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The Carrell-Chapuy recurrence formulas dramatically improve the efficiency of counting orientable rooted maps by genus, either by number of edges alone or by number of edges and vertices. This paper presents an implementation of these…
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a $\log$ mapping to Laguerre polynomials. We develop basic approximation…
Occupancy grids are the most common framework when it comes to creating a map of the environment using a robot. This paper studies occupancy grids from the motion planning perspective and proposes a mapping method that provides richer data…
We present LOOM (Line-Ordering Optimized Maps), a fully automatic generator of geographically accurate transit maps. The input to LOOM is data about the lines of a given transit network, namely for each line, the sequence of stations it…
We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain structured cut-generating functions. This has the consequence of…
Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with…
There are numerous applications which require the ability to take certain actions (e.g. distribute money, medicines, people etc.) over a geographic region. A disaster relief organization must allocate people and supplies to parts of a…
The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…
Wave maps (or Lorentzian-harmonic maps) from a $1+1$-dimensional Lorentz space into the $2$-sphere are associated to constant negative Gaussian curvature surfaces in Euclidean 3-space via the Gauss map, which is harmonic with respect to the…
For area-preserving H\'enon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For constructing such perturbations, we use two methods, the…
We propose a novel non-linear extension to the Orienteering Problem (OP), called the Correlated Orienteering Problem (COP). We use COP to model the planning of informative tours for the persistent monitoring of a spatiotemporal field with…
This paper presents Latent Sampling-based Motion Planning (L-SBMP), a methodology towards computing motion plans for complex robotic systems by learning a plannable latent representation. Recent works in control of robotic systems have…
The repeated execution of reasoning tasks is desirable in many applicative scenarios, such as stream reasoning and event processing. When using answer set programming in such contexts, one can avoid the iterative generation of ground…
Offline map matching involves aligning historical trajectories of mobile objects, which may have positional errors, with digital maps. This is essential for applications in intelligent transportation systems (ITS), such as route analysis…
The Simple Plant Location Problem with Order (SPLPO) is a variant of the Simple Plant Location Problem (SPLP), where the customers have preferences over the facilities which will serve them. In particular, customers define their preferences…
The aim of this paper is to further explore an idea from J.-L. Loday briefly exposed in [5]. We impose a natural and simple symmetry on a unit action over the most general quadratic relation which can be written. This leads us to two…
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying…
We study the iterations of a class of curvature image operators $\Lambda_p^{\varphi}$ introduced by the author in (J. Funct. Anal. 271 (2016) 2133--2165). The fixed points of these operators are the solutions of the $L_p$ Minkowski problems…
In this paper, we prove that the set of triangulations of a polygon can be equipped with an order to become a lattice. First, we define this order. In [HN99], authors defined the flip operator and then prove some properties of the graph of…
We study one of the key tools in data approximation and optimization: low-discrepancy colorings. Formally, given a finite set system $(X,\mathcal S)$, the \emph{discrepancy} of a two-coloring $\chi:X\to\{-1,1\}$ is defined as $\max_{S \in…