It is becoming a mainstream feature fusion approach for speech-visual emotion recognition (SVER) by directly using neural networks to fuse the extracted speech and visual features. However, the heterogeneity between speech and visual modalities usually results in a distribution gap and information redundancy between the extracted speech and visual features, thus affecting the performance of the SVER. To this end, this paper proposes a SVER method based on the modal decomposition learning. It leverages the shared, private and reconstructed modal learning with a specifically designed loss to decompose the extracted speech and visual features into the shared and private subspaces to obtain the shared and private features, which effectively reduces the distribution gap and information redundancy between the extracted speech and visual features. Experiments on the BAUM-1s, RAVDESS and eNTERFACE05 datasets also show that the proposed method achieves a better result.

This paper investigates Tullock group contests with the possibility of a draw in which the winner, if any, shares the prize with other players in his group, and each group's sharing rule is private. Considering the draw is exogenously determined, we investigate the strategic choice of the sharing rules and individual effort. We find that introducing the draw into the contest has negative effects on individual payoff, while players would increase the sharing rule. When groups are symmetric, the possibility of a draw decreases all group's individual effort. In the model with asymmetric groups, the draw has a non-monotonic effect on the aggregate effort and individual effort of the strong group with larger value for the prize. Next, considering the draw is endogenously given, we investigate the strategy for maximizing aggregate effort. In the asymmetric model, when groups' values of the prize are dispersed enough or the organizer cares much more about the strong group, introducing a draw into the contest would increase the aggregate effort. However, no draw is most beneficial to the aggregate effort if the organizer puts more weight on the weak group. Finally, a numerical example is given to analyze and illustrate the results.