US market entry by Spanish pharmaceutical firms

This work explores the factors that spur firms’ propensity to enter in international markets. Among the whole population of Spanish firms active in the pharmaceutical sector (over the period 1995-2004), we identify those firms that have entered the US market by assessing whether they have filed at least a trademark in the US Patents and Trademarks Office. By means of a hazard model, we empirically estimate which firm’s characteristics affect the probability of entry in the US market in a given year. Results show that technological capabilities (breadth and depth of firms’ patent base), and the firm’s cost structure explain the entry in the US market with a branded product. Moreover, our evidence shows that entry strategies based on differentiation advantage (technological diversification) and strategies based on cost advantage (scale economies) are exclusive and do not mix well each otherForeign market entry, Internationalization strategies, Firm-Specific advantages, Competitive advantage, Innovation and R&D, Patents, Trademarks

Is 0716+714 a superluminal blazar?

We present an analysis of new and old high frequency VLBI data collected during the last 10 years at 5--22 GHz. For the jet components in the mas-VLBI jet, two component identifications are possible. One of them with quasi-stationary components oscillating about their mean positions. Another identification scheme, which formally gives the better expansion fit, yields motion with $\sim 9$ $c$ for $H_0=65$ km s$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$. This model would be in better agreement with the observed rapid IDV and the expected high Lorentz-factor, deduced from IDV.Comment: 2 pages, 3 figures, appears in: Proceedings of the 6th European VLBI Network Symposium held on June 25th-28th in Bonn, Germany. Edited by: E. Ros, R.W. Porcas, A.P. Lobanov, and J.A. Zensu

Analysing the behaviour of robot teams through relational sequential pattern mining

This report outlines the use of a relational representation in a Multi-Agent domain to model the behaviour of the whole system. A desired property in this systems is the ability of the team members to work together to achieve a common goal in a cooperative manner. The aim is to define a systematic method to verify the effective collaboration among the members of a team and comparing the different multi-agent behaviours. Using external observations of a Multi-Agent System to analyse, model, recognize agent behaviour could be very useful to direct team actions. In particular, this report focuses on the challenge of autonomous unsupervised sequential learning of the team's behaviour from observations. Our approach allows to learn a symbolic sequence (a relational representation) to translate raw multi-agent, multi-variate observations of a dynamic, complex environment, into a set of sequential behaviours that are characteristic of the team in question, represented by a set of sequences expressed in first-order logic atoms. We propose to use a relational learning algorithm to mine meaningful frequent patterns among the relational sequences to characterise team behaviours. We compared the performance of two teams in the RoboCup four-legged league environment, that have a very different approach to the game. One uses a Case Based Reasoning approach, the other uses a pure reactive behaviour.Comment: 25 page

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

Classification of symmetric periodic trajectories in ellipsoidal billiards

We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are defined as periodic trajectories passing through some symmetry set. We prove that there are exactly 2^{2n}(2^{n+1}-1) classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (R^2) and each of the 112 classes in the 3D case (R^3). They have periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We display a selection of 3D minimal SPTs. Some of them have properties that cannot take place in the 2D case.Comment: 26 pages, 77 figures, 17 table

Blow-up behaviour of a fractional Adams-Moser-Trudinger type inequality in odd dimension

Given a smoothly bounded domain $\Omega\Subset\mathbb{R}^n$ with $n\ge 1$ odd, we study the blow-up of bounded sequences $(u_k)\subset H^\frac{n}{2}_{00}(\Omega)$ of solutions to the non-local equation $$(-\Delta)^\frac n2 u_k=\lambda_k u_ke^{\frac n2 u_k^2}\quad \text{in }\Omega,$$ where $\lambda_k\to\lambda_\infty \in [0,\infty)$, and $H^{\frac n2}_{00}(\Omega)$ denotes the Lions-Magenes spaces of functions $u\in L^2(\mathbb{R}^n)$ which are supported in $\Omega$ and with $(-\Delta)^\frac{n}{4}u\in L^2(\mathbb{R}^n)$. Extending previous works of Druet, Robert-Struwe and the second author, we show that if the sequence $(u_k)$ is not bounded in $L^\infty(\Omega)$, a suitably rescaled subsequence $\eta_k$ converges to the function $\eta_0(x)=\log\left(\frac{2}{1+|x|^2}\right)$, which solves the prescribed non-local $Q$-curvature equation $$(-\Delta)^\frac n2 \eta =(n-1)!e^{n\eta}\quad \text{in }\mathbb{R}^n$$ recently studied by Da Lio-Martinazzi-Rivi\`ere when $n=1$, Jin-Maalaoui-Martinazzi-Xiong when $n=3$, and Hyder when $n\ge 5$ is odd. We infer that blow-up can occur only if $\Lambda:=\limsup_{k\to \infty}\|(-\Delta)^\frac n4 u_k\|_{L^2}^2\ge \Lambda_1:= (n-1)!|S^n|$