at possible diachronic trends in the appropriation by B'sscribe of his exemplar. We argue that scribal takeovers in the exemplar impactsthe practice of the copying scribe, while transitions to a different contentmatter cause little to no effect
A Generalization of Iseki's Formula and The Jacobi Theta Function
No full textIn this paper we give a generalization of Iseki's formula and use it to prove the transformation law of
Results on of general quadratic groups
No full textIn the first part of this article we discuss the relative cases ofQuillen-Suslin's local-global principle for the general quadratic (Bak'sunitary) groups, and its applications for the (relative) stable and unstable-groups. The second part is dedicated to the graded version ofthe local-global principle for the general quadratic groups and its applicationto deduce a result for Bass' nil groups.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:2101.0702
A Complete Diagrammatic Calculus for Boolean Satisfiability
No full textWe propose a calculus of string diagrams to reason about satisfiability ofBoolean formulas, and prove it to be sound and complete. We then showcase ourcalculus in a few case studies. First, we consider SAT-solving. Second, weconsider Horn clauses, which leads us to a new decision method forpropositional logic programs equivalence under Herbrand model semantics
A Categorical Normalization Proof for the Modal Lambda-Calculus
No full textWe investigate a simply typed modal -calculus,, due to Pfenning, Wong and Davies, where we define awell-typed term with respect to a context stack that captures the possibleworld semantics in a syntactic way. It provides logical foundation formulti-staged meta-programming. Our main contribution in this paper is anormalization by evaluation (NbE) algorithm for which weprove sound and complete. The NbE algorithm is a moderate extension to thestandard presheaf model of simply typed -calculus. However, central tothe model construction and the NbE algorithm is the observation of Kripke-stylesubstitutions on context stacks which brings together two previously separateconcepts, structural modal transformations on context stacks and substitutionsfor individual assumptions. Moreover, Kripke-style substitutions allow us togive a formulation for contextual types, which can represent open code in ameta-programming setting. Our work lays the foundation for extending thelogical foundation by Pfenning, Wong, and Davies towards building a practical,dependently typed foundation for meta-programming
The Internal Operads of Combinatory Algebras
No full textWe argue that operads provide a general framework for dealing withpolynomials and combinatory completeness of combinatory algebras, including theclassical -algebras, linear -algebras, planar-algebras as well as the braided \mathbf{BC^\pmI}-algebras. We show that every extensional combinatory algebra gives rise toa canonical closed operad, which we shall call the internal operad of thecombinatory algebra. The internal operad construction gives a left adjoint tothe forgetful functor from closed operads to extensional combinatory algebras.As a by-product, we derive extensionality axioms for the classes of combinatoryalgebras mentioned above
FTMPST: Fault-Tolerant Multiparty Session Types
No full textMultiparty session types are designed to abstractly capture the structure ofcommunication protocols and verify behavioural properties. One important suchproperty is progress, i.e., the absence of deadlock. Distributed algorithmsoften resemble multiparty communication protocols. But proving theirproperties, in particular termination that is closely related to progress, canbe elaborate. Since distributed algorithms are often designed to cope withfaults, a first step towards using session types to verify distributedalgorithms is to integrate fault-tolerance. We extend multiparty session typesto cope with system failures such as unreliable communication and processcrashes. Moreover, we augment the semantics of processes by failure patternsthat can be used to represent system requirements (as, e.g., failuredetectors). To illustrate our approach we analyse a variant of the well-knownrotating coordinator algorithm by Chandra and Toueg
Computing square roots in quaternion algebras
No full textWe present an explicit algorithmic method for computing square roots inquaternion algebras over global fields of characteristic different from 2.Comment: Final version of the paper formatted by the editorial board to appear in Fundamenta Informatica
Gossiping with interference in radio ring networks
No full textIn this paper, we study the problem of gossiping with interference constraint in radio ring networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and algorithms that attain this makespan. We focus on the case where the transmission network is a ring network. We consider synchronous protocols where it takes one unit of time (step) to transmit a unit-length message. During one step, a node receives at most one message only through one of its two neighbors. We also suppose that, during one step, a node cannot be both a sender and a receiver (half duplex model). Moreover communication is subject to interference constraints. We use a primary node interference model where, if a node receives a message from one of its neighbors, its other neighbor cannot send at the same time. With these assumptions we completely solve the problem for ring networks. We first show lower bounds and then give gossiping algorithms which meet these lower bounds and so are optimal. The number of rounds depends on the congruences of n modulo 12