The Price of Anarchy for Network Formation in an Adversary Model

We study network formation with n players and link cost \alpha > 0. After the network is built, an adversary randomly deletes one link according to a certain probability distribution. Cost for player v incorporates the expected number of players to which v will become disconnected. We show existence of equilibria and a price of stability of 1+o(1) under moderate assumptions on the adversary and n \geq 9. As the main result, we prove bounds on the price of anarchy for two special adversaries: one removes a link chosen uniformly at random, while the other removes a link that causes a maximum number of player pairs to be separated. For unilateral link formation we show a bound of O(1) on the price of anarchy for both adversaries, the constant being bounded by 10+o(1) and 8+o(1), respectively. For bilateral link formation we show O(1+\sqrt{n/\alpha}) for one adversary (if \alpha > 1/2), and \Theta(n) for the other (if \alpha > 2 considered constant and n \geq 9). The latter is the worst that can happen for any adversary in this model (if \alpha = \Omega(1)). This points out substantial differences between unilateral and bilateral link formation

A Synthesis of Literature Examining the Structured Teaching Components of the TEACCH Model Employing the Use of a Visual Conceptual Model

A synthesis of research on the TEACCH Model was conducted to determine which components of Structured Teaching under the TEACCH model meet criteria as evidenced based practices using the Reichow, Volkmar, and Cicchetti criteria (2007) along with reporting on the findings of the National Autism Center report (2009). The critical components of the Structured Teaching approach under the TEACCH model as defined by Schopler et al. (1995) are: physical structure; visual schedules; work systems; and task organization. Our analysis found visual schedules met the Reichow et al. (2008) criteria and a case can be made for task organization. A secondary purpose of the synthesis was to visually represent the integration and separation of what researchers mean when they refer to the implementation of the TEACCH model. Components of the Structured Teaching approach under the TEACCH model along with the TEACCH philosophy /model are depicted using a proposed conceptual model

The Price of Anarchy and Computation of Equilibria in Non-atomic Consumption-Relevance Congestion Games

We present an extension to the model of non-atomic congestion games (NCG). NCGs enforce a symmetry between the consumption of elements (e.g., network links) and their relevance for the players: players utilizing an element e through a strategy S (e.g., a multicast tree) with rate of consumption C_{eS}>0 experience the element's latency amplified by that same factor C_{eS}. Our extension instead allows a factor R_{eS}, independent of C_{eS}, to express the amplification of the element's latency from the players' perspective, or, in other words, the relevance of element e for strategy S. We therefore call the extended model non-atomic consumption-relevance congestion games (NCRCG). NCRCGs exhibit new phenomena, including multiple Nash equilibria of different social cost and -- even from a worst-case point of view -- a dependence of the price of anarchy on structural parameters not limited to the class of element latency functions used. It poses new computational challenges. We prove almost tight lower, upper, and bicriteria bounds for the price of anarchy for super-homogeneous classes of element latency functions. We show a positive computational result for affine element latency functions. A summary of experimental results is given, which suggest that our lower bound is the best possible

Experimental Studies of the Price of Anarchy in Non-atomic Consumption-Relevance Congestion Games

The model of non-atomic consumption-relevance congestion games (NCRCG) is an extension of the well-known non-atomic congestion games (NCG). We introduced the NCRCG model in a previous report (0814) and proved worst-case lower and upper bounds on the price of anarchy. These bounds are are tight up to a factor of gamma, where gamma is a new structural parameter of the game; we have gamma=1 for NCGs. This experimental work substantiates our conjecture that the worst-case lower bound is the best possible, i.e., that it actually also is an upper bound

#Bilingualkids : what are people on instagram teaching about raising a bilingual kid?

O bilinguismo sempre foi tratado como uma parte muito importante para alguém se dar “bem na vida”, ou para ter um bom “lugar no mundo” e, hoje em dia, essa necessidade de ser bilíngue está surgindo cada vez mais cedo, chegando ao grupo das crianças. Juntamente com isso, a internet e as redes sociais também têm crescido muito e, especialmente, as páginas de influenciadores de todos os tipos, desde coisas simples e comuns, como maquiagens e outfits, mas também para coisas mais sérias, como o ensino e a aquisição de uma segunda língua. Na junção dessas duas coisas - a necessidade de as crianças começarem a aprender uma segunda língua desde cedo e o crescimento desenfreado das páginas de influenciadores em redes sociais -, muitas páginas que “ensinam” a transformar seus filhos em crianças bilíngues começaram a aparecer. Dessa forma, é possível começar a se questionar o quanto o conteúdo dessas páginas é verdadeiro e teoricamente embasado em boas e respeitadas teorias. Foi nesse contexto que surgiu a presente pesquisa, que visa a responder à pergunta “O que o Instagram está ensinando sobre criar crianças bilíngues ?”. Para responder essa questão , foi realizada uma revisão sistemática da literatura acadêmica sobre bilinguismo e sobre a aquisição da linguagem , principalmente com as ideias de Yule (2017) e Cunningham (2011) e, por meio de uma abordagem qualitativa , postagens e conteúdo de perfis relevantes do Instagram foram coletados e analisados , identificando os temas centrais abordados e as estratégias de comunicação utilizadas por eles. Dessa forma , a análise comparativa revela similaridades e discrepâncias entre a representação nas mídias sociais e as abordagens acadêmicas, fornecendo insights sobre a disseminação de informações sobre bilinguismo e sua influência nas percepções populares . Ao compreender melhor como o discurso online interage com as bases acadêmicas, este estudo pretende contribuir para uma compreensão mais abrangente do bilinguismo e da aquisição da linguagem na sociedade contemporânea, com o objetivo de ajudar os pais e os responsáveis a selecionarem o melhor conteúdo para prepararem seus filhos para adquirir uma segunda língua.Bilingualism has always been treated as a very important part for someone to do “well in life”, or to have a “good place in the world” and, nowadays, this need to be bilingual is appearing earlier and earlier, reaching the children's group. Along with this, the internet and social media have also grown a lot and, especially, the pages of influencers of all kinds, from simpler things, such as makeup and outfits, but also for more serious things, such as teaching and acquiring a second language. In the combination of these two things - the need for children to start learning a second language from an early age and the unbridled growth of pages on social networks -, many pages that "teach" how to turn their children into bilingual children, have appeared. In this way, it is possible to start questioning how much the content of these pages is true and theoretically based on good and respected theories. Therefore , this research aims to answer the question “What is Instagram teaching about raising bilingual kids ?”. To answer this question , I performed a systematic review of academic literature on bilingualism and language acquisition, mainly by Yule (2017) and Cunningham (2011), and through a qualitative approach, I collected and analyzed posts and content from relevant profiles. of Instagram, identifying the central themes addressed and the communication strategies used by them. Thus, the comparative analysis revealed similarities and discrepancies between representation in social media and academic approaches, providing insights into the dissemination of information about bilingualism and its influence on popular perceptions. By better understanding how online discourse interacts with academic foundations , this study contributes to a more comprehensive understanding of bilingualism and language acquisition in contemporary society, with the aim of helping parents and guardians select the best content to pass on to your children