Related papers: Method of Asymptotics beyond All Orders and Restri…
Path planning is an active area of research essential for many applications in robotics. Popular techniques include graph-based searches and sampling-based planners. These approaches are powerful but have limitations. This paper continues…
How to divide floor plans or navigation maps into semantic representations, such as rooms and corridors, is an important research question in fields such as human-robot interaction, place categorization, or semantic mapping. While most…
It has recently become clear that simulations under amorphpous boundary conditions (ABCs) can provide valuable information on the dynamics and thermodynamics of disordered systems with no obvious ordered parameter. In particular, they allow…
Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion…
This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…
We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data?…
Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used…
Sequential detection of independent anomalous processes among K processes is considered. At each time, only M processes can be observed, and the observations from each chosen process follow two different distributions, depending on whether…
When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…
A navigation on a set of points $S$ is a rule for choosing which point to move to from the present point in order to progress toward a specified target. We study some navigations in the plane where $S$ is a non uniform Poisson point process…
This is a proof of an asymptotic formula which describes exponentially small splitting of separatrices in a generic analytic family of area-preserving maps near a Hamiltonian saddle-centre bifurcation. As a particular case and in…
We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
We assume that a symplectic real-analytic map has an invariant normally hyperbolic cylinder and an associated transverse homoclinic cylinder. It is well known that such cylinder is preserved under small perturbations. We prove that for a…
We present a unified general method for the asymptotic study of graphs from the so-called "subcritical"$ $ graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works…
In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems…
We carry out the asymptotic analysis as $n \to \infty$ of a class of orthogonal polynomials $p_{n}(z)$ of degree $n$, defined with respect to the planar measure \begin{equation*} d\mu(z) = (1-|z|^{2})^{\alpha-1}|z-x|^{\gamma}\mathbf{1}_{|z|…
Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…
Recent results concerning asymptotic Bayes-optimality under sparsity (ABOS) of multiple testing procedures are extended to fairly generally distributed effect sizes under the alternative. An asymptotic framework is considered where both the…