A duality approach to the genealogies of discrete nonneutral Wright-Fisher models.
A general framework for stability analysis of gene regulatory networks with delay.
A Hopf Bifurcation Theorem for Difference Equations Approximating a Differential Equation.
A mathematical model of HIV transmission in homosexuals with genetic heterogeneity.
A model for gene activation.
A new model for evolution in a spatial continuum.
A statistical variance components framework for mapping imprinted quantitative trait locus in experimental crosses.
An asymptotic test for quantitative gene detection
Application of Cauchy's equation in combinatorics and genetics.
Application of occupancy and ordering theory in genetics of autopolyploids
Application of the Rasch model in categorical pedigree analysis using MCEM: I binary data
An extension of the Rasch model with correlated latent variables is proposed to model correlated binary data within families. The latent variables have the classical correlation structure of Fisher (1918) and the model parameters thus have genetic interpretations. The proposed model is fitted to data using a hybrid of the Metropolis-Hastings algorithm and the MCEM modification of the EM-algorithm and is illustrated using genotype-phenotype data on a psychological subtest in families where some members...
Applications of topology to DNA
The following is an expository article meant to give a simplified introduction to applications of topology to DNA.
Building the library of RNA 3D nucleotide conformations using the clustering approach
An increasing number of known RNA 3D structures contributes to the recognition of various RNA families and identification of their features. These tasks are based on an analysis of RNA conformations conducted at different levels of detail. On the other hand, the knowledge of native nucleotide conformations is crucial for structure prediction and understanding of RNA folding. However, this knowledge is stored in structural databases in a rather distributed form. Therefore, only automated methods...
Cálculo de probabilidades en el análisis de perfiles genéticos compatibles.
Un hecho delictivo ha sido cometido por una o más personas. Para descubrir el número de presuntos delincuentes, se determina el perfil genético de la evidencia forense encontrada en el lugar del delito, mediante el estudio de marcadores de tipo STR. En el presente artículo se desarrollan diversos algoritmos. En el primero se considera la probabilidad de que n personas elegidas aleatoriamente de la población de referencia contengan un perfil genético compatible, en el segundo se calcula la evidencia...
Complete polynomial vector fields in simplexes with application to evolutionary dynamics.
Contributi delle Scienze Matematiche ed Informatiche al sequenziamento genomico su larga scala
Nel panorama della scienza contemporanea, la biologia molecolare ha recentemente assunto un ruolo di fondamentale importanza. Il bisognocrescente di conoscere intere sequenze genomiche e l’esigenza, ancora piùpressante, di analizzare e confrontare tali sequenze per poter dedurre funzionalità e discendenze comuni, ha reso necessaria l’integrazione delleusuali tecniche sperimentali, proprie della ricerca biologica, con le metodologie formali della matematica e dell’informatica. Queste motivazioni...
Data mining methods for gene selection on the basis of gene expression arrays
The paper presents data mining methods applied to gene selection for recognition of a particular type of prostate cancer on the basis of gene expression arrays. Several chosen methods of gene selection, including the Fisher method, correlation of gene with a class, application of the support vector machine and statistical hypotheses, are compared on the basis of clustering measures. The results of applying these individual selection methods are combined together to identify the most often selected...
Description combinatoire des ultramétriques
Deterministic and stochastic simulations of simple genetic circuits
We analyze three simple genetic circuits which involve transcriptional regulation and feedback: the autorepressor, the switch and the repressilator, that consist of one, two and three genes, respectively. Such systems are commonly simulated using rate equations, that account for the concentrations of the mRNAs and proteins produced by these genes. Rate equations are suitable when the concentrations of the relevant molecules in a cell are large and fluctuations are negligible. However, when some...
Diffusion limit for the phenomenon of random genetic drift
The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as...