First and second-order derivatives for CP and INDSCAL

In this paper we provide the means to analyse the second-order differential structure of optimization functions concerning CANDECOMP/PARAFAC and INDSCAL. Closed-form formulas are given under two types of constraint: unit-length columns or orthonormality of two of the three component matrices. Some numerical problems that might occur during the computation of the Jacobian and Hessian matrices are addressed. The use of these matrices is illustrated in three applications. (C) 2010 Elsevier B.V. All rights reserved

Beyond the ontological turn: affirming the relative autonomy of politics

In this article, I critically evaluate a characteristic tendency that is found across the various traditions of poststructuralism, both narrowly and more broadly defined. This is an increasing propensity to be preoccupied with ontological questions and seemingly at the expense of either a refinement of political concepts or a concrete analysis of forms of power and domination. I consider the reasons for this development and stress how this characteristic feature of poststructuralism appears to follow from the very fact of ontological pluralism. What we see in contemporary continental thought is a proliferation of different traditions, and each side seeks to defend their position in ontological terms. Following this, I advance the idea of a relative autonomy between ontology and politics, where the former does not determine the latter in any direct or straightforward fashion. I argue that we need to stress this relative autonomy to open a little space between ontology and politics, space where we can return poststructuralism to a more concrete engagement with ‘the political’

Historical literacy and consciousness

A ideia de literacia histórica - enquanto conjunto de competências de interpretação e compreensão do passado - surge associada à proposta de desenvolvimento da consciência histórica, tal como defende Peter Lee. Esta necessidade de orientação temporal exige identificações múltiplas, a várias escalas (do local ao global), e a consideração de pontos de vista diversificados, apresentados quer por historiadores quer por outras fontes para a História. Assumindo a relevância desta problemática para a formação da consciência histórica, é pertinente interrogarmo-nos acerca de como desenvolvem os alunos universitários (futuros professores de História) as suas competências de literacia histórica. No âmbito da disciplina de Metodologia do Ensino da História, no 4º ano da Licenciatura em Ensino de História (Universidade do Minho), explorararam-se as seguintes questões de investigação: 1) Que critérios utilizam os futuros professores de História quando decidem entre versões históricas diferentes? 2) Como é que estes futuros professores fundamentam os seus argumentos a favor ou contra uma determinada versão? Aos dezoito alunos do curso participantes neste estudo, foi proposta uma tarefa de avaliação de dois textos históricos, um de Luís de Albuquerque, historiador português, outro de Sanjay Subrahmanyam, historiador indiano, sobre a primeira viagem marítima dos portugueses à Índia (com suporte em várias fontes, nomeadamente um excerto do diário de viagem de Gama). Conjugando-se as dimensões de interpretação substantiva das mensagens com a de uso de critérios históricos, os dados sugeriram uma categorização global constituída por cinco níveis de ideias. Os padrões mais observados ligam-se a noções de viés (a validade histórica depende de uma maior ou menor neutralidade) ou de influência do contexto de produção nos historiadores. A aceitação da validade de versões diferentes, enquanto algo genuíno no conhecimento histórico, emergiu entre alguns poucos alunos universitários. Esta tipologia coincide com os níveis de idéias observados em adolescentes e crianças portuguesas, em estudos anteriores, embora os níveis mais elaborados apareçam mais frequentemente entre os alunos universitários.The idea of historical literacy - as a set of competences of historical interpretation and understanding - is emerging as linked to the proposal of developing historical consciousness, as Peter Lee argues. This need for temporal orientation demands multiple identifications at several scales (from the local up to the global scale) as well as the consideration of diversified points of view, given either by historians or many other sources of history. Assuming the relevance of this issue, it is pertinent to question about the way university students (preservice history teachers) are developing their own competences of historical literacy. In the context of the Methodology of History Teaching subject, at year 4 of the Teaching of History Graduate Course (University of Minho), the following research questions were explored: 1) What criteria do the preservice history teachers employ when deciding about different historical versions? 2) How those preservice history teachers support their arguments for or against a given version? An assessment task of two historical texts, one written by Luís de Albuquerque, Portuguese historian, another by Sanjay Subrahmanyam, Indian historian, was accomplished by the 18 participants of this study. The historical texts focussed on the first Portuguese maritime voyage to India (and they were grounded on several evidence, namely an excerpt of the Gama trip log). Combining the dimensions of substantive interpretation of messages and use of historical criteria, data suggested a global categorization with five levels of ideas. The most observed patterns are related to notions of bias (historical validity depends on neutrality) or notions of influence of the historical production context). The recognition of validity of different versions as a genuine element of the historical knowledge emerged just among a few university students. Such a tipology matches with the levels of ideas observed among Portuguese children and adolescents in former studies, although the most elaborate levels appear more frequently among the university students