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Curvilinear structures are present in various fields in image processing such as blood vessels in medical imaging or roads in remote sensing. Their detection is crucial for many applications. In this article, we propose an unsupervised…
Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at…
We study the dynamics of a single chain polymer confined to a two dimensional cell. We introduce a kinetically constrained lattice gas model that preserves the connectivity of the chain, and we use this kinetically constrained model to…
A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was…
A new line clipping algorithm against convex polyhedron in E3 with an expected complexity O(1) is presented. The suggested approach is based on two orthogonal projections to E2 co-ordinate system and on pre-processing of the given…
An unfolding of a polyhedron along its edges is called a vertex unfolding if adjacent faces are allowed to be connected at not only an edge but also a vertex. Demaine et al showed that every triangulated polyhedron has a vertex unfolding.…
We make use of the previously developed formalism for a monomer ensemble and include angular dependence of the segments of the polymer chains thus described. In particular we show how to deal with stiffness when the polymer chain is…
Each element in tensioned structural networks -- such as tensegrity, architectural fabrics, or medical braces/meshes -- requires a specific tension level to achieve and maintain the desired shape, stability, and compliance. These structures…
Extracting shape information from object bound- aries is a well studied problem in vision, and has found tremen- dous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying…
Simple cycles on a digraph form a trace monoid under the rule that two such cycles commute if and only if they are vertex disjoint. This rule describes the spatial configuration of simple cycles on the digraph. Cartier and Foata have showed…
In this paper, we present a theory to efficiently deal with mechanical properties of heterogeneous polymer chain in free space and the central problem is to evaluate the diffusion equation and orientation-orientation correlation function,…
Guarding a polygon with few guards is an old and well-studied problem in computational geometry. Here we consider the following variant: We assume that the polygon is orthogonal and thin in some sense, and we consider a point $p$ to guard a…
When the boundary of a familiar object is shown by a series of isolated dots, humans can often recognize the object with ease. This ability can be sustained with addition of distracting dots around the object. However, such capability has…
Inverse kinematics is a fundamental problem for articulated robots: fast and accurate algorithms are needed for translating task-related workspace constraints and goals into feasible joint configurations. In general, inverse kinematics for…
This paper studies the problem of using a robot arm to manipulate a uniformly rotating chain with its bottom end fixed. Existing studies have investigated ideal rotational shapes for practical applications, yet they do not discuss how these…
We report simulation results on melts of entangled linear polymers confined in a free-standing thin film. We study how the geometric constraints imposed by the confinement alter the entanglement state of the system compared to the…
In $2013$ a novel self-assembly strategy for polypeptide nanostructure design which could lead to significant developments in biotechnology was presented in [Design of a single-chain polypeptide tetrahedron assembled from coiled-coil…
In biology, there are several processes in which unfolded protein chains are transported along narrow-tube channels. Normally, without such a severe configurational constraint, unfolded polypeptides would not bind to each other. However,…
We prove that every 2-dimensional polygonal complex, where each polygon is given a constant curvature metric and belongs to one of finitely many isometry classes can be triangulated using only acute simplices. There is no requirement on the…
We consider guarding classes of simple polygons using mobile guards (polygon edges and diagonals) under the constraint that no two guards may see each other. In contrast to most other art gallery problems, existence is the primary question:…