Theoretical understanding of how a deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse graining. It reminds us of the basic renormalization group (RG) concept in statistical physics. In order to explore possible relations between DNN and RG, we use the restricted Boltzmann machine (RBM) applied to an Ising model and construct a flow of model parameters (in particular, temperature) generated by the RBM. We show that the unsupervised RBM trained by spin configurations at various temperatures from T=0 to T=6 generates a flow along which the temperature approaches the critical value T_{c}=2.27. This behavior is the opposite of the typical RG flow of the Ising model. By analyzing various properties of the weight matrices of the trained RBM, we discuss why it flows towards T_{c} and how the RBM learns to extract features of spin configurations.

In this note, we investigate the electromagnetic radiation emitted from a revolving point charge in a compact space. If the point charge is circulating with an angular frequency ω 0 on the (x, y)-plane at z = 0 with boundary conditions, x ∼ x + 2πR and y ∼ y + 2πR, it emits radiation into the z-direction of z ∈ [−∞, +∞]. We find that the radiation shows discontinuities as a function of ω 0 R at which a new propagating mode with a different Fourier component appears. For a small radius limit ω 0 R 1, all the Fourier modes except the zero mode on (x, y)-plane are killed, but an effect of squeezing the electric field totally enhances the radiation. In the large volume limit ω 0 R → ∞, the energy flux of the radiation reduces to the expected Larmor formula.