Symbolically integrating tensor networks over various random tensors by the second version of Python RTNI

We are upgrading the Python-version of RTNI, which symbolically integrates tensor networks over the Haar-distributed unitary matrices. Now, PyRTNI2 can treat the Haar-distributed orthogonal matrices and the real and complex normal Gaussian tensors as well. Moreover, it can export tensor networks in the format of TensorNetwork so that one can make further calculations with concrete tensors, even for low dimensions, where the Weingarten functions differ from the ones for high dimensions. The tutorial notebooks are found at GitHub: https://github.com/MotohisaFukuda/PyRTNI2. In this paper, we explain maths behind the program and show what kind of tensor network calculations can be made with it. For the former, we interpret the element-wise moment calculus of the above random matrices and tensors in terms of tensor network diagrams, and argue that the view is natural, relating delta functions in the calculus to edges in tensor network diagrams.

Central object segmentation by deep learning for fruits and other roundish objects

We present CROP (Central Roundish Object Painter), which identifies and paints the object at the center of an RGB image. Primarily CROP works for roundish fruits in various illumination conditions, but surprisingly, it could also deal with images of other organic or inorganic materials, or ones by optical and electron microscopes, although CROP was trained solely by 172 images of fruits. The method involves image segmentation by deep learning, and the architecture of the neural network is a deeper version of the original U-Net. This technique could provide us with a means of automatically collecting statistical data of fruit growth in farms. Our trained neural network CROP is available on GitHub, with a user-friendly interface program.