A framework for navigating environments with spatially correlated obstacles and uncertain blockage status.
problem Navigation in environments with spatially correlated obstacles of uncertain blockage status.
method Modeling spatial correlation with Gaussian Random Field, developing Bayesian belief updates, proposing a two-stage learning framework with offline and online phases.
result Consistent performance gains over baselines in environments with adversarial interruptions or clustered natural hazards.
Method recovers obstacles from travel times on curved surfaces.
problem Recovering obstacles from travel times on curved surfaces.
method Extending Noakes and Stoyanov's method to Riemannian surfaces with curvature constraints.
result Obstacles can be recovered from travel times on Riemannian surfaces under certain curvature conditions.
Study finds a limiting distribution for free path lengths on flat surfaces with circular obstacles.
problem Understanding free path lengths on flat surfaces with circular obstacles.
method Proved the existence of a limiting distribution using radius of obstacles as a parameter.
result Relates the limiting distribution to heights of zippered rectangle decompositions.
Study on elastic curves pinned at the boundary, focusing on minimizers and their interaction with obstacles.
problem Minimizing elastic bending energy for open planar curves with obstacles.
method Investigation of global minimizers and explicit solutions for different values of the penalization parameter.
result Explicit threshold for λ above which minimizers touch the obstacle, regardless of obstacle shape. Study of mean curvature flow with obstacles using singular perturbation.
problem Obstacle problem associated to mean curvature flow.
method Geometric vanishing-viscosity approximation with singular perturbation.
result Generic level sets are distributional solutions of the obstacle problem.
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two obstacles satisfy some generic regularity conditions and have (almost) the same trave…
New approach for obstacle avoidance in robotics using learned representations.
problem Challenges in sensor-based motion planning for new and dynamic environments.
method Proposes a new obstacle representation using PointNet architecture trained jointly with policies for obstacle avoidance.
result Significant improvements in accuracy and efficiency compared to state of the art.
The paper finds local minimizers for obstacle avoidance on curved spaces.
problem Finding optimal paths on curved spaces avoiding obstacles.
method Minimizing an action functional with bi-Jacobi fields and biconjugate points.
result Local minimizers are classified into two categories with local uniqueness results.
Same travelling times imply identical obstacles in Riemannian manifolds.
problem Determining if two sets of obstacles are identical based on travel times.
method Analyzing curvature conditions and geodesic intersections.
result Disjoint convex obstacles with identical travel times are identical.
The paper simplifies conditions for optimal paths on manifolds avoiding obstacles.
problem Finding optimal paths on manifolds avoiding obstacles.
method Study of sufficient conditions for optimality on Riemannian manifolds and Lie groups.
result New conditions for optimality are provided in terms of matrix invertibility.
Study anisotropic obstacle problem for minimal surfaces using Cahn-Hoffman transform.
problem Anisotropic obstacle problem for minimal surfaces.
method Cahn-Hoffman transform to convert to isotropic problem with generalized Robin boundary condition.
result Optimal regularity of the solution and C1,1 regularity of the free boundary. Study proves uniqueness for ray transform on surfaces with obstacles.
problem Uniqueness of functions and 1-forms on surfaces with reflecting obstacles.
method Broken ray transform on twisted geodesics with nonpositive curvature and reflecting boundary.
result Proves uniqueness result for sums of functions and 1-forms.
We consider the broken ray transform on Riemann surfaces in the presence of an obstacle, following earlier work of Mukhometov. If the surface has nonpositive curvature and the obstacle is strictly convex, we show that a function is determined by its integrals over broken geodesic rays that reflect on the boundary of th…
Anisotropic obstacle problems and Stefan problem studied with evolving surfaces.
problem Anisotropic parabolic obstacle problems and Stefan problem.
method Cahn-Hoffman transform and anisotropic mean curvature flow.
result Optimal regularity of the solution and C1,α-regularity of the evolving free boundary. Geometric optics describes wave behavior near convex obstacles.
problem Wave behavior near convex obstacles.
method Geometric optics in L2 and H1 spaces. result Oscillations transport along grazing rays to any order.
We consider an obstacle problem for elastic curves with fixed ends. We attempt to extend the graph approach provided in [8]. More precisely, we investigate nonexistence of graph solutions for special obstacles and extend the class of admissible curves in a way that an existence result can be obtained by a penalization …
We show short time existence and uniqueness of $\C^{1,1}$ solutions to the mean curvature flow with obstacles, when the obstacles are of class $\C^{1,1}$. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.
In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator f has quadratic growth in the z-variable. In particular, we obtain existence, comparison, and stability results, and consider the opti…
This paper presents preliminary work on learning the search heuristic for the optimal motion planning for automated driving in urban traffic. Previous work considered search-based optimal motion planning framework (SBOMP) that utilized numerical or model-based heuristics that did not consider dynamic obstacles. Optimal…
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In this work, we attack non-convexity by first introducing the concept of \emph{probab…
Billiard trajectories in curved spaces have predictable travel times.
problem Understanding travel times in billiard trajectories on curved surfaces.
method Analyzing geodesic flows and sectional curvature to prove time-preserving conjugacy.
result Billiard trajectories with almost identical obstacles have identical shapes.
In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits obstacles (or barriers) when the noise is given by Brownian motion and a Poisson random measure mutually independent. The jumps of the obstacle processes could be either predictable or inaccessible. W…
Many mobile robots rely on 2D laser scanners for localization, mapping, and navigation. However, those sensors are unable to correctly provide distance to obstacles such as glass panels and tables whose actual occupancy is invisible at the height the sensor is measuring. In this work, instead of estimating the distance…
Billiard trajectories (broken generalised geodesics) are considered in the exterior of an obstacle K with smooth boundary on an arbitrary Riemannian manifold. We prove a generalisation of the well-known Santalo's formula. As a consequence, it is established that if the set of trapped points has positive measure, then…
We consider the problem of evolving hypersurfaces by mean curvature flow in the presence of obstacles, that is domains which the flow is not allowed to enter. In this paper, we treat the case of complete graphs and explain how the approach of M. Saez and the second author yields a global weak solution to the original p…
GP-ND avoids obstacles in trajectory planning using Gaussian Process regression.
problem Avoiding obstacles in trajectory planning for real-world systems.
method GP-ND models negative data pairs using Gaussian distributions and maximizes their KL divergence from the GP to avoid them.
result GP-ND outperforms traditional GP learning in obstacle-aware trajectory planning.
Flow adjusts curvature to avoid a fixed region, proving bounds and regularity.
problem Adjusting curvature flow to avoid a fixed region.
method Flow by powers of Gauss curvature, proving optimal curvature bounds and regularity.
result Proves optimal curvature bounds and long time existence for all dimensions and powers.
DPERC efficiently estimates covariance matrices for mixed data with missing values.
problem Estimating covariance matrices for datasets with missing values and mixed features.
method Direct Parameter Estimation for Randomly Missing Data with Categorical Features (DPERC).
result DPERC outperforms other methods in estimating covariance matrices for mixed data with missing values.
Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerat…
We prove that if two non-trapping obstacles in Rn satisfy some rather weak non-degeneracy conditions and the scattering rays in their exteriors have (almost) the same travelling times or (almost) the same scattering length spectrum, then they coincide.
Paper studies optimal control for a specific geometric problem.
problem Optimal control problem associated with the Paneitz obstacle problem.
method Existence and regularity results for optimal controls.
result Existence of optimal controls and their properties.
Study on semiconcavity of solutions to gradient obstacle problems on compact manifolds.
problem Gradient obstacle problems on compact Riemannian manifolds.
method Uniform semiconcavity estimates and fine convergence results for solutions and free boundaries.
result The elastic and λ-elastic sets of solutions converge to the cut locus and λ-cut locus of the manifold. We develop some of the basic theory for the obstacle problem on Riemannian Manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.
Coordinated defensive escorts can aid a navigating payload by positioning themselves in order to maintain the safety of the payload from obstacles. In this paper, we present a novel, end-to-end solution for coordinating an escort team for protecting high-value payloads. Our solution employs deep reinforcement learning …
Rigidity of travel times for convex obstacles in Riemannian manifolds is proven.
problem Rigidity of travel times for strictly convex obstacles in Riemannian manifolds.
method Analysis of billiard trajectories and comparison of travel times.
result If travel times are equal, then obstacles are identical in dimensions greater than or equal to 3.
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bending energy is used as a stabilizing term in Tikhonov regularization to gain independence of the parametrization. Moreover, we discuss how se…
The paper studies the properties of maps with free boundaries, focusing on the obstacle case.
problem Properties of the projected image and its regularity in maps with free boundaries.
method Dividing the map into distance and projected image parts; applying classical obstacle problem methods and proving higher regularity for the projected image.
result The projected image is at most of class C2,1 and globally of class W3,BMO, locally of C2,1 around the regular part of the free boundary. Investigates polar tangential angles of curves and their monotonicity.
problem Behavior of polar tangential angles of plane curves.
method Proof of monotonicity for certain curves of monotone curvature.
result Nonexistence results for an obstacle problem involving free elasticae.
Optimal controls for conformal Laplacian obstacle problems on spheres and manifolds.
problem Optimal control of conformal metrics with constant scalar curvature.
method Analysis of optimal control problem on Riemannian manifolds with positive Yamabe invariant.
result Existence of smooth optimal controls inducing metrics with constant scalar curvature.
The paper tackles stock prediction models by improving their generalizability to out-of-sample domains using causal representation learning.
problem Low signal-to-noise ratio and nonstationary nature of financial markets lead to poor performance of stock prediction models.
method The paper investigates Domain Generalization techniques, focusing on causal representation learning to improve model generalizability. It introduces a novel error bound and a causal discovery technique to mitigate spurious correlations.
result The proposed approach enhances the generalizability of stock prediction models, as demonstrated by numerical results.
We study periodic wind-tree models, billiards in the plane endowed with Z2-periodically located identical connected symmetric right-angled obstacles. We show asymptotic formulas for the number of (isotopy classes of) closed billiard trajectories (up to Z2-translations) on the wind-tree billiard.…
Deep network learns Obstacle Tower challenge without human demonstrations.
problem Master procedurally generated levels that get progressively harder.
method Deep Reinforcement Learning with a simple feed-forward network.
result Performed competitively in a reinforcement learning competition.
We give background which shows the connection between the mean value theorem and the obstacle problem, and then we prove that a set is a mean value set for an elliptic operator of the form Lu:=∂i(aij(x)∂ju(x)) if and only if it arises as the noncontact set of an obstacle problem involving the …
Quantum method detects financial stress regimes from market data.
problem Detecting financial stress regimes from market data.
method Adapted Pauli Correlation Encoding to quantum topological data analysis.
result Quantum method can recover Betti numbers exactly at every scale.
Study minimizers in large volume isoperimetric problems with a new flatness criterion.
problem Minimizers in isoperimetric problems with a compact obstacle.
method Study Plateau-type problem with free boundary, develop mesoscale flatness criterion.
result Identify isoperimetric residue in energy expansion for large volume.
We study a notion of relative entropy motivated by self-expanders of mean curvature flow. In particular, we obtain the existence of this quantity for arbitrary hypersurfaces trapped between two disjoint self-expanders asymptotic to the same cone. This allows us to begin to develop the variational theory for the relativ…
One of the main obstacles regarding Barky Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds …