Geodesic-Preserving Polygon Simplification

Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-to-describe linear-time method to replace an input polygon $\mathcal{P}$ by a polygon $\mathcal{P}'$ such that (1) $\mathcal{P}'$ contains $\mathcal{P}$, (2) $\mathcal{P}'$ has its reflex vertices at the same positions as $\mathcal{P}$, and (3) the number of vertices of $\mathcal{P}'$ is linear in the number of reflex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both $\mathcal{P}$ and $\mathcal{P}'$, our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reflex vertices rather than on the size of $\mathcal{P}$

Packing Plane Spanning Trees and Paths in Complete Geometric Graphs

We consider the following question: How many edge-disjoint plane spanning trees are contained in a complete geometric graph $GK_n$ on any set $S$ of $n$ points in general position in the plane? We show that this number is in $\Omega(\sqrt{n})$. Further, we consider variants of this problem by bounding the diameter and the degree of the trees (in particular considering spanning paths).Comment: This work was presented at the 26th Canadian Conference on Computational Geometry (CCCG 2014), Halifax, Nova Scotia, Canada, 2014. The journal version appeared in Information Processing Letters, 124 (2017), 35--4

System and method for determining velocity of electrically conductive fluid

A flowing electrically-conductive fluid is controlled between an upstream and downstream location thereof to insure that a convection timescale of the flowing fluid is less than a thermal diffusion timescale of the flowing fluid. First and second nodes of a current-carrying circuit are coupled to the fluid at the upstream location. A current pulse is applied to the current-carrying circuit so that the current pulse travels through the flowing fluid to thereby generate a thermal feature therein at the upstream location. The thermal feature is convected to the downstream location where it is monitored to detect a peak associated with the thermal feature so-convected. The velocity of the fluid flow is determined using a time-of-flight analysis

Packing Short Plane Spanning Trees in Complete Geometric Graphs

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is very long (when compared to the minimum length needed to obtain a spanning graph). We consider two different approaches: first we show an almost optimal centralized approach to extract two trees. Then we show a constant factor approximation for a distributed model in which each point can compute its adjacencies using only local information. This second approach may create cycles, but maintains planarity

Workshop on immunotherapy combinations. Society for immunotherapy of cancer annual meeting Bethesda, November 3, 2011

Although recent FDA approvals on ipilimumab and sipuleucel-T represent major milestones, the ultimate success of immunotherapy approaches will likely benefit from appropriate combinations with other immunotherapeutic and/or non-immunotherapeutic approaches. However, implementation of ideal combinations in the clinic may still face formidable challenges in regulatory, drug-availability and intellectual property aspects. The 2011 SITC annual meeting hosted a workshop on combination immunotherapy to discuss: 1) the most promising combinations found in the laboratory; 2) early success of combination immunotherapy in clinical trials; 3) industry perspectives on combination approaches, and 4) relevant regulatory issues. The integrated theme was how to accelerate the implementation of efficacious combined immunotherapies for cancer patients. Rodent animal models are providing many examples of synergistic combinations that typically include more than two agents. However, mouse and human immunology differ in a significant number of mechanisms and hence we might be missing opportunities peculiar to humans. Nonetheless, incisive animal experimentation with deep mechanistic insight remains the best compass that we can use to guide our paths in combinatorial immunotherapy. Combination immunotherapy clinical trials are already in progress and preliminary results are extremely promising. As a key to translate promising combinations into clinic, real and “perceived” business and regulatory hurdles were debated. A formidable step forward would be to be able to test combinations of investigational agents prior to individual approval. Taking together the FDA and the industrial perspective on combinatorial immunotherapy, the audience was left with the clear message that this is by no means an impossible task. The general perception is that the road ahead of us is full of combination clinical trials which hopefully will bring clinical benefit to our cancer patients at a fast pace

Cell-paths in mono- and bichromatic line arrangements in the plane

We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no cell is revisited). When all lines have the same color, and hence the preceding alternating constraint is dropped, we prove that the dual graph of the arrangement always contains a path of length (n2).Peer ReviewedPostprint (author’s final draft

Workshop on immunotherapy combinations. Society for Immunotherapy of Cancer annual meeting

Abstract Although recent FDA approvals on ipilimumab and sipuleucel-T represent major milestones, the ultimate success of immunotherapy approaches will likely benefit from appropriate combinations with other immunotherapeutic and/or non-immunotherapeutic approaches. However, implementation of ideal combinations in the clinic may still face formidable challenges in regulatory, drug-availability and intellectual property aspects. The 2011 SITC annual meeting hosted a workshop on combination immunotherapy to discuss: 1) the most promising combinations found in the laboratory; 2) early success of combination immunotherapy in clinical trials; 3) industry perspectives on combination approaches, and 4) relevant regulatory issues. The integrated theme was how to accelerate the implementation of efficacious combined immunotherapies for cancer patients. Rodent animal models are providing many examples of synergistic combinations that typically include more than two agents. However, mouse and human immunology differ in a significant number of mechanisms and hence we might be missing opportunities peculiar to humans. Nonetheless, incisive animal experimentation with deep mechanistic insight remains the best compass that we can use to guide our paths in combinatorial immunotherapy. Combination immunotherapy clinical trials are already in progress and preliminary results are extremely promising. As a key to translate promising combinations into clinic, real and "perceived" business and regulatory hurdles were debated. A formidable step forward would be to be able to test combinations of investigational agents prior to individual approval. Taking together the FDA and the industrial perspective on combinatorial immunotherapy, the audience was left with the clear message that this is by no means an impossible task. The general perception is that the road ahead of us is full of combination clinical trials which hopefully will bring clinical benefit to our cancer patients at a fast pace