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.

Visual and optical performance and quality of life after implantation of posterior chamber phakic intraocular lens

Purpose To evaluate visual, optical, and quality of life (QoL) outcomes and intercorrelations after bilateral implantation of posterior chamber phakic intraocular lenses. Methods Twenty eyes with high to moderate myopia of 10 patients that underwent PRL implantation (Phakic Refractive Lens, Carl Zeiss Meditec AG) were examined. Refraction, visual acuity, photopic and low mesopic contrast sensitivity (CS) with and without glare, ocular aberrations, as well as QoL outcomes (National Eye Institute Refractive Error Quality of Life Instrument-42, NEI RQL-42) were evaluated at 12 months postoperatively. Results Significant improvement in uncorrected (UDVA) and best-corrected distance (CDVA) visual acuities were found postoperatively (p < 0.01), with significant reduction in spherical equivalent (p < 0.01). Low mesopic CS without glare was significantly better than measurements with glare for 1.5, 3, and 6 cycles/degree (p < 0.01). No significant correlations between higher order root mean square (RMS) with CDVA (r = −0.26, p = 0.27) and CS (r ≤ 0.45, p ≥ 0.05) were found. Postoperative binocular photopic CS for 12 cycles/degree and 18 cycles/degree correlated significantly with several RQL-42 scales. Glare index correlated significantly with CS measures and scotopic pupil size (r = −0.551, p = 0.04), but not with higher order RMS (r = −0.02, p = 0.94). Postoperative higher order RMS, postoperative primary coma and postoperative spherical aberration was significant higher for 5-mm pupil diameter (p < 0.01) compared with controls. Conclusions Correction of moderate to high myopia by means of PRL implantation had a positive impact on CS and QoL. The aberrometric increase induced by the surgery does not seem to limit CS and QoL. However, perception of glare is still a relevant disturbance in some cases possibly related to the limitation of the optical zone of the PRL.

The posterior chamber phakic refractive lens (PRL): a review

Implantation of phakic intraocular lenses (pIOLs) is a reversible refractive procedure, preserving the patient’s accommodative function with minimal induction of higher order aberrations compared with corneal photoablative procedures. Despite this, as an intraocular procedure, it has potential risks such as cataracts, chronic uveitis, pupil ovalization, corneal endothelial cell loss, pigmentary dispersion syndrome, pupillary block glaucoma, astigmatism, or endophthalmitis. Currently, only two models of posterior chamber pIOLs are commercially available, the implantable collammer lens (STAAR Surgical Co.) and the phakic refractive lens (PRL; Zeiss Meditec). The number of published reports on the latter is very low, and some concerns still remain about its long-term safety. The present article reviews the published literature on the outcomes after PRL implantation in order to provide a general overview and evaluate its real potential as a surgical refractive option.

No. 14 Actual amount of chamber rent & board, [1799]

One folio-sized leaf containing a handwritten table with information about student boarders in Cambridge residences listing the names of the heads of families, student names, the annual rent of chambers, the board per week, and a total amount.

Description of a College Chamber (manuscript copy), ca. 1744

This humorous, rhyming poem appears to have been co-authored by Thomas Handcock of Massachusetts and Richard Waterman of Warwick, Rhode Island. The document is also signed by Catharine Waterman. Neither of the authors attended Harvard College, and the circumstances of this poem's creation are not known. The poem suggests that they composed the poem while visiting - uninvited - the room of "honest Bob." The poem describes the contents of this college chamber, including the following items: an oak table with a broken leg; paper, a pen, and sand for writing; books, including "Scotch songs," philosophy, Euclid, a book of prayer, Tillotson, and French romances; pipes and tobacco; mugs; a broken violin; copperplate and mezzotint prints; a cat; clothes; two globes; a pair of bellows; a broom; a chamber pot; a candle in a bottle; tea; cups and saucers; a letter to Chloe, to whom the room's inhabitant apparently owed money; a powder horn; a fishing net; a rusty gun; a battledore; a shuttlecock; a cannister; a pair of shoes; and a coffee mill. The poem references events related to the War of Austrian Succession (1740-1748); British Vice Admiral Edward Vernon's siege of Portobello (in present-day Panama) in 1739; the "Rushian War" (perhaps the Russo-Swedish War of 1741-1743); and the War of Jenkins' Ear (the cat in the college chamber, like British Captain Robert Jenkins, has lost an ear).

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.

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.