Score Prediction of Sports Events Based on Parallel Self-Organizing Nonlinear Neural Network

This paper introduces the basic concepts and main characteristics of parallel self-organizing networks and analyzes and predicts parallel self-organizing networks through neural networks and their hybrid models. First, we train and describe the law and development trend of the parallel self-organizing network through historical data of the parallel self-organizing network and then use the discovered law to predict the performance of the new data and compare it with its true value. Second, this paper takes the prediction and application of chaotic parallel self-organizing networks as the main research line and neural networks as the main research method. Based on the summary and analysis of traditional neural networks, it jumps out of inertial thinking and first proposes phase space. Reconstruction parameters and neural network structure parameters are unified and optimized, and then, the idea of dividing the phase space into multiple subspaces is proposed. The multi-neural network method is adopted to track and predict the local trajectory of the chaotic attractor in the subspace with high precision to improve overall forecasting performance. During the experiment, short-term and longer-term prediction experiments were performed on the chaotic parallel self-organizing network. The results show that not only the accuracy of the simulation results is greatly improved but also the prediction performance of the real data observed in reality is also greatly improved. When predicting the parallel self-organizing network, the minimum error of the self-organizing difference model is 0.3691, and the minimum error of the self-organizing autoregressive neural network is 0.008, and neural network minimum error is 0.0081. In the parallel self-organizing network prediction of sports event scores, the errors of the above models are 0.0174, 0.0081, 0.0135, and 0.0381, respectively.

Simulation of convective transport during frequency chirping of a TAE using the MEGA code

We present a procedure to examine energetic particle phase-space during long range frequency chirping phenomena in tokamak plasmas. To apply the proposed method, we have performed self-consistent simulations using the MEGA code and analyzed the simulation data. We demonstrate a travelling wave in phase-space and that there exist specific slices of phase-space on which the resonant particles lie throughout the wave evolution. For non-linear evolution of an n=6 toroidicity-induced Alfven eigenmode (TAE), our results reveal the formation of coherent phase-space structures (holes/clumps) after coarse-graining of the distribution function. These structures cause a convective transport in phase-space which implies a radial drift of the resonant particles. We also demonstrate that the rate of frequency chirping increases with the TAE damping rate. Our observations of the TAE behaviour and the corresponding phase-space dynamics are consistent with the Berk-Breizman (BB) theory.

Four-mode squeezed states: two-field quantum systems and the symplectic group $$\mathrm {Sp}(4,{\mathbb {R}})$$

We construct the four-mode squeezed states and study their physical properties. These states describe two linearly-coupled quantum scalar fields, which makes them physically relevant in various contexts such as cosmology. They are shown to generalise the usual two-mode squeezed states of single-field systems, with additional transfers of quanta between the fields. To build them in the Fock space, we use the symplectic structure of the phase space. For this reason, we first present a pedagogical analysis of the symplectic group $$\mathrm {Sp}(4,{\mathbb {R}})$$ Sp ( 4 , R ) and its Lie algebra, from which we construct the four-mode squeezed states and discuss their structure. We also study the reduced single-field system obtained by tracing out one of the two fields. This procedure being easier in the phase space, it motivates the use of the Wigner function which we introduce as an alternative description of the state. It allows us to discuss environmental effects in the case of linear interactions. In particular, we find that there is always a range of interaction coupling for which decoherence occurs without substantially affecting the power spectra (hence the observables) of the system.