The Cartesian product of graphs with loops

We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one unlooped vertex. We also prove that this factorization can be computed in O(m) time, where m is the number of edges of the given graph.Comment: 8 pages, 1 figur

Towards an evolutionary environmental regulation of capitalism : sustainable development 20 years after

The paper argues that by combining ecological economics, IPE and regulation approaches more closely, one may provide an account of the apparent contradiction between the utopian aspect of sustainable development and the ability of capitalism to pragmatically deal with ecological crises. It explores how ensuing institutional forms inevitably take sustainability claims into account. It assumes that such forms revolve around the emergence of a new type of evolutionary environmental regulation whose coherence is paradoxically at once open-ended, fragmented and hybrid. This feature clearly reinforces the extreme difficulty in thinking about ecological regularities. The paper analyses core elements of such institutional forms and how far they can be identified as a new type of fragmented evolutionary environmental regulation. Section 1 provides background on the notion of sustainable development. Sections 2 examines the prospects and limits of regulation theory on global ecological issues and presents lessons could be drawn from ecological economics and international political economy approaches for opening new routes to appraise current and future environmental concerns of capitalism. Section 3 explores the emerging form of evolutionary environmental regulation reflecting the apparently paradoxical situation we have reached, in which disillusion regarding sustainable development goes hand in hand with increasing awareness of the inescapability of a policy shift in its favour.SUSTAINABLE DEVELOPMENT

Three cotyledons on Schinziophyton rautanenii seedlings

During a study of seedling growth in Schinziophyton rautanenii (Schinz) Hutch. Ex Radcl.-Sm. some anomalous seedlings developed from a batch of seeds collected in the Rundu area of northern Namibia. These seedlings had three cotyledons instead of the usual two. This report of tricotyly in Euphorbiaceae is the first for the family

Prognostic Ability of Practitioners of Traditional Arabic Medicine: Comparison with Western Methods Through a Relative Patient Progress Scale

The ancient Greek medical theory based on balance or imbalance of humors disappeared in the western world, but does survive elsewhere. Is this survival related to a certain degree of health care efficiency? We explored this hypothesis through a study of classical Greco-Arab medicine in Mauritania. Modern general practitioners evaluated the safety and effectiveness of classical Arabic medicine in a Mauritanian traditional clinic, with a prognosis/follow-up method allowing the following comparisons: (i) actual patient progress (clinical outcome) compared with what the traditional ‘tabib’ had anticipated (= prognostic ability) and (ii) patient progress compared with what could be hoped for if the patient were treated by a modern physician in the same neighborhood. The practice appeared fairly safe and, on average, clinical outcome was similar to what could be expected with modern medicine. In some cases, patient progress was better than expected. The ability to correctly predict an individual's clinical outcome did not seem to be better along modern or Greco-Arab theories. Weekly joint meetings (modern and traditional practitioners) were spontaneously organized with a modern health centre in the neighborhood. Practitioners of a different medical system can predict patient progress. For the patient, avoiding false expectations with health care and ensuring appropriate referral may be the most important. Prognosis and outcome studies such as the one presented here may help to develop institutions where patients find support in making their choices, not only among several treatment options, but also among several medical systems