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We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

We measure the geometry of a crumpled sheet of paper with laser-aided topography and discuss its statistical properties. The curvature of an elasto-plastic fold scales linearly with applied force. The curvature distribution follows an…

It is shown that the number of pages required for a book embedding of a graph is the maximum of the numbers needed for any of the maximal nonseparable subgraphs and that a plane graph in which every triangle bounds a face has a two-page…

The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all the vertices. It is known that the cover time on any n-vertex, connected graph is at least (1+o(1)) n…

A rapidly increasing portion of internet traffic is dominated by requests from mobile devices with limited and metered bandwidth constraints. To satisfy these requests, it has become standard practice for websites to transmit small and…

Presentation of folded documents is not an uncommon case in modern society. Digitizing such documents by capturing them with a smartphone camera can be tricky since a crease can divide the document contents into separate planes. To unfold…

Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…

A rectangular thin elastic sheet is deformed by forcing a contact between two points at the middle of its length. A transition to buckling with stress focusing is reported for the sheets sufficiently narrow with a critical width…

Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…

The determination of the reading sequence of text is fundamental to document understanding. This problem is easily solved in pages where the text is organized into a sequence of lines and vertical alignment runs the height of the page…

Motivated by recent experiments, we consider theoretically the compression of droplets pinned at the bottom on a surface of finite area. We show that if the droplet is sufficiently compressed at the top by a surface, it will always develop…

In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to…

When people explore large document collections to build understanding, they face a challenge: existing AI tools help them see what is central but tend to hide what is unusual. Summarization and topic modeling optimize for coverage,…

For an angle $\alpha\in (0,\pi)$, we consider plane graphs and multigraphs in which the edges are either (i) one-bend polylines with an angle $\alpha$ between the two edge segments, or (ii) circular arcs of central angle $2(\pi-\alpha)$. We…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

We consider two- and three-dimensional lattice models of proteins which were characterized previously. We coarse grain their folding dynamics by reducing it to transitions between effective states. We consider two methods of selection of…

Observing certain patches in an image reduces the uncertainty of others. Their realization lowers the distribution entropy of each remaining patch feature, analogous to collapsing a particle's wave function in quantum mechanics. This…

We consider information diffusion on Web-like networks and how random walks can simulate it. A well-studied problem in this domain is Partial Cover Time, i.e., the calculation of the expected number of steps a random walker needs to visit a…