Motzkin decomposition of closed convex sets via truncation

A nonempty set F is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set C with a closed convex cone D. In that case, the sets C and D are called compact and conic components of F. This paper provides new characterizations of the Motzkin decomposable sets involving truncations of F (i.e., intersections of FF with closed halfspaces), when F contains no lines, and truncations of the intersection F̂ of F with the orthogonal complement of the lineality of F, otherwise. In particular, it is shown that a nonempty closed convex set F is Motzkin decomposable if and only if there exists a hyperplane H parallel to the lineality of F such that one of the truncations of F̂ induced by H is compact whereas the other one is a union of closed halflines emanating from H. Thus, any Motzkin decomposable set F can be expressed as F=C+D, where the compact component C is a truncation of F̂. These Motzkin decompositions are said to be of type T when F contains no lines, i.e., when C is a truncation of F. The minimality of this type of decompositions is also discussed.

On the stability of the Motzkin representation of closed convex sets

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple (C,D) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.

Relationship between static and dynamic elastic modulus of calcarenite heated at different temperatures: the San Julián's stone

The San Julián’s stone is the main material used to build the most important historical buildings in Alicante city (Spain). This paper describes the analysis developed to obtain the relationship between the static and the dynamic modulus of this sedimentary rock heated at different temperatures. The rock specimens have been subjected to heating processes at different temperatures to produce different levels of weathering on 24 specimens. The static and dynamic modulus has been measured for every specimen by means of the ISRM standard and ultrasonic tests, respectively. Finally, two analytic formulas are proposed for the relationship between the static and the dynamic modulus for this stone. The results have been compared with some relationships proposed by different researchers for other types of rock. The expressions presented in this paper can be useful for the analysis, using non-destructive techniques, of the integrity level of historical constructions built with San Julián’s stone affected by fires.

The EU and Syria – Time to Play behind Closed Doors. Jean Monnet/Robert Schuman Paper Series Special Issue, September 13, 2013

From the Introduction. Since the – presumed – utilization of chemical weapons against civilians by the Assad regime late August, the members of the Euro-Atlantic community have been building the case for a military intervention, a punishing mission against Bashar al-Assad. Despite evidences that sarin gas was used, the UK and Germany seem to be out of the race – for a similar reason: domestic politics –, leaving the US and France in the starting blocks. French President Hollande has expressed his commitment to go to war. The world is now on hold waiting for the US as President Obama, after asking US Congress to postpone a vote on a military intervention, is working on a possible diplomatic solution with Russian President Putin. Since Kerry’s comments in London earlier this week, Russian President Putin has been seeking for a diplomatic solution that would put all Syrian chemical arsenals under international supervision.

Lymphatic vessel function in atherosclerosis

L'athérosclérose est une maladie inflammatoire chronique caractérisée par l'accumulation de cholestérol dans la paroi artérielle et associée à une réponse immunitaire anormale dans laquelle les macrophages jouent un rôle important. Récemment, il a été démontré que les vaisseaux lymphatiques jouent un rôle primordial dans le transport inverse du cholestérol (Martel et al. JCI 2013). L’objectif global de mon stage de maîtrise a été de mieux caractériser la dysfonction lymphatique associée à l’athérosclérose, en étudiant de plus près l’origine physiologique et temporelle de ce mauvais fonctionnement. Notre approche a été d’étudier, depuis l’initiation de l’athérosclérose jusqu’à la progression d’une lésion athérosclérotique tardive, la physiologie des deux constituants principaux qui forment les vaisseaux lymphatiques : les capillaires et collecteurs lymphatiques. En utilisant comme modèle principal des souris Ldlr-/-; hApoB100+/+, nous avons pu démontrer que la dysfonction lymphatique est présente avant même l’apparition de l’athérosclérose, et que cette dysfonction est principalement associée avec un défaut au niveau des vaisseaux collecteurs, limitant ainsi le transport de la lymphe des tissus périphériques vers le sang. De plus, nous avons démontré pour la première fois l’expression du récepteur au LDL par les cellules endothéliales lymphatiques. Nos travaux subséquents démontrent que ce défaut de propulsion de la lymphe pourrait être attribuable à l’absence du récepteur au LDL, et que la dysfonction lymphatique observée précocement dans l’athérosclérose peut être limitée par des injections systémiques de VEGF (vascular endothelial growth factor) –C. Ces résultats suggèrent que la caractérisation fonctionnelle de la capacité de pompage des vaisseaux collecteurs serait une condition préalable à la compréhension de l'interaction entre la fonction du système lymphatique et la progression de l'athérosclérose. Ultimement, nos travaux nous ont amené à considérer de nouvelles cibles thérapeutiques potentielles dans la prévention et le traitement de l’athérosclérose.

Overthrowing Secrecy: The Spitzenkandidaten experiment and a new chance for a European party system. CEPS Commentary, 4 August 2014

The Spitzenkandidaten experiment has been at the centre of a heated debate for several months now, prompting much speculation as to the changes it will bring to the balance of power between the EU institutions. But the real coup d’état has been directed against the old process of appointing the European Commission President behind closed doors. Although the new procedure entails “a number of political, institutional and ‘thus’ constitutional ambiguities”, according to the authors of this commentary, it has rendered that process more transparent, if not more democratic – and will almost certainly endure to the next European elections in 2019 and beyond. As a result, they conclude that the new procedure is likely to trigger important changes in Europe’s political parties and elections.

Clinical prediction of large vessel occlusion in anterior circulation stroke: mission impossible?

Simple clinical scores to predict large vessel occlusion (LVO) in acute ischemic stroke would be helpful to triage patients in the prehospital phase. We assessed the ability of various combinations of National Institutes of Health Stroke Scale (NIHSS) subitems and published stroke scales (i.e., RACE scale, 3I-SS, sNIHSS-8, sNIHSS-5, sNIHSS-1, mNIHSS, a-NIHSS items profiles A-E, CPSS1, CPSS2, and CPSSS) to predict LVO on CT or MR arteriography in 1085 consecutive patients (39.4 % women, mean age 67.7 years) with anterior circulation strokes within 6 h of symptom onset. 657 patients (61 %) had an occlusion of the internal carotid artery or the M1/M2 segment of the middle cerebral artery. Best cut-off value of the total NIHSS score to predict LVO was 7 (PPV 84.2 %, sensitivity 81.0 %, specificity 76.6 %, NPV 72.4 %, ACC 79.3 %). Receiver operating characteristic curves of various combinations of NIHSS subitems and published scores were equally or less predictive to show LVO than the total NIHSS score. At intersection of sensitivity and specificity curves in all scores, at least 1/5 of patients with LVO were missed. Best odds ratios for LVO among NIHSS subitems were best gaze (9.6, 95 %-CI 6.765-13.632), visual fields (7.0, 95 %-CI 3.981-12.370), motor arms (7.6, 95 %-CI 5.589-10.204), and aphasia/neglect (7.1, 95 %-CI 5.352-9.492). There is a significant correlation between clinical scores based on the NIHSS score and LVO on arteriography. However, if clinically relevant thresholds are applied to the scores, a sizable number of LVOs are missed. Therefore, clinical scores cannot replace vessel imaging.

Innovation and Development in the Age of Climate Change Adaptation: Open or Closed?

Change Adaptation: Open or Closed? Paper read at the Second African International Economic Law Network Conference, 7-8 March 2013, Wits School of Law, Johannesburg, South Africa. In a time of rapid convergence of technologies, goods, services, hardware, software, the traditional classifications that informed past treaties fail to remove legal uncertainty, or advance welfare and innovation. As a result, we turn our attention to the role and needs of the public domain at the interface of existing intellectual property rights and new modes of creation, production and distribution of goods and services. The concept of open culture would have it that knowledge should be spread freely and its growth should come from further developing existing works on the basis of sharing and collaboration without the shackles of intellectual property. Intellectual property clauses find their way into regional, multilateral, bilateral and free trade agreements more often than not, and can cause public discontent and incite unrest. Many of these intellectual property clauses raise the bar on protection beyond the clauses found in the WTO Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS). In this paper we address the question of the protection and development of the public domain in service of open innovation in accord with Article 15 of the International Covenant on Economic, Social and Cultural Rights (ICESCR) in light of the Objectives (Article 7) and Principles (Article 8) set forth in TRIPS. Once areas of divergence and reinforcement between the intellectual property regime and human rights have been discussed, we will enter into options that allow for innovation and prosperity in the global south. We then conclude by discussing possible policy developments.