This thesis didactically maps and describes new didactical mathematic environment and the possibilities of its application in teaching in the first grade of primary education. In this thesis I describe the process of an experiment conducted with pupils of the 1st - 5th year of elementary school, with whom I have tried and verified a series of new environment exercises. Based on the reflection of this experiment, and the analysis of pupils' solutions, I formulated a final version of these exercises. I led the process of the whole experiment in line with the constructivist educational style. In the theory part, I am mentioning the important terms of mathematics and its didactics, that are necessary for the purposes of this thesis, and that I refer to the relevant professional literature. This thesis also contains the analysis of chosen textbook collections that are related to its topic. The last part of this thesis is the final and complete series of exercises useful for teaching mathematics in the 1st grade of elementary school, especially if the teacher aims to purposefully develop the pupils' understanding of the terminology and relations from the mathematical areas of analytic geometry, functions and sequences.

L’axe cerveau-intestin désigne l’interaction bidirectionnelle entre le cerveau et le tube digestif. Bien que la leptine, hormone produite par le tissu adipeux, participe à la régulation de cet axe, son mode d’action dans le système nerveux entérique a été peu étudié. A l’heure actuelle, une relation étroite entre une perturbation de l’axe cerveau-intestin et la schizophrénie est supposée. Par conséquent, les objectifs de ce travail étaient d’évaluer 1) les effets ex vivo de la leptine dans la neurotransmission entérique chez le rat et 2) les altérations périphériques dans un modèle neurodéveloppemental de la schizophrénie (NVHL) chez le rat. Nous avons montré que la leptine module l’activité des neurones entériques inhibiteurs et excitateurs dans le jéjunum et le côlon proximal. L’implication des neurones afférents primaires intrinsèques a été discutée. Chez les rats NVHL, nous avons mis en évidence une réduction de la masse corporelle, des variations hormonales, une inflammation du jéjunum et des altérations motrices digestives. La relation entre les troubles périphériques, notamment vagaux, et la physiopathologie de la schizophrénie a été discutée. / The brain-gut axis refers to the bidirectional interaction between the gut and the brain. Although leptin, a hormone released from fat tissue, is involved in the brain-gut axis control, its mechanism of action in the enteric nervous system has not been studied so far. Nowadays, brain-gut axis dysfunctions are supposed to be in close connection with schizophrenia. Therefore, the goals of this work were to determine 1) the effects of leptin on rat enteric nervous system neurotransmission and 2) peripheral alterations in the NVHL neurodevelopmental rat model of schizophrenia. We showed that leptin modulates inhibitory and excitatory enteric motor neurons activity in jejunum and proximal colon. Implication of intrinsic primary afferent neurons was discussed. In NVHL rats, we showed a decrease in body mass, some hormonal variations, jejunal inflammation and gastro-intestinal mechanical activities alterations. The relation peripheral alterations, like vagus nerve dysfunction, and the physiopathology of schizophrenia was discussed.

An exploratory study was undertaken to investigate the relationship between emotional intelligence based on Mayer and Salovey's (1990) trait model of emotional intelligence and cognitive thinking styles based on the theory of mental selfgovernment. Emphasis was placed on the influence of emotional intelligence and thinking styles on choice of study field. Participants were 309 students from a Gauteng university. Students registered with the humanities (n=99), management (n=41), sciences (n=131) and engineering (n=38) faculties were compared on the Schutte Self-Report Inventory for emotional intelligence (Schutte et al., 1998) and on the Thinking Styles Inventory (Sternberg & Wagner, 1992). A relationship was found between complex and creative thinking styles and high emotional intelligence. Results from the stepwise multiple regression analysis procedures indicated that the subscales of thinking styles could be significant predictors of emotional intelligence. Students from different faculties were found to have the same level of emotional intelligence and similar thinking styles. / Psychology / MA (Social Sciences) (Psychology)

Submitted by Alane dos Santos Viana (alane.viana@ucsal.br) on 2016-09-27T13:19:32Z No. of bitstreams: 1 Banca Final - REVISÃO 30-6 WEB.pdf: 2344802 bytes, checksum: ff6e72625bf497ce41d99b272a337d3a (MD5) / Approved for entry into archive by Maria Emília Carvalho Ribeiro (maria.ribeiro@ucsal.br) on 2016-09-30T19:42:06Z (GMT) No. of bitstreams: 1 Banca Final - REVISÃO 30-6 WEB.pdf: 2344802 bytes, checksum: ff6e72625bf497ce41d99b272a337d3a (MD5) / Made available in DSpace on 2016-09-30T19:42:06Z (GMT). No. of bitstreams: 1 Banca Final - REVISÃO 30-6 WEB.pdf: 2344802 bytes, checksum: ff6e72625bf497ce41d99b272a337d3a (MD5) Previous issue date: 2014-02-18 / A presente dissertação tem como objetivo analisar a expansão da cidade de Salvador/BA e os agentes modeladores do espaço urbano, no vetor caracterizado pelo eixo viário da Avenida Paralela (Salvador/BA), como é conhecida a Avenida Luis Viana Filho, no período de 1968 a 2013. A metodologia utilizada, fundamentada em conceitos e teorias, consistiu em pesquisa quantitativa, a partir da análise da dinâmica de implantação de empreendimentos ao longo desta avenida, tendo por base o levantamento de dados constantes nos alvarás de construção emitidos pela Prefeitura Municipal de Salvador e em dados censitários do IBGE (2010), que se traduziram em mapas temáticos, tabelas e gráficos. As informações obtidas foram posteriormente cruzadas com fotos aéreas, e confrontadas por pesquisa de campo na área de estudo. A hipótese que se buscou comprovar foi que este território vem se caracterizando e conformando como um eixo de expansão urbana da cidade de Salvador, o qual, concebido inicialmente como elo de ligação entre centralidades metropolitanas, passou a desempenhar o papel de eixo de conexão entre empreendimentos aí implantados. Recentemente vem sendo requalificado com vistas à retomar este papel no novo sistema viário metropolitano que se configura no cenário atual. De forma breve, foram reconstruídas as transformações espaciais ocorridas na cidade como um todo e nesta localidade de forma mais específica, remontando à implantação da avenida na década de 1970 e as repercussões sobre o território contextualizadas historicamente em períodos definidos por marcos histórico-urbanos na trajetória política de Salvador. Como resultado, ratificou-se a hipótese levantada, comprovando-se a ação dos agentes sociais nesse vetor urbanizado na intenção da produção de novos espaços urbanos. Com o presente trabalho busca-se, pois enriquecer e despertar o interesse pela produção de novos estudos e/ou intervenções sobre esta área da cidade, até então pouco investigada no âmbito acadêmico. / This thesis aims to analyze the expansion of the city of Salvador / BA and the modeling agents of urban space, at the vector axis of Avenida Paralela (Salvador/BA), as is known the Avenida Luis Viana Filho, between 1968 and 2013. The methodology consisted of quantitative research, based on concepts and theories from the analysis of the dynamics of implementation of projects along this avenue, based on the survey data contained in building permits issued by the city administration of Salvador and census data of IBGE (2010), which were translated into thematic maps, tables and graphs. The information obtained was subsequently crossed with aerial photos, and confronted by field research in the study area. The hypothesis that sought to prove was that this territory has been characterized as an expansion axis of Salvador and, as it was conceived at the very beginning, as a link between Salvador and other cities of the metropolitan region. Subsequently acting as a point of connection between the ventures deployed there, it has been remodeled to get back to it’s original function. In brief, spatial transformations that occurred in the city were rebuilt as a whole, and in this location more specifically, dating back to the construction of this avenue in the 1970s and the repercussions on the territory historically contextualized. As a result, the hypothesis raised was confirmed by the action of social agents in the urbanized vector intending the production of new urban spaces. With this present work, one looks foward to enrich and awaken interest in the production of new studies and/or interventions in this area of town, though little investigation was found about it in the academic area.

A infraestrutura viária desempenha um papel importante na eficiência do transporte urbano. O sistema de transporte é um desafio para os gestores públicos. Em Uberlândia (MG), as autoridades municipais discutem propostas na busca de sua melhoria para a mobilidade urbana. O objetivo deste trabalho é analisar a rede de infraestrutura urbana de um eixo viário na região Sudeste de Uberlândia, considerando o fluxo veicular, os projetos implantados e as condições de circulação dos veículos, comparando a capacidade viária existente e ampliada. Foram discutidos diferentes elementos da via e suas consequências para a malha viária do eixo. Os resultados foram obtidos a partir da contagem volumétrica classificada veicular em 8 postos de pesquisa com maior fluxo veicular nos períodos de 6:15h às 8:15h e de 17:30h às 19:30h, e o local com maior volume de tráfego encontrou-se na interseção da Avenida Jaime de Barros com a Rua Pascoal Bruno, em direção ao Terminal Santa Luzia. Na maioria dos postos pesquisados ocorreram medidas paliativas que adiaram a concretização dos projetos previstos nos Planos Diretores e foram encontrados problemas envolvendo sinalizações horizontal e vertical. Foi possível verificar que os projetos viários, embora presentes em diferentes gestões públicas, nem sempre foram viabilizados, sendo um dos entraves encontrados à dificuldade nas indenizações pelas desapropriações de lotes. O eixo estudado é uma mistura de obras finalizadas e outras não conclusas. Dos acidentes de trânsito em 2014 com vítimas, 77,78% envolveu resgate de motociclistas, com maior incidência nos bairros São Jorge e Santa Luzia. O volume veicular nas vias arteriais foi menor do que o estabelecido por Vasconcellos (2005), onde conclui-se que os motoristas utilizam vias fora do eixo como outras opções viáveis para os deslocamentos na região, alterando a dinâmica urbana no eixo estudado. / Road infrastructure plays an important role in urban transport system efficiency. The transportation plan is a challenge for public managers. In Uberlândia (MG), the city authorities are searching for alternatives in the urban mobility. The objective of this study is to analyze the urban road infrastructure network of an axis road in the southeast region of Uberlândia, considering the traffic flow, implemented roadworks and the vehicle circulation conditions, comparing the current and future road capacity. The discussion includes different road components and the consequences for the axis road routes. Vehicle volume counts were carried out at 8 different research points with the volume counts showed more intense traffic during 2 (two) periods - from 6:15 to 8:15am and from 17:30 to 19:30pm. The most intense traffic volume occurred in the intersection of Jaime de Barros Avenue and Pascoal Bruno Street, in direction of the Santa Luzia Terminal. The major research points received only palliative measures that caused a delay in the implementation of projects included in the main Transportation Plan and problems related to horizontal and vertical traffic signs. Some of the roadworks were not completed although they were included in different public administrations. One of the main obstacles was the difficulty related to properties compensation in the area. The analyzed axis road is a mixture of finished and unfinished roadworks. Of traffic accidents in 2014 with victims, 77.78% involved rescue of motorcyclists, with greater incidence in the São Jorge and Santa Luzia neighborhoods. The vehicular flow counted on the main roads are lower than established by Vasconcellos (2005), for the results that drivers use off-axis routes as other viable options for the displacements in the region, changing the urban dynamic in the analysed axis road. / Dissertação (Mestrado)

(EN) GH/IGF-1 axis components (GH, growth hormone receptor (GH-R), IGF-1, IGF-1 receptor (IGF-1R), IGF-binding proteins (IGFBPs)) participate in the control of glucose metabolism, inflammatory processes as well as cell proliferation and differentiation, including adipocytes and monocytes. The aim of the present study was to evaluate the role of local mRNA expression of GH/IGF-1 axis components in subcutaneous adipose tissue (SCAT) and peripheral monocytes (PM) in the development of insulin resistance and differences of adipose tissue mass in following groups of patients: obese females with and without type 2 diabetes mellitus and subjects with active untreated acromegaly. A total number of 66 subjects were included in the study: obese females without type 2 diabetes mellitus (OB), obese females with type 2 diabetes mellitus (T2DM), acromegalic patients (AC) and healthy lean control subjects (C). T2DM underwent 2 weeks of very-low- calorie diet (VLCD - energy content 2500 kJ/day). According to our results we suggest that decreased mRNA expression of IGF-1, IGF-1R, IGFBP-2 and IGFBP-3 in adipose tissue of T2DM subjects may contribute to changes of fat differentiation capacity and the increased IGF-1R mRNA expression in peripheral monocytes in these patients may play a role in the regulation of...

As interações entre o sistema nervoso central e os sistemas imune e endócrino são o objeto de estudo da psiconeuroimunologia. Protocolos de indução de estresse têm sido amplamente utilizados como métodos confiáveis de investigação da relação entre transtornos psiquiátricos, aspectos psicológicos, traços de personalidade, ansiedade e a resposta imune. O procedimento de simulação de falar em público (SFP) é um protocolo experimental validado que reconhecidamente é capaz de ativar o eixo hipotálamo-hipófise-adrenal (HPA) e produzir respostas de estresse em sujeitos humanos. Esse método foi utilizado para: 1) Comparar a reatividade imunológica de indivíduos com diagnóstico de fobia social com a de indivíduos sem qualquer diagnóstico psiquiátrico; 2) Investigar se ocorrem alterações imunes subseqüentes à exposição a um estressor agudo induzido em laboratório e 3) identificar e correlacionar parâmetros imunológicos com traços de personalidade, humor, níveis de ansiedade e medidas fisiológicas. Os traços de personalidade foram investigados por meio dos seguintes instrumentos: Inventário de Temperamento e Caráter (TCI), Escala de Afeto Positivo e Negativo (PANAS), Inventário de Ansiedade Traço (IDATE-T), Inventário de Depressão de Beck (BDI), Inventário de Estratégias de ?Coping? de Folkman e Lazarus e Adaptação da Escala de Percepção de Estresse (PSS). Os sintomas de ansiedade foram avaliados por meio da Escala Analógica Visual de Humor (VAMS), da Escala de Sintomas Somáticos (ESS) e do IDATE-Estado. As variáveis psicofisiológicas avaliadas foram pressão arterial sistólica (PAS), diastólica (PAD), batimentos cardíacos (BPM), resposta galvânica da pele (GSR) e temperatura. Os níveis plasmáticos de catecolaminas (adrenalina, noradrenalina e dopamina) e hormônios do eixo HPA (cortisol e ACTH) também foram dosados. Realizou-se a contagem de células imunes polimorfonucleares e mononucleares no sangue periférico e mediu-se a atividade citotóxica de células NK e neutrófilos. Dosou-se proteínas de fase aguda e imunoglobulinas (A, D, G, M e E) a produção de citocinas no sangue por ELISA e RT-PCR. Os dados foram submetidos a análises de variância para dados com medidas repetidas testando efeitos de grupo, sexo, momento experimental e interações. As correlações entre as variáveis foram testadas por regressões múltiplas e coeficientes de correlação de Pearson. Os resultados apontam que o SFP foi eficiente para induzir estresse e produzir alterações detectáveis em diversos dos parâmetros investigados. As diferenças entre fóbicos sociais e controles são significativas para traços de personalidade e atuam ao longo do tempo para as medidas psicofisiológicas. Alterações imunes e hormonais estiveram mais frequentemente associadas ao gênero do que ao grupo experimental, e afetaram mais homens. Além disso, as alterações imunes foram de pequena magnitude afetando componentes inespecíficos da resposta imune. Conjuntamente, os resultados apontam uma relativa ativação do eixo HPA em fóbicos mas que não corresponde a alterações imunes de mesma magnitude. Mais estudos com uma amostra maior e a investigação de outros parâmetros são necessários para compreender melhor como a fobia social afeta o sistema imune de homens e mulheres e investigar se as alterações podem aumentar a susceptibilidade a doenças nesse grupo de sujeitos. Uma vez que essa interação seja melhor compreendida poderá subsidiar estratégias mais adequadas para abordar e elaborar estratégias de prevenção e intervenção capazes de promover comportamentos saudáveis. / Interactions among the nervous, immune and endocrine systems are the object of study of Psychoneuroimmunology. Stress protocols have been broadly used as reliable means to investigate the relationship among psychiatric disorders, psychological aspects, personality traits, anxiety and immune response has been studied using these interactions. The Simulated Public Speaking (SPS) is a validated experimental procedure known to activate the Hypothalamus-Pituitary-Adrenal (HPA) axis and produce stress responses in human subjects. This method was used to: 1) compare the immune reactions of individuals with a diagnosis of social phobia to that of individuals without any psychiatric diagnosis; 2) investigate if immune alterations occur subsequent to the exposure to an acute laboratory induced stressor; 3) identify and correlate immune parameters with personality traits, mood, anxiety levels and physiologic measures. Personality traits were investigated with Cloninger?s Temperament and Character?s Inventory (TCI), Positive and Negative Affects Scale (PANAS), State-Trait Anxiety Scale (STAI?T), Beck?s Depression Inventory (BDI), Lazarus?s Coping Strategies Inventory, Perceived Stress Scale (PSS). Anxiety symptoms were investigated along the procedure with the Bodily Symptoms Scale (ESS), STAI-E and the Visual Analogue Mood Scale (VAMS). Psychophysiologic variables assessed were Systolic (PAS) and Diastolic (PAD) Blood Pressure, Heart Rate (BPM), Galvanic Skin Response (GSR) and temperature. Plasmatic circulating levels of cathecolamines (Adrenaline, Noradrenaline and Dopamine) and HPA axis hormones (Cortisol, ACTH) were assessed. Peripheral blood cell population counts were obtained for polymorphonuclear (PMN) and mononuclear cells. Cytotoxic activity of neutrophils and NK cells was assessed, as well as cytokine production by ELISA and RT-PCR. Acute phase proteins and immunoglobulins (A, D, G, M, and E) were dosed on peripheral blood. Data was submitted to variance analysis for data with repeated measures testing effects of group, sex, experimental moment and interactions on variables. Correlations among variables were tested by multiple regressions and Pearson?s correlation deltas. The results show SPS was efficient in inducing stress and produce detectable alterations in several of the parameters investigated. Differences between social phobics and controls are significant for personality traits and, along time for psychophysiologic measures. Hormonal and immune alterations were more often associated to gender rather than to the group subjects belonged to, with men being more susceptible to the procedure. Also, immune changes were of small magnitude, usually affecting inespecific components of the response. Together, the results point to a relatively higher activation of the HPA-axis in social phobics, but one that does not correspond to immune responses of the same magnitude. Further studies with a larger sample and investigation of other parameters are necessary to better understand how social phobia affects the immune system of men and women and to investigate if the alterations can increase susceptibility to diseases in this group of individuals. Once this interaction is better understood it may provide the basis for an improved design to approach and elaborate prevention/intervention strategies and promote healthy behaviours.

O sistema NADPH oxidase é um complexo enzimático gerador de superóxido. O NF-kB é um fator de transcrição envolvido no controle da expressão de diversos genes ligados à resposta inflamatória. Defeitos no eixo IL-12/23-IFN-g resultam em infecções recorrentes e à susceptibilidade mendeliana a micobacterioses, podendo diminuir a expressão do componente gp91-phox da NADPH oxidase. Estudamos qual é a relação direta do NF-kB e de defeitos no eixo IL-12/23-IFN-g na regulação dos genes CYBA, NCF1, NCF2 e NCF4 do sistema NADPH oxidase humano em células U937, células B EBV transformadas provenientes de pacientes com EDA-ID, DGC, ou de pacientes com defeitos no eixo IL-12/23-IFN-g. A expressão dos genes NCF1 e NCF2 foi diminuída em células com defeitos no eixo (IFNGR1 e INFGR2) e em células U937 IkB S32A/S36A. A expressão do gene NCF1 também foi diminuída em células EDA-ID S32I e em células EDA-ID NEMO/IKKg W420X. O NF-kB e os IFNGR1 e INFGR2 são necessários para a expressão dos genes NCF1 e NCF2 e para a ativação do sistema NADPH oxidase humano neste sistema modelo. / The NADPH oxidase system is an enzymatic complex that generates superoxide. The NF-kB is a transcriptional factor involved in the expression of several genes related to the inflammatory response. The IL-12/23-IFN-g axis defects lead to recurrent infections and to the mendelian susceptibility of mycobacterial disease (MSMD), and they can decrease the gp91-phox expression (a NADPH oxidase component). We studied the NF-kB and the IL-12/23-IFN-g axis defects consequences on the regulation of CYBA, NCF1, NCF2 and NCF4 genes of the human NADPH oxidase system in U937 cells, and in B EBV cells from patients with EDA-ID, DGC, or patients with IL-12/23-IFN-g axis defects. The NCF1 and NCF2 gene expression was decreased in IL-12/23-IFN-g axis defects cells (IFNGR1 and INFGR2) and in U937 IkB S32A/S36A cells. NCF1 gene expression was decreased in EDA-ID S32I and in EDA-ID NEMO/IKKg W420X cell lineages. The NF-kB and the IFNGR1 and INFGR2 are necessary for NCF1 and NCF2 gene expression and activation of the human NADPH oxidase in this model system.

O objetivo deste estudo foi comparar o eixo de rotação verdadeiro com o anatômico em ambiente virtual 3D, e seus efeitos sobre dois pontos anatômicos mandibulares. O eixo verdadeiro foi determinado em 14 indivíduos por meio de axiografia, e transferido para o ambiente virtual por TCFC, e posteriormente determinado anatomicamente, onde foram medidas as distâncias entre ambos. Foram simuladas rotações de 2º, 5º e 8º da mandíbula nos dois eixos, tanto para abertura como fechamento, e quantificadas as diferenças nos pontos da linha média inferior (LMI) e pogônio (Pg). O teste t pareado foi utilizado para examinar as diferenças entre as médias nas posições desses pontos (p<0,05). Os eixos verdadeiros localizaram-se dentro de um raio de 5 mm do anatômico em 67,86% da amostra. A distância absoluta média entre os eixos foi de 4,79 mm, enquanto que a vetorial foi de 2,33 no plano horizontal e 3,03 mm no vertical, resultando na direção anteroinferior em 71,43% dos eixos verdadeiros. Houve diferença estatisticamente significante na posição dos pontos LMI e Pg para todas as magnitudes e direções, entre os eixos. O eixo verdadeiro está localizado na direção anteroinferior em relação ao anatômico. Os efeitos na mandíbula são significantes e diferentes em todas as amplitudes, tanto para abertura como fechamento, porém com possível pequena relevância clínica. / The aim of this study was to compare the true hinge axis to the anatomic one in a virtual 3D environment, and also their respective effects on two mandibular anatomic points. The true axis has been determined in 14 individuals by means of axiography, and later transferred to a virtual environment by CBTC, where the anatomical axis was determined, and measured the distances between them. Mandibular rotation of 2º, 5º and 8º in both axes were performed, both for opening and closing, as well as the quantification of the difference found in the points of the lower midline (LM) and pogonion (Pg). Paired t-test was used to examine differences between the average values in the position of those points (p<0,05). The true axis was located within a 5mm-radius of the anatomic axis throughout 67.86% of the sample. The average absolute distance between the axes was 4.79 mm, while the vector distance was 2.33 mm in the horizontal plane e 3.03mm in the vertical plane, amounting to an anteriorinferior direction of 71.43% of the true axis. There was significant difference in the position of points LM and Pg to all magnitudes and directions within the axes. The true hinge axis is located in the anterior-inferior direction in relation to the anatomic axis. The effects observed onto the mandible are significant and different in all amplitudes, both for opening and closing positions, however they present small clinical relevance.

Given a set of n points P ⊂ R2, the Delaunay graph of P for a family of geometric objects C is a graph defined as follows: the vertex set is P and two points p, p' ∈ P are connected by an edge if and only if there exists some C ∈ C containing p, p' but no other point of P. Delaunay graph of circle is often called as Delaunay triangulation as each of its inner face is a triangle if no three points are co-linear and no four points are co-circular. The dual of the Delaunay triangulation is the Voronoi diagram, which is a well studied structure. The study of graph theoretic properties on Delaunay graphs was motivated by its application to wireless sensor networks, meshing, computer vision, computer graphics, computational geometry, height interpolation, etc. The problem of finding an optimal vertex cover on a graph is a classical NP-hard problem. In this thesis we focus on the vertex cover problem on Delaunay graphs for geometric objects like axis-parallel slabs and circles(Delaunay triangulation). 1. We consider the vertex cover problem on Delaunay graph of axis-parallel slabs. It turns out that the Delaunay graph of axis-parallel slabs has a very special property — its edge set is the union of two Hamiltonian paths. Thus, our problem reduces to solving vertex cover on the class of graphs whose edge set is simply the union of two Hamiltonian Paths. We refer to such a graph as a braid graph. Despite the appealing structure, we show that deciding k-vertex cover on braid graphs is NP-complete. This involves a rather intricate reduction from the problem of finding a vertex cover on 2-connected cubic planar graphs. 2. Having established the NP-hardness of the vertex cover problem on braid graphs, we pursue the question of improved fixed parameter algorithms on braid graphs. The best-known algorithm for vertex cover on general graphs has a running time of O(1.2738k + kn) [CKX10]. We propose a branching based fixed parameter tractable algorithm with running time O⋆(1.2637k) for graphs with maximum degree bounded by four. This improves the best known algorithm for this class, which surprisingly has been no better than the algorithm for general graphs. Note that this implies faster algorithms for the class of braid graphs (since they have maximum degree at most four). 3. A triangulation is a 2-connected plane graph in which all the faces except possibly the outer face are triangles, we often refer to such graphs as triangulated graphs. A chordless-NST is a triangulation that does not have chords or separating triangles (non-facial triangles). We focus on the computational problem of optimal vertex covers on triangulations, specifically chordless-NST. We call a triangulation Delaunay realizable if it is combinatorially equivalent to some Delaunay triangulation. Characterizations of Delaunay triangulations have been well studied in graph theory. Dillencourt and Smith [DS96] showed that chordless-NSTs are Delaunay realizable. We show that for chordless-NST, deciding the vertex cover problem is NP-complete. We prove this by giving a reduction from vertex cover on 3-connected, triangle free planar graph to an instance of vertex cover on a chordless-NST. 4. If the outer face of a triangulation is also a triangle, then it is called a maximal planar graph. We prove that the vertex cover problem is NP-complete on maximal planar graphs by reducing an instance of vertex cover on a triangulated graph to an instance of vertex cover on a maximal planar graph.