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Technological innovations accompanying advances in medicine have given rise to the possibility of obtaining better-defined fetal images that assist in medical diagnosis and contribute toward genetic counseling offered to parents during the prenatal care. 3D printing is an emerging technique with a variety of medical applications such as surgical planning, biomedical research and medical education.Clinical Relevance: 3D physical and virtual models from ultrasound and magnetic resonance imaging have been used for educational, multidisciplinary discussion and plan therapeutic approaches. The authors describe techniques that can be applied at different stages of pregnancy and constitute an innovative contribution to research on fetal abnormalities. We will show that physical models in fetal medicine can help in the tactile and interactive study of complex abnormalities in multiple disciplines. They may also be useful for prospective parents because a 3D physical modelwith the characteristics of the fetus should allow a more direct emotional connection to their unborn child.

This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.