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Brief introduction to tropical geometry 
Posted on 20150228
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The paper consists of lecture notes for a minicourse given by the authors at the G\"okova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves in the plane and their applications to problems in classical enumerative geometry, and continue with a look at more general tropical varieties and their homology theories. . . . . 






Dark Energy: Observational Evidence and Theoretical Models 
Posted on 20150223
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The book elucidates the current state of the dark energy problem and presents the results of the authors, who work in this area. It describes the observational evidence for the existence of dark energy, the methods and results of constraining of its parameters, modeling of dark energy by scalar fields, the spacetimes with extra spatial dimensions, especially KaluzaKlein models, the braneworld models with a single extra dimension as well as the problems of positive definition of gravitational energy in General Relativity, energy conditions a . . . . 






Superradiance 
Posted on 20150222
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Superradiance is a radiation enhancement process that involves dissipative systems. With a 60 yearold history, superradiance has played a prominent role in optics, quantum mechanics and especially in relativity and astrophysics. In General Relativity, blackhole superradiance is permitted by dissipation at the event horizon, that allows for energy and angular momentum extraction from the vacuum, even at the classical level. Blackhole superradiance is intimately connected to the blackhole area theorem, Penrose process, tidal forces and even H . . . . 










Advanced Topics of Theoretical Physics I: The electronic structure of matter 
Posted on 20150217
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This book is work in progress. This book is not completed and not proofread. You can use this book
currently as a basis for following through the material presented in the course. However, you should
never blindly copy formulas an apply them. The chances that there are still errors is too large.
This book provides an introduction into the quantum mechanics of the interacting electron gas.
It aims at students at the graduate level, that already have a good understanding on oneparticle
quantum mechanics. My aim is to include all proofs in a . . . . 






Lecture Notes in Machine Learning 
Posted on 20150217
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Contents: Introduction; Concept learning; Languages for learning; Version space learning; Induction of Decision trees; Covering strategies; Searching the generalization/specialization graph; Inductive Logic Progrogramming; Unsupervised Learning; Explanationbased Learning. . . . . 






