In this paper we investigate the combinatorial complexity of an algorithm to determine the geometry and the topology related to an arrangement of hyperplanes in multi-dimensional Euclidean space from the “probing” on the arrangement. The “probing” by a flat means the operation from which we can obtain the intersection of the flat and the arrangement. For a finite set H of hyperplanes in Ed, we ...

Ghosh [2,3 j has introduced a very economic method of organizing records in an information retrieval system : the records relevant to a query are stored in consecutive locations and cne location may be significant for several queries (see also Ghosh [5], Lipski [7] and Lipski and Marek [S]). Thus, the record sets corresponding to queries form overlapping segments in storage. In general, repetit...

To every affine real arrangement of hyperplanes AR we associate a family of diagrams of spaces over the face poset of the arrangement. We show that any cover of the complement of the complexification of AR is homotopy equivalent to the homotopy colimit of one of the diagrams. More precisely, we show that any cover of the Salvetti complex is isomorphic to the order complex of the poset limit of ...

Introduction: Non-linear local gradients have been introduced for high-magnetic fields to alleviate problems arising from fast gradient switching and resulting peripheral nerve stimulation [1]. This work is focused on the implementation of a selfconstructed four-channel phased-array coil for multi-parallel PatLoc imaging to study the non-linear geometry of these fields under realistic condition...

We consider a natural analogue of the graph linear arrangement problem for posets. Let P = (X,≺) be a poset that is not an antichain, and let : X → [n] be an order-preserving bijection, that is, a linear extension of P . For any relation a ≺ b of P , the distance between a and b in is (b)− (a). The average relational distance of , denoted distP ( ), is the average of these distances over all re...

The "inflammatory linear verrucous epidermal nevus" is a rare disease, consisting of hyperplasia of the normal components of the epidermis. Its clinical features include erythematous and hyperkeratosic, warty, sometimes psoriasiform or lichenoid patches with a typical linear arrangement. At present, there are no effective medical therapies available. Currently, the best therapeutic results are ...

We consider the Minimum Linear Arrangement problem and the (Uniform) Sparsest Cut problem. So far, these two notorious NP-hard graph problems have resisted all attempts to prove inapproximability results. We show that they have no polynomial time approximation scheme, unless NP-complete problems can be solved in randomized subexponential time. Furthermore, we show that the same techniques can b...

Parallel mechanisms driven by fixed linear actuators promise high speed and high output, thanks to lightweight movable parts. Several types of mechanism applying this mechanical principle are already known. Although these have different methods of actuator arrangement, they may be considered the same mechanism since they can be treated using the same kinematics. However, it is not known how the...

Divide-and-conquer approximation algorithms for vertex ordering problems partition the vertex set of graphs, compute recursively an ordering of each part, and “glue” the orderings of the parts together. The computed ordering is specified by a decomposition tree that describes the recursive partitioning of the subproblems. At each internal node of the decomposition tree, there is a degree of fre...