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The goal of the present paper is to highlight the fundamental differences of so-called synchronization or consensus algorithms when the agents to synchronize evolve on a compact homogeneous manifold (like the circle, sphere or the group of…
We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are…
Mobile devices increasingly require the parallel execution of several computing tasks offloaded at the wireless edge. Existing communication systems only support parallel transmissions at the bit level, which fundamentally limits the number…
Recent advances in pixel-level tasks (e.g. segmentation) illustrate the benefit of of long-range interactions between aggregated region-based representations that can enhance local features. However, such aggregated representations, often…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
The system presented here shows the feasibility of modeling the knowledge involved in a complex musical activity by integrating sub-symbolic and symbolic processes. This research focuses on the question of whether there is any advantage in…
Word embeddings are rich word representations, which in combination with deep neural networks, lead to large performance gains for many NLP tasks. However, word embeddings are represented by dense, real-valued vectors and they are therefore…
Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in…
Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…
Music can be represented in multiple forms, such as in the audio form as a recording of a performance, in the symbolic form as a computer readable score, or in the image form as a scan of the sheet music. Music synchronisation provides a…
Let $\mathfrak g$ be an infinite-dimensional Lie algebra and $G$ be the algebraic completion of its module. Using a geometric interpretation in terms of sewing two Riemann spheres with a number of marked points, we introduce a…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
The goal of the present paper is to provide a detailed study of irreducible representations of the algebra generated by the symmetries of the generic quantum superintegrable system on the $d$-sphere. Appropriately normalized, the symmetry…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
The ability to perform mathematical computations using metastructures is an emergent paradigm that carries the potential of wave-based analog computing to the realm of near-speed-of-light, low-loss, compact devices. We theoretically…
Models trained on semantically related datasets and tasks exhibit comparable inter-sample relations within their latent spaces. We investigate in this study the aggregation of such latent spaces to create a unified space encompassing the…
Neural networks trained on natural language processing tasks capture syntax even though it is not provided as a supervision signal. This indicates that syntactic analysis is essential to the understating of language in artificial…
We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to prove via algebraic geometry a recursion between the…