Attractors in spacetimes and time functions

We develop a new approach to the existence of time functions on Lorentzian manifolds, based on Conley's work regarding Lyapunov functions for dynamical systems. We recover Hawking's result that a stably causal admits a time function through a more general result giving the existence of a continuous function that is non decreasing along all future directed causal curves, and increasing along such curves that lie outside a special region of the spacetime, called the chain recurrent set, which is empty for stably causal spacetimes. The construction is based on a notion of attractive sets in spacetimes.Comment: 26 pages, 2 figure

Convergence groups and semi conjugacy

We study a simple problem that arises from the study of Lorentz surfaces and Anosov flows. For a non decreasing map of degree one $h:\mathbb{S}^1\to \mathbb{S}^1$, we are interested in groups of circle diffeomorphisms that act on the complement of the graph of $h$ in $\mathbb{S}^1\times \mathbb{S}^1$ by preserving a volume form. We show that such groups are semi conjugate to subgroups of $\mathrm{PSL}(2,\mathbb{R})$, and that when $h\in \mathrm{Homeo}(\mathbb{S}^1)$, we have a topological conjugacy. We also construct examples, where $h$ is not continuous, for which there is no such conjugacy.Comment: 27 pages, 7 figures. arXiv admin note: text overlap with arXiv:1402.042

Regularity of limit sets of AdS quasi-Fuchsian groups

Limit sets of $\mathrm{AdS}$-quasi-Fuchsian groups of $\mathrm{PO}(n,2)$ are always Lipschitz submanifolds. The aim of this article is to show that they are never $\mathcal{C}^1$, except for the case of Fuchsian groups. As a byproduct we show that $\mathrm{AdS}$-quasi-Fuchsian groups that are not Fuchsian are Zariski dense in $\mathrm{PO}(n,2)$

Hausdorff dimension of limit sets for projective Anosov representations

We study the relation between critical exponents and Hausdorff dimensions of limit sets for projective Anosov representations. We prove that the Hausdorff dimension of the symmetric limit set in $\mathbf{P}(\mathbb{R}^{n}) \times \mathbf{P}({\mathbb{R}^{n}}^*)$ is bounded between two critical exponents associated respectively to a highest weight and a simple root

Gromov-Thurston manifolds and anti-de Sitter geometry

We consider hyperbolic and anti-de Sitter (AdS) structures on $M\times (0,1)$, where $M$ is a $d$-dimensional Gromov-Thurston manifold. If $M$ has cone angles greater than $2\pi$, we show that there exists a "quasifuchsian" (globally hyperbolic maximal) AdS manifold such that the future boundary of the convex core is isometric to $M$. When $M$ has cone angles less than $2\pi$, there exists a hyperbolic end with boundary a concave pleated surface isometric to $M$. Moreover, in both cases, if $M$ is a Gromov-Thurston manifold with $2k$ pieces (as defined below), the moduli space of quasifuchsian AdS structures (resp. hyperbolic ends) satisfying this condition contains a submanifold of dimension $2k-3$. When $d=3$, the moduli space of quasifuchsian AdS (resp. hyperbolic) manifolds diffeomorphic to $M\times (0,1)$ contains a submanifold of dimension $2k-2$, and extends up to a "Fuchsian" manifold, that is, an AdS (resp. hyperbolic) warped product of a closed hyperbolic manifold by~$\R$. We use this construction of quasifuchsian AdS manifolds to obtain new compact quotients of \O(2d,2)/\U(d,1). The construction uses an explicit correspondence between quasifuchsian $2d+1$-dimensional AdS manifolds and compact quotients of \O(2d,2)/\U(d,1) which we interpret as the space of timelike geodesic Killing fields of \AdS^{2d+1}.Comment: 48 page

Análise da importância de atributos do serviço no mercado de streaming de vídeo : um estudo aplicado através de experimento de escolhas discretas

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Faculdade de Economia, Administração, Contabilidade e Gestão de Políticas Públicas, Departamento de Administração, 2021.O presente artigo buscou analisar a importância dos atributos dos serviços de streaming audiovisual online (mais especificamente, dos serviços SVOD – Subscription Video on Demand, em que o usuário paga uma taxa mensal ou anual para ter acesso a conteúdo de entretenimento audiovisual por meio de uma plataforma online). Para isso, foi utilizado o método DCE – Discrete Choice Experiment, ou Experimento de Escolha Discreta, que busca medir o peso de cada um dos vários atributos que um produto ou serviço podem ter na decisão de compra de um consumidor, ao apresentar cenários de escolha que combinam diferentes níveis de cada atributo. Os atributos avaliados foram definidos com base em um levantamento qualitativo com 10 usuários de plataformas de streaming de vídeo e, em seguida, foi feito um survey com 250 pessoas a fim de aplicar o experimento de escolha discreta e obter a importância relativa de cada atributo e a disposição a pagar a mais por cada um deles. Os resultados revelam que os atributos mais importantes para os consumidores desse tipo de serviço são “qualidade do vídeo”, “velocidade de lançamentos” e “variedade de conteúdo”, sendo que os dois últimos são, ainda, os atributos pelos quais as pessoas estão dispostas a pagar mais. Além disso, também foi observado que os fatores sociodemográficos “idade” e “renda familiar” têm influência nessa avaliação, de forma que os atributos “variedade de conteúdo” e “estabilidade da conexão” são mais importantes a medida que a renda familiar é mais alta e, por outro lado, os atributos “facilidade de uso”, “estabilidade da conexão” e “preço” são mais importantes para pessoas com mais idade. Esses resultados são especialmente relevantes para as empresas do segmento contemplado por permitirem um maior embasamento nas decisões relacionadas ao serviço, segmentação e precificação, mas também contribuem para a literatura acadêmica ao aplicar, de forma inovadora, o método DCE a um serviço digital.This article aimed to analyze the importance of online video streaming service's attributes (more specifically the SVOD - Subscription Videos on Demand, in wich the user pays a monthly or annual fee to have access to audiovisual entertainment content via an online platform). To achieve that, the DCE (Discrete Choice Experiment) method was chosen, wich measures the impact of each one of the various attributes that a product or a service may have on a consumer's purchase decision, by presenting a selection of scenarios that combine different levels of each attribute. The assessed attributes were chosen on the grounds of a qualitative survey with 10 SVOD users, and then, another survey was done, with a 250 people sample, with the intent of applying the DCE and obtain the relative importance of each attribute and the inclination to pay more for each one of them. The results reveal that the most important attributes to the consumers of this type of service are "video quality", "speed of new releases" and "variety of content", the last two being the ones that people are willing to pay more. Also, it was observed that the sociodemographic factors "age" and "family income" exert influence on the evaluation in a way that the attributes "variety of content" and "stability of the connection" become more important as family income gets higher and, on the other hand, the "easiness of use", "stability of the connection" and "price" are more important to older people. These results are especially important to companies in the contemplated segment, as they allow a better foundation in the decisions related to the services, segmentation and pricing, but also contributes to the academic literature by applying to a digital service, in an innovative manner, the DCE method

Development of an open-source, flexible framework for complex inter-institutional disparate data sharing and collaboration

Clinical information, “-omic” datasets, and tissue samples are difficult to harmonize and manage for data mining. We have developed a platform for storing clinical research data while providing access to associated data from other information stores. Data on 34 metrics from 11,000 neuroblastoma patients were instantiated into a database. The Django web framework was used to create a model for rapid development of tools and views with a front-end interface for generating complex queries. Working with Nationwide Children’s Hospital, we can now consume their tissue inventory data through an API. The end-user sees the number of patients who both match their search and have tissue available. Since initial implementation, the current tasks revolve around developing a governance structure and the necessary data use agreements. Efforts now are to (1) update the data with 5000 more patients, and (2) link to genomic data stores, facilitating disparate data acquisition for research studies

Recommendations for the standardization of bone marrow disease assessment and reporting in children with neuroblastoma; on behalf of the International Neuroblastoma Response Criteria Bone Marrow Working Group

BACKGROUND: The current study was conducted to expedite international standardized reporting of bone marrow disease in children with neuroblastoma and to improve equivalence of care. METHODS: A multidisciplinary International Neuroblastoma Response Criteria Bone Marrow Working Group was convened by the US National Cancer Institute in January 2012 with representation from Europe, North America, and Australia. Practical transferable recommendations to standardize the reporting of bone marrow disease were developed. RESULTS: To the authors' knowledge, the current study is the first to comprehensively present consensus criteria for the collection, analysis, and reporting of the percentage area of bone marrow parenchyma occupied by tumor cells in trephine-biopsies. The quantitative analysis of neuroblastoma content in bone marrow aspirates by immunocytology and reverse transcriptase-quantitative polymerase chain reaction are revised. The inclusion of paired-like homeobox 2b (PHOX2B) for immunohistochemistry and reverse transcriptase-quantitative polymerase chain reaction is recommended. Recommendations for recording bone marrow response are provided. The authors endorse the quantitative assessment of neuroblastoma cell content in bilateral core needle biopsies-trephines and aspirates in all children with neuroblastoma, with the exception of infants, in whom the evaluation of aspirates alone is advised. It is interesting to note that 5% disease is accepted as an internationally achievable level for disease assessment. CONCLUSIONS: The quantitative assessment of neuroblastoma cells is recommended to provide data from which evidence-based numerical criteria for the reporting of bone marrow response can be realized. This is particularly important in the minimal disease setting and when neuroblastoma detection in bone marrow is intermittent, where clinical impact has yet to be validated. The wide adoption of these harmonized criteria will enhance the ability to compare outcomes from different trials and facilitate collaborative trial design