The classical clique tree approach to chordal graphs (and, more recently, to strongly chordal graphs) can be generalized to show a common structure for other classes of graphs, including clique graphs of chordal graphs, outerplanar graphs, distance-hereditary graphs, and chordal bipartite graphs. c © 2003 Elsevier B.V. All rights reserved.

A C♯ implementation of a generalized k-means variant called relational k-means is described here. Relational k-means is a generalization of the well-known k-means clustering method which works for non-Euclidean scenarios as well. The input is an arbitrary distance matrix, as opposed to the traditional k-means method, where the clustered objects need to be identified with vectors.

Configuration space (C-space) plays an important role not only in motion planning but also in geometric modeling, shape and kinematic reasoning, and is fundamental to several basic geometric operations, such as continuous collision detection and generalized penetration depth estimation, that also find their applications in motion planning, animation and simulation. In this paper, we developed a...

We consider certain spaces of linear signals equipped with a standard prefix relation and a suitably defined generalized distance function. We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and prove a representation theorem stating that every generalized ultrametric semilattice with a totally ordered distance set is isomorphic to a space of th...

a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

A new method for simulating the folding process of a protein is reported. The method is based on the essential dynamics sampling technique. In essential dynamics sampling, a usual molecular dynamics simulation is performed, but only those steps, not increasing the distance from a target structure, are accepted. The distance is calculated in a configurational subspace defined by a set of general...

In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations. 2010 MSC: 14M25, 14G50,...