Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs

The purpose of the present paper is to set up a formalism inspired from non-Archimedean geometry to study K-stability. We first provide a detailed analysis of Duistermaat-Heckman measures in the context of test configurations, characterizing in particular the trivial case. For any normal polarized variety (or, more generally, polarized pair in the sense of the Minimal Model Program), we introduce and study the non-Archimedean analogues of certain classical functionals in K\"ahler geometry. These functionals are defined on the space of test configurations, and the Donaldson-Futaki invariant is in particular interpreted as the non-Archimedean version of the Mabuchi functional, up to an explicit error term. Finally, we study in detail the relation between uniform K-stability and singularities of pairs, reproving and strengthening Y. Odaka's results in our formalism. This provides various examples of uniformly K-stable varieties.Comment: Small changes. To appear in Ann. Inst. Fourie

Uniform K-stability and asymptotics of energy functionals in K\"ahler geometry

Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in K\"ahler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability.Comment: New version with errata (an error was found in the proof of Theorem 5.6). The affected parts of the paper are marked in re

Behavior and Thought to Attention: Change of Behavior Therapy and Mindfulness

Behavior therapy of the first generation was designed to influence maladjusted behavior. Cognitive therapy as the second generation of behavior therapy was designed to improve emotions/moods by influencing thoughts away from the necessity of treating unpleasant emotions like depression. Behavior therapy of the third generation is mindfulness therapy that is designed to control emotions/moods by operating on attension. It introduces mindfulness-based stress reduction and mindfulness-based cognitive therapy as examples of mindfulness therapy.第１世代の行動療法は、不適応行動を改善するために行動を操作しようするものであった。さらにうつのような不快な気分や感情を治療する必要から、思考を操作することによって気分や感情を改善しようとする第２世代の認知療法が生まれた。そして、第３世代の行動療法として注意を操作し、気分や感情をコントロールするマインドフルネスな治療法が生まれてきた。マインドフルネスな治療の具体例として、マインドフルネス・ストレス低減法とマインドフルネス認知療法を紹介した。感情心理学の応