In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing modular tensor categories and fusion rings. Rather than providing an in-depth mathematical development we concentrate instead on presenting the "highlights for a physicist".

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Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent neural networks, based on dissipative quantum neural networks, capable of learning general causal quantum automata. A quantum training algorithm is proposed and classical simulations for the case of product outputs with the fidelity as cost function are carried out. We thereby demonstrate the potential of these algorithms to learn complex quantum processes with memory in terms of the exemplary delay channel, the time evolution of quantum states governed by a time-dependent Hamiltonian, and highand low-frequency noise mitigation. Numerical simulations indicate that our quantum recurrent neural networks exhibit a striking ability to generalise from small training sets.

The distinctive feature of modern musical art is the constant search for new expressive means. Innovations infiltrated all aspects of composition, including the writing technique, understanding of the genre, style, form, and instrumental interpretation. These efforts are aimed at a true diverse and multifaceted embodiment of reality, which is constantly changing due to grand social upheavals. “Creative experiment, inquisitive search, and desire for renewal are inevitable and necessary in modern music. Without these experiments, artistic creativity becomes shallow, declines, and is subjected to sclerotic necrosis”. The growing need for a highly spiritual society requires a rapprochement to teaching and educating the younger generation to develop its spiritual and cultural values, personal and artistic orientations. These trends are primarily related to maintaining and increasing the intellectual and creative potential of a person who can express oneself through professional activities. In this case, the modern socio-cultural stage of development of musical-pedagogical education brings attention to new quality requirements to training of the experts that supposes the necessity and urgency of updating a problem of methodological training of music teachers.

The article pays special attention to the need to use active teaching methods in the process of forming the professionally necessary ensemble skills of the future music teacher.