Existence of parabolic minimizers to the total variation flow on metric measure spaces

We give an existence proof for variational solutions u associated to the total variation flow. Here, the functions being considered are defined on a metric measure space $$({\mathcal {X}}, d, \mu )$$ ( X , d , μ ) satisfying a doubling condition and supporting a Poincaré inequality. For such parabolic minimizers that coincide with a time-independent Cauchy–Dirichlet datum $$u_0$$ u 0 on the parabolic boundary of a space-time-cylinder $$\Omega \times (0, T)$$ Ω × ( 0 , T ) with $$\Omega \subset {\mathcal {X}}$$ Ω ⊂ X an open set and $$T > 0$$ T > 0 , we prove existence in the weak parabolic function space $$L^1_w(0, T; \mathrm {BV}(\Omega ))$$ L w 1 ( 0 , T ; BV ( Ω ) ) . In this paper, we generalize results from a previous work by Bögelein, Duzaar and Marcellini by introducing a more abstract notion for $$\mathrm {BV}$$ BV -valued parabolic function spaces. We argue completely on a variational level.

Localising urbanism

<p>This research began as a personal dissatisfaction with how the notion of indeterminacy very commonly gets used in contemporary landscape architectural design discourse and practice, most strongly associated with but not limited to what gets termed ‘landscape urbanism’. The dominant use of this notion is associated with design preoccupations such as change over time, bodily movement, the inability to predict, allowing for change and ecological growth or succession - and uses of representation related to these ideas. Peter Connolly has termed this conception the ‘abstract’ notion of indeterminacy. This notion was inspired by the writings of Deleuze and Guattari, however Connolly’s examination of the literature, and my field studies and design investigations point to an alternative version, a ‘concrete’ notion of indeterminacy¹ as being more relevant to designers. The abstract version will only ever be indirectly relevant to the human involvement in landscape. The ‘concrete’ is affectual and intensive and is directly relevant to human spatiality and life. Instead of change in space or over time, the concrete version is, in contrast, about the liveliness and shiftiness of affect (the shiftiness of affects / affordances, / propensities / capabilities…)—the shiftiness of powers. This research attempts to move beyond the attractive ambiguity and confusion associated with the abstract version and engage with the concrete ‘indeterminacy-of-affect’ by focusing on a very restricted realm of small urban spaces, which might be considered incidental spaces, in Wellington city. Through this intentionally limited attempt to directly engage with concrete indeterminacy there emerged, a way to engage with a type of localness associated with these spaces. This process has involved the development of aesthetic and representational techniques and it is suggested that this work is not just relevant to the question of indeterminacy and the local, but is very relevant to the newly emergent interest by landscape architects in design aesthetics².</p>

Localising urbanism

<p>This research began as a personal dissatisfaction with how the notion of indeterminacy very commonly gets used in contemporary landscape architectural design discourse and practice, most strongly associated with but not limited to what gets termed ‘landscape urbanism’. The dominant use of this notion is associated with design preoccupations such as change over time, bodily movement, the inability to predict, allowing for change and ecological growth or succession - and uses of representation related to these ideas. Peter Connolly has termed this conception the ‘abstract’ notion of indeterminacy. This notion was inspired by the writings of Deleuze and Guattari, however Connolly’s examination of the literature, and my field studies and design investigations point to an alternative version, a ‘concrete’ notion of indeterminacy¹ as being more relevant to designers. The abstract version will only ever be indirectly relevant to the human involvement in landscape. The ‘concrete’ is affectual and intensive and is directly relevant to human spatiality and life. Instead of change in space or over time, the concrete version is, in contrast, about the liveliness and shiftiness of affect (the shiftiness of affects / affordances, / propensities / capabilities…)—the shiftiness of powers. This research attempts to move beyond the attractive ambiguity and confusion associated with the abstract version and engage with the concrete ‘indeterminacy-of-affect’ by focusing on a very restricted realm of small urban spaces, which might be considered incidental spaces, in Wellington city. Through this intentionally limited attempt to directly engage with concrete indeterminacy there emerged, a way to engage with a type of localness associated with these spaces. This process has involved the development of aesthetic and representational techniques and it is suggested that this work is not just relevant to the question of indeterminacy and the local, but is very relevant to the newly emergent interest by landscape architects in design aesthetics².</p>

Semigroups for flows on limits of graphs

We use a version of the Trotter-Kato approximation theorem for strongly continuous semigroups in order to study ows on growing networks. For that reason we use the abstract notion of direct limits in the sense of category theory

The Iraqw society reflected in their language

A close inspection of the anthropological literature on Iraqw (Cushitic, Tanzania) reveals that central properties in their culture include the relative importance of social relations and hence community over kinship relations, the relevance of relative rather than absolute time, the centrality of space in culture and the importance of ritual cleansiness. The paper investigates to what extend the Iraqw language reflects this. Language being a social construct is expected to reflect social structure over time, both in lexicon and in grammar. Indeed the Iraqw language reflects their social structure in a number of way. Their verbal art emphasizes the need for peace in the community and is strongly communal in performance. This is evident, for example, in the rituals for lifting a curse. The centrality of community is reflected in various part of the lexicon. expression for pride being one of them, or the factor of companionship in possession. It is also grammaticalised in an extension of the function of the impersonal subject pronoun to express actions done together. Iraqw mythology and tales never attempt to indicate a point on time and only report chronology of event. This conceptualisation of time is reflected in the absence of lexical elements for absolute time and the abstract notion time. Furthermore the language forces specification of gender in any direct address: the second person pronoun is gender specified, kinship terms used for address are all gender specified as is the interjection for attention. Iraqw shows signs for a disappearing in-law respect register.

Copula-based software metrics aggregation

A quality model is a conceptual decomposition of an abstract notion of quality into relevant, possibly conflicting characteristics and further into measurable metrics. For quality assessment and decision making, metrics values are aggregated to characteristics and ultimately to quality scores. Aggregation has often been problematic as quality models do not provide the semantics of aggregation. This makes it hard to formally reason about metrics, characteristics, and quality. We argue that aggregation needs to be interpretable and mathematically well defined in order to assess, to compare, and to improve quality. To address this challenge, we propose a probabilistic approach to aggregation and define quality scores based on joint distributions of absolute metrics values. To evaluate the proposed approach and its implementation under realistic conditions, we conduct empirical studies on bug prediction of ca. 5000 software classes, maintainability of ca. 15000 open-source software systems, and on the information quality of ca. 100000 real-world technical documents. We found that our approach is feasible, accurate, and scalable in performance.

LINGUISTIC AND CULTURAL UNIVERSALS, CONCEPTS, DEFINITIONS: PHENOMENOLOGY OF CONCEPTOLOGY

В статье обсуждаются дискуссионные вопросы лингвокультурологии, концептологии, языковой картины мира, национального коммуникативного поведения. Рассматриваются не получившие пока однозначного решения дефиниции концепта, различные подходы к отождествлению концепта и понятия, значения и концепта (и основания таких отождествлений). Дискуссионной, по мнению критиков лингвокультурологии, является и методика выделения концепта, преодоление порочного круга рассуждения типа «концепты выделяются по признаку непереводимости, а основным свойством концептов является непереводимость». Неясным предстает вопрос, является ли концепт абстракцией общности говорящих или индивидуальной эмоционально окрашенной единицей сознания. Представлена идея национального языка как фикции, состоящей из множества динамично меняющихся социолектов, что не свидетельствует в пользу возможности выделения «национальных концептов». Обсуждается линия критики концептологии, связанная с обсуждением спорных вопросов этнологии, «национального характера», этноса, народа, нации. Продемонстрирована линия критики лингвокультурологии концептов, исходя из тезиса о невозможности отождествления языка и мышления и языка и культуры. Принципиальная переводимость, синонимия, возможность эквивалентной субституции, билингвизм свидетельствуют в пользу отсутствия непереводимых национальных концептов. Критики лингокультурологии считают, что национальный язык - часто не источник сведений о культуре и мышлении народа. Целый народ не разговаривает на едином национальном языке, который диктует этому народу, как ему мыслить, а также предопределяет модели его поведения. Дискуссионной для критиков концептологии предстает и языковая картина мира. The article discusses the debatable questions of linguistic cultural studies, studies of concepts in linguistics, linguistic cognitive maps, national communicative behavior. The paper scrutinizes the definitions of the concept that are still far from being universally acknowledged and final, looks at different approaches identifying linguistic concepts with meanings and notions ( and at facts that are the foundations of such extrapolations). The mute point for those who criticize conceptual studies is the method of identifying the concept, overcoming the vicious circle in argumentation that «concepts are singled out ad the key elements of the language that cannot be translated properly, and the main characteristic of the concepts is the absence of such adequate translation». It is still not clear whether the concept is the abstract notion of the community or the emotional individual element in the consciousness of the individual user of the language. The paper highlights the idea of representing the national language as a fiction consisting of varieties of social dialects, which are characterized by dynamic changes. This idea is contradicting the possibility of singling out national concepts in national mentality, judging by the language knowledge. Discussed in the paper are the questions of national character, ethnos, nation, ethnology. The paper describes the criticism of conceptology that stresses the fallacies of identifying the language with the culture, and language with the peoples’ character and thinking. The possibility of translation for every word and concept, the status of bilingual consciousness, the possibility of finding synonymous ways of rendering everything are the arguments against unique non-translatable national concepts. The criticism of linguistic conceptual studies states that quite often the language is not a source of national culture and thinking of a whole nation (ethnic group). That ethic group does not possess the language as a mechanism that prompts all the members of the ethnic group how to think and behave. One more debatable question is the existence of the linguistic map of the universe.

Pseudofinite Structures and Counting Dimensions

The thesis pseudofinite structures and counting dimensions is about the model theory of pseudofinite structures with the focus on groups and fields. The aim is to deepen our understanding of how pseudofinite counting dimensions can interact with the algebraic properties of underlying structures and how we could classify certain classes of structures according to their counting dimensions. Our approach is by studying examples. We treat three classes of structures: The first one is the class of H-structures, which are generic expansions of existing structures. We give an explicit construction of pseudofinite H-structures as ultraproducts of finite structures. The second one is the class of finite difference fields. We study properties of coarse pseudofinite dimension in this class, show that it is definable and integer-valued and build a partial connection between this dimension and transformal transcendence degree. The third example is the class of pseudofinite primitive permutation groups. We generalise Hrushovski’s classical classification theorem for stable permutation groups acting on a strongly minimal set to the case where there exists an abstract notion of dimension, which includes both the classical model theoretic ranks and pseudofinite counting dimensions. In this thesis, we also generalise Schlichting’s theorem for groups to the case of approximate subgroups with a notion of commensurability.Abstract prepared by Tingxiang Zou.E-mail: [email protected]: https://tel.archives-ouvertes.fr/tel-02283810/document

Diversity without Race

This article examines how a sample of 62 higher education institutions in Canada, the United States and the United Kingdom discuss international students in their official institutionalization strategies, focusing on how ideas of race and diversity are addressed. We find that institutional strategies connect international students to an abstract notion of diversity, using visual images to portray campus environments as inclusive of racial, ethnic and religious diversity. Yet, strategy documents rarely discuss race, racialization, or racism explicitly, despite the fact that most international students in all three countries are non-white. Moreover, racial injustice is externalized as a global issue and racial diversity is instrumentalized as a source of improving institutional reputation or diversity metrics. We argue that a first step to creating more inclusive and anti-racist campuses is to acknowledge international students’ racial identities and experiences with racism in official discourses and strategies.

GOOD BAD TIME

The article discloses the axiological potential of the qualitative metaphor of time on the example of emotive prose and poetry of German-speaking authors. Time as an abstract notion is rendered metaphorically. Metaphor, taken as an image, is a universal pattern that is used to form emotional and evaluative categories. It encompasses an image representation, evaluation information and attitude expression, both positive and negative. There is an attempt to assess the correlation between ameliorative and pejorative evaluation of time in poetry and emotive prose discourse in the German-language literature. However, besides positive and negative modes, evaluation may also have some other semantic features, which can contribute to its more detailed classification. We analyzed the possibility of using the classification by N.D. Arutyunova to identify and distribute these semantic features among the suggested sets.