Octopus arm movements provide an extreme example of controlled movements of a flexible arm with virtually unlimited degrees of freedom. This study aims to identify general principles in the organization of these movements. Video records of the movements of Octopus vulgaris performing the task of reaching toward a target were studied. The octopus extends its arm toward the target by a wave-like ...

From the early days of computational geometry, practitioners have looked for faster ways to triangulate a simple polygon. Several near-linear time algorithms have been devised and implemented. However, the true linear time algorithms of Chazelle and Amato et al. are considered impractical for actual use despite their faster asymptotic running time. In this paper, I examine the latter of these i...

Batagelj and Zaversnik proposed a linear algorithm for the wellknown k-core decomposition problem. However, when k-cores are desired for a given k, we find that a simple linear algorithm requiring no sorting works for mining k-cores. In addition, this algorithm can be extended to mine (k1, k2, . . . , kp)-cores from p-partite graphs in linear time, and this mining approach can be efficiently im...

Packrat parsing is a novel technique for implementing parsers in a lazy functional programming language. A packrat parser provides the power and flexibility of top-down parsing with backtracking and unlimited lookahead, but nevertheless guarantees linear parse time. Any language defined by an LL(k) or LR(k) grammar can be recognized by a packrat parser, in addition to many languages that conven...

Triangulating a simple polygon has been one of the most outstanding open problems in two-dimensional computational geometry. It is a basic primitive in computer graphics and, generally, seems the natural preprocessing step for most nontrivial operations on simple polygons [5,13]. Recall that to triangulate a polygon is t o partition it into triangles without adding any new vertices. Despite its...

The first polynomial time algorithm (O(n)) for modular decomposition appeared in 1972 [8] and since then there have been incremental improvements, eventually resulting in linear-time algorithms [22, 7, 23, 9]. Although having optimal time complexity these algorithms are quite complicated and difficult to implement. In this paper we present an easily implementable linear-time algorithm for modul...

There exists a bijection between the configuration space of a linear pentapod and all points (u,v,w, px, py, pz)∈R located on the singular quadric Γ : u2+v2+w2 = 1, where (u,v,w) determines the orientation of the linear platform and (px, py, pz) its position. Then the set of all singular robot configurations is obtained by intersecting Γ with a cubic hypersurface Σ in R6, which is only quadrati...

A simple linear loop is a simple while loop with linear assignments and linear loop guards. If a simple linear loop has only two program variables, we give a complete algorithm for computing the set of all the inputs on which the loop does not terminate. For the case of more program variables, we show that the non-termination set cannot be described by Tarski formulae in general.