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A System of Interaction and Structure III: The Complexity of BV and Pomset Logic
No full textPomset logic and BV are both logics that extend multiplicative linear logic(with Mix) with a third connective that is self-dual and non-commutative.Whereas pomset logic originates from the study of coherence spaces and proofnets, BV originates from the study of series-parallel orders, cographs, andproof systems. Both logics enjoy a cut-admissibility result, but for neitherlogic can this be done in the sequent calculus. Provability in pomset logic canbe checked via a proof net correctness criterion and in BV via a deep inferenceproof system. It has long been conjectured that these two logics are the same. In this paper we show that this conjecture is false. We also investigate thecomplexity of the two logics, exhibiting a huge gap between the two. Whereasprovability in BV is NP-complete, provability in pomset logic is-complete. We also make some observations with respect to possiblesequent systems for the two logics
Degrees in random -ary hooking networks
No full textThe theme in this paper is a composition of random graphs and P\'olya urns.The random graphs are generated through a small structure called the seed. ViaP\'olya urns, we study the asymptotic degree structure in a random -aryhooking network and identify strong laws. We further upgrade the result tosecond-order asymptotics in the form of multivariate Gaussian limit laws. Wegive a few concrete examples and explore some properties with a fullrepresentation of the Gaussian limit in each case. The asymptotic covariancematrix associated with the P\'olya urn is obtained by a new method thatoriginated in this paper and is reported in [25].Comment: 21 pages, 5 figure
Galois cohomology of reductive algebraic groups over the field of real numbers
No full textWe describe functorially the first Galois cohomology set of a connected reductive algebraic group over the field of realnumbers in terms of a certain action of the Weyl group on the real points oforder dividing 2 of the maximal torus containing a maximal compact torus. Thisresult was announced with a sketch of proof in the author's 1988 note. Here wegive a detailed proof.Comment: V.1, v.2, v.3: 6 pages. V.4, v.5: 11 pages, the final version to appear in Communicationa in Mathematics. In this final version, Theorem 9 (the main result) of versions 1-3 became Theorem 3.
Being loyal to fieldwork: on building the "contract of silence"
No full textThe aim of the present contribution is to analyze how relations of loyalty emerge between researcher and researched during ethnographic fieldwork and to defend a perspective against the principle of open science. I discuss methodological issues with respect to my several years of multi-sited fieldwork experience in various labs, research centers and medical institutions, during which I inquired into the design and use of exoskeletal devices. Exoskeletal devices are technologies applied to three fields of application: rehabilitation, industry and the armed forces. Their invention is the subject of high levels of economic and scientific competition. Given these constraints, I was compelled to develop "loyalty strategies", one of which I call the "contract of silence". I associate this category with an ethnographic exercise in how to address one's interlocutors during fieldwork. I conceive of this process as a result of consciously retaining the information obtained from interviewees that might endanger the position of the researcher in the field. Although a tacit contract with one's interlocutors during ethnographic fieldwork implies anonymity, certain sensitive fields and research situations require forms of auto-censorship and the control of published results. I associate these strategies with the fabrication of fieldwork secrecy
Implicative models of set theory
No full textIn this paper we show that using implicative algebras one can produce modelsof set theory generalizing Heyting/Boolean-valued models and realizabilitymodels of (I)ZF, both in intuitionistic and classical logic. This has asconsequence that any topos which is obtained from a Set-based tripos as theresult of the tripos-to-topos construction hosts a model of intuitionistic orclassical set theory, provided a large enough strongly inaccessible cardinalexists.Comment: arXiv admin note: substantial text overlap with arXiv:2301.1174
Les ordres mendiants et l’eau: Deux facteurs liés dans la croissance des villes de Savoie du nord (XIIIe-XVIIIe siècles)
No full textCet article propose un aperçu du lien unissant ordres mendiants (dominicains, franciscains, carmes et augustins) et gestion de l'eau dans les principales villes de l'ancien diocèse de Genève au cours du bas Moyen Âge et de l'époque moderne. Tributaires de cet élément lors des implantations et du développement de leurs établissements, ils ont également su le maîtriser et contribuer ainsi à modifier, plus ou moins en profondeur, les différents faciès urbains les environnant
The Effects of Political Martyrdom on Election Results: The Assassination of Abe
No full textIn developed nations assassinations are rare and thus the impact of such actson the electoral and political landscape is understudied. In this paper, wefocus on Twitter data to examine the effects of Japan's former Primer MinisterAbe's assassination on the Japanese House of Councillors elections in 2022. Weutilize sentiment analysis and emotion detection together with topic modelingon over 2 million tweets and compare them against tweets during previouselection cycles. Our findings indicate that Twitter sentiments were negativelyimpacted by the event in the short term and that social media attention spanhas shortened. We also discuss how "necropolitics" affected the outcome of theelections in favor of the deceased's party meaning that there seems to havebeen an effect of Abe's death on the election outcome though the findingswarrant further investigation for conclusive results
Perverse-Hodge complexes for Lagrangian fibrations
No full textPerverse-Hodge complexes are objects in the derived category of coherentsheaves obtained from Hodge modules associated with Saito's decompositiontheorem. We study perverse-Hodge complexes for Lagrangian fibrations andpropose a symmetry between them. This conjectural symmetry categorifies the"Perverse = Hodge" identity of the authors and specializes to Matsushita'stheorem on the higher direct images of the structure sheaf. We verify ourconjecture in several cases by making connections with variations of Hodgestructures, Hilbert schemes, and Looijenga-Lunts-Verbitsky Lie algebras.Comment: 20 pages. Final versio
Discrete complex reflection groups
No full textHere are reproduced slightly edited notes of my lectures on theclassification of discrete groups generated by complex reflections of Hermitianaffine spaces delivered in October of 1980 at the University of Utrecht.Comment: Final version. 73 page
Extended commutator algebra for the -oscillator and a related Askey-Wilson algebra
No full textLet be a nonzero complex number that is not a root of unity. In the-oscillator with commutation relation , it is known thatthe smallest commutator algebra of operators containing the creation andannihilation operators and is the linear span of and ,together with all operators of the form , and, where is a nonnegative integer and is apositive integer. That is, linear combinations of operators of the form or with or are outside the commutator algebragenerated by and . This is a solution to the Lie polynomialcharacterization problem for the associative algebra generated by and . In this work, we extend the Lie polynomial characterization into theassociative algebra generated by , , andthe operator for some nonzero real parameter , where is the number operator, and we relate this to a -oscillator representationof the Askey-Wilson algebra