254 research outputs found
Star Structure Connectivity of Folded hypercubes and Augmented cubes
The connectivity is an important parameter to evaluate the robustness of a
network. As a generalization, structure connectivity and substructure
connectivity of graphs were proposed. For connected graphs and , the
-structure connectivity (resp. -substructure connectivity
) of is the minimum cardinality of a set of subgraphs
of that each is isomorphic to (resp. to a connected subgraph of ) so
that is disconnected or the singleton. As popular variants of hypercubes,
the -dimensional folded hypercubes and augmented cubes are
attractive interconnected network prototypes for multiple processor systems. In
this paper, we obtain that
for , , and
for
The star-structure connectivity and star-substructure connectivity of hypercubes and folded hypercubes
As a generalization of vertex connectivity, for connected graphs and ,
the -structure connectivity (resp. -substructure
connectivity ) of is the minimum cardinality of a set of
subgraphs of that each is isomorphic to (resp. to a connected
subgraph of ) so that is disconnected. For -dimensional hypercube
, Lin et al. [6] showed
and
for
and . Sabir et al. [11] obtained that
for
, and for -dimensional folded hypercube ,
,
with and . They proposed an open problem of
determining -structure connectivity of and for general
. In this paper, we obtain that for each integer ,
and
for all integers larger than in quare scale. For , we
separately confirm the above result holds for in the remaining cases
Defect-induced fracture topologies in Al<sub>2</sub>O<sub>3</sub> ceramic-graphene nanocomposites
Models of ceramic-graphene nanocomposites are used to study how the manufacturing process-dependent arrangement of reduced graphene oxide (rGO) inclusions governs nano-crack network development. The work builds upon recent studies of such composites where a novel combinatorial approach was used to investigate the effect of rGO arrangements on electrical conductivity and porosity. This approach considers explicitly the discrete structure of the composite and represents it as a collection of entities of different dimensions - grains, grain boundaries, triple junctions, and quadruple points. Here, the combinatorial approach is developed further by considering the effects of rGO agglomerations, stress concentrators and adhesion energies on intergranular cracking. The results show that the fracture networks can be effectively controlled by the local ordering of rGO inclusions to allow for a concurrent increase in the strength and conductivity of the ceramic composites. It is shown that the ratio of local stress concentrators related to rGO inclusions and cracks is the most significant factor affecting the nano-crack network topology. The local spatial arrangement of rGO inclusions becomes an effective tool for controlling nano-crack network topology only when this ratio approaches one. It is anticipated that these results will inform future design of toughness-enhanced composites
Sequence-structure relations of pseudoknot RNA
<p>Abstract</p> <p>Background</p> <p>The analysis of sequence-structure relations of RNA is based on a specific notion and folding of RNA structure. The notion of coarse grained structure employed here is that of canonical RNA pseudoknot contact-structures with at most two mutually crossing bonds (3-noncrossing). These structures are folded by a novel, <it>ab initio </it>prediction algorithm, cross, capable of searching all 3-noncrossing RNA structures. The algorithm outputs the minimum free energy structure.</p> <p>Results</p> <p>After giving some background on RNA pseudoknot structures and providing an outline of the folding algorithm being employed, we present in this paper various, statistical results on the mapping from RNA sequences into 3-noncrossing RNA pseudoknot structures. We study properties, like the fraction of pseudoknot structures, the dominant pseudoknot-shapes, neutral walks, neutral neighbors and local connectivity. We then put our results into context of molecular evolution of RNA.</p> <p>Conclusion</p> <p>Our results imply that, in analogy to RNA secondary structures, 3-noncrossing pseudoknot RNA represents a molecular phenotype that is well suited for molecular and in particular neutral evolution. We can conclude that extended, percolating neutral networks of pseudoknot RNA exist.</p
Self-assembly in polyoxometalate and metal coordination-based systems: synthetic approaches and developments
Utilizing new experimental approaches and gradual understanding of the underlying chemical processes has led to advances in the self-assembly of inorganic and metalâorganic compounds at a very fast pace over the last decades. Exploitation of unveiled information originating from initial experimental observations has sparked the development of new families of compounds with unique structural characteristics and functionalities. The main source of inspiration for numerous research groups originated from the implementation of the design element along with the discovery of new chemical components which can self-assemble into complex structures with wide range of sizes, topologies and functionalities. Not only do self-assembled inorganic and metalâorganic chemical systems belong to families of compounds with configurable structures, but also have a vast array of physical properties which reflect the chemical information stored in the various âmodularâ molecular subunits. The purpose of this short review article is not the exhaustive discussion of the broad field of inorganic and metalâorganic chemical systems, but the discussion of some representative examples from each category which demonstrate the implementation of new synthetic approaches and design principles
From surfaces to objects : Recognizing objects using surface information and object models.
This thesis describes research on recognizing partially obscured objects using
surface information like Marr's 2D sketch ([MAR82]) and surface-based geometrical
object models. The goal of the recognition process is to produce a fully
instantiated object hypotheses, with either image evidence for each feature or
explanations for their absence, in terms of self or external occlusion.
The central point of the thesis is that using surface information should be
an important part of the image understanding process. This is because surfaces
are the features that directly link perception to the objects perceived (for
normal "camera-like" sensing) and because surfaces make explicit information
needed to understand and cope with some visual problems (e.g. obscured features).
Further, because surfaces are both the data and model primitive, detailed
recognition can be made both simpler and more complete.
Recognition input is a surface image, which represents surface orientation and
absolute depth. Segmentation criteria are proposed for forming surface patches
with constant curvature character, based on surface shape discontinuities which
become labeled segmentation- boundaries.
Partially obscured object surfaces are reconstructed using stronger surface based
constraints. Surfaces are grouped to form surface clusters, which are 3D
identity-independent solids that often correspond to model primitives. These are
used here as a context within which to select models and find all object features.
True three-dimensional properties of image boundaries, surfaces and surface
clusters are directly estimated using the surface data.
Models are invoked using a network formulation, where individual nodes
represent potential identities for image structures. The links between nodes are
defined by generic and structural relationships. They define indirect evidence relationships
for an identity. Direct evidence for the identities comes from the data
properties. A plausibility computation is defined according to the constraints inherent
in the evidence types. When a node acquires sufficient plausibility, the
model is invoked for the corresponding image structure.Objects are primarily represented using a surface-based geometrical model.
Assemblies are formed from subassemblies and surface primitives, which are
defined using surface shape and boundaries. Variable affixments between assemblies
allow flexibly connected objects.
The initial object reference frame is estimated from model-data surface relationships,
using correspondences suggested by invocation. With the reference
frame, back-facing, tangential, partially self-obscured, totally self-obscured and
fully visible image features are deduced. From these, the oriented model is used
for finding evidence for missing visible model features. IT no evidence is found,
the program attempts to find evidence to justify the features obscured by an unrelated
object. Structured objects are constructed using a hierarchical synthesis
process.
Fully completed hypotheses are verified using both existence and identity
constraints based on surface evidence.
Each of these processes is defined by its computational constraints and are
demonstrated on two test images. These test scenes are interesting because they
contain partially and fully obscured object features, a variety of surface and solid
types and flexibly connected objects. All modeled objects were fully identified
and analyzed to the level represented in their models and were also acceptably
spatially located.
Portions of this work have been reported elsewhere ([FIS83], [FIS85a], [FIS85b],
[FIS86]) by the author
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