Witness (Delaunay) Graphs

Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome with suitable generalizations. We introduce a generalization, witness graphs, that encompasses both the goal of more power and flexibility for graph drawing issues and a wider spectrum for neighborhood analysis. We study in detail two concrete examples, both related to Delaunay graphs, and consider as well some problems on stabbing geometric objects and point set discrimination, that can be naturally described in terms of witness graphs.Comment: 27 pages. JCCGG 200

Extended high dimensional indexing approach for reachability queries on very large graphs

Given a directed acyclic graph G = (V,A) and two vertices u, v ∈ V , the reachability problem is to answer if there is a path from u to v in the graph. In the context of very large graphs, with millions of vertices and a series of queries to be answered, it is not practical to search the graph for each query. On the other hand, the storage of the full transitive closure of the graph is also impractical due to its O(|V |2) size. Scalable approaches aim to create indices used to prune the search during its execution. Negative indices may be able to determine (in constant time) that a query has a negative answer while positive indices may determine (again in constant time) that a query has a positive answer. In this paper we propose novel scalable approach called LYNX that uses a large number of topological sorts of G as a negative cut index without degrading the query time. A similar strategy is applied regarding a positive cut index. In addition, LYNX proposes a user-defined index size that enables the user to control the ratio between negative and positive cuts depending on the expected query pattern. We show by computational experiments that LYNX consistently outperforms the state-of-the-art approach in terms of query-time using the same index-size for graphs with high reachability ratio. In intelligent computer systems that rely on frequent tests of connectivity in graphs, LYNX can reduce the time delay experience by end users through a reduced query time. This comes at the expense of an increased setup time whenever the underlying graph is updated. Keywords: directed acyclic graphs, topological sorts, reachability queries, graph indexingpublishedVersio

Acoustic interactions between an altitude test facility and jet engine plumes: Theory and experiments

The overall objective of the described effort was to develop an understanding of the physical mechanisms involved in the flow/acoustic interactions experienced in full-scale altitude engine test facilities. This is done by conducting subscale experiments and through development of a theoretical model. Model cold jet experiments with an axisymmetric convergent nozzle are performed in a test setup that stimulates a supersonic jet exhausting into a cylindrical diffuser. The measured data consist of detailed flow visualization data and acoustic spectra for a free and a ducted plume. It is shown that duct resonance is most likely responsible by theoretical calculations. Theoretical calculations also indicate that the higher discrete tones observed in the measurements are related to the screech phenomena. Limited experiments on the sensitivity of a free 2-D, C-D nozzle to externally imposed sound are also presented. It is shown that a 2-D, C-D nozzle with a cutback is less excitable than a 2-D C-D nozzle with no cutback. At a pressure ratio of 1.5 unsteady separation from the diverging walls of the nozzle is noticed. This separation switches from one wall to the opposite wall thus providing an unsteady deflection of the plume. It is shown that this phenomenon is related to the venting provided by the cutback section

Early experience, binocular competition, and the sculpting of relay cell morphology in the cat lateral geniculate nucleus

Perturbations of early visual experience imposed by either monocular deprivation (MD) or artificially induced strabismus (squint) affect the morphological development of cells in the lateral geniculate nucleus (LGN) of cats. These morphological anomalies are thought to arise from competitive mechanisms which control many features of LGN cell development. Competition between the axon terminals of LGN cells innervated by the right and left eyes for establishing and maintaining synaptic contacts with cells in the visual cortex (i.e., binocular competition) is known to be a very important mechanism for controlling the development of LGN cells. Much of our present understanding regarding the importance of binocular competition is based on the effects of MD and squint on LGN somata. The objective of the present study was to further explore the role of binocular competition in the somatic development of LGN cells and extend these observations to determine the role of binocular competition in the dendritic development of LGN cells. Binocular competition was eliminated in some of the animals reared with either MD or squint by concomitant sagittal transection of the optic chiasm (OX), performed on either postnatal day 27 or 28

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group