282 research outputs found
Macropolyhedral boron-containing cluster chemistry: two-electron variations in intercluster bonding intimacy. Contrasting structures of 19-vertex [(eta(5)-C5Me5)HIrB18H19(PHPh2)] and [(eta(5) -C5Me5)IrB18H18(PH2Ph)]
Fused double-cluster [(5-C5Me5)IrB18H18(PH2Ph)]8, from syn-[(5-C5Me5)IrB18H20] 1 and PH2Ph, retains the three-atoms-in-common cluster fusion intimacy of 1, in contrast to [(5-C5Me5)HIrB18H19(PHPh2)]6, from PHPh2 with 1, which exhibits an opening to a two atoms-in-common cluster fusion intimacy. Compound 8 forms via spontaneous dihydrogen loss from its precursor [(5-C5Me5)HIrB18H19(PH2Ph)]7, which has two-atoms-in-common cluster-fusion intimacy and is structurally analogous to 6
A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem
The clustered planarity problem (c-planarity) asks whether a hierarchically
clustered graph admits a planar drawing such that the clusters can be nicely
represented by regions. We introduce the cd-tree data structure and give a new
characterization of c-planarity. It leads to efficient algorithms for
c-planarity testing in the following cases. (i) Every cluster and every
co-cluster (complement of a cluster) has at most two connected components. (ii)
Every cluster has at most five outgoing edges.
Moreover, the cd-tree reveals interesting connections between c-planarity and
planarity with constraints on the order of edges around vertices. On one hand,
this gives rise to a bunch of new open problems related to c-planarity, on the
other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure
Three-dimensional reconstruction from projections
summary:Computerized tomograhphy is a technique for computation and visualization of density (i.e. X- or -ray absorption coefficients) distribution over a cross-sectional anatomic plane from a set of projections. Three-dimensional reconstruction may be obtained by using a system of parallel planes.
For the reconstruction of the transverse section it is necessary to choose an appropriate method taking into account the geometry of the data collection, the noise in projection data, the amount of data, the computer power available, the accuracy required etc.
In the paper the theory related to the convolution reconstruction methods is reviewed. The principal contribution consists in the exact mathematical treatment of Radon's inverse transform based on the concepts of the regularization of a function and the generalized function. This approach naturally leads to the employment of the generalized Fourier transform. Reconstructions using simulated projection data are presented for both the parallel and divergent-ray collection geometries
The Minimum Shared Edges Problem on Grid-like Graphs
We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide
whether it is possible to route paths from a start vertex to a target
vertex in a given graph while using at most edges more than once. We show
that MSE can be decided on bounded (i.e. finite) grids in linear time when both
dimensions are either small or large compared to the number of paths. On
the contrary, we show that MSE remains NP-hard on subgraphs of bounded grids.
Finally, we study MSE from a parametrised complexity point of view. It is known
that MSE is fixed-parameter tractable with respect to the number of paths.
We show that, under standard complexity-theoretical assumptions, the problem
parametrised by the combined parameter , , maximum degree, diameter, and
treewidth does not admit a polynomial-size problem kernel, even when restricted
to planar graphs
A new multi-center approach to the exchange-correlation interactions in ab initio tight-binding methods
A new approximate method to calculate exchange-correlation contributions in
the framework of first-principles tight-binding molecular dynamics methods has
been developed. In the proposed scheme on-site (off-site) exchange-correlation
matrix elements are expressed as a one-center (two-center) term plus a {\it
correction} due to the rest of the atoms. The one-center (two-center) term is
evaluated directly, while the {\it correction} is calculated using a variation
of the Sankey-Niklewski \cite{Sankey89} approach generalized for arbitrary
atomic-like basis sets. The proposed scheme for exchange-correlation part
permits the accurate and computationally efficient calculation of corresponding
tight-binding matrices and atomic forces for complex systems. We calculate bulk
properties of selected transition (W,Pd), noble (Au) or simple (Al) metals, a
semiconductor (Si) and the transition metal oxide Ti with the new method
to demonstrate its flexibility and good accuracy.Comment: 17 pages, 5 figure
Hierarchical Partial Planarity
In this paper we consider graphs whose edges are associated with a degree of
{\em importance}, which may depend on the type of connections they represent or
on how recently they appeared in the scene, in a streaming setting. The goal is
to construct layouts of these graphs in which the readability of an edge is
proportional to its importance, that is, more important edges have fewer
crossings. We formalize this problem and study the case in which there exist
three different degrees of importance. We give a polynomial-time testing
algorithm when the graph induced by the two most important sets of edges is
biconnected. We also discuss interesting relationships with other
constrained-planarity problems.Comment: Conference version appeared in WG201
Planar Octilinear Drawings with One Bend Per Edge
In octilinear drawings of planar graphs, every edge is drawn as an
alternating sequence of horizontal, vertical and diagonal ()
line-segments. In this paper, we study octilinear drawings of low edge
complexity, i.e., with few bends per edge. A -planar graph is a planar graph
in which each vertex has degree less or equal to . In particular, we prove
that every 4-planar graph admits a planar octilinear drawing with at most one
bend per edge on an integer grid of size . For 5-planar
graphs, we prove that one bend per edge still suffices in order to construct
planar octilinear drawings, but in super-polynomial area. However, for 6-planar
graphs we give a class of graphs whose planar octilinear drawings require at
least two bends per edge
Bipartite Entanglement in Continuous-Variable Cluster States
We present a study of the entanglement properties of Gaussian cluster states,
proposed as a universal resource for continuous-variable quantum computing. A
central aim is to compare mathematically-idealized cluster states defined using
quadrature eigenstates, which have infinite squeezing and cannot exist in
nature, with Gaussian approximations which are experimentally accessible.
Adopting widely-used definitions, we first review the key concepts, by
analysing a process of teleportation along a continuous-variable quantum wire
in the language of matrix product states. Next we consider the bipartite
entanglement properties of the wire, providing analytic results. We proceed to
grid cluster states, which are universal for the qubit case. To extend our
analysis of the bipartite entanglement, we adopt the entropic-entanglement
width, a specialized entanglement measure introduced recently by Van den Nest M
et al., Phys. Rev. Lett. 97 150504 (2006), adapting their definition to the
continuous-variable context. Finally we add the effects of photonic loss,
extending our arguments to mixed states. Cumulatively our results point to key
differences in the properties of idealized and Gaussian cluster states. Even
modest loss rates are found to strongly limit the amount of entanglement. We
discuss the implications for the potential of continuous-variable analogues of
measurement-based quantum computation.Comment: 22 page
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