Equations defining probability tree models

Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of context-specific Bayesian networks. In this paper, we study the algebraic properties of their ideal of model invariants. The generators of this ideal can be easily read from the tree graph and have a straightforward interpretation in terms of the underlying model: they are differences of odds ratios coming from conditional probabilities. One of the key findings in this analysis is that the tree is a convenient tool for understanding the exact algebraic way in which the sum-to-1 conditions on the parameter space translate into the sum-to-one conditions on the joint probabilities of the statistical model. This enables us to identify necessary and sufficient graphical conditions for a staged tree model to be a toric variety intersected with a probability simplex.Comment: 22 pages, 4 figure

Identity Negotiation through the Lens of Language Rights: Refugee and Migrant Children and Youths in MissionPlace*, Budapest

This dissertation is a qualitative study that aims at investigating the potential tensions and conflicts among languages and cultures of refugee and migrant children in the Hungarian educational context and how they solve them by negotiating their identities. The study examines one main research question and four sub-questions: (1) How do refugee and migrant children and youths negotiate their identities when facing potentially contradictory linguistic and other cultural needs in their daily activities in school? (a) How do these children perceive themselves in the school as new arrivals in Hungary? (b) What roles do the languages spoken by these children play in their construction and negotiation of identity? (c) How do school teachers understand the education and integration process of migrant and refugee children in Hungary? (d) What is the role of MissionPlace* in the social inclusion of these children? In order to address these research questions, the sociocultural linguistic approach (Bucholtz & Hall, 2005) and the narrative inquiry (Connelly & Clandinin, 2006) were used. Three groups of participants were part of the study. The first group was comprised of 22 children and youths with migrant backgrounds. The other two groups comprised eight school teachers and principals and 12 members of the staff in MissionPlace*. The instruments used to generate data were interviews. Unstructured interviews with children and youths, semi-structured interviews with school teachers and principals, and ethnographic interviews with the staff in MissionPlace*. Three sets of data resulted from the three groups. The data set corresponding to the narratives of the children and youths was analyzed under the narrative approach, and the other two sets of data were examined using thematic analysis. The setting of the study is an NGO in Budapest that is protected under the pseudonym of MissionPlace*. For the narrative analysis, the five principles underlying the sociocultural linguistic approach were used to explore the constructions of identity. These five principles are (1) emergence, (2) positionality, (3) indexicality, (4) relationality, and (5) partialness. Data are categorized according to processes of identity negotiation found in the narratives, with the names of (1) fleeing from war and envisioning their future, (2) acting as conduits for understanding between Hungarian and their mother tongue, (3) navigating between two cultures, (4) overcoming the language barrier in school, and (5) empowerment, integration, and recognition through Hungarian. For the thematic analysis used to examine the interviews with school teachers and staff in MissionPlace*, three categories were organized under the titles of (1) invisibility of refugee and migrant children in the educational policies, (2) building boundaries in the classroom through monolingual teaching practices; and (3) MissionPlace* as the place of mediation between children, family, and school. Although there are studies on the topic of migration in Europe, this study is different from other studies as it is related to the identity construction of migrant children in Hungary. This is due to the fact that Hungary is a country that is not considered as an immigration country within the EU but rather a transit country for asylum seekers. In terms of research in applied linguistics, this study continues the debate on how from the narrative analysis, the process of integration through education in Europe can be better understood for the design and implementation of strategies of coexistence in multicultural settings. Issues in the relations between linguistic diversity and social justice can be considered as a way forward for such a future. The findings revealed that education in the multilingual context of Europe has not received enough attention in Hungary. Although the Hungarian official policy is hostile to immigration, it still receives migrants from different backgrounds. The education policy continues to be based on principles of the monolingual habitus, which puts distance between the goal of integration and the teaching practices that are implemented in the classroom. As these migrant children do not know Hungarian, the language of the host country, they are not able to follow the contents of the subjects in the school and are left behind, making their integration very difficult. This is a conflicting situation that calls for a comparative analysis of the language policies of the member states of the European Union in the future in order to recognize and accept a philosophy of language that is aware of the diversity as an investment to strengthen the economic and social structures of the society

Algebraic geometry of discrete interventional models

We investigate the algebra and geometry of general interventions in discrete DAG models. To this end, we develop the formalism to study these models as subvarieties of multiprojective space and introduce a theory for modeling soft interventions in the more general family of staged tree models. We then consider the problem of finding their defining equations, and we derive a combinatorial criterion for identifying interventional staged tree models for which the defining ideal is toric. This criterion, when combined with a new characterization of decomposable DAG models in terms of their associated staged trees, specializes to a graphical criterion in the case of discrete interventional DAG models.Comment: Comments welcom

Autobiografías: una herramienta para representar experiencias de aprendizaje del idioma inglés

This article contains a description of a research project carried out with a group of English Language Pre-service Teachers (ELPTs) of a state University in Bogotá, Colombia. The purpose of the study was to portray the experiences the ELPTs went through as English language learners, their feelings and insights as such. The main source to collect data was the autobiographies. The results show that the English language learners’ process of learning has a strong influence of the language policies connected to the National Program of Bilingualism. They also show that it is necessary to create a cumulative program of English for each phase of schooling in order to avoid overlapping and to provide a more motivating learning process.  Este artículo contiene la descripción de un proyecto de investigación que se llevó a cabo con 26 estudiantes de un programa de licenciatura en inglés de una universidad pública en Bogotá, Colombia. El propósito del estudio fue retratar las experiencias de los estudiantes como aprendices de lengua, sus sentimientos y puntos de vista al respecto. La investigadora utilizó la autobiografía como la fuente principal para la recolección de datos. Los resultados muestran que el proceso de aprendizaje de lengua tiene una fuerte influencia de las políticas de lenguaje del Programa Nacional de Bilingüismo. También evidencian la necesidad de crear un programa de inglés que tenga en cuenta lo aprendido en las diferentes etapas de la escuela para evitar la repetición de contenidos y propiciar un aprendizaje más motivador

Algebraic Geometry of Quantum Graphical Models

Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical models are families of quantum states satisfying certain locality or correlation conditions encoded by a graph. We lay out several ways to associate an algebraic variety to a quantum graphical model. The classical graphical models can be recovered from most of these varieties by restricting to quantum states represented by diagonal matrices. We study fundamental properties of these varieties and provide algorithms to compute their defining equations. Moreover, we study quantum information projections to quantum exponential families defined by graphs and prove a quantum analogue of Birch's Theorem.Comment: 20 pages, comments welcome

Estudiantes de inglés en Hungría y licenciatura en inglés en Colombia: Una investigación narrativa sobre identidades imaginadas

This article reports on a qualitative study that aims to explore on how the notion of imagined communities elucidates issues concerning identity and foreign language learning and teaching. The research questions that frame this study are the following: (1) What are the imagined identities (English as a Foreign Language (EFL)) students have constructed to learn English when enrolling in an English bachelor programme?, (2) How are these imagined identities connected to the imagined community they feel affiliated with? and (3) How are these imagined identities linked to the language practices of the EFL classroom? Narrative inquiry was used as the research method to answer these questions. Autobiographies were also written by the 26 participants enrolled in an English teacher education programme at a university in Colombia. Furthermore, written narratives and interviews were conducted with 15 students from an English bachelor programme at a university in Hungary. The study was conducted during one academic semester. The L2 motivational self-system theory, the theory of possible selves and the concepts of imagined communities and identities framed this research. Three salient categories emerged from the analysis of the narratives, namely, (1) bicultural identity: belonging to a worldwide community, (2) possible selves: broadening the scope of possibilities and (3) becoming an English teacher: an ongoing process.Este artículo informa sobre un estudio cualitativo cuyo propósito fue explorar cómo la noción de comunidades imaginadas aclara los problemas relacionados con la identidad y el aprendizaje y la enseñanza de lenguas extranjeras. Las preguntas de investigación que enmarcan este estudio fueron (1) ¿Cuáles son las identidades imaginadas de los estudiantes de inglés como lengua extranjera cuando cursan un pregrado de inglés? (2) ¿Cómo estas identidades están conectadas a la comunidad imaginada a la que quieren pertenecer? (3) ¿Cómo están vinculadas a las prácticas de lengua dentro de la clase? El método utilizado para dar respuesta a estos interrogantes fue la investigación narrativa.  Los 26 participantes inscritos en un programa de formación de profesores de inglés en una universidad de Colombia escribieron autobiografías. Se realizaron narraciones escritas y entrevistas con 15 estudiantes de un programa de pregrado de inglés en una universidad de Hungría. El estudio se realizó durante un semestre académico. La teoría de auto-sistema de motivación en L2, la teoría de los posibles sí mismos y los conceptos de comunidades e identidades imaginadas enmarcan esta investigación. Del análisis de las narrativas surgieron tres categorías destacadas: (1) Identidad bicultural: pertenecer a una comunidad mundial, (2) Posibles sí mismos: ampliar el alcance de las posibilidades y (3) Convertirse en un profesor de inglés: un proceso continuo

¿Marcar o superar fronteras? Estudio de construcción de identidad de profesores colombianos en escuelas públicas de Estados Unidos

In the framework of the present colloquium on Transnational Americas, this talk aims to explain how language ideologies and linguistic hierarchies are involved in indexing speakers to spaces of belonging that draw ideological and social boundaries around human beings from the use of the word “we”. With this purpose, a small-scale study with Colombian teachers in public schools of USA was carried out. These teachers answered an online questionnaire and participated in an interview via Skype. The results were analyzed taking into account the principle of indexicality, proposed by Bucholtz and Hall (2010). Contemporary discourse studies have shown that social identities are not fixed, but constructed according to the positioning speakers seek to inhabit temporarily in the course of a linguistic interaction to achieve specific social goals in the negotiation of belonging with the others. Thus the concept of boundary is not either fixed, but it is understood as a symbolic construction that is founded on a subjectivity that circumscribes the world of “one” and “other”, from the cultural, social and linguistic practices.Teniendo en cuenta el marco teórico del presente coloquio sobre Américas Transnacionales, esta ponencia busca explicar cómo las jerarquías lingüísticas y las ideologías del lenguaje están involucradas en la indexicalidad de espacios de pertenencia de los hablantes y cómo a partir del uso de la palabra “nosotros” se marcan fronteras sociales e ideológicas alrededor de los seres humanos. Para esto se realizó un estudio a menor escala con profesores colombianos que se encuentran vinculados laboralmente con escuelas públicas en Estados Unidos. Los profesores respondieron un cuestionario en línea y participaron de una entrevista por Skype. Los resultados se analizaron teniendo en cuenta el principio de indexicalidad dentro del estudio de identidad, propuesto por Bucholtz y Hall (2010). Los estudios de discurso contemporáneos argumentan que las identidades sociales no son fijas, sino que se construyen de acuerdo al posicionamiento que el hablante busca habitar en el curso de una interacción lingüística para alcanzar una meta específica en las negociaciones de pertenencia con los demás. De aquí que el concepto de frontera tampoco sea fijo, sino que se entiende como una construcción simbólica que se funda en una subjetividad que circunscribe al mundo del “uno” y el “otro”, desde las prácticas culturales, sociales y lingüísticas