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To achieve the popularization of more innovative teaching modes and promote the rapid development of intelligent classroom teaching technology, it is necessary to design and develop the education and training platform more deeply, integrate with new teaching methods, and achieve an efficient teaching environment. We propose a load-balancing strategy based on deep reinforcement learning considering the problem of classroom terminal load. Based on the embedded classroom teaching platform, in the communication process, this strategy will let the reinforcement learning module model analyze the network. Then, through the advantages of the SDN global view, it obtains the status and information of the whole network, realizing the classroom interaction’s learning process. Optimizing the teaching structure is closer to the key and difficult points of teaching. The fuzzy perception clustering model is designed to improve teaching quality. By the embedded system, we process the data of the fuzzy perception model. Then, we combine fuzzy logic reasoning with the classroom teaching evaluation and utilize the fuzzy neural network to analyze the teaching situation. By training the network to get the optimal migration action decision, it can not only effectively improve the load-balancing effect of multiple controllers, but also reduce the balancing time and enhance the overall performance and stability of the network. Through the experimental analysis, compared with the traditional fuzzy neural network method, the mapping effect of the fuzzy clustering perception classification activation function used in this paper on the output of the normalized layer is verified. The clustering effect is 15.22% higher than that of the PE method and 9.32% higher than that of the SHKwon method. Besides, the improved algorithm improves the prediction rate of the network operation situation awareness. It is especially suitable for embedded systems with limited computing power.

We study the fuzzy structure of the general Kähler coset space G/S ⊗ U(1)^k deformed by the Fedosov formalism. It is shown that the Killing potentials satisfy the fuzzy algebras working in the Darboux coordinates.

A dynamical fuzzy space might be described by a three-index variable , which determines the algebraic relations among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. We study equations for the three-index variable invariant under the general linear transformation and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, we study SO(3) symmetric solutions and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parametrized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.

Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator, and the 3-ary algebra symmetry reported in the previous paper is just a single sector of the whole structure. The condition for the Leibnitz rules of the n-ary algebras is discussed from the perspective of the invariance of the underlying algebra under the n-ary transformations. It is shown that the n-ary transformations which keep the underlying algebraic structure invariant form closed finite n-ary Lie subalgebras. It is also shown that, in physical settings, the 3-ary transformation practically generates only local infinitesimal symmetry transformations, and the other more nonlocal infinitesimal symmetry transformations of the tensor models are generated by higher n-ary transformations.

By extending the algebraic description of the bosonic rank-three tensor models, a general framework for super rank-three tensor models and correspondence to super fuzzy spaces is proposed. The corresponding super fuzzy spaces must satisfy a certain cyclicity condition on the algebras of functions on them. Due to the cyclicity condition, the symmetry of the super rank-three tensor models are represented by super n-ary transformations. The Leibnitz rules and the fundamental identities for the super n-ary transformations are discussed from the perspective of the symmetry of the algebra of a fuzzy space. It is shown that the super n-ary transformations of finite orders which conserve the algebra of a fuzzy space form a finite closed n-ary super Lie algebra. Super rank-three tensor models would be of physical interest as background independent models for dynamical generation of supersymmetric fuzzy spaces, in which quantum corrections are under control.

Canonical formalism of the rank-three tensor model has recently been proposed, in which "local" time is consistently incorporated by a set of first class constraints. By brute-force analysis, this paper shows that there exist only two forms of a Hamiltonian constraint which satisfies the following assumptions: (i) A Hamiltonian constraint has one index. (ii) The kinematical symmetry is given by an orthogonal group. (iii) A consistent first class constraint algebra is formed by a Hamiltonian constraint and the generators of the kinematical symmetry. (iv) A Hamiltonian constraint is invariant under time reversal transformation. (v) A Hamiltonian constraint is an at most cubic polynomial function of canonical variables. (vi) There are no disconnected terms in a constraint algebra. The two forms are the same except for a slight difference in index contractions. The Hamiltonian constraint which was obtained in the previous paper and behaved oddly under time reversal symmetry can actually be transformed to one of them by a canonical change of variables.