522 research outputs found
Rigid ball-polyhedra in Euclidean 3-space
A ball-polyhedron is the intersection with non-empty interior of finitely
many (closed) unit balls in Euclidean 3-space. One can represent the boundary
of a ball-polyhedron as the union of vertices, edges, and faces defined in a
rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at
every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a
standard ball-polyhedron if its vertex-edge-face structure is a lattice (with
respect to containment). To each edge of a ball-polyhedron one can assign an
inner dihedral angle and say that the given ball-polyhedron is locally rigid
with respect to its inner dihedral angles if the vertex-edge-face structure of
the ball-polyhedron and its inner dihedral angles determine the ball-polyhedron
up to congruence locally. The main result of this paper is a Cauchy-type
rigidity theorem for ball-polyhedra stating that any simple and standard
ball-polyhedron is locally rigid with respect to its inner dihedral angles.Comment: 11 pages, 2 figure
Contact numbers for congruent sphere packings in Euclidean 3-space
Continuing the investigations of Harborth (1974) and the author (2002) we
study the following two rather basic problems on sphere packings. Recall that
the contact graph of an arbitrary finite packing of unit balls (i.e., of an
arbitrary finite family of non-overlapping unit balls) in Euclidean 3-space is
the (simple) graph whose vertices correspond to the packing elements and whose
two vertices are connected by an edge if the corresponding two packing elements
touch each other. One of the most basic questions on contact graphs is to find
the maximum number of edges that a contact graph of a packing of n unit balls
can have in Euclidean 3-space. Our method for finding lower and upper estimates
for the largest contact numbers is a combination of analytic and combinatorial
ideas and it is also based on some recent results on sphere packings. Finally,
we are interested also in the following more special version of the above
problem. Namely, let us imagine that we are given a lattice unit sphere packing
with the center points forming the lattice L in Euclidean 3-space (and with
certain pairs of unit balls touching each other) and then let us generate
packings of n unit balls such that each and every center of the n unit balls is
chosen from L. Just as in the general case we are interested in finding good
estimates for the largest contact number of the packings of n unit balls
obtained in this way.Comment: 18 page
Noise-robust method for image segmentation
Segmentation of noisy images is one of the most challenging problems in image analysis and any improvement of segmentation methods can highly influence the performance of many image processing applications. In automated image segmentation, the fuzzy c-means (FCM) clustering has been widely used because of its ability to model uncertainty within the data, applicability to multi-modal data and fairly robust behaviour. However, the standard FCM algorithm does not consider any information about the spatial linage context and is highly sensitive to noise and other imaging artefacts. Considering above mentioned problems, we developed a new FCM-based approach for the noise-robust fuzzy clustering and we present it in this paper. In this new iterative algorithm we incorporated both spatial and feature space information into the similarity measure and the membership function. We considered that spatial information depends on the relative location and features of the neighbouring pixels. The performance of the proposed algorithm is tested on synthetic image with different noise levels and real images. Experimental quantitative and qualitative segmentation results show that our method efficiently preserves the homogeneity of the regions and is more robust to noise than other FCM-based methods
Pixel and Voxel Representations of Graphs
We study contact representations for graphs, which we call pixel
representations in 2D and voxel representations in 3D. Our representations are
based on the unit square grid whose cells we call pixels in 2D and voxels in
3D. Two pixels are adjacent if they share an edge, two voxels if they share a
face. We call a connected set of pixels or voxels a blob. Given a graph, we
represent its vertices by disjoint blobs such that two blobs contain adjacent
pixels or voxels if and only if the corresponding vertices are adjacent. We are
interested in the size of a representation, which is the number of pixels or
voxels it consists of.
We first show that finding minimum-size representations is NP-complete. Then,
we bound representation sizes needed for certain graph classes. In 2D, we show
that, for -outerplanar graphs with vertices, pixels are
always sufficient and sometimes necessary. In particular, outerplanar graphs
can be represented with a linear number of pixels, whereas general planar
graphs sometimes need a quadratic number. In 3D, voxels are
always sufficient and sometimes necessary for any -vertex graph. We improve
this bound to for graphs of treewidth and to
for graphs of genus . In particular, planar graphs
admit representations with voxels
Locked and Unlocked Chains of Planar Shapes
We extend linkage unfolding results from the well-studied case of polygonal
linkages to the more general case of linkages of polygons. More precisely, we
consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are
hinged together sequentially at rotatable joints. Our goal is to characterize
the families of planar shapes that admit locked chains, where some
configurations cannot be reached by continuous reconfiguration without
self-intersection, and which families of planar shapes guarantee universal
foldability, where every chain is guaranteed to have a connected configuration
space. Previously, only obtuse triangles were known to admit locked shapes, and
only line segments were known to guarantee universal foldability. We show that
a surprisingly general family of planar shapes, called slender adornments,
guarantees universal foldability: roughly, the distance from each edge along
the path along the boundary of the slender adornment to each hinge should be
monotone. In contrast, we show that isosceles triangles with any desired apex
angle less than 90 degrees admit locked chains, which is precisely the
threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof
details. (Fixed crash-induced bugs in the abstract.
Autonomous clustering using rough set theory
This paper proposes a clustering technique that minimises the need for subjective
human intervention and is based on elements of rough set theory. The proposed algorithm is
unified in its approach to clustering and makes use of both local and global data properties to
obtain clustering solutions. It handles single-type and mixed attribute data sets with ease and
results from three data sets of single and mixed attribute types are used to illustrate the
technique and establish its efficiency
Regular packings on periodic lattices
We investigate the problem of packing identical hard objects on regular
lattices in d dimensions. Restricting configuration space to parallel alignment
of the objects, we study the densest packing at a given aspect ratio X. For
rectangles and ellipses on the square lattice as well as for biaxial ellipsoids
on a simple cubic lattice, we calculate the maximum packing fraction \phi_d(X).
It is proved to be continuous with an infinite number of singular points X^{\rm
min}_\nu, X^{\rm max}_\nu, \nu=0, \pm 1, \pm 2,... In two dimensions, all
maxima have the same height, whereas there is a unique global maximum for the
case of ellipsoids. The form of \phi_d(X) is discussed in the context of
geometrical frustration effects, transitions in the contact numbers and number
theoretical properties. Implications and generalizations for more general
packing problems are outlined.Comment: 5 pages, 4 figures, accepted for publication in Physical Review
Letter
Sybil tolerance and probabilistic databases to compute web services trust
© Springer International Publishing Switzerland 2015. This paper discusses how Sybil attacks can undermine trust management systems and how to respond to these attacks using advanced techniques such as credibility and probabilistic databases. In such attacks end-users have purposely different identities and hence, can provide inconsistent ratings over the same Web Services. Many existing approaches rely on arbitrary choices to filter out Sybil users and reduce their attack capabilities. However this turns out inefficient. Our approach relies on non-Sybil credible users who provide consistent ratings over Web services and hence, can be trusted. To establish these ratings and debunk Sybil users techniques such as fuzzy-clustering, graph search, and probabilistic databases are adopted. A series of experiments are carried out to demonstrate robustness of our trust approach in presence of Sybil attacks
Prioritization of the launch of ICT products and services through linguistic multi-criteria decision-making
The market launch of new products and services is a basic pillar for large and medium-sized companies in the ICT (Information and Communications Technology) sector. Choosing the right moment for it is usually a differentiating factor in terms of competition, since it is a source of competitive advantage. There are several mechanisms and strategies to address this problem from the market perspective. However, the criteria of the different actors involved – managers, sales representatives, experts, etc. – coexist in the corporate sphere and they often differ, causing difficulties in priority setting processes in the launch of a product or service. The assessment of the prioritization of these criteria is usually expressed in natural language, thus adding a great deal of uncertainty. Fuzzy linguistic models have proved to be an efficient tool for managing the intrinsic uncertainty of this type of information. This paper presents a linguistic multi-criteria decision-making model, able to reconcile the different requirements and viewpoints existing in the corporate sector when planning the launch of new products and services. The proposed model is based on the fuzzy 2-tuple linguistic model, aimed at managing linguistic data expressing different corporate criteria, without compromising accuracy in the calculation of said data. In order to illustrate this, a practical case study is presented, in which the model is applied for scheduling the launch prioritization of several new products and services by a telecommunications company, within the deadlines set in its strategic planning.The authors would like to acknowledge the financial support received from the European Regional Development Fund (ERDF) for the Research Projects TIN2016-75850-R, TIN2016-79484-R and TIN2013-40658-P
Evidential Clustering: A Review
International audienceIn evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibilistic and rough partitions, which are recovered as special cases. Three algorithms to generate a credal partition are reviewed. Each of these algorithms is shown to implement a decision-directed clustering strategy. Their relative merits are discussed
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