Advances on Matroid Secretary Problems: Free Order Model and Laminar Case

The most well-known conjecture in the context of matroid secretary problems claims the existence of a constant-factor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secretaries is not adversarial but uniformly random (Soto [SODA 2011], Oveis Gharan and Vondr\'ak [ESA 2011]). However, so far, there was no variant of the matroid secretary problem with adversarial weight assignment for which a constant-factor approximation was found. We address this point by presenting a 9-approximation for the \emph{free order model}, a model suggested shortly after the introduction of the matroid secretary problem, and for which no constant-factor approximation was known so far. The free order model is a relaxed version of the original matroid secretary problem, with the only difference that one can choose the order in which secretaries are interviewed. Furthermore, we consider the classical matroid secretary problem for the special case of laminar matroids. Only recently, a constant-factor approximation has been found for this case, using a clever but rather involved method and analysis (Im and Wang, [SODA 2011]) that leads to a 16000/3-approximation. This is arguably the most involved special case of the matroid secretary problem for which a constant-factor approximation is known. We present a considerably simpler and stronger $3\sqrt{3}e\approx 14.12$-approximation, based on reducing the problem to a matroid secretary problem on a partition matroid

Islam and private property

Cet article soutient que la faiblesse des libertés économiques dans les pays de l'aire musulmane (1) s'explique par l'histoire du droit musulman et plus particulièrement sa conception des droits de propriété. Il montre que la principale résistance à l'avènement de la propriété privée fût le statut de la terre hérité de la domination des premiers califats. Il rappelle, d'une part, les effets des inégalités formelles entre les hommes (homme – femme, homme – esclave, musulman – non musulman) en droit musulman et, d'autre part, des restrictions sur la propriété sur le développement économique (2), mais soutient que le cœur du blocage est le statut juridique de la terre. Ce statut protège la propriété publique et l'étend à l'eau. Il enferme l'économie dans une logique d'enrichissement où les opportunités de profit sont artificiellement créées par les rentes saisies par la classe dirigeante (3). La conclusion est consacrée à l'avenir de la liberté économique dans cette aire (4).développement économique, droit de propriété, Islam et prédation

Identity and Islamic Radicalization in Western Europe

This paper argues that both socio-economic disadvantage and political factors, such as the West’s foreign policy with regard to the Muslim world, along with historical grievances, play a part in the development of Islamic radicalized collective action in Western Europe. We emphasise the role of group identity based individual behaviour in organising collective action within radicalized Muslim groups. Inasmuch as culture plays any role at all in radicalization, it is because individuals feel an imperative to act on the basis of their Muslim identity, something to which different individuals will attach varying degrees of salience, depending on how they place their Muslim identity based actions in the scheme of their multiple identities. We also emphasize the role of the opportunistic politician, from the majority European community, in fomenting hatred for Muslims, which also produces a backlash from radicalized political Islam. We present comparative evidence on socio-economic, political and cultural disadvantage faced by Muslim minorities in five West European countries: Germany, the UK, France, Spain and the Netherlands.Peacekeeping; Identity, Radicalization, Clash of civilizations, Terrorism

Identity and Islamic Radicalization in Western Europe

This paper argues that both socio-economic disadvantage and political factors, such as the West's foreign policy with regard to the Muslim world, along with historical grievances, play a part in the development of Islamic radicalized collective action in Western Europe. We emphasise the role of group identity based individual behaviour in organising collective action within radicalized Muslim groups. Inasmuch as culture plays any role at all in radicalization, it is because individuals feel an imperative to act on the basis of their Muslim identity, something to which different individuals will attach varying degrees of salience, depending on how they place their Muslim identity based actions in the scheme of their multiple identities. We also emphasize the role of the opportunistic politician, from the majority European community, in fomenting hatred for Muslims, which also produces a backlash from radicalized political Islam. We present comparative evidence on socio-economic, political and cultural disadvantage faced by Muslim minorities in five West European countries: Germany, the UK, France, Spain and the Netherlands.Identity, Radicalization, Clash of civilizations, Terrorism

Islamic headscarves and female circumcision: Unveiling the threat posed by Islam to human rights

This paper is, in part, a response to the NZPGLeJ Editor-in-Chief Herman Salton’s article,“‘Veiled Threats?’ Islam, Headscarves and Freedom of Religion in France and the United States”, which was published in the first issue of this journal. However, it moves beyond Salton’s article as it seeks to address familiar assumptions regarding the inherent incompatibility of Islam with human rights, particularly women’s rights. By focusing on two distinct issues, the Islamic headscarf and the practice of female circumcision, questions are raised as to whether Islam and human rights, especially women’s rights, are truly incompatible or whether there are other issues at stake. It also discusses the defamation of religions, particularly Islam, and the recent steps taken by the United Nations Commission on Human Rights in relation to this issue. The paper concludes by providing some insights into the likely future direction that the headscarf debate may take in New Zealand

Prophet Inequalities: Separating Random Order from Order Selection

Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values online, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on the model. When observing each value, the gambler either accepts it as a reward or irrevocably rejects it and proceeds to observe the next value. The goal of the gambler, who cannot see the future, is maximising the expected value of the reward while competing against the expectation of a prophet (the offline maximum). In other words, one seeks to maximise the gambler-to-prophet ratio of the expectations. The model, in which the gambler selects the arrival order first, and then observes the values, is known as Order Selection. Recently it has been shown that in this model a ratio of $0.7251$ can be attained for any instance. If the gambler chooses the arrival order (uniformly) at random, we obtain the Random Order model. The worst case ratio over all possible instances has been extensively studied for at least $40$ years. Still, it is not known if carefully choosing the order, or simply taking it at random, benefits the gambler. We prove that, in the Random Order model, no algorithm can achieve a ratio larger than $0.7235$, thus showing for the first time that there is a real benefit in choosing the order.Comment: 36 pages, 2 figure

International Human Rights: Islam\u27s Friend or Foe? Algeria as an Example of the Compatibility of International Human Rights Regarding Women\u27s Equality and Islamic Law

Part I of this Note briefly discusses the development of International Human Rights Law as embodied in international covenants today. Part I also discusses Islamic law, the traditional role of women under Islamic law and culture, Algeria\u27s Constitution and Family Code, and other dynamics specific to Algeria that have hindered women\u27s obtainment of equal rights in the modern era. Part II presents the debate between conservative Islamists who argue that international principles of human rights law are incompatible with Islamic law and the scholars who assert that the two are compatible. Part III, by focusing on fundamental principles underlying the provisions in both the international human rights doctrine and Islamic law, argues that international human rights provisions granting women equal status with men comport with Islamic law principles as much as do legal documents that the Algerian Government has drafted. This Note concludes that the deprivation of women\u27s equal rights based on the claim of conflict with Islamic law is unjustified and that the example of Algeria proves that Islamic countries can and should protect human rights without regard to gender