相关论文: Symbolic dynamical scales: modes, orbitals, and tr…

This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…

It is shown how to model any automorphism of a totally disconnected, locally compact group by a symbolic dynamical system. The model is an inverse limit of a product of a full-shift, on a finite number of symbols, with one of two types of…

Research on style transfer and domain translation has clearly demonstrated the ability of deep learning-based algorithms to manipulate images in terms of artistic style. More recently, several attempts have been made to extend such…

Dynamical quantum phase transitions (DQPTs), which serve as a theoretical framework for understanding far-from-equilibrium physics in quantum many-body systems, have recently been observed experimentally. Their topological properties are…

In this paper we propose the Music Note Ontology, an ontology for modelling music notes and their realisation. The ontology addresses the relation between a note represented in a symbolic representation system, and its realisation, i.e. a…

Although a variety of transformers have been proposed for symbolic music generation in recent years, there is still little comprehensive study on how specific design choices affect the quality of the generated music. In this work, we…

Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal…

This paper investigates the learning of 3rd-order tensors representing the semantics of transitive verbs. The meaning representations are part of a type-driven tensor-based semantic framework, from the newly emerging field of compositional…

In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…

Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…

We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…

Winding number transitions from quantum to classical behavior are studied in the case of the {1+1} dimensional Mottola-Wipf model with the space coordinate on a circle for exploring the possibility of obtaining transitions of second order.…

We test a segmentation algorithm, based on the calculation of the Jensen-Shannon divergence between probability distributions, to two symbolic sequences of literary and musical origin. The first sequence represents the successive appearance…

The musical realm is a promising area in which to expect to find nontrivial topological structures. This paper describes several kinds of metrics on musical data, and explores the implications of these metrics in two ways: via techniques of…

Symbolic Music Generation relies on the contextual representation capabilities of the generative model, where the most prevalent approach is the Transformer-based model. The learning of musical context is also related to the structural…

We study a class of singular dynamical systems which generalise the classical N-centre problem of Celestial Mechanics to the case in which the configuration space is a Riemannian surface. We investigate the existence of topological…

Music is a repetition of patterns and rhythms. It can be composed by repeating a certain number of bars in a structured way. In this paper, the objective is to generate a loop of 8 bars that can be used as a building block of music. Even…

Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…

We introduce O-systems (Definition \ref{DO}) of orthogonal transformations of ${\Bbb R}^{m}$, and establish $1-1$ correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and…

Characteristic modes of arbitrary two-dimensional periodic systems are analyzed using scattering parameter data. This approach bypasses the need for periodic integral equations and allows for characteristic modes to be computed from generic…