In the heart of representable metric jets

Here, I aim to immerse myself in the heart of the metric jets, more precisely of those which are representable, restricting myself to the main basic concepts, while going deeper into some notions already mentionned in our previous papers; this will give me the opportunity of lightening the previous texts (including some proofs), while precising some ideas and giving new examples (as the bifractal wave function) with a proof at the end of this paper. Concerning the concrete examples found all along this paper: they play the "starring role" in the understanding of our metric Differential Calculus!Comment: 18 pages, 10 figure

Termination orders for 3-polygraphs

This note presents the first known class of termination orders for 3-polygraphs, together with an application.Comment: 4 pages, 12 figure

Theories of analytic monads

We characterize the equational theories and Lawvere theories that correspond to the categories of analytic and polynomial monads on Set, and hence also the categories of the symmetric and rigid operads in Set. We show that the category of analytic monads is equivalent to the category of regular-linear theories. The category of polynomial monads is equivalent to the category of rigid theories, i.e. regular-linear theories satisfying an additional global condition. This solves a problem A. Carboni and P. T. Johnstone. The Lawvere theories corresponding to these monads are identified via some factorization systems.Comment: 29 pages. v2: minor correction

A split-gesture, competitive, coupled oscillator model of syllable structure predicts the emergence of edge gemination and degemination

The phonological mechanisms responsible for the emergence of edge geminates in phonological processes like the Italian Raddoppiamento (Fono-)Sintattico (RS) are an open issue. Previous analyses of Italian treat gemination of (i) word initial consonants, (ii) morpheme-final consonants, and (iii) word final consonants as separate processes brought about by dedicated rule/constraints. We argue that these edge gemination processes result from the same, independently established principles. Through computational simulation of the split-gesture, competitive, coupled oscillator model of syllable structure of Articulatory Phonology, we show that increases in closure duration typical of geminates arise from changes to consonant/vowel couplings. Word initial gemination follows from coupling of a closure gesture to a preceding vowel across a word boundary. Word final gemination follows from coupling of a release gesture to a following vowel. In both cases, the posited structures reflect changes in syllabification hypothesized in previous work. The model simulation also predict different durations for resyllabified edge geminates and medial lexical geminates, in line with experimental findings on the topic. Changes to consonant/vowel couplings also account for the opposite effect: word initial degemination. Thus, the coupled oscillator model of Articulatory Phonology, originally developed to model intergestural timing, predicts the emergence of edge gemination/degemination

Dynamic provisioning: rationale, functioning, and prudential treatment

Current policy debate has renewed interest in countercyclical provisioning policies; dynamic provisions are regarded as a valuable device for pursuing this goal. Last July, Ecofin supported “the introduction of forward-looking provisioning, which consists in constituting provisions deducted from profits in good times for expected losses on loan portfolios, and which would contribute to limiting procyclicalityâ€. This paper describes: i) how dynamic provisions work in a general framework based on expected losses; ii) how they work according to the Spanish system, which is the only real example of countercyclical provisioning; iii) the differences and similarities between the expected loss model and the Spanish approach. Building on proposals currently under discussion in the international community, it also suggests a possible way forward for introducing a system of dynamic provisions that, while meeting the prudential goal of having more conservative provisioning policies, would not clash with accounting standards.dynamic provisions, capital buffers, Basel 2, credit risk, procyclicality

Two polygraphic presentations of Petri nets

This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and transitions as rewriting rules on it: this setting is totally equivalent to Petri nets, but lacks any graphical intuition. The second one considers places as 1-dimensional cells and transitions as 2-dimensional ones: this translation recovers a graphical meaning but raises many difficulties since it uses explicit permutations. Finally, the third translation sees places as degenerated 2-dimensional cells and transitions as 3-dimensional ones: this is a setting equivalent to Petri nets, equipped with a graphical interpretation.Comment: 28 pages, 24 figure