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Atoms in quasilocal integral domainsBombardier, Kevin Wilson 01 May 2019 (has links)
Let R be an integral domain. An atom is a nonzero nonunit x of R where x = yz implies that either y or z is a unit. We say that R is an atomic domain if each nonzero nonunit is a finite product of atoms. An atomic domain with only finitely many nonassociate atoms is called a Cohen-Kaplansky (CK) domain. We will investigate atoms in integral domains R with a unique maximal ideal M. Of particular interest will be atoms that are not in M^2.
After studying the atoms in integral domains, we will narrow our focus to CK domains with a unique maximal ideal M. In this pursuit, we investigate atoms in M^2 for these CK domains. We will show that the minimal number of atoms needed to have an atom in M^2 is exactly eight. This disproves a conjecture given by Cohen and Kaplansky in 1946 that the minimal number would be ten. We then classify complete local CK domains with exactly three atoms.
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Interakcia fytohormónov a vonkajšich faktorov v dormacii hľúz ľuľka zemiakového (Solanum tuberosum L.) odvodených v explantátovej kultúreMaco, Roman January 2016 (has links)
Microtubers were obtained from potato plants (Solanum tuberosum L.) cultured in vitro, they were used in following experiments. The impact of growth regulators (FLD, AgNO3, BA, ABA) was monitored in length of dormancy. The content of ABA in the budding tubers and the content of endogenous CK (BA, IP, DHZ, DHZR, Z) was determined during the dormancy as well. Production of ACC, ethylene, O2, CO2 and ethane was determined by gas chromatography. Variants containing FLD, AgNO3 and BA had a significant impact in the shortening of dormancy and stimulation the growth of buds microtubers. When they were used the occurrence of budding tubers was increased by 30-40 % over the control. Variant of ABA inhibited the growth of buds. ABA content correlated with the process of dormancy and the occurrence of budding tubers. The highest content of ABA was in variant with freshly collected dormant tubers. Concentration of various CK was dependent on the type of CK and monitored variant. Generally, It was slightly increased with occurrence of budding tubers.
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A simetria de reflexão: elementos de concepções mobilizadas por alunos do ensino fundamentalMELO, Diógenes Maclyne Bezerra de 31 January 2010 (has links)
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Previous issue date: 2010 / Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco / Esta pesquisa se inscreve na problemática da modelização de conhecimentos, em particular, ao estudo das concepções que os alunos do ensino fundamental mobilizam quando resolvem problemas de simetria de reflexão. Para realizar o estudo, utilizamos o Modelo cK¢ (BALACHEFF, 1995) que é ancorado na Teoria das Situações Didáticas (BROUSSEAU, 1998). As concepções dos alunos foram analisadas a partir das estruturas de controle. Inicialmente, estudamos a simetria de reflexão do ponto de vista do ensino, a saber, livros didáticos e documentos que orientam o ensino do objeto matemático estudado. A pesquisa está baseada, também, nos resultados de pesquisas sobre a temática abordada (GRENIER, 1988 e LIMA, 2006). Os resultados dos estudos realizados subsidiaram a escolha dos problemas propostos na experimentação e na análise a priori, bem como a construção dos instrumentos de coleta e análise dos dados. A experimentação foi implementada com 51 alunos do 9° ano de escolas das redes pública, municipal e estadual de ensino do agreste pernambucano. Os estudantes resolveram problemas de construção e de identificação de figuras simétricas em relação a um eixo de simetria. A pesquisa confirma resultados de estudos precedentes como, por exemplo, os alunos mobilizaram controles ligados a direção vertical e horizontal, independentemente da orientação do eixo de simetria. Controles ligados à conservação de forma e de tamanho das figuras também foram bastante mobilizados pelos alunos, isso dá indícios de que as respostas estão baseadas na visualização das figuras
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Faktory indukce tvorby hlíz lilku bramboru (Solanum tuberosum L.) v in vitro podmínkáchKůrková, Jana January 2017 (has links)
This thesis deals with the factors responsible for induction of the formation of tuber potato (Solanum tuberosum L.) in in vitro conditions. The aim was to observe cultivation of the nodal segments of stems on the induction medium with reduced content of inorganic nitrogen 12 umol, 80 g/l sucrose and the addition of 10 mg/l BA for the for-mation of tubers. The frequency of tuberisation was evaluated, as well as morfological changes, size and weight of the tubers. Three groups of explants were established diffe-ring in lenght of cultivation on the induction medium. These were monitored for chan-ges in the content of endogenous ABA in the nodal segments of stem and stolon. Moni-toring of the changes in content of endogenous cytokinin, nitrogen content, production of ethylene, ethane and CO2 was performed as well. Permanent microscopic preparations were prepared to detect transformation of the axillary bud into stolon, resp. tuber. Increased content of ABA during the tuber formation demonstrates its effect on tuberi-zation. Amongs cytokinins, the biggest effect of cytokinins on tuberization has BA, iP and iPR. Conversely, Z and ZR had no influence. Contents of ethylene, ethane,CO2 and nitrogen are related to the lenght of culturing on the induction medium.
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Perfil metabólico de cabras submetidas a transporte rodoviário / Metabolic profile of goats submitted to road transportationStorillo, Vanessa Martins 05 September 2012 (has links)
O transporte leva os animais ao estresse, que pode comprometer a saúde e bem estar destes, além de elevar a geração de substâncias reativas, aumentando a necessidade de antioxidantes. A idade também influencia o metabolismo, pois o envelhecimento causa modificações no organismo, levando a prejuízos funcionais. O objetivo deste estudo foi avaliar a influência do transporte rodoviário e da idade em cabras, tratadas ou não vitaminas A, D, e E. Foram utilizadas 20 cabras, da raça Boer, com cerca de 60 dias pós-parto, hígidas, manejo e dietas idênticos, de duas faixas etárias (de 1 até 4 anos de idade e entre 4 e 7 anos) e distribuídas em grupos de 10 animais. O transporte rodoviário teve duração de 4h. O exame físico e as coletas de sangue foram efetuados nos tempos T0 (-15d); T1 (-8d); T2 (-3d); T3 (0h); T4 (4h); T5 (5h); T6 (7h) e T7 (6d) do transporte. Em T1 e T2, 10 cabras receberam, via IM, 2mL de complexo com vitaminas A, D e E e 10 receberam solução fisiológica. Foram determinadas temperatura retal (TR); peso vivo (PV); escore de condição corporal (ECC); lactato L; ácidos graxos não esterificados (AGNEs); beta hidroxibutirato (BHB); ureia; creatinina; proteína total (PT); albumina; globulina; creatina fosfoquinase (cK); AST; GGT; glicose; eritrograma; concentrações eritrocitárias da superóxido dismutase (SOD) e o status antioxidante total (TAS). As variáveis PT, albumina, globulina, PV, ECC, AGNEs, AST, GGT, creatinina, ureia e eritrograma não se alteraram. O transporte diminuiu o BHB, não interferiu no TAS, mas em T4, as cabras mais jovens apresentaram menor TAS do que as com mais de 4 anos. A SOD não foi influenciada por transporte ou tratamento, sua concentração foi maior nas cabras jovens, e, nestas, quanto maior o ECC, menor a concentração de SOD. O estresse foi maior nas cabras de 1 a 4 anos. O transporte rodoviário de caprinos, mesmo de curta duração, causou estresse, verificado pelo aumento da glicemia, TR e lactato, independente da administração das vitaminas A, D e E, porém estas evitaram o aumento da cK, evidente nos grupos controles. / Animal transportation can trigger stress. Stress could compromise health and livestock welfare, as well increases the generation of reactive substances and raise the need for antioxidants. Age also affect the metabolism, because aging causes organic modifications that lead to functional impairment. The aim of this study was to analyze the influence of short road transportation and age in goats, treated or not, with vitamins A, D and E. It were used 20 healthy female Boer goats, calved two months ago, with identical diet and management, divided in groups by age (1 to 4 years of age and 4 to 7 years) and distributed in groups of 10 animals. The transportation lasted 4 hours. Physical examination and blood collection were performed in times T0 (-15d); T1 (-8d); T2 (-3d); T3 (0h); T4 (4h); T5 (5h); T6 (7h) and T7 (6d) from transportation. In T1 and T2, 10 goats received, by intramuscular injection, 2 mL of complex with vitamins A, D and E and 10 animals received saline solution. It were collected the followings parameters: rectal temperature (RT); body weight (BW), body condition score (BCS); non esterified fatty acids (NEFA); β hydroxybutyrate (BHB); lactate L; urea; creatinine; total protein (TP); albumin; globulin; creatine phosphokinase (cK); AST; GGT; glucose; erithrogram; erythrocyte concentrations of superoxide dismutase (SOD) and total antioxidant status (TAS). There were no differences for the parameters TP, albumin, globulin, BW, BCS, NEFA, AST, GGT, creatinine, urea and erithrogram. The transportation decreased BHB, and it had shown no influence on TAS, but in T4, the younger goats had lower TAS than older ones. SOD was not affected by transport or treatment, but show greater concentration in young goats, and, only in this category, higher ECC leads to lower SOD. The stress was higher in 1 to 4 years goats. Road transportation of goats, even in appropriate conditions, trigger stress, verified by elevated blood glucose, lactate and RT, regardless of the administration of vitamins A, D and E, but they prevented the increase of cK, evident in the control groups.
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Dosagem sérica da enzima creatinafosfoquinase-isoenzima MB (CK-MB) e de troponina I (cTnI) de cães eletrocardiograficamente normais e naqueles com desníveis (infra e supra) do segmento ST, utilizando ensaio imunométrico por quimioluminescência / Serum determination of creatinephosphokinase-isoenzyme MB (CK-MB) enzyme and of troponin I (cTnI) in electrocardiographic normal dogs and in those with ST deviation (elevation or depression) by a chemiluminescent immunometric assaySantos, Andre Luis Fernandes dos 11 March 2005 (has links)
Ao contrário do homem, as cardiopatias de natureza hipóxica/isquêmica são pouco relatadas nos cães. Raros são os relatos de infarto agudo do miocárdio (IAM) nesses espécimes; entretanto, existem achados eletrocardiográficos que indicam hipóxia/isquemia miocárdica, como os desníveis (infra e supra) do segmento ST. Com o intuito de constatar algum dano nas células do miocárdio em condições de má perfusão, utilizaram-se 38 cães, dos quais 20 com traçados eletrocardiográficos normais e 18 com desníveis (infra e supra) do segmento ST, na derivação DII, velocidade de 50 mm/s e sensibilidade N. Nos animais normais (grupo 1), a dosagem sérica da enzima creatinafosfoquinase isoenzima MB (CK-MB) e da troponina I (cTnI) destinou-se à obtenção dos valores de referência (em ng/mL). Estes valores de referência foram confrontados com os obtidos de cães portadores de desnível (grupo 2), permitindo confirmar ou não a injúria miocárdica. Em relação à CK-MB, os cães do grupo 1 apresentaram média de 0,54 ng/mL e desvio-padrão de 0,89 ng/mL e os do grupo 2 apresentaram média de 0,44 ng/mL e desvio-padrão de 1,106 ng/mL. A média e o desvio-padrão foram, respectivamente, de 0,16 ng/mL e 0,110 ng/mL e de 0,20 ng/mL e 0,111 ng/mL, nos grupos 1 e 2. Houve 18 valores nulos de CK-MB, igualmente distribuídos entre ambos os grupos. O grupo 1 apresentou três valores nulos para cTnI. Houve diferença marcante em relação à idade, sendo o grupo 1 constituído por animais, preponderantemente, abaixo de 7 anos; o contrário ocorreu no grupo 2. São significativas, ao nível de significância de 5%, as associações da variável CK-MB com as variáveis idade, massa e CK-T (creatinafosfoquinase total) no grupo 1, e com a variável CK-T no grupo 2. A variável cTnI não apresentou evidências de associação, ao nível de significância de 5% , com as variáveis idade, massa, CK-T e nível sérico de potássio, para cada um dos níveis da variável grupo. Tanto para a variável CK-MB quanto para a cTnI, não houve diferenças significativas, ao nível de 5%, entre os grupos 1 e 2. Conclui-se que é possível a utilização do \"kit\" de ensaio imunométrico quimioluminescente humano para a espécie canina e que a hipóxia/isquemia, revelada pelo desnível do segmento ST, não acarreta dano miocárdico, ou que este é mínimo. / Although very often in men, hypoxic and ischemic heart diseases are poorly documented in dogs. There are few reports of acute myocardial infarction (AMI) in this species. However, some electrocardiographic findings may suggest myocardium hypoxia/ischemia, like ST segment elevation or depression. In order to investigate myocardial cells injury in poor perfusion conditions, 38 dogs, being 20 with normal electrocardiogram and 18 with ST segment elevation or depression in lead II, at a paper speed of 50 mm/sec and N sensibility (1 mV = 1cm), were included. Serum measurement of creatinephosphokinase isoenzyme MB (CK-MB) enzym and troponin I (cTnI) in normal dogs (group 1) determined reference values (in ng/ml). These values were compared to those obtained in dogs with deviation (group 2), which allowed confirmation or not of myocardial injury. CK-MB mean values obtained from dogs in groups 1 and 2 was 0,54 ng/mL (SD±0,54 ng/mL) and 0,44 ng/mL (SD±1,106), respectively. Mean cTnI values in groups 1 and 2 was 0,16 ng/mL (SD±0,110 ng/mL) and 0,20 ng/mL (SD±0,111 ng/mL) respectively. Three cTnI null values were found in group 1. There was a marked difference concerning to age, being group 1 composed, mainly, by animals ageing under 7 years, on the contrary of group 2. At a significance level of 5%, was significant the relation of CK-MB with age, mass and total creatinephosphokinase (CK-T) in group 1 and with CK-T in group 2. There is no relation, at a significance level of 5%, of cTnI with age, mass, CK-T or serum potassium concentration, for each level of group variable. Both CK-MB and cTnI variables showed no difference, at 5% level, between groups 1 and 2. In conclusion, it is possible to use the human chemiluminescent immunometric assay kit in canine species and that hypoxia/ischemia revealed by ST segment deviation does not mean significant myocardium injury.
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Dosagem sérica da enzima creatinafosfoquinase-isoenzima MB (CK-MB) e de troponina I (cTnI) de cães eletrocardiograficamente normais e naqueles com desníveis (infra e supra) do segmento ST, utilizando ensaio imunométrico por quimioluminescência / Serum determination of creatinephosphokinase-isoenzyme MB (CK-MB) enzyme and of troponin I (cTnI) in electrocardiographic normal dogs and in those with ST deviation (elevation or depression) by a chemiluminescent immunometric assayAndre Luis Fernandes dos Santos 11 March 2005 (has links)
Ao contrário do homem, as cardiopatias de natureza hipóxica/isquêmica são pouco relatadas nos cães. Raros são os relatos de infarto agudo do miocárdio (IAM) nesses espécimes; entretanto, existem achados eletrocardiográficos que indicam hipóxia/isquemia miocárdica, como os desníveis (infra e supra) do segmento ST. Com o intuito de constatar algum dano nas células do miocárdio em condições de má perfusão, utilizaram-se 38 cães, dos quais 20 com traçados eletrocardiográficos normais e 18 com desníveis (infra e supra) do segmento ST, na derivação DII, velocidade de 50 mm/s e sensibilidade N. Nos animais normais (grupo 1), a dosagem sérica da enzima creatinafosfoquinase isoenzima MB (CK-MB) e da troponina I (cTnI) destinou-se à obtenção dos valores de referência (em ng/mL). Estes valores de referência foram confrontados com os obtidos de cães portadores de desnível (grupo 2), permitindo confirmar ou não a injúria miocárdica. Em relação à CK-MB, os cães do grupo 1 apresentaram média de 0,54 ng/mL e desvio-padrão de 0,89 ng/mL e os do grupo 2 apresentaram média de 0,44 ng/mL e desvio-padrão de 1,106 ng/mL. A média e o desvio-padrão foram, respectivamente, de 0,16 ng/mL e 0,110 ng/mL e de 0,20 ng/mL e 0,111 ng/mL, nos grupos 1 e 2. Houve 18 valores nulos de CK-MB, igualmente distribuídos entre ambos os grupos. O grupo 1 apresentou três valores nulos para cTnI. Houve diferença marcante em relação à idade, sendo o grupo 1 constituído por animais, preponderantemente, abaixo de 7 anos; o contrário ocorreu no grupo 2. São significativas, ao nível de significância de 5%, as associações da variável CK-MB com as variáveis idade, massa e CK-T (creatinafosfoquinase total) no grupo 1, e com a variável CK-T no grupo 2. A variável cTnI não apresentou evidências de associação, ao nível de significância de 5% , com as variáveis idade, massa, CK-T e nível sérico de potássio, para cada um dos níveis da variável grupo. Tanto para a variável CK-MB quanto para a cTnI, não houve diferenças significativas, ao nível de 5%, entre os grupos 1 e 2. Conclui-se que é possível a utilização do \"kit\" de ensaio imunométrico quimioluminescente humano para a espécie canina e que a hipóxia/isquemia, revelada pelo desnível do segmento ST, não acarreta dano miocárdico, ou que este é mínimo. / Although very often in men, hypoxic and ischemic heart diseases are poorly documented in dogs. There are few reports of acute myocardial infarction (AMI) in this species. However, some electrocardiographic findings may suggest myocardium hypoxia/ischemia, like ST segment elevation or depression. In order to investigate myocardial cells injury in poor perfusion conditions, 38 dogs, being 20 with normal electrocardiogram and 18 with ST segment elevation or depression in lead II, at a paper speed of 50 mm/sec and N sensibility (1 mV = 1cm), were included. Serum measurement of creatinephosphokinase isoenzyme MB (CK-MB) enzym and troponin I (cTnI) in normal dogs (group 1) determined reference values (in ng/ml). These values were compared to those obtained in dogs with deviation (group 2), which allowed confirmation or not of myocardial injury. CK-MB mean values obtained from dogs in groups 1 and 2 was 0,54 ng/mL (SD±0,54 ng/mL) and 0,44 ng/mL (SD±1,106), respectively. Mean cTnI values in groups 1 and 2 was 0,16 ng/mL (SD±0,110 ng/mL) and 0,20 ng/mL (SD±0,111 ng/mL) respectively. Three cTnI null values were found in group 1. There was a marked difference concerning to age, being group 1 composed, mainly, by animals ageing under 7 years, on the contrary of group 2. At a significance level of 5%, was significant the relation of CK-MB with age, mass and total creatinephosphokinase (CK-T) in group 1 and with CK-T in group 2. There is no relation, at a significance level of 5%, of cTnI with age, mass, CK-T or serum potassium concentration, for each level of group variable. Both CK-MB and cTnI variables showed no difference, at 5% level, between groups 1 and 2. In conclusion, it is possible to use the human chemiluminescent immunometric assay kit in canine species and that hypoxia/ischemia revealed by ST segment deviation does not mean significant myocardium injury.
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Perfil metabólico de cabras submetidas a transporte rodoviário / Metabolic profile of goats submitted to road transportationVanessa Martins Storillo 05 September 2012 (has links)
O transporte leva os animais ao estresse, que pode comprometer a saúde e bem estar destes, além de elevar a geração de substâncias reativas, aumentando a necessidade de antioxidantes. A idade também influencia o metabolismo, pois o envelhecimento causa modificações no organismo, levando a prejuízos funcionais. O objetivo deste estudo foi avaliar a influência do transporte rodoviário e da idade em cabras, tratadas ou não vitaminas A, D, e E. Foram utilizadas 20 cabras, da raça Boer, com cerca de 60 dias pós-parto, hígidas, manejo e dietas idênticos, de duas faixas etárias (de 1 até 4 anos de idade e entre 4 e 7 anos) e distribuídas em grupos de 10 animais. O transporte rodoviário teve duração de 4h. O exame físico e as coletas de sangue foram efetuados nos tempos T0 (-15d); T1 (-8d); T2 (-3d); T3 (0h); T4 (4h); T5 (5h); T6 (7h) e T7 (6d) do transporte. Em T1 e T2, 10 cabras receberam, via IM, 2mL de complexo com vitaminas A, D e E e 10 receberam solução fisiológica. Foram determinadas temperatura retal (TR); peso vivo (PV); escore de condição corporal (ECC); lactato L; ácidos graxos não esterificados (AGNEs); beta hidroxibutirato (BHB); ureia; creatinina; proteína total (PT); albumina; globulina; creatina fosfoquinase (cK); AST; GGT; glicose; eritrograma; concentrações eritrocitárias da superóxido dismutase (SOD) e o status antioxidante total (TAS). As variáveis PT, albumina, globulina, PV, ECC, AGNEs, AST, GGT, creatinina, ureia e eritrograma não se alteraram. O transporte diminuiu o BHB, não interferiu no TAS, mas em T4, as cabras mais jovens apresentaram menor TAS do que as com mais de 4 anos. A SOD não foi influenciada por transporte ou tratamento, sua concentração foi maior nas cabras jovens, e, nestas, quanto maior o ECC, menor a concentração de SOD. O estresse foi maior nas cabras de 1 a 4 anos. O transporte rodoviário de caprinos, mesmo de curta duração, causou estresse, verificado pelo aumento da glicemia, TR e lactato, independente da administração das vitaminas A, D e E, porém estas evitaram o aumento da cK, evidente nos grupos controles. / Animal transportation can trigger stress. Stress could compromise health and livestock welfare, as well increases the generation of reactive substances and raise the need for antioxidants. Age also affect the metabolism, because aging causes organic modifications that lead to functional impairment. The aim of this study was to analyze the influence of short road transportation and age in goats, treated or not, with vitamins A, D and E. It were used 20 healthy female Boer goats, calved two months ago, with identical diet and management, divided in groups by age (1 to 4 years of age and 4 to 7 years) and distributed in groups of 10 animals. The transportation lasted 4 hours. Physical examination and blood collection were performed in times T0 (-15d); T1 (-8d); T2 (-3d); T3 (0h); T4 (4h); T5 (5h); T6 (7h) and T7 (6d) from transportation. In T1 and T2, 10 goats received, by intramuscular injection, 2 mL of complex with vitamins A, D and E and 10 animals received saline solution. It were collected the followings parameters: rectal temperature (RT); body weight (BW), body condition score (BCS); non esterified fatty acids (NEFA); β hydroxybutyrate (BHB); lactate L; urea; creatinine; total protein (TP); albumin; globulin; creatine phosphokinase (cK); AST; GGT; glucose; erithrogram; erythrocyte concentrations of superoxide dismutase (SOD) and total antioxidant status (TAS). There were no differences for the parameters TP, albumin, globulin, BW, BCS, NEFA, AST, GGT, creatinine, urea and erithrogram. The transportation decreased BHB, and it had shown no influence on TAS, but in T4, the younger goats had lower TAS than older ones. SOD was not affected by transport or treatment, but show greater concentration in young goats, and, only in this category, higher ECC leads to lower SOD. The stress was higher in 1 to 4 years goats. Road transportation of goats, even in appropriate conditions, trigger stress, verified by elevated blood glucose, lactate and RT, regardless of the administration of vitamins A, D and E, but they prevented the increase of cK, evident in the control groups.
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Ocenění hodnoty vybrané cestovní kanceláře / Evaluation of the selected travel agencyMarešová, Monika January 2010 (has links)
The main goal of the thesis is to settle the value of the travel agency CK FISCHER, a.s. according the most used methods of evaluation. After the short determination of main problems the thesis is focused on strategic and financial analyzes of the company. The practical part is devoted to the evaluation of the company. Three methods are used there -- accounting evaluation method, approach using Discounted Cash Flow FCFF and the third method with the Economic Value Added. These last two techniques are the most exploited in working routine. Lastly the brand value is analyzed, because it is in this case very important part of the firm value. In the conclusion all methods are compared according the possibility of using in different purpose of evaluation.
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Applications of branching processes to cancer evolution and initiationNicholson, Michael David January 2018 (has links)
There is a growing appreciation for the insight mathematical models can yield on biological systems. In particular, due to the challenges inherent in experimental observation of disease progression, models describing the genesis, growth and evolution of cancer have been developed. Many of these models possess the common feature that one particular type of cellular population initiates a further, distinct population. This thesis explores two models containing this feature, which also employ branching processes to describe population growth. Firstly, we consider a deterministically growing wild type population which seeds stochastically developing mutant clones. This generalises the classic Luria- Delbruck model of bacterial evolution. We focus on how differing wild type growth manifests itself in the distribution of clone sizes. In our main result we prove that for a large class of wild type growth, the long-time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law. In the second model, we consider a fully stochastic system of cells in a growing population that can undergo birth, death and transitions. New cellular types appear via transitions, examples of which are genetic mutations or migrations bringing cells into a new environment. We concentrate on the scenario where the original cell type has the largest net growth rate, which is relevant for modelling drug resistance, due to fitness costs of resistance, or cells migrating into contact with a toxin. Two questions are considered in our main results. First, how long do we wait until a cell with a specific target type, an arbitrary number of transitions from the original population, exists. Second, which particular sequence of transitions initiated the target population. In the limit of small final transition rates, simple, explicit formulas are given to answer these questions.
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