Critical percolation on certain non-unimodular graphs

An important conjecture in percolation theory is that almost surely no infinite cluster exists in critical percolation on any transitive graph for which the critical probability is less than 1. Earlier work has established this for the amenable cases Z^2 and Z^d for large d, as well as for all non-amenable graphs with unimodular automorphism groups. We show that the conjecture holds for the basic classes of non-amenable graphs with non-unimodular automorphism groups: for decorated trees and the non-unimodular Diestel-Leader graphs. We also show that the connection probability between two vertices decay exponentially in their distance. Finally, we prove that critical percolation on the positive part of the lamplighter group has no infinite clusters.Comment: 15 pages, 5 figures. Several corrections to previous versio

Tempo e educação em Platão

This paper aims to present some views about Plato's reflection on education and its temporality, emphasizing the "inner" time involved in questions of areté, knowledge and teleology of human life. The dignity of living as an aim dependant on normative reason (lógos), is a base to the action of those who have Philosophy as an specific reflection for the education of the soul, as the Philosopher regarded it.Neste texto pretende-se mostrar certos ângulos da reflexão de Platão sobre a educação e sua temporalidade, privilegiando o tempo "interno" imbricado nas questões da areté, do conhecimento e da teleologia da vida humana. A dignidade do viver como meta dependente da razão normativa (lógos) estrutura a ação daqueles que têm a Filosofia como reflexão específica para a educação da alma, conforme a pensou o filósofo

Freedom of religion or belief: Group right or individual right?

Freedom of religious and belief is a recognized right in international law. In order to understand, interpret, develop and implement this right, it is important to go back and analyse the fundamental reasoning behind this right. Freedom of religion and belief is a contradictory right: a freedom for self-constraint. It is a double-sided right, a right of expression and a right of identity, two aspects related to individual and group perceptions of this right. Therefore, this right must be understood through a conflict between competing conceptions of individual and group rights. International law should protect the religious freedoms of individuals, and should protect groups only as derivative from the rights of individuals, and never in contravention of them, and generally does so. Current tendencies towards recognising group rights raise concerns, highlighting the importance of this determination. The conceptual analysis of the right serves as a critical tool for discussion of specific conflicts of rights regarding religious freedom, in different area of legal regulation. Different state constitutional structures concerning religion have important implications for analysis of the group/individual conflict. A categorization of constitutional arrangements shows that each presents problems for guaranteeing religious freedom. The constitutional analysis shows religions have public characteristics, and so must abide by human rights norms. The recognition of group rights compromises state neutrality, central to liberal theory. Whatever their constitutional arrangement, states must allow participation in religious communities while protecting individual rights. Particular conflicts are analysed: A conflict between group and individual rights exists between community religious autonomy and women's rights. While international law has been decisive in mandating supremacy of individual rights in this conflict, it has not addressed some of the root causes undermining women's individual rights. Children's religious freedom, in conflict between state, religious group, family, and child, has not always been amply protected in international law, due to absence of differentiation between group and individual interests. Lastly, use of speech by individuals directed against, or in conflict with, religious groups, such as blasphemy, proselytism or hate speech, is addressed. Discussion of these conflicts examines difficulties created, and shows that although some states, based on their respective histories, religions, and cultures, protect the group over the individual, ultimately only an individualistic approach of international law is a coherent way of protecting religious freedom as a human right

As grandes revoluções no judaísmo

O artigo apresenta um breve panorama da evolução do judaísmo, desde o século XIII antes da era cristã até os dias atuais, focalizando as diversas correntes de pensamento que nele floresceram ao longo dos séculos. São abordados os eventos sociopolíticos envolvidos na transição do hebraísmo bíblico ao judaísmo talmúdico, bem como o subsequente surgimento do caraísmo, da cabalá, do judaísmo filosófico de Maimônides, da Haskalá, do chassidismo, da Reforma e do sionismo, que culminou com a criação do Estado de Israel. The great revolutions of Judaism - Abstract: This article presents a brief overview of the evolution of Judaism, from the 13th century before the Christian era to the present day, focusing on the diverse currents of thought that flourished in it throughout the centuries. The sociopolitical events involved in the transition from Biblical Hebraism to Talmudic Judaism are addressed, as well as the subsequent emergence of Karaism, Kabbalah, the philosophy of Maimonides, Haskalah, Hasidism, Reform and Zionism, which culminated in the creation of the State of Israel

Judaisation in the first Hebrew translation of Romeo and Juliet

Ram and Jael (Salkinson 1878), the earliest Hebrew version of Romeo and Juliet, is a highly domesticating translation containing numerous Jewish cultural elements. This is attributable to the fact that the translation formed part of an ideologically loaded Jewish Enlightenment initiative to establish a European-style literary canon in Hebrew and reflecting Jewish values at a time when the language was still almost solely a written medium prior to its late nineteenth-century re-vernacularisation in Palestine. This chapter discusses the unusual sociolinguistic background to Ram and Jael and analyses its main Judaising features, which include the treatment of non-Jewish names; holidays and rituals; establishments; oaths and expressions; mythological figures; and foreign languages, as well as the insertion of biblical verses

RE: pedagogy – after neutrality

Within the UK and in many parts of the world, official accounts of what it is to make sense of religion are framed within a rhetorics of neutrality in which such study is premised upon the possibility of dispassionate engagement and analysis. This paper, which is largely theoretical in scope, explores both the affordances and the costs of such an approach which has become ‘black boxed’ on account of the work that it achieves. A series of new orientations within the academy that are broadly associated with post-structuralist philosophies, feminist and post-colonial studies, together with insights from Science and Technology Studies, question the plausibility of these claims for neutrality whilst in turn raising a series of new questions and priorities. It therefore becomes necessary to re-think and re-frame what it is to make sense of religious and cultural difference after neutrality. The gathering and co-ordination of new planes of sense-making that are responsive to an emergent series of epistemological, ontological, and ethical orientations are considered. Some of the distinctive pedagogical implications of such an approach that engages material practice, difference and uncertainty are then entertained