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Exploring Formalisation
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ISBN: 9783031146497 9783031146480 9783031146503 Year: 2022 Publisher: Cham Springer International Publishing :Imprint: Springer

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Abstract

This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean. After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers. Subsequently, typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher-dimensional generalisation of graph theory). Finally, the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers. Informed by the author's recent teaching and research experience, this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter, familiarity with elementary category theory and algebraic topology is recommended.


Book
Identification and other probabilistic models : Rudolf Ahlswede's lectures on information theory 6
Authors: ---
ISBN: 3030650723 3030650707 Year: 2021 Publisher: Cham, Switzerland : Springer,


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Parallel-in-time integration methods : 9th parallel-in-time workshop, June 8-12 2020
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ISBN: 3030759334 3030759326 Year: 2021 Publisher: Cham, Switzerland : Springer,


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Intelligent algorithms for packing and cutting problem
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ISBN: 9811959153 9811959161 Year: 2022 Publisher: Gateway East, Singapore : Springer,


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Frontiers in Psychiatry : Artificial Intelligence, Precision Medicine, and Other Paradigm Shifts
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ISBN: 9813297212 9813297204 Year: 2019 Publisher: Singapore : Springer Singapore : Imprint: Springer,

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Abstract

This book reviews key recent advances and new frontiers within psychiatric research and clinical practice. These advances either represent or are enabling paradigm shifts in the discipline and are influencing how we observe, derive and test hypotheses, and intervene. Progress in information technology is allowing the collection of scattered, fragmented data and the discovery of hidden meanings from stored data, and the impacts on psychiatry are fully explored. Detailed attention is also paid to the applications of artificial intelligence, machine learning, and data science technology in psychiatry and to their role in the development of new hypotheses, which in turn promise to lead to new discoveries and treatments. Emerging research methods for precision medicine are discussed, as are a variety of novel theoretical frameworks for research, such as theoretical psychiatry, the developmental approach to the definition of psychopathology, and the theory of constructed emotion. The concluding section considers novel interventions and treatment avenues, including psychobiotics, the use of neuromodulation to augment cognitive control of emotion, and the role of the telomere-telomerase system in psychopharmacological interventions.

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