Apparently noninvariant terms of U(N)×U(N)U(N)\times U(N) nonlinear sigma model in the one-loop approximation

We show how the Apparently Noninvariant Terms (ANTs), which emerge in perturbation theory of nonlinear sigma models, are consistent with the nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the form of an inhomogeneous Zinn-Justin equation). In the literature the discussions on ANTs are confined to the SU(2) case. We generalize them to the U(N) case and demonstrate explicitly at the one-loop level that despite the presence of divergent ANTs in the effective action of the "pions", the symmetry is preserved.Comment: two paragraphs added in Introduction, typos in Eqs. fixe

Degeneration of the Julia set to singular loci of algebraic curves

We show that, when a non-integrable rational map changes to an integrable one continuously, a large part of the Julia set of the map approach indeterminate points (IDP) of the map along algebraic curves. We will see that the IDPs are singular loci of the curves.Comment: 12 pages, 5 figure

Autism-related traits are related to effectiveness of immersive visual guidance on spatial cognitive ability: a pilot study

A head-mounted display could potentially restrict users’ visual fields and thereby impair their spatial cognitive ability. Spatial cognition can be assisted with immersive visual guidance. However, whether this technique is useful for individuals with autism-spectrum disorder (ASD) remains unclear. Given the recent virtual reality (VR) contents targeting individuals with ASD, the relationship between ASD-related traits and the effectiveness of immersive visual guidance should be clarified. This pilot study evaluated how ASD-related traits (autistic traits and empathizing–systemizing cognitive styles) among typically developing individuals are related to the effectiveness of visual guidance. Participants performed visual search and spatial localization tasks while using immersive visual guidance. In the visual search task, participants searched immersive VR environments for a target object and pushed a button according to the target color as quickly as possible. In the localization task, they viewed immersive visual guidance for a short duration and localized the guided direction via a controller. Results showed that visual search times were hastened with systemizing cognition. However, ASD-related traits were not significantly related to localization accuracy. These findings suggest that immersive visual guidance is generally useful for individuals with higher ASD-related traits