Curry-Howard for sequent calculus at last!

This paper tries to remove what seems to be the remaining stumbling blocks in the way to a full understanding of the Curry-Howard isomorphism for sequent calculus, namely the questions: What do variables in proof terms stand for? What is co-control and a co-continuation? How to define the dual of Parigot's mu-operator so that it is a co-control operator? Answering these questions leads to the interpretation that sequent calculus is a formal vector notation with first-class co-control. But this is just the "internal" interpretation, which has to be developed simultaneously with, and is justified by, an "external" one, offered by natural deduction: the sequent calculus corresponds to a bi-directional, agnostic (w.r.t. the call strategy), computational lambda-calculus. Next, the duality between control and co-control is studied and proved in the context of classical logic, where one discovers that the classical sequent calculus has a distortion towards control, and that sequent calculus is the de Morgan dual of natural deduction.

Charakterisierung von Kartoffelpflanzen mit reduzierter THT-Genexpression

Diese Masterarbeit wurde im Verlauf des Sommersemesters 2014 am Leibniz Institut für Pflanzenbiochemie (IPB) in Halle angefertigt. Gegenstand dabei war die Charakterisierung von Kartoffelpflanzen (Solanum tuberosum cv Désirée), welche durch RNA-Interferenz reduzierte Mengen der Tyramin-Hydroxyzimtsäure-Transferase (THT) besaßen. Durch Southern- und Northern-Blot-Analysen wurden die korrekte Insertion als auch der RNAi-Effekt überprüft und bestätigt. Infizierte Blätter und die dazugehörenden Infektionstropfen wurden in Methanol gelöst und massenspektrometrisch nachgewiesen. Darauf aufbauend wurde das Wachstum von Phytophthora infestans auf transformierten Linien untersucht, wobei dessen Biomasse nach 3-tägiger Infektion durch qPCR bestimmt wurde. Während der Betreuung der transformierten Linien in Sterilkultur wurde ein Phänotyp ersichtlich. Nach Dokumentation der äußeren Erscheinungen und nach Prüfung auf Einfluss von Pathogenen, wurden diese Pflanzen für Knollenversuche im Gewächshaus ausgepflanzt und analysiert. Zuletzt wurde die Sequenz von THT analysiert und kloniert, woraufhin drei Fragmente generiert wurden, welche für weitere Versuche genutzt werden können.

RECASTING THE ELLIOTT CONJECTURE

Let A be a simple, unital, finite, and exact C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomor phism, and prove the conjecture in several cases. In these same cases - Z-stable algebras all - we prove that the Elliott conjecture in its strongest form is equivalent to a conjecture which appears much weaker. Outside the class of Z-stable C*-algebras, this weaker conjecture has no known counterexamples, and it is plausible that none exist. Thus, we reconcile the still intact principle of Elliott's classification conjecture -that K-theoretic invariants will classify separable and nuclear C*-algebras- with the recent appearance of counterexamples to its strongest concrete form.

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

La Phoronomia (1716) de Jacob Hermann (1678 -1733): entre la filosofía natural y la mecánica analítica

La "Phoronomia", primer libro de mecánica escrito tras los "Principia", es representativo del proceso de transición que transformó la dinámica a principios del XVIII y que concluye con la "Mecánica" de Euler (1736). Está escrita en estilo geométrico y algebraico, y mezcla los conceptos y métodos de Leibniz y Newton de forma idiosincrásica. En esta obra se encuentra por primera vez la segunda ley de Newton escrita en la forma en que hoy la conocemos, así como un intento de construcción de la estática y la dinámica de sólidos y fluidos basado en reglas generales diferenciales.

Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofi brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications.

Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators,and, as a by-product, recover the known graphs E4, E6 and E8 describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give sufficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.

Mètodes algebraics i de teoria de la prova per a la formalització del raonament vague

Projecte de recerca elaborat a partir d’una estada a la Università degli studi di Siena, Italy , entre 2007 i 2009. El projecte ha consistit en un estudi de la formalització lògica del raonament en presència de vaguetat amb els mètodes de la Lògica Algebraica i de la Teoria de la Prova. S'ha treballat fonamental en quatre direccions complementàries. En primer lloc, s'ha proposat un nou plantejament, més abstracte que el paradigma dominant fins ara, per l'estudi dels sistemes de lògica borrosa. Fins ara en l'estudi d'aquests sistemes l'atenció havia recaigut essencialment en l'obtenció de semàntiques basades en tnormes contínues (o almenys contínues per l'esquerra). En primer nivell de major abstracció hem estudiat les propietats de completesa de les lògiques borroses (tant proposicionals com de primer ordre) respecte de semàntiques definides sobre qualsevol cadena de valors de veritat, no necessàriament només sobre l'interval unitat dels nombres reals. A continuació, en un nivell encara més abstracte, s’ha pres l'anomenada jerarquia de Leibniz de la Lògica Algebraica Abstracta que classifica tots els sistemes lògics amb un bon comportament algebraic i s'ha expandit a una nova jerarquia (que anomenem implicacional) que permet definir noves classes de lògiques borroses que contenen quasi totes les conegudes fins ara. En segon lloc, s’ha continuat una línia d'investigació iniciada els darrers anys consistent en l'estudi de la veritat parcial com a noció sintàctica (és a dir, com a constants de veritat explícites en els sistemes de prova de les lògiques borroses). Per primer cop, s’ha considerat la semàntica racional per les lògiques proposicionals i la semàntica real i racional per les lògiques de primer ordre expandides amb constants. En tercer lloc, s’ha tractat el problema més fonamental del significat i la utilitat de les lògiques borroses com a modelitzadores de (part de) els fenòmens de la vaguetat en un darrer article de caràcter més filosòfic i divulgatiu, i en un altre més tècnic en què defensem la necessitat i presentem l'estat de l'art de l'estudi de les estructures algèbriques associades a les lògiques borroses. Finalment, s’ha dedicat la darrera part del projecte a l'estudi de la complexitat aritmètica de les lògiques borroses de primer ordre.

Equivariant semiprojectivity

We define equivariant semiprojectivity for C* -algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: A. Arbitrary finite dimensional C*-algebras with arbitrary actions of compact groups. - B. The Cuntz algebras Od and extended Cuntz algebras Ed, for finite d, with quasifree actions of compact groups. - C. The Cuntz algebra O∞ with any quasifree action of a finite group. For actions of finite groups, we prove that equivariant semiprojectivity is equiv- alent to a form of equivariant stability of generators and relations. We also prove that if G is finite, then C*(G) is graded semiprojective.

Space-time within general relativity : a structural realist understanding

ABSTRACT This dissertation investigates the, nature of space-time as described by the theory of general relativity. It mainly argues that space-time can be naturally interpreted as a physical structure in the precise sense of a network of concrete space-time relations among concrete space-time points that do not possess any intrinsic properties and any intrinsic identity. Such an interpretation is fundamentally based on two related key features of general relativity, namely substantive general covariance and background independence, where substantive general covariance is understood as a gauge-theoretic invariance under active diffeomorphisms and background independence is understood in the sense that the metric (or gravitational) field is dynamical and that, strictly speaking, it cannot be uniquely split into a purely gravitational part and a fixed purely inertial part or background. More broadly, a precise notion of (physical) structure is developed within the framework of a moderate version of structural realism understood as a metaphysical claim about what there is in the world. So, the developement of this moderate structural realism pursues two main aims. The first is purely metaphysical, the aim being to develop a coherent metaphysics of structures and of objects (particular attention is paid to the questions of identity and individuality of these latter within this structural realist framework). The second is to argue that moderate structural realism provides a convincing interpretation of the world as described by fundamental physics and in particular of space-time as described by general relativity. This structuralist interpretation of space-time is discussed within the traditional substantivalist-relationalist debate, which is best understood within the broader framework of the question about the relationship between space-time on the one hand and matter on the other. In particular, it is claimed that space-time structuralism does not constitute a 'tertium quid' in the traditional debate. Some new light on the question of the nature of space-time may be shed from the fundamental foundational issue of space-time singularities. Their possible 'non-local' (or global) feature is discussed in some detail and it is argued that a broad structuralist conception of space-time may provide a physically meaningful understanding of space-time singularities, which is not plagued by the conceptual difficulties of the usual atomsitic framework. Indeed, part of these difficulties may come from the standard differential geometric description of space-time, which encodes to some extent this atomistic framework; it raises the question of the importance of the mathematical formalism for the interpretation of space-time.

Tea consumption and incidence of type 2 diabetes in Europe: the EPIC-InterAct case-cohort study.

BACKGROUND In previous meta-analyses, tea consumption has been associated with lower incidence of type 2 diabetes. It is unclear, however, if tea is associated inversely over the entire range of intake. Therefore, we investigated the association between tea consumption and incidence of type 2 diabetes in a European population. METHODOLOGY/PRINCIPAL FINDINGS The EPIC-InterAct case-cohort study was conducted in 26 centers in 8 European countries and consists of a total of 12,403 incident type 2 diabetes cases and a stratified subcohort of 16,835 individuals from a total cohort of 340,234 participants with 3.99 million person-years of follow-up. Country-specific Hazard Ratios (HR) for incidence of type 2 diabetes were obtained after adjustment for lifestyle and dietary factors using a Cox regression adapted for a case-cohort design. Subsequently, country-specific HR were combined using a random effects meta-analysis. Tea consumption was studied as categorical variable (0, >0-<1, 1-<4, ≥ 4 cups/day). The dose-response of the association was further explored by restricted cubic spline regression. Country specific medians of tea consumption ranged from 0 cups/day in Spain to 4 cups/day in United Kingdom. Tea consumption was associated inversely with incidence of type 2 diabetes; the HR was 0.84 [95%CI 0.71, 1.00] when participants who drank ≥ 4 cups of tea per day were compared with non-drinkers (p(linear trend) = 0.04). Incidence of type 2 diabetes already tended to be lower with tea consumption of 1-<4 cups/day (HR = 0.93 [95%CI 0.81, 1.05]). Spline regression did not suggest a non-linear association (p(non-linearity) = 0.20). CONCLUSIONS/SIGNIFICANCE A linear inverse association was observed between tea consumption and incidence of type 2 diabetes. People who drink at least 4 cups of tea per day may have a 16% lower risk of developing type 2 diabetes than non-tea drinkers.

L'aportació de Tomàs Cerdà en la introducció del càlcul diferencial i integral a l'Espanya del segle XVIII

El desenvolupament del càlcul diferencial i integral com a disciplina científica a Europa durant el segle XVIII no és un tema nou. Però s’ha acostumat a enfocar la visió d’aquesta formació molt sovint des del “centre” i a partir de les grans figures com Isaac Newton o Gottfried Wilhelm Leibniz. En el present treball el protagonista potser, per a molts, no és una figura de primera línia; Tomàs Cerdà, és un ensenyant a Barcelona i a Madrid durant la segona meitat del segle XVIII, que “tradueix” al castellà autors anglesos, però que amb la seva pràctica està realment introduint el nou càlcul a Espanya i donant, de fet, una orientació d’aquesta nova disciplina als seus deixebles. El com i per què Cerdà decideix quin serà el seu guia en la introducció del càlcul diferencial i integral i quines seran les seves pròpies aportacions en aquesta labor seran els temes centrals del nostre treball. La nostra tasca ha anat, així doncs, a entendre millor, el procés de divulgació del coneixement científic, veient-lo en tot moment com formant part activa del mateix procés de construcció d’aquest coneixement.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method