6 research outputs found

    How Fast Can We Play Tetris Greedily With Rectangular Pieces?

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    Consider a variant of Tetris played on a board of width ww and infinite height, where the pieces are axis-aligned rectangles of arbitrary integer dimensions, the pieces can only be moved before letting them drop, and a row does not disappear once it is full. Suppose we want to follow a greedy strategy: let each rectangle fall where it will end up the lowest given the current state of the board. To do so, we want a data structure which can always suggest a greedy move. In other words, we want a data structure which maintains a set of O(n)O(n) rectangles, supports queries which return where to drop the rectangle, and updates which insert a rectangle dropped at a certain position and return the height of the highest point in the updated set of rectangles. We show via a reduction to the Multiphase problem [P\u{a}tra\c{s}cu, 2010] that on a board of width w=Θ(n)w=\Theta(n), if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time O(n1/2ϵ)O(n^{1/2-\epsilon}) simultaneously. The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture. On the other hand, we show that there is a data structure supporting both operations in O(n1/2log3/2n)O(n^{1/2}\log^{3/2}n) time on boards of width nO(1)n^{O(1)}, matching the lower bound up to a no(1)n^{o(1)} factor.Comment: Correction of typos and other minor correction

    Complete lattice projection autoassociative memories

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    Orientador: Marcos Eduardo Ribeiro do Valle MesquitaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: A capacidade do cérebro humano de armazenar e recordar informações por associação tem inspirado o desenvolvimento de modelos matemáticos referidos na literatura como memórias associativas. Em primeiro lugar, esta tese apresenta um conjunto de memórias autoassociativas (AMs) que pertecem à ampla classe das memórias morfológicas autoassociativas (AMMs). Especificamente, as memórias morfológicas autoassociativas de projeção max-plus e min-plus (max-plus e min-plus PAMMs), bem como suas composições, são introduzidas nesta tese. Tais modelos podem ser vistos como versões não distribuídas das AMMs propostas por Ritter e Sussner. Em suma, a max-plus PAMM produz a maior combinação max-plus das memórias fundamentais que é menor ou igual ao padrão de entrada. Dualmente, a min-plus PAMM projeta o padrão de entrada no conjunto de todas combinações min-plus. Em segundo, no contexto da teoria dos conjuntos fuzzy, esta tese propõe novas memórias autoassociativas fuzzy, referidas como classe das max-C e min-D FPAMMs. Uma FPAMM representa uma rede neural morfológica fuzzy com uma camada oculta de neurônios que é concebida para o armazenamento e recordação de conjuntos fuzzy ou vetores num hipercubo. Experimentos computacionais relacionados à classificação de padrões e reconhecimento de faces indicam possíveis aplicações dos novos modelos acima mencionadosAbstract: The human brain¿s ability to store and recall information by association has inspired the development various mathematical models referred to in the literature as associative memories. Firstly, this thesis presents a set of autoassociative memories (AMs) that belong to the broad class of autoassociative morphological memories (AMMs). Specifically, the max-plus and min-plus projection autoassociative morphological memories (max-plus and min-plus PAMMs), as well as their compositions, are introduced in this thesis. These models are non-distributed versions of the AMM models developed by Ritter and Sussner. Briefly, the max-plus PAMM yields the largest max-plus combination of the stored vectors which is less than or equal to the input pattern. Dually, the min-plus PAMM projects the input pattern into the set of all min-plus combinations. In second, in the context of fuzzy set theory, this thesis proposes new fuzzy autoassociative memories mentioned as class of the max-C and min-D FPAMMs. A FPAMM represents a fuzzy morphological neural network with a hidden layer of neurons that is designed for the storage and retrieval of fuzzy sets or vectors on a hypercube. Computational experiments concerning pattern classification and face recognition indicate possible applications of the aforementioned new AM modelsDoutoradoMatematica AplicadaDoutor em Matemática AplicadaCAPE

    Expressões proverbiais do português - usos, variação formal e identificação automática

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    Os provérbios são uma expressão da cultura de uma sociedade e estão ligados às mais diversas áreas da experiência humana. Este tipo de expressões surge nos mais variados tipos de texto e desempenha diferentes funções retóricas no discurso, nele se integrando por meio de diferentes mecanismos, nem sempre fáceis de detetar formalmente. A interferência nos processos de coerência e de coesão discursivas, p. ex., a referência, e a sua variação formal, constituem sérios desafios ao processamento da linguagem natural (PLN), exigindo a sua identificação e delimitação precisas. Este projeto visa a identificação automática de provérbios portugueses (e as suas variantes) em textos, a fim de melhor caracterizar a sua utilização, tanto qualitativa como quantitativamente. Tal permitirá a definição de índices de frequência e, a partir destes, bem como de outros critérios, a determinação da disponibilidade lexical das unidades paremiológicas (o provérbio e as suas variantes). Estas informações são elementos relevantes a considerar, por exemplo, no desenvolvimento de instrumentos complementares de diagnóstico ou terapia de determinadas patologias da linguagem; ou mesmo para a construção de jogos didáticos para o ensino-aprendizagem de português, língua materna e língua não materna, eventualmente assistido por computador.Proverbs are an expression of the culture of a society and are connected to the most diverse areas of human experience. This type of expression occurs in the most diverse types of text and performs different rhetorical functions in the discourse, integrating it through several mechanisms, not always easy to detect formally. Interference in the processes of discursive coherence and cohesion, e.g. reference, and its formal variation, constitute serious challenges to Natural Language Processing (NLP), requiring its precise identification and delimitation. This project aims at the automatic identification of Portuguese proverbs (and their variants) in texts, to effectively characterize their use, both qualitatively and quantitatively. This will allow the definition of frequency indices and, from these, as well as other criteria, the determination of the lexical availability of the paremiological units (the proverb and its variants). This information is relevant elements to consider, for example, in the development of complementary diagnostic or therapeutic instruments for certain language pathologies; or even for the construction of didactic games for the teaching-learning of Portuguese, either as a Mother Tongue or as a Foreign Language, eventually assisted by computer

    Proceedings of the International Congress on Interdisciplinarity in Social and Human Sciences

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    Interdisciplinarity is the main topic and the main goal of this conference. Since the sixteen century with the creation of the first Academy of Sciences, in Napoles (Italy) (1568), and before that with the creation of the Fine Arts Academies, the world of science and arts began to work independently, on the contrary of the Academy of Plato, in Classical Antiquity, where science, art and sport went interconnected. Over time, specific sciences began to be independent, and the specificity of sciences caused an increased difficulty in mutual understanding. The same trend has affected the Human and Social Sciences. Each of the specific sciences gave rise to a wide range of particular fields. This has the advantage of allowing the deepening of specialised knowledge, but it means that there is often only a piecemeal approach of the research object, not taking into account the its overall complexity. So, it is important to work for a better understanding of the scientific phenomena with the complementarity of the different sciences, in an interdisciplinary perspective. With this growing specialisation of sciences, Interdisciplinarity acquired more relevance for scientists to find moreencompassing and useful answers for their research questions.info:eu-repo/semantics/publishedVersio

    Proceedings of the International Congress on Interdisciplinarity in Social and Human Sciences

    Get PDF
    Interdisciplinarity is the main topic and the main goal of this conference. Since the sixteen century with the creation of the first Academy of Sciences, in Napoles (Italy) (1568), and before that with the creation of the Fine Arts Academies, the world of science and arts began to work independently, on the contrary of the Academy of Plato, in Classical Antiquity, where science, art and sport went interconnected. Over time, specific sciences began to be independent, and the specificity of sciences caused an increased difficulty in mutual understanding. The same trend has affected the Human and Social Sciences. Each of the specific sciences gave rise to a wide range of particular fields. This has the advantage of allowing the deepening of specialised knowledge, but it means that there is often only a piecemeal approach of the research object, not taking into account the its overall complexity. So, it is important to work for a better understanding of the scientific phenomena with the complementarity of the different sciences, in an interdisciplinary perspective. With this growing specialisation of sciences, Interdisciplinarity acquired more relevance for scientists to find moreencompassing and useful answers for their research questions.info:eu-repo/semantics/publishedVersio
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