Labour productivity in the Nordic EU countries - a comparative overview and explanatory factors – 1998-2004

This paper analyses the differences in hourly labour productivity growth rates and levels between the Nordic EU countries (Denmark, Finland and Sweden) and four larger euro area countries (Germany, France, Italy and Spain). Additional information for the euro area as a whole, the UK and the US is also provided. Given that the economic and social models developed in the Nordic EU countries are in many ways closer to those of the larger euro area countries than that of the US, the experience of these countries is particularly interesting. Since the mid-1990s, the Nordic EU countries, particularly Sweden and Finland, have experienced stronger labour productivity growth than the larger euro countries. Like in the US, innovation and technological changes have played a major role in explaining the higher labour productivity growth in the Nordic EU countries compared with the larger euro area economies. Information and Communication Technology (ICT) diffusion is a key element to explain these differences. A number of institutional indicators, relating to market regulation, human capital, R&D investments and venture capital, show that the Nordic EU economies are better positioned than some of the larger euro area countries to exploit the opportunities provided by ICT in terms of productivity growth. However, remaining labour market rigidities may not allow the Nordic EU countries to fully enjoy the benefits of ICT diffusion in terms of increased employment.

Two-Level Type Theory and Applications

We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is homotopy type theory (HoTT) which may include univalent universes and higher inductive types. The outer theory is a traditional form of type theory validating uniqueness of identity proofs (UIP). One point of view on it is as internalised meta-theory of the inner type theory. There are two motivations for 2LTT. Firstly, there are certain results about HoTT which are of meta-theoretic nature, such as the statement that semisimplicial types up to level $n$ can be constructed in HoTT for any externally fixed natural number $n$. Such results cannot be expressed in HoTT itself, but they can be formalised and proved in 2LTT, where $n$ will be a variable in the outer theory. This point of view is inspired by observations about conservativity of presheaf models. Secondly, 2LTT is a framework which is suitable for formulating additional axioms that one might want to add to HoTT. This idea is heavily inspired by Voevodsky's Homotopy Type System (HTS), which constitutes one specific instance of a 2LTT. HTS has an axiom ensuring that the type of natural numbers behaves like the external natural numbers, which allows the construction of a universe of semisimplicial types. In 2LTT, this axiom can be stated simply be asking the inner and outer natural numbers to be isomorphic. After defining 2LTT, we set up a collection of tools with the goal of making 2LTT a convenient language for future developments. As a first such application, we develop the theory of Reedy fibrant diagrams in the style of Shulman. Continuing this line of thought, we suggest a definition of (infinity,1)-category and give some examples.Comment: 53 page

Adventures in Formalisation: Financial Contracts, Modules, and Two-Level Type Theory

We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language for financial contracts (the CL language). The code in CL is translated into a simple expression language well-suited for integration with software components implementing Monte Carlo simulation techniques (pricing engines). The compilation procedure is accompanied with formal proofs of correctness carried out in Coq. The second project presents techniques that allow for formal reasoning with nested and mutually inductive structures built up from finite maps and sets. The techniques, which build on the theory of nominal sets combined with the ability to work with isomorphic representations of finite maps, make it possible to give a formal treatment, in Coq, of a higher-order module system, including the ability to eliminate at compile time abstraction barriers introduced by the module system. The development is based on earlier work on static interpretation of modules and provides the foundation for a higher-order module language for Futhark, an optimising compiler targeting data-parallel architectures. The third project presents an implementation of two-level type theory, a version of Martin-Lof type theory with two equality types: the first acts as the usual equality of homotopy type theory, while the second allows us to reason about strict equality. In this system, we can formalise results of partially meta-theoretic nature. We develop and explore in details how two-level type theory can be implemented in a proof assistant, providing a prototype implementation in the proof assistant Lean. We demonstrate an application of two-level type theory by developing some results on the theory of inverse diagrams using our Lean implementation.Comment: PhD thesis defended in January 2018 at University of Copenhagen, Department of Computer Scienc

Definition of a family of tissue-protective cytokines using functional cluster analysis: a proof-of-concept study

The discovery of the tissue-protective activities of erythropoietin (EPO) has underlined the importance of some cytokines in tissue-protection, repair, and remodeling. As such activities have been reported for other cytokines, we asked whether we could define a class of tissue-protective cytokines. We therefore explored a novel approach based on functional clustering. In this pilot study, we started by analyzing a small number of cytokines (30). We functionally classified the 30 cytokines according to their interactions by using the bioinformatics tool STRING (Search Tool for the Retrieval of Interacting Genes), followed by hierarchical cluster analysis. The results of this functional clustering were different from those obtained by clustering cytokines simply according to their sequence. We previously reported that the protective activity of EPO in a model of cerebral ischemia was paralleled by an upregulation of synaptic plasticity genes, particularly early growth response 2 (EGR2). To assess the predictivity of functional clustering, we tested some of the cytokines clustering close to EPO (interleukin-11, IL-11; kit ligand, KITLG; leukemia inhibitory factor, LIF; thrombopoietin, THPO) in an in vitro model of human neuronal cells for their ability to induce EGR2. Two of these, LIF and IL-11, induced EGR2 expression. Although these data would need to be extended to a larger number of cytokines and the biological validation should be done using more robust in vivo models, rather then just one cell line, this study shows the feasibility of this approach. This type of functional cluster analysis could be extended to other fields of cytokine research and help design biological experiments

Peinture et révolution : propos de Lénine et de Trotsky sur l’art pictural d’après les souvenirs d’un portraitiste officiel

Une brève présentation des Vies et Œuvres (au pluriel) d’Iouri Pavlovitch (dit Georges) Annenkov (1889-1974) constitue simplement un défi au bon sens : l’homme a en effet touché à tout, à la fois portraitiste, peintre, lithographe, illustrateur, décorateur de théâtre, costumier de cinéma, caricaturiste, écrivain, critique, metteur en scène... Il a été l’ami de nombreuses célébrités — russes, françaises, italiennes —, l’admirateur de nombreuses cultures — russe, japonaise, finlandaise et médit..