We investigate linear and nonlinear dynamics of spherically symmetric perturbations on a static configuration in scalar-tensor theories focusing the chameleon screening mechanism. particularly address two questions: how much can source fifth force when background is well screened, whether resultant change stability structure configuration. For perturbations, we derive lower bound for square Fou...

To study incremental machine learning in tensor space, this paper proposes incremental tensor discriminant analysis. The algorithm employs tensor representation to carry on discriminant analysis and combine incremental learning to alleviate the computational cost. This paper proves that the algorithm can be unified into the graph framework theoretically and analyzes the time and space complexit...

Techniques from representation theory, symbolic computational algebra, and numerical algebraic geometry are used to find the minimal generators of the ideal of the trifocal variety. An effective test for determining whether a given tensor is a trifocal tensor is also given.

Using the integration by parts method we derive a closed analytical expression for the result of the integration of an arbitrary dimensionally regulated tadpole diagram composed of a massless propagator and two massive ones, each raised into an arbitrary power, and including an arbitrary tensor numerator. We also briefly discuss the implementation of the formula in the algebraic manipulation la...

Magnetic resonance imaging (MRI) has allowed the unprecedented capability to measure the human brain in vivo. This technique has paved the way for longitudinal studies exploring brain changes across the entire life span. Results from these studies have given us a glimpse into the remarkably extended and multifaceted development of our brain, converging with evidence from anatomical and histolog...