Related papers: Inverting the signature of a path
A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is…
The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…
Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally…
The restoration lemma is a classic result by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [PODC '01], which relates the structure of shortest paths in a graph $G$ before and after some edges in the graph fail. Their work shows that, after…
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…
Let a and b be two positive integers. A culminating path is a path of Z^2 that starts from (0,0), consists of steps (1,a) and (1,-b), stays above the x-axis and ends at the highest ordinate it ever reaches. These paths were first…
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
Parallel transport, or path development, provides a rich characterization of paths which preserves the underlying algebraic structure of concatenation. The path signature is universal among such maps: any (translation-invariant) parallel…
Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory…
Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference…
Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…
A path or a polygonal domain is C-oriented if the orientations of its edges belong to a set of C given orientations; this is a generalization of the notable rectilinear case (C = 2). We study exact and approximation algorithms for…
In this paper we give a criterion by which one can conclude that every reduction of a basic term to normal form has the same length. As a consequence, the number of steps to reach the normal form is independent of the chosen strategy. In…
The treatment of equality as a type in type theory gives rise to an interesting type-theoretic structure known as `identity type'. The idea is that, given terms $a,b$ of a type $A$, one may form the type $Id_{A}(a,b)$, whose elements are…
The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be…
We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially…
Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data…
This paper presents methodologies to discretize nominal robot paths extracted from 3-D CAD drawings. Behind robot path discretization is the ability to have a robot adjusting the traversed paths so that the contact between robot tool and…
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…
The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define…