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We present several new results on the combinatorial properties of a locally restricted version of monomino-domino coverings of rectilinear regions. These are monomino-domino tatami coverings, and the restriction is that no four tiles may meet at any point. The global structure that the tatami restriction induces has numerous implications, and provides a powerful tool for solving enumeration problems on tatami coverings. Among these we address the enumeration of coverings of rectangles, with various parameters, and we develop algorithms for exhaustive generation of coverings, in constant amortised time per covering. We also con- sider computational complexity on two fronts; firstly, the structure shows that the space required to store a covering of the rectangle is linear in its longest dimension, and secondly, it is NP-complete to decide whether an arbitrary polyomino can be tatami-covered only with dominoes. / Graduate / 0984 / 0405 / alejandro.erickson@gmail.com

Made available in DSpace on 2015-03-03T15:36:09Z (GMT). No. of bitstreams: 1 JoseRAB_DISSERT.pdf: 776491 bytes, checksum: bef691e2a550b6345b490b668bd8cb38 (MD5) Previous issue date: 2013-02-22 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Humans, as well as some animals are born gifted with the ability to perceive quantities. The needs that came from the evolution of societies and technological resources make the the optimization of such counting methods necessary. Although necessary and useful, there are a lot of diculties in the teaching of such methods.In order to broaden the range of available tools to teach Combinatorial Analysis, a owchart is presented in this work with the goal of helping the students to x the initial concepts of such subject via pratical exercises / Os seres humanos, assim como alguns animais, nascem dotados da capacidade de perceber quantidades. Portanto t?cnicas para contar quantidades foi um passo natural no desenvolvimento do homem. As necessidades provindas da evolu??o das sociedades e recursos tecnol?gicos tornam necess?rio a otimiza??o de tais m?todos de contagem. Apesar de necess?rio e ?til, o estudo desses m?todos no Ensino M?dio esbarram em dificuldades did?ticas. Com o objetivo de ampliar o leque de ferramentas dispon?veis aos professores para o ensino de An?lise Combinat?ria apresentamos neste trabalho um fluxograma que pretende dinamizar o processo de fixa??o dos conceito via resolu??o de exerc?cios

Orientador: José Plínio de Oliveira Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T04:32:08Z (GMT). No. of bitstreams: 1 BrasilJunior_NelsonGomes_M.pdf: 980636 bytes, checksum: dd8d61baeb633d5f598abc3523def800 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho, estudamos a sequência dos Números de Catalan, uma sequência que aparece como solução de vários problemas de contagem envolvendo árvores, palavras, grafos e outras estruturas combinatórias. Atualmente, são conhecidas cerca de 200 interpretações combinatórias distintas para os Números de Catalan, o que motiva o estudo de relações entre estas interpretações, isto é, entre conjuntos cuja cardinalidade é dada pelos termos desta sequência. O principal objetivo do nosso trabalho é, portanto, mostrar bijeções entre esses conjuntos. No início do texto fazemos uma pequena introdução histórica aos números de Catalan, assim como definimos algumas formas de representar a sequência estudada. Depois mostramos algumas bijeções clássicas entre conjuntos contados pela sequência de Catalan. Além disso, apresentamos outras bijeções entre conjuntos envolvendo diversos objetos combinatórios. No total, são exibidas 29 bijeções / Abstract: In this work, we study the sequence of Catalan Numbers, which appears as a solution of many counting problems involving trees, words, graphs and other combinatorial structures. Nowadays, about 200 different combinatorial interpretations of the Catalan Numbers are known and that motivates the study between them, i. e., the study between sets whose cardinality is given by the terms of this sequence. The main objective of our work is therefore to show bijections between these sets. In the beginning, we make a short historical introduction of the Catalan Numbers and define some ways to represent the sequence. After that, we show some classical bijections between sets counted by the Catalan Numbers. Additionally, we exhibit other bijections between sets involving several combinatorial objects. Altogether, 29 bijections are presented / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

High variety and low volume manufacturing environment always been a challenge for organisations to maintain their overall performance especially because of the high level of variability induced by ever changing customer demand, high product variety, cycle times, routings and machine failures. All these factors consequences poor flow and degrade the overall organisational performance. For most of the organisations, therefore, process improvement has evidently become the core component for long term survival. The aim of this research here is to develop a methodology for automating operations in process improvement as a part of lean creative problem solving process. To achieve the stated aim, research here has investigated the job sequence and buffer management problem in high variety/low volume manufacturing environment, where lead time and total inventory holding cost are used as operational performance measures. The research here has introduced a novel approach through integration of genetic algorithms based multi-objective combinatorial optimisation and discrete event simulation modelling tool to investigate the effect of variability in high variety/low volume manufacturing by considering the effect of improvement of selected performance measures on each other. Also, proposed methodology works in an iterative manner and allows incorporating changes in different levels of variability. The proposed framework improves over exiting buffer management methodologies, for instance, overcoming the failure modes of drum-buffer-rope system and bringing in the aspect of automation. Also, integration of multi-objective combinatorial optimisation with discrete event simulation allows problem solvers and decision makers to select the solution according to the trade-off between selected performance measures.

Conditional preference networks (CP-nets) exploit the power of ceteris paribus rules to represent preferences over combinatorial decision domains compactly. CP-nets have much appeal. However, their study has not yet advanced sufficiently for their widespread use in real-world applications. Known algorithms for deciding dominance---whether one outcome is better than another with respect to a CP-net---require exponential time. Data for CP-nets are difficult to obtain: human subjects data over combinatorial domains are not readily available, and earlier work on random generation is also problematic. Also, much of the research on CP-nets makes strong, often unrealistic assumptions, such as that decision variables must be binary or that only strict preferences are permitted. In this thesis, I address such limitations to make CP-nets more useful. I show how: to generate CP-nets uniformly randomly; to limit search depth in dominance testing given expectations about sets of CP-nets; and to use local search for learning restricted classes of CP-nets from choice data.

It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems.

Thesis (PhD (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2004. / Suppose a lottery scheme consists of randomly selecting an unordered winning n-subset from a universal set of m numbers, while a player participates in the scheme by purchasing a playing set of any number of unordered n-subsets from the same universal set prior to a winning draw, and is awarded a prize if ...

Until very recently, synthetic chemistry has focussed on the creation of chemical entities with desirable properties through the programmed application of isolated chemical reactions, either individually or in a cascade that afford a target compound selectively. By contrast, biological systems operate using a plethora of complex interconnected signaling and metabolic networks with multiple checkpoint controls and feedback loops allowing biological systems to adapt and respond rapidly to external stimuli. Systems chemistry attempts to capture the complexity and emergent phenomena prevalent in the life sciences within a wholly synthetic chemical framework. In this approach, complex phenomena are expressed by a group of synthetic chemical entities designed to interact and react with many partners within the ensemble in programmed ways. In this manner, it should be possible to create synthetic chemical systems whose properties are not simply the linear sum of the attributes of the individual components. Chapter 1 discusses the role of complex networks in various aspects of chemistry- related research from the origin of life to nanotechnology. Further, it introduces the concept of Systems chemistry, giving various examples of dynamic covalent networks, self-replicating systems and molecular logic gates, showing the applications of complex system research. Chapter 2 discusses the components of replicator design. Further, it introduces a network based on recognition mediated reactions that is implemented by length- segregation of the substrates and displays properties of self-sorting. Chapter 3 presents a fully addressable chemical system based on auto- and cross- catalytic properties of product templates. The system is described by Boolean logic operations with different template inputs giving different template outputs. Chapter 4 introduces a dynamic network which fate is determined by a single recognition event. The replicator is capable of exploiting and dominating the exchanging pool of reagents in order to amplify its own formation at the expense of other species through the non-linear kinetics inherent in minimal replication. Chapter 5 focuses on the development of complex dynamic systems from structurally simple molecules. The new approach allows creating multicomponent networks with many reaction pathways operating simultaneously from readily available substrates.

<p>This thesis describes recombinant proteins that have been generated by rational and combinatorial protein engineering strategies for use in subunit vaccine delivery and tumor targeting.</p><p>In a first series of studies, recombinant methods for incorporating immunogens into an adjuvant formulation, e.g. immunostimulating complexes (iscoms), were evaluated. Protein immunogens, which are not typically immunogenic in themselves, are normally administered with an adjuvant to improve their immunogenicity. To accomplish iscom incorporation of a <i>Toxoplasma gondii</i> surface antigen through hydrophobic interaction, lipids were added either <i>in vivo</i> via <i>E. coli</i> expression, or <i>in vitro</i> via interaction of an introduced hexahistidyl (His6) peptide and a chelating lipid. The possibility of exploiting the strong interaction between biotin and streptavidin was also explored, in order to couple a<i> Neospora caninum</i> surface antigen to iscom matrix, i.e. iscom particles without any antigen. Subsequent analyses confirmed that the immunogens were successfully incorporated into iscoms by the investigated strategies. In addition, immunization of mice with the recombinant Neospora antigen NcSRS2, associated with iscoms through the biotin-streptavidin interaction, induced specific antibodies to native NcSRS2 and reduced clinical symptoms following challenge infection. The systems described in this thesis might offer convenient and efficient methods for incorporating recombinant immunogens into adjuvant formulations that might be considered for the generation of future recombinant subunit vaccines.</p><p>In a second series of studies, Affibody® (affibody) ligands directed to the extracellular domain of human epidermal growth factor receptor 2 (HER2/neu), which is known to be overexpressed in ∼ 20-30% of breast cancers, were isolated by phage display <i>in vitro</i> selection from a combinatorial protein library based on the 58 amino acid residue staphylococcal protein A-derived Z domain. Biosensor analyses demonstrated that one of the variants from the phage selection, denoted His₆-Z_HER2/neu:4, selectively bound with nanomolar affinity (KD ≈ 50 nM) to the extracellular domain of HER2/neu (HER2-ECD) at a different site than the monoclonal antibody trastuzumab. In order to exploit avidity effects, a bivalent affibody ligand was constructed by head-to-tail dimerization, resulting in a 15.6 kDa affibody ligand, termed His₆-(Z_HER2/neu:4)₂, that was shown to have an improved apparent affinity to HER2-ECD (KD ≈ 3 nM) compared to the monovalent affibody. Moreover, radiolabeled monovalent and bivalent affibody ligands showed specific binding in vitro to native HER2/neu molecules expressed in human cancer cells. Biodistribution studies in mice carrying SKOV-3 xenografted tumors revealed that significant amounts of radioactivity were specifically targeted to the tumors <i>in vivo</i>, and the tumors could easily be visualized with a gamma camera. These results suggest that affibody ligands would be interesting candidates for specific tumor targeting in clinical applications, such as <i>in vivo</i> imaging and radiotherapy.</p>