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In this paper, we study the Rosenzweig-MacArthur predator-prey model with predator-taxis and time delay defined on a disk. Theoretically, we studied the equivariant Hopf bifurcation around the positive constant steady-state solution. Standing and rotating waves have been investigated through the theory of isotropic subgroups and Lyapunov-Schmidt reduction. The existence conditions, the formula for the periodic direction and the periodic variation of bifurcation periodic solutions are obtained. Numerically, we select appropriate parameters and conduct numerical simulations to illustrate the theoretical results and reveal quite complicated dynamics on the disk. Different types of rotating and standing waves, as well as more complex spatiotemporal patterns with random initial values, are new dynamic phenomena that do not occur in one-dimensional intervals.

With the emergence of large language models (LLMs), multimodal models based on LLMs have demonstrated significant potential. Models such as LLaSM, X-LLM, and SpeechGPT exhibit an impressive ability to comprehend and generate human instructions. However, their performance often falters when faced with complex tasks like end-to-end speech translation (E2E-ST), a cross-language and cross-modal translation task. In comparison to single-modal models, multimodal models lag behind in these scenarios. This paper introduces LST, a Large multimodal model designed to excel at the E2E-ST task. LST consists of a speech frontend, an adapter, and a LLM backend. The training of LST consists of two stages: (1) Modality adjustment, where the adapter is tuned to align speech representation with text embedding space, and (2) Downstream task fine-tuning, where both the adapter and LLM model are trained to optimize performance on the E2EST task. Experimental results on the MuST-C speech translation benchmark demonstrate that LST-13B achieves BLEU scores of 30.39/41.55/35.33 on En-De/En-Fr/En-Es language pairs, surpassing previous models and establishing a new state-of-the-art. Additionally, we conduct an in-depth analysis of single-modal model selection and the impact of training strategies, which lays the foundation for future research. We will open up our code and models after review.

Turing bifurcation and Hopf bifurcation are two important kinds of transitions giving birth to inhomogeneous solutions, in spatial or temporal ways. On a disk, these two bifurcations may lead to equivariant Turing-Hopf bifurcations. In this paper, normal forms for three kinds of Turing-Hopf bifurcations are given and the breathing, standing wave-like, and rotating wave-like patterns are found in numerical examples.

Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a two-dimensional disk. The properties of these bifurcations around equilibriums are analyzed rigorously by studying the equivariant normal forms. Two reaction-diffusion systems with discrete time delays are selected as numerical examples to verify the theoretical results, in which spatially inhomogeneous periodic solutions including standing waves and rotating waves, and spatially homogeneous periodic solutions are found near the bifurcation points.

The end-to-end speech translation (E2E-ST) model has gradually become a mainstream paradigm due to its low latency and less error propagation. However, it is non-trivial to train such a model well due to the task complexity and data scarcity. The speech-and-text modality differences result in the E2E-ST model performance usually inferior to the corresponding machine translation (MT) model. Based on the above observation, existing methods often use sharingmechanisms to carry out implicit knowledge transfer by imposing various constraints. However, the final model often performs worse on the MT task than the MT model trained alone, which means that the knowledge transfer ability of this method is also limited. To deal with these problems, we propose the FCCL (Fine- and Coarse- Granularity Contrastive Learning) approach for E2E-ST, which makes explicit knowledge transfer through cross-modal multi-grained contrastive learning. A key ingredient of our approach is applying contrastive learning at both sentence- and frame-level to give the comprehensive guide for extracting speech representations containing rich semantic information.In addition, we adopt a simple whitening method to alleviate the representation degeneration in the MT model, which adversely affects contrast learning. Experiments on the MuST-C benchmark show that our proposed approach significantly outperforms the state-of-the-art E2E-ST baselines on all eight language pairs. Further analysis indicates that FCCL can free up its capacity from learning grammatical structure information and force more layers to learn semantic information.

Existing techniques often attempt to make knowledge transfer from a powerful machine translation (MT) to speech translation (ST) model with some elaborate techniques, which often requires transcription as extra input during training. However, transcriptions are not always available, and how to improve the ST model performance without transcription, i.e., data efficiency, has rarely been studied in the literature. In this paper, we propose Decoupled Non-parametric Knowledge Distillation (DNKD) from data perspective to improve the data efficiency. Our method follows the knowledge distillation paradigm. However, instead of obtaining the teacher distribution from a sophisticated MT model, we construct it from a non-parametric datastore via k-Nearest-Neighbor (kNN) retrieval, which removes the dependence on transcription and MT model. Then we decouple the classic knowledge distillation loss into target and non-target distillation to enhance the effect of the knowledge among non-target logits, which is the prominent "dark knowledge". Experiments on MuST-C corpus show that, the proposed method can achieve consistent improvement over the strong baseline without requiring any transcription., Comment: Accepted by ICASSP 2023