For a graph G=(V, E) and a set of vertices S⊆ V, a vertex v∈S is said to be very cost effective if it is adjacent to more vertices in V{set minus}. S than in S. A bipartition π= {S, V{set minus}. S} is called very cost effective if both S and V{set minus}. S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We characterize the cactus graphs having a very cost effective bipartition. Also, we show that if a graph G or H has a very cost effective bipartition, then so does the Cartesian product G□ H.

In this thesis we investigate different domination-related graph polynomials, like the connected domination polynomial, the independent domination polynomial, and the total domination polynomial. We prove some basic properties of these polynomials and obtain formulas for the calculation in special graph classes. Furthermore, we also prove results about the calculation of the different graph polynomials in product graphs and different representations of the graph polynomials. One focus of this thesis lays on the generalization of domination-related polynomials. In this context the trivariate domination polynomial is defined and some results about the bipartition polynomial, which is also a generalization of the domination polynomial, is presented. These two polynomials have many useful properties and interesting connections to other graph polynomials. Furthermore, some more general domination-related polynomials are defined in this thesis, which shows some possible directions for further research. / In dieser Dissertation werden verschiedene, zum Dominationspolynom verwandte, Graphenpolynome, wie das zusammenhängende Dominationspolynom, das unabhängige Dominationspolynom und das totale Dominationspolynom, untersucht. Es werden grundlegende Eigenschaften erforscht und Sätze für die Berechnung dieser Polynome in speziellen Graphenklassen bewiesen. Weiterhin werden Ergebnisse für die Berechnung in Produktgraphen und verschiedene Repräsentationen für diese Graphenpolynome gezeigt. Ein Fokus der Dissertation liegt auf der Verallgemeinerung der verschiedenen Dominationspolynome. In diesem Zusammenhang wird das trivariate Dominationspolynom definiert. Außerdem werden Ergebnisse für das Bipartitionspolynom bewiesen. Diese beiden Polynome haben viele interessante Eigenschaften und Beziehungen zu anderen Graphenpolynomen. Darüber hinaus werden weitere multivariate Graphenpolynome definiert, die eine mögliche Richtung für weitere Forschung auf diesem Gebiet aufzeigen.

L‟étude porte sur la systématique de l‟endofaune microbienne des Oligochètes terricoles Megascolecidae et Glossoscolecidae de la région de Yaoundé et ses environs, avec un accent particulier sur l‟analyse morphologique et génétique des Ciliés Astomes présents dans leur tractus digestif. Une révision taxonomique de la famille des Radiophryidae de Puytorac 1972 est menée, avec la description de cinq espèces nouvelles de la sous-famille des Metaracoelophryinae de Puytorac, 1972. Elle permet de confirmer d‟une part, la présence des genres Paracoelophrya et Dicoelophrya dans le tube digestif des Oligochètes du genre Alma du Cameroun et de confirmer l‟homogénéité de ce groupe d‟autre part. La question de la parenté phylogénétique des Hoplitophryida est exposée. La diversité d‟organisation de l‟appareil nucléaire dans le genre Almophrya a été étudiée à travers des observations sur ses variations morphologiques après coloration des spécimens au Diamidino Phényl Indol (Johnson et al., 1982), au Feulgen ou au carbonate d‟argent ammoniacal (Fernandez Galiano, 1994). Une nouvelle espèce d‟Almophrya à vacuoles axiales est décrite, Almophrya nkoldaensis n. sp., imposant une révision des clés d‟identification des espèces au sein de ce genre. Bien plus, le processus de morphogenèse de bipartition chez trois espèces d‟Astomes a été étudié, montrant diverses variantes de cette division : à côté de la fission binaire classique chez Eudrilophrya complanata, la palintomie radiaire et distale chez Buchneriella eupolytoreuti n. sp. a été précisée. De plus, le processus de la conjugaison a été exploré chez Eudrilophrya simplex n.sp. L‟analyse des séquences de gènes RNA de la petite sous unité ribosomale (SSrRNA) chez Anoplophrya marylandensis Conklin, 1930 montre l‟appartenance de cette espèce d‟Astome à la Classe des Oligohymenophora (Affa‟a et al., 2004). Cependant, la séquence de gènes d‟une seule espèce est insuffisante pour établir avec certitude, les relations phylétiques dans un grand groupe. Par conséquent, nous avons obtenu les séquences de gènes SSrRNA de neuf espèces additionnelles distribuées dans six genres appartenant aux trois ordres de la sous-classe des Astomatia : Hoplitophryida Cheissin, 1930 em., de Puytorac, 1972 ; Anoplophryida Cépède, 1910 et Haptophryida Cépède, 1923. Dans le cadre de l‟analyse moléculaire, un nouveau genre de Clausilocolidae de Puytorac in Corliss, 1979 est proposé : Paraclausilocola nov. gen., avec deux espèces nouvelles : P. elongata n. sp. et P. constricta n. sp. Ce nouveau genre est représentatif de l‟ordre des Haptophryida. Le cladogramme obtenu montre une forte affinité des séquences des nouveaux Astomes étudiés avec celle d‟A. marylandensis Conklin, 1930. La branche de l‟arbre contenant les Astomes est précise et montre une distance génétique considérable avec les autres sous-classes des Oligohymenophorea. Cet arbre établit les Astomes comme un clade frère des Scuticociliés, confirmant l‟hypothèse selon laquelle les Astomes forment une sous-classe monophylétique appartenant à la classe des Oligohymenophora (de Puytorac, 1954 ; Affa‟a et al., 2004). Dans la sous-classe des Astomatia, nous observons deux branches bien distinctes : l‟une avec les genres Anoplophrya, Almophrya et Metaracoelophrya, la seconde avec les genres restants : Eudrilophrya, Metaradiophrya, Paraclausilocola et Njinella. Au regard de ce regroupement, les attributions ordinales et les assignations des genres aux familles dans les deux classifications actuelles, celle de de Puytorac (1994) et de Lynn (2008), ne semblent plus respectées.

O diabetes mellitus tipo 2 (DM2) é uma doença de prevalência crescente na população mundial, sendo associado ao aumento de diversas comorbidades. A relação entre o trato digestivo e o DM2 tem sido fortalecida a partir dos resultados das diferentes cirurgias metabólicas frente à remissão do distúrbio endócrino. Alterações morfológicas hipertróficas no epitélio intestinal são percebidas nos estágios iniciais da doença e parece ter papel primordial na instalação da hiperglicemia crônica. O gene p53 participa ativamente dos processos de regulação do crescimento epitelial intestinal e pode sofrer alteração de sua expressão em estados diabéticos. Objetiva-se avaliar os resultados clínicos e laboratoriais de pacientes DM2 e com índice de Massa Corpórea (IMC) >25 e <35 Kg/m2 submetidos a cirurgia metabólica denominada adaptação digestiva com duodenal switch parcial (DSP) e avaliar o comportamento da expressão do gene p53 na mucosa intestinal no período pré e pós-operatório. Nove pacientes DM2, com IMC<35Kg/m2 foram operados pela técnica DSP. Biópsias de duodeno e íleo foram colhidas no estado diabético (pré e transoperatório respectivamente) e, 3 meses após a cirurgia, através de endoscopia digestiva alta. Foram comparados os dados de evolução antropométrica (IMC) e laboratorial no período pré e pós-operatório. Através do método enzyme-linked immunosorbent assay (ELISA) foram determinados os níveis dos entero-hormônios glucagon-like peptide-1 (GLP-1) e glucose-dependent insulinotropic peptide (GIP), no pré e pós-operatório, em jejum e pós-prandial nos períodos 30',60',90' e 120'. A expressão do gene p53, foi avaliada por real time polymerase chain reaction (qrt-PCR) e western blot, nos dois diferentes momentos. As variáveis: glicemia de jejum e pós-prandial (2 horas), trigliceridemia de jejum, hemoglobina glicada (HbAc1) e peptídeo C foram analisadas. As médias dos parâmetros laboratoriais foram comparadas pela análise multivariada ANOVA e após teste-Tukey. A média de expressão relativa do gene p53 foi comparada nos dois períodos pelo teste t-student. Os resultados evidenciaram que entre maio e dezembro de 2010, nove pacientes (4 homens, 5 mulheres) DM2 e com IMC entre 26 e 34Kg/m2 foram submetidos a DSP. A média de IMC do grupo operado foi de 31,3. Houve queda do IMC média de 23% após um ano. Houve queda significativa (p<0,05) nos níveis de triglicerídeos, glicemia de jejum e pós-prandial (2 horas), HbA1c assim como aumento do peptídeo-C (p<0,05), quando comparados os períodos pré e pós-operatório. Os níveis séricos de GLP-1 foram significativamente maiores no pós-operatório (p<0,05), tanto em jejum como pós-prandial sendo que houve diminuição dos níveis de GIP, contudo sem significância estatística. O gene p53 sofreu aumento significativo de sua expressão relativa (qrt-PCR)(p<0,05) no período pós-operatório na mucosa duodenal e uma tendência de aumento no íleo, contudo sem significância estatística. A análise da expressão ao nível proteico foi bem sucedida somente no íleo, também mostrando tendência de aumento. Concluí-se que a DSP foi capaz de controlar satisfatoriamente o DM2 em pacientes com IMC<35 Kg/m2. Houve aumento da secreção de GLP-1 e tendência de diminuição do GIP. Houve aumento da expressão do p53 na mucosa intestinal, no período pós-operatório, após o controle do diabetes, quando comparada ao período pré-operatório. / Diabetes mellitus type 2 (DM2) is a worldwide increasing prevalence disease, being related to a variety of comorbidities. The relationship between the digestive tract and DM2 has been strengthened by the results of different metabolic surgery procedures on resolution of the endocrine disorder, before weigh loss achievement. Hypertrophic morphological changes in the intestinal epithelium are observed in the early stages of disease development and seems to have a pivotal role in the establishment of chronic hyperglicemia. The p53 gene directly participates on regulation of growth processes of the intestinal epithelium, and its expression has been shown to be altered in diabetic states.The objectives were to evaluate clinical and laboratory results in DM2 patients, presenting Body Mass Index(BMI)>25 and <35Kg/m2, undergoing a metabolic surgery procedure called digestive adaptation with partial duodenal switch(DSP). To assess p53 gene expression behavior in intestinal mucosa, on pre and postoperative period. Nine patients presenting DM2 and BMI below 35Kg/m2 underwent DSP.Biopsies of the duodenum and intermediate portion of the ileum were undertaken in diabetic state (pre and transoperative respectively) and 3 months after surgery by upper gastrointestinal endoscopy. The evolution of anthropometric (BMI) and laboratory parameters were acessed on postoperative period. Serum levels of enterohormones glucagon-like peptide-1(GLP-1) and glucose-dependent insulinotropic peptide (GIP) were determined by the method enzyme-linked immunosorbent assay (ELISA), pre and postoperatively, on fasting and postprandial state (30',60'90 and 120') after ingestion of a standart meal.The p53 gene expression was evaluated by real time polymerase chain reaction (qrt-PCR) and western blot, on two different periods. The variables: fasting and postprandial (2 hours) glicemia, fasting triglycerides (TG), glycosylated hemoglobin (HbA1c) and C-peptide were undertaken. The mean levels of laboratorial parameters were compared by mulivariate analyses (ANOVA) and Tukey test. The mean expression of the p53 gene was compared in two different periods by T test. Between may and December 2010, four men and 5 women were operated on. The mean BMI was 31,1. There was a decrease in BMI of 23% after one year of surgery. There was a significant decrease (p<0,05) on fasting TG and HbA1c levels as well as glucose levels on fasting and postprandial state (2 hours) when compared pre and postoperatively. There was an increase (p<0,05) in C-peptide levels after surgery. Serum levels of GLP-1 were significantly higher postorperatively (p<0,05), on both fasting and postprandial condition, and there was a decrease,not significant, on GIP levels. The p53 relative gene expression showed a significant increase (p<0,05) in the postoperative period in duodenal mucosa (transcriptional state) and showed an increasing trend in the ileum, but not statistically significant. Only ileum portion results were succesfully acessed by western blot analisys, showing an increasing trend as well. The DSP procedure was succesfully capable to control type 2 diabetes in patients presenting BMI<35 Kg/m2. There was a significant enhancement of GLP-1 secretion and a decreasing trend for GIP on postoperative period. There was increased expression of mucosal p53 in the postoperative period after the control of DM2, when compared to diabetic pre-operative state.

O diabetes mellitus tipo 2 (DM2) é uma doença de prevalência crescente na população mundial, sendo associado ao aumento de diversas comorbidades. A relação entre o trato digestivo e o DM2 tem sido fortalecida a partir dos resultados das diferentes cirurgias metabólicas frente à remissão do distúrbio endócrino. Alterações morfológicas hipertróficas no epitélio intestinal são percebidas nos estágios iniciais da doença e parece ter papel primordial na instalação da hiperglicemia crônica. O gene p53 participa ativamente dos processos de regulação do crescimento epitelial intestinal e pode sofrer alteração de sua expressão em estados diabéticos. Objetiva-se avaliar os resultados clínicos e laboratoriais de pacientes DM2 e com índice de Massa Corpórea (IMC) >25 e <35 Kg/m2 submetidos a cirurgia metabólica denominada adaptação digestiva com duodenal switch parcial (DSP) e avaliar o comportamento da expressão do gene p53 na mucosa intestinal no período pré e pós-operatório. Nove pacientes DM2, com IMC<35Kg/m2 foram operados pela técnica DSP. Biópsias de duodeno e íleo foram colhidas no estado diabético (pré e transoperatório respectivamente) e, 3 meses após a cirurgia, através de endoscopia digestiva alta. Foram comparados os dados de evolução antropométrica (IMC) e laboratorial no período pré e pós-operatório. Através do método enzyme-linked immunosorbent assay (ELISA) foram determinados os níveis dos entero-hormônios glucagon-like peptide-1 (GLP-1) e glucose-dependent insulinotropic peptide (GIP), no pré e pós-operatório, em jejum e pós-prandial nos períodos 30',60',90' e 120'. A expressão do gene p53, foi avaliada por real time polymerase chain reaction (qrt-PCR) e western blot, nos dois diferentes momentos. As variáveis: glicemia de jejum e pós-prandial (2 horas), trigliceridemia de jejum, hemoglobina glicada (HbAc1) e peptídeo C foram analisadas. As médias dos parâmetros laboratoriais foram comparadas pela análise multivariada ANOVA e após teste-Tukey. A média de expressão relativa do gene p53 foi comparada nos dois períodos pelo teste t-student. Os resultados evidenciaram que entre maio e dezembro de 2010, nove pacientes (4 homens, 5 mulheres) DM2 e com IMC entre 26 e 34Kg/m2 foram submetidos a DSP. A média de IMC do grupo operado foi de 31,3. Houve queda do IMC média de 23% após um ano. Houve queda significativa (p<0,05) nos níveis de triglicerídeos, glicemia de jejum e pós-prandial (2 horas), HbA1c assim como aumento do peptídeo-C (p<0,05), quando comparados os períodos pré e pós-operatório. Os níveis séricos de GLP-1 foram significativamente maiores no pós-operatório (p<0,05), tanto em jejum como pós-prandial sendo que houve diminuição dos níveis de GIP, contudo sem significância estatística. O gene p53 sofreu aumento significativo de sua expressão relativa (qrt-PCR)(p<0,05) no período pós-operatório na mucosa duodenal e uma tendência de aumento no íleo, contudo sem significância estatística. A análise da expressão ao nível proteico foi bem sucedida somente no íleo, também mostrando tendência de aumento. Concluí-se que a DSP foi capaz de controlar satisfatoriamente o DM2 em pacientes com IMC<35 Kg/m2. Houve aumento da secreção de GLP-1 e tendência de diminuição do GIP. Houve aumento da expressão do p53 na mucosa intestinal, no período pós-operatório, após o controle do diabetes, quando comparada ao período pré-operatório. / Diabetes mellitus type 2 (DM2) is a worldwide increasing prevalence disease, being related to a variety of comorbidities. The relationship between the digestive tract and DM2 has been strengthened by the results of different metabolic surgery procedures on resolution of the endocrine disorder, before weigh loss achievement. Hypertrophic morphological changes in the intestinal epithelium are observed in the early stages of disease development and seems to have a pivotal role in the establishment of chronic hyperglicemia. The p53 gene directly participates on regulation of growth processes of the intestinal epithelium, and its expression has been shown to be altered in diabetic states.The objectives were to evaluate clinical and laboratory results in DM2 patients, presenting Body Mass Index(BMI)>25 and <35Kg/m2, undergoing a metabolic surgery procedure called digestive adaptation with partial duodenal switch(DSP). To assess p53 gene expression behavior in intestinal mucosa, on pre and postoperative period. Nine patients presenting DM2 and BMI below 35Kg/m2 underwent DSP.Biopsies of the duodenum and intermediate portion of the ileum were undertaken in diabetic state (pre and transoperative respectively) and 3 months after surgery by upper gastrointestinal endoscopy. The evolution of anthropometric (BMI) and laboratory parameters were acessed on postoperative period. Serum levels of enterohormones glucagon-like peptide-1(GLP-1) and glucose-dependent insulinotropic peptide (GIP) were determined by the method enzyme-linked immunosorbent assay (ELISA), pre and postoperatively, on fasting and postprandial state (30',60'90 and 120') after ingestion of a standart meal.The p53 gene expression was evaluated by real time polymerase chain reaction (qrt-PCR) and western blot, on two different periods. The variables: fasting and postprandial (2 hours) glicemia, fasting triglycerides (TG), glycosylated hemoglobin (HbA1c) and C-peptide were undertaken. The mean levels of laboratorial parameters were compared by mulivariate analyses (ANOVA) and Tukey test. The mean expression of the p53 gene was compared in two different periods by T test. Between may and December 2010, four men and 5 women were operated on. The mean BMI was 31,1. There was a decrease in BMI of 23% after one year of surgery. There was a significant decrease (p<0,05) on fasting TG and HbA1c levels as well as glucose levels on fasting and postprandial state (2 hours) when compared pre and postoperatively. There was an increase (p<0,05) in C-peptide levels after surgery. Serum levels of GLP-1 were significantly higher postorperatively (p<0,05), on both fasting and postprandial condition, and there was a decrease,not significant, on GIP levels. The p53 relative gene expression showed a significant increase (p<0,05) in the postoperative period in duodenal mucosa (transcriptional state) and showed an increasing trend in the ileum, but not statistically significant. Only ileum portion results were succesfully acessed by western blot analisys, showing an increasing trend as well. The DSP procedure was succesfully capable to control type 2 diabetes in patients presenting BMI<35 Kg/m2. There was a significant enhancement of GLP-1 secretion and a decreasing trend for GIP on postoperative period. There was increased expression of mucosal p53 in the postoperative period after the control of DM2, when compared to diabetic pre-operative state.

In this thesis we investigate different domination-related graph polynomials, like the connected domination polynomial, the independent domination polynomial, and the total domination polynomial. We prove some basic properties of these polynomials and obtain formulas for the calculation in special graph classes. Furthermore, we also prove results about the calculation of the different graph polynomials in product graphs and different representations of the graph polynomials. One focus of this thesis lays on the generalization of domination-related polynomials. In this context the trivariate domination polynomial is defined and some results about the bipartition polynomial, which is also a generalization of the domination polynomial, is presented. These two polynomials have many useful properties and interesting connections to other graph polynomials. Furthermore, some more general domination-related polynomials are defined in this thesis, which shows some possible directions for further research. / In dieser Dissertation werden verschiedene, zum Dominationspolynom verwandte, Graphenpolynome, wie das zusammenhängende Dominationspolynom, das unabhängige Dominationspolynom und das totale Dominationspolynom, untersucht. Es werden grundlegende Eigenschaften erforscht und Sätze für die Berechnung dieser Polynome in speziellen Graphenklassen bewiesen. Weiterhin werden Ergebnisse für die Berechnung in Produktgraphen und verschiedene Repräsentationen für diese Graphenpolynome gezeigt. Ein Fokus der Dissertation liegt auf der Verallgemeinerung der verschiedenen Dominationspolynome. In diesem Zusammenhang wird das trivariate Dominationspolynom definiert. Außerdem werden Ergebnisse für das Bipartitionspolynom bewiesen. Diese beiden Polynome haben viele interessante Eigenschaften und Beziehungen zu anderen Graphenpolynomen. Darüber hinaus werden weitere multivariate Graphenpolynome definiert, die eine mögliche Richtung für weitere Forschung auf diesem Gebiet aufzeigen.