arXiv subjects
Publications and source records attributed to Francisco Martin.
We construct new expanders for mean curvature flow that are smoothly asymptotic to cones arising from certain shrinkers. For each such cone, we prove the existence of expanders of arbitrarily large genus. Thus, for a fixed incoming shrinker, the genus of the outgoing expander can be chosen much larger than the genus before the singularity, contrary to Ilmanen's genus-reduction conjecture.
We prove existence for many examples of shrinkers by producing compact, smoothly embedded surfaces that, under mean curvature flow, develop singularities at which the shrinkers occur as blowups.
Executing temporal plans in the real and open world requires adapting to uncertainty both in the environment and in the plan actions. A plan executor must therefore be flexible to dispatch actions based on the actual execution conditions. In general, this involves considering both event and time-based constraints between the actions in the plan. A simple temporal network (STN) is a convenient framework for specifying the constraints between actions in the plan. Likewise, a behavior tree (BT) is a convenient framework for controlling the execution flow of the actions in the plan. The principle contributions of this paper are i) an algorithm for transforming a plan into an STN, and ii) an algorithm for transforming an STN into a BT. When combined, these algorithms define a systematic approach for executing total-order (time-triggered) plans in robots operating in the real world. Our approach is based on creating a graph describing a deordered (state-triggered) plan and then creating a BT representing a partial-order (determined at runtime) plan. This approach ensures the correct execution of plans, including those with required concurrency. We demonstrate the validity of our approach within the PlanSys2 framework on real robots.
The latest trends in cancer research and nanomedicine focus on using nanocarriers to target cancer stem cells (CSCs). Specifically, lipid liquid nanocapsules are usually developed as nanocarriers for lipophilic drug delivery. Here, we developed olive oil liquid NCs (O2LNCs) functionalized by covalent coupling of an anti-CD44-fluorescein isothiocyanate antibody (αCD44). First, O2LNCs are formed by a core of olive oil surrounded by a shell containing phospholipids, a nonionic surfactant, and deoxycholic acid molecules. Then, O2LNCs were coated with an αCD44 antibody (αCD44-O2LNC). The optimization of an αCD44 coating procedure, a complete physicochemical characterization, as well as clear evidence of their efficacy in vitro and in vivo were demonstrated. Our results indicate the high targeted uptake of these αCD44-O2LNCs, and the increased antitumor efficacy (up to four times) of paclitaxel-loaded-αCD44-O2LNC compared to free paclitaxel in pancreatic CSCs (PCSCs). Also, αCD44-O2LNCs were able to selectively target PCSCs in an orthotopic xenotransplant in vivo model.
The accelerated deployment of service robots have spawned a number of algorithm variations to better handle real-world conditions. Many local trajectory planning techniques have been deployed on practical robot systems successfully. While most formulations of Dynamic Window Approach and Model Predictive Control can progress along paths and optimize for additional criteria, the use of pure path tracking algorithms is still commonplace. Decades later, Pure Pursuit and its variants continues to be one of the most commonly utilized classes of local trajectory planners. However, few Pure Pursuit variants have been proposed with schema for variable linear velocities - they either assume a constant velocity or fails to address the point at all. This paper presents a variant of Pure Pursuit designed with additional heuristics to regulate linear velocities, built atop the existing Adaptive variant. The Regulated Pure Pursuit algorithm makes incremental improvements on state of the art by adjusting linear velocities with particular focus on safety in constrained and partially observable spaces commonly negotiated by deployed robots. We present experiments with the Regulated Pure Pursuit algorithm on industrial-grade service robots. We also provide a high-quality reference implementation that is freely included ROS 2 Nav2 framework at https://github.com/ros-planning/navigation2 for fast evaluation.
Self-localization is a fundamental capability that mobile robot navigation systems integrate to move from one point to another using a map. Thus, any enhancement in localization accuracy is crucial to perform delicate dexterity tasks. This paper describes a new location that maintains several populations of particles using the Monte Carlo Localization (MCL) algorithm, always choosing the best one as the sytems's output. As novelties, our work includes a multi-scale match matching algorithm to create new MCL populations and a metric to determine the most reliable. It also contributes the state-of-the-art implementations, enhancing recovery times from erroneous estimates or unknown initial positions. The proposed method is evaluated in ROS2 in a module fully integrated with Nav2 and compared with the current state-of-the-art Adaptive ACML solution, obtaining good accuracy and recovery times.
We prove the existence of horizontal Jenkins-Serrin graphs that are translating solitons of the mean curvature flow in Riemannian product manifolds $M\times\mathbb{R}$. Moreover, we give examples of these graphs in the cases of $\mathbb{R}^3$ and $\mathbb{H}^2\times\mathbb{R}$.
The so called Jenkins-Serrin problem is a kind of Dirichlet problem for graphs with prescribed mean curvature that combines, at the same time, continuous boundary data with regions of the boundary where the boundary values explodes either to $+\infty$ or to $-\infty.$ We give a survey on the development of Jenkins-Serrin type problems over domains on Riemannian manifolds. The existence of this type of graphs imposes restrictions on the geometry of the boundary of these domains. We also improve some earlier results by proving Theorem 1.8, and prove the existence of translating Jenkins-Serrin graphs (Theorem 1.9).
In this paper we study the moduli space of properly Alexandrov-embedded, minimal annuli in $\mathbb{H}^2 \times \mathbb{R}$ with horizontal ends. We say that the ends are horizontal when they are graphs of $\mathcal{C}^{2, α}$ functions over $\partial_\infty \mathbb{H}^2$. Contrary to expectation, we show that one can not fully prescribe the two boundary curves at infinity, but rather, one can prescribe the bottom curve, but the top curve only up to a translation and a tilt, along with the position of the neck and the vertical flux of the annulus. We also prove general existence theorems for minimal annuli with discrete groups of symmetries.
A translating soliton is a hypersurface $M$ in $\mathbb{R}^{n+1}$ such that the family $M_t= M- t \,\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such that normal component of the velocity at each point is equal to the mean curvature at that point $\mathbf{H}=\mathbf{e}_{n+1}^{\perp}.$ In this paper we obtain a characterization of hyperplanes which are parallel to $\mathbf{e}_{n+1}$ and the family of tilted grim reaper cylinders as the only translating solitons in $\mathbb{R}^{n+1}$ which are $C^1$-asymptotic to two half-hyperplanes outside a non-vertical cylinder. This result was proven for translators in $\mathbb{R}^3$ by the second author, Perez-Garcia, Savas-Halilaj and Smoczyk under the additional hypotheses that the genus of the surface was locally bounded and the cylinder was perpendicular to the translating velocity.
In this paper we provide a full classification of complete translating graphs in $\mathbf{R}^3$. We also construct two $(n-1)$-parameter families of new examples of translating graphs in $\mathbf{R}^{n+1}$.
In this paper we study solitons invariant with respect to the flow generated by a complete Killing vector field in a ambient Riemannian manifold. A special case occurs when the ambient manifold is the Riemannian product $(\mathbb{R} \times P, {\rm d}t^2+g_0)$ and the Killing field is $X=\partial_t$. Similarly to what happens in the Euclidean setting, we call them translating solitons. We see that a translating soliton in $\mathbb{R} \times P$ can be seen as a minimal submanifold for a weighted volume functional. Moreover we show that this kind of solitons appear in a natural way in the context of a monotonicity formula for the mean curvature flow in $\mathbb{R} \times P$. When $g_0$ is rotationally invariant and its sectional curvature is non-positive, we are able to characterize all the rotationally invariant translating solitons. Furthermore, we use these families of new examples as barriers to deduce several non-existence results.
In this article we prove that a connected and properly embedded translating soliton in $\mathbb{R}^3$ with uniformly bounded genus on compact sets which is $C^1$-asymptotic to two planes outside a cylinder, either is flat or coincides with the grim reaper cylinder.
In the present article we obtain classification results and topological obstructions for the existence of translating solitons of the mean curvature flow.
We prove prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space $\mathbb{H}^3$, and we use it to prove that any open, connected, orientable surface can be properly embedded in $\mathbb{H}^3$ as an area-minimizing surface. Moreover, the embedding can be constructed in such a way that the limit sets of different ends are disjoint.
We construct the first examples of complete, properly embedded minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$ with finite total curvature and positive genus. These are constructed by gluing copies of horizontal catenoids or other nondegenerate summands. We also establish that every horizontal catenoid is nondegenerate. Finally, using the same techniques, we are able to produce properly embedded minimal surfaces with infinitely many ends. Each annular end has finite total curvature and is asymptotic to a vertical totally geodesic plane.
We construct a complete bounded immersed null holomorphic curve in C^3, which is a recovery of the previous version of the paper Calc. Var. and PDE's vol 36 (2009); Erratum: to appear in Calc. Var. and PDE's, doi:10.1007/s00526-009-0226-5 by the last three authors on this subject.
We construct a complete, bounded Legendrian immersion in C^3. As direct applications of it, we show the first examples of a weakly complete bounded flat front in hyperbolic 3-space, a weakly complete bounded flat front in de Sitter 3-space, and a weakly complete bounded improper affine front in R^3.