Related papers: Interval Superposition Arithmetic
Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supplementing a given sequence of values of an approximate…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
The integral image, an intermediate image representation, has found extensive use in multi-scale local feature detection algorithms, such as Speeded-Up Robust Features (SURF), allowing fast computation of rectangular features at constant…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which…
Exemplar-based inpainting is the process of reconstructing missing parts of an image by searching the remaining data for patches that fit seamlessly. The image is completed to a plausible-looking solution by repeatedly inserting the patch…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…
The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence,…
Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
Given a factorable function f, we propose a procedure that constructs a concave underestimator of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is…
This paper presents a factor analysis model for symbolic data, focusing on the particular case of interval-valued variables. The proposed method describes the correlation structure among the measured interval-valued variables in terms of a…
The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…
Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…