Gametes are cells that have the unique ability to give rise to new individuals as well as transmit (epi)genetic information across generations. Generation of functionally competent gametes, oocytes... Show moreGametes are cells that have the unique ability to give rise to new individuals as well as transmit (epi)genetic information across generations. Generation of functionally competent gametes, oocytes and sperm cells, depends to some extent on several fundamental processes that occur during fetal development. Direct studies on human fetal germ cells remain hindered by ethical considerations and inaccessibility to human fetal material. Therefore, the majority of our current knowledge of germ cell development still comes from an invaluable body of research performed using different mammalian species. During the last decade, our understanding of human fetal germ cells has increased due to the successful use of human pluripotent stem cells to model aspects of human early gametogenesis and advancements on single-cell omics. Together, this has contributed to determine the cell types and associated molecular signatures in the developing human gonads. In this review, we will put in perspective the knowledge obtained from several mammalian models (mouse, monkey, pig). Moreover, we will discuss the main events during human fetal (female) early gametogenesis and how the dysregulation of this highly complex and lengthy process can link to infertility later in life. Show less
This thesis studies principal algebraic actions of the discrete Heisenberg group. There are two main questions which are investigated. The first question deals with the problem of finding criteria... Show moreThis thesis studies principal algebraic actions of the discrete Heisenberg group. There are two main questions which are investigated. The first question deals with the problem of finding criteria for a principal algebraic action to be expansive. Expansiveness is directly related to questions about invertibility in the convolution algebra of the discrete Heisenberg group. The results presented in this thesis give a variety of tools which allow one to decide whether an element in the convolution algebra is invertible or not. These findings are based on local principles and the representation theory of the convolution algebra. The second main question which has been addressed is concerned with the search of summable homoclinic points of non expansive actions. This problem was first linked to a deconvolution problem. A method has been introduced to solve such deconvolution problems with the help of abstract harmonic analysis. This method was successfully applied to a certain class of examples. Show less
