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A discretisation of differential geometry using the Whitney forms of algebraic topology is consistently extended via the introduction of a pairing on the space of chains. This pairing of chains enables us to give a definition of the…
The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered. We first use the quadrature-based finite difference schemes…
We provide novel deterministic distributed vertex coloring algorithms. As our main result, we give a deterministic distributed algorithm to compute a $(\Delta+1)$-coloring of an $n$-node graph with maximum degree $\Delta$ in…
A method is presented for producing analytical results applicable to the standard two-party deterministic dense coding protocol, wherein communication of K perfectly distinguishable messages is attainable with the aid of K selected local…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument, series and electrical moves. We show that given a…
Image ordinal classification refers to predicting a discrete target value which carries ordering correlation among image categories. The limited size of labeled ordinal data renders modern deep learning approaches easy to overfit. To tackle…
Differential privacy (DP) has arisen as the gold standard in protecting an individual's privacy in datasets by adding calibrated noise to each data sample. While the application to categorical data is straightforward, its usability in the…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
In this work, following the discrete de Rham (DDR) approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary…
How is it possible to read the dynamical properties (ie when the time goes to infinity) of a system on numerical simulations? To try to answer this question, we study in this manuscript a model reflecting what happens when the orbits of a…
We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization…
Conventional tomographic reconstruction typically depends on centralized servers for both data storage and computation, leading to concerns about memory limitations and data privacy. Distributed reconstruction algorithms mitigate these…
In this work, we consider a class of $n$-dimensional, $n\geq2$, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may…
This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…
This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with…
Many tasks require mapping continuous input data (e.g. images) to discrete task outputs (e.g. class labels). Yet, how neural networks learn to perform such discrete computations on continuous data manifolds remains poorly understood. Here,…
In regular dynamics, discrete maps are model presentations of discrete dynamical systems, and they may approximate continuous dynamical systems. Maps are used to investigate general properties of dynamical systems and to model various…