Related papers: On The Euclidean Algorithm: Rhythm Without Recursi…

A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…

Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…

In this case study in ``fully automated enumeration'', we illustrate how to take full advantage of symbolic computation by developing (what we call) `symbolic-dynamical-programming' algorithms for computing many terms of `hard to compute…

We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…

We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…

We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…

The nonlinear, or warped, resolvent recently explored by Giselsson and B\`ui-Combettes has been used to model a large set of existing and new monotone inclusion algorithms. To establish convergent algorithms based on these resolvents,…

We propose a novel stochastic optimization algorithm called STOchastic Recursive Momentum for Compositional (STORM-Compositional) optimization that minimizes the composition of expectations of two stochastic functions, the latter being an…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

Transformer architectures offer significant advantages regarding the generation of symbolic music; their capabilities for incorporating user preferences toward what they generate is being studied under many aspects. This paper studies the…

We propose a new unsupervised and non-parametric method to detect change points in intricate quasi-periodic signals. The detection relies on optimal transport theory combined with topological analysis and the bootstrap procedure. The…

Musical counterpoint, a musical technique in which two or more independent melodies are played simultaneously with the goal of creating harmony, has been around since the baroque era. However, to our knowledge computational generation of…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…

Rhythm is a fundamental aspect of human behaviour, present from infancy and deeply embedded in cultural practices. Rhythm anticipation is a spontaneous cognitive process that typically occurs before the onset of actual beats. While most…

In this work, we generalized and unified two recent completely different works of~\cite{shi2015large} and~\cite{cartis2012adaptive} respectively into one by proposing the cyclic incremental Newton-type gradient descent with cubic…

We build and study a recursive algorithm based on the occupation measure of an Euler scheme with decreasing step for the numerical approximation of the quasistationary distribution (QSD) of an elliptic diffusion in a bounded domain. We…

In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…

Bayesian nonparametric mixture models provide a flexible framework for data analysis but are often hindered by the computational expense of traditional inference methods like MCMC. A fast, recursive algorithm proposed by Newton (2002)…

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…