Abstract: Let G = (V,E) be a connected graph and distance
between any two vertices a and b in G is a−b geodesic and is denoted
by d(a, b). A set of vertices W resolves a graph G if each vertex is
uniquely determined by its vector of distances to the vertices in W.
A metric dimension of G is the minimum cardinality of a resolving
set of G. In this paper line graph of honeycomb network has been
derived and then we calculated the metric dimension on line graph
of honeycomb network.
Abstract: The P300 from Event related potential (ERP) explains the psycho-physiological phenomenon in human body. The present study aims to identify the differences of amplitude and latency of P300 component from auditory stimuli, between ambiversion and extraversion types of personality. Ambivert (N=20) and extravert (N=20) undergoing ERP recording at the Hospital Universiti Sains Malaysia (HUSM) laboratory. Electroencephalogram data was recorded with oddball paradigm, counting auditory standard and target tones, from nine electrode sites (Fz, Cz, Pz, T3, T4, T5, T6, P3 and P4) by using the 128 HydroCel Geodesic Sensor Net. The P300 latency of the target tones at all electrodes were insignificant. Similarly, the P300 latency of the standard tones were also insignificant except at Fz and T3 electrode. Likewise, the P300 amplitude of the target and standard tone in all electrode sites were insignificant. Extravert and ambivert indicate similar characteristic in cognition processing from auditory task.
Abstract: In this paper, we present an application of Riemannian
geometry for processing non-Euclidean image data. We consider the
image as residing in a Riemannian manifold, for developing a new
method to brain edge detection and brain extraction. Automating this
process is a challenge due to the high diversity in appearance brain
tissue, among different patients and sequences. The main contribution, in this paper, is the use of an edge-based
anisotropic diffusion tensor for the segmentation task by integrating
both image edge geometry and Riemannian manifold (geodesic,
metric tensor) to regularize the convergence contour and extract
complex anatomical structures. We check the accuracy of the
segmentation results on simulated brain MRI scans of single
T1-weighted, T2-weighted and Proton Density sequences. We
validate our approach using two different databases: BrainWeb
database, and MRI Multiple sclerosis Database (MRI MS DB). We
have compared, qualitatively and quantitatively, our approach with
the well-known brain extraction algorithms. We show that using
a Riemannian manifolds to medical image analysis improves the
efficient results to brain extraction, in real time, outperforming the
results of the standard techniques.
Abstract: In this paper, we present a comparative study of three
methods of 2D face recognition system such as: Iso-Geodesic Curves
(IGC), Geodesic Distance (GD) and Geodesic-Intensity Histogram
(GIH). These approaches are based on computing of geodesic
distance between points of facial surface and between facial curves.
In this study we represented the image at gray level as a 2D surface in
a 3D space, with the third coordinate proportional to the intensity
values of pixels. In the classifying step, we use: Neural Networks
(NN), K-Nearest Neighbor (KNN) and Support Vector Machines
(SVM). The images used in our experiments are from two wellknown
databases of face images ORL and YaleB. ORL data base was
used to evaluate the performance of methods under conditions where
the pose and sample size are varied, and the database YaleB was used
to examine the performance of the systems when the facial
expressions and lighting are varied.
Abstract: The purpose of this paper is to give a combinatorial characterization and construct representations of the chaotic fundamental groups of the chaotic submanifolds of chaotic flat space by using some geometrical transformations. The chaotic homotopy groups of the limit folding for chaotic flat space are presented. The chaotic fundamental groups of some types of chaotic geodesics in chaotic flat space are deduced.
Abstract: In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus.
Abstract: The distance between two objects is an important
problem in CAGD, CAD and CG etc. It will be presented in this paper
that a simple and quick method to estimate the distance between a
point and a Bezier curve on a Bezier surface.
Abstract: We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, and that enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. Unlike most methods that incorporate global information, the proposed approach automatically handles non-convexity of the data manifold. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data.
Abstract: The class of geometric deformable models, so-called
level sets, has brought tremendous impact to medical imagery. In
this paper we present yet another application of level sets to medical
imaging. The method we give here will in a way modify the speed
term in the standard level sets equation of motion. To do so we
build a potential based on the distance and the gradient of the
image we study. In turn the potential gives rise to the force field:
F~F(x, y) = P
∀(p,q)∈I
((x, y) - (p, q)) |ÔêçI(p,q)|
|(x,y)-(p,q)|
2 . The direction
and intensity of the force field at each point will determine the
direction of the contour-s evolution. The images we used to test
our method were produced by the Univesit'e de Sherbrooke-s PET
scanners.
Abstract: The analytical solutions for geodesic acoustic
eigenmodes in tokamak plasmas with circular concentric magnetic
surfaces are found. In the frame of ideal magnetohydrodynamics the
dispersion relation taking into account the toroidal coupling between
electrostatic perturbations and electromagnetic perturbations with
poloidal mode number |m| = 2 is derived. In the absence of such
a coupling the dispersion relation gives the standard continuous
spectrum of geodesic acoustic modes. The analysis of the existence
of global eigenmodes for plasma equilibria with both off-axis
and on-axis maximum of the local geodesic acoustic frequency is
performed.
Abstract: In this paper, we studied some properties of geodesic on some open surfaces: Hyperboloid, Paraboloid and Funnel Surface. Geodesic equation in the v-Clairaut parameterization was calculated and reduced to definite integral. Some geodesics on some open surfaces as mention above were classified by Clairaut's relation.
Abstract: It is an important problem to compute the geodesics on
a surface in many fields. To find the geodesics in practice, however,
the traditional discrete algorithms or numerical approaches can only
find a list of discrete points. The first author proposed in 2010 a new,
elegant and accurate method, the geodesic-like method, for
approximating geodesics on a regular surface. This paper will present
by use of this method a computation of the Bezier geodesic-like curves
on spheres.
Abstract: Earlier studies in kinship networks have primarily
focused on observing the social relationships existing between family
relatives. In this study, we pre-identified hubs in the network to
investigate if they could play a catalyst role in the transfer of physical
information. We conducted a case study of a ceremony performed in
one of the families of a small Hindu community – the Uttar Rarhi
Kayasthas. Individuals (n = 168) who resided in 11 geographically
dispersed regions were contacted through our hub-based
representation. We found that using this representation, over 98% of
the individuals were successfully contacted within the stipulated
period. The network also demonstrated a small-world property, with
an average geodesic distance of 3.56.
Abstract: This paper proposes a method to improve the shortest
path problem on a NURBS (Non-uniform rational basis spline) surfaces.
It comes from an application of the theory in classic differential
geometry on surfaces and can improve the distance problem not only
on surfaces but in the Euclidean 3-space R3 .
Abstract: The topic of surface flattening plays a vital role in the field of computer aided design and manufacture. Surface flattening enables the production of 2D patterns and it can be used in design and manufacturing for developing a 3D surface to a 2D platform, especially in fashion design. This study describes surface flattening based on minimum energy methods according to the property of different fabrics. Firstly, through the geometric feature of a 3D surface, the less transformed area can be flattened on a 2D platform by geodesic. Then, strain energy that has accumulated in mesh can be stably released by an approximate implicit method and revised error function. In some cases, cutting mesh to further release the energy is a common way to fix the situation and enhance the accuracy of the surface flattening, and this makes the obtained 2D pattern naturally generate significant cracks. When this methodology is applied to a 3D mannequin constructed with feature lines, it enhances the level of computer-aided fashion design. Besides, when different fabrics are applied to fashion design, it is necessary to revise the shape of a 2D pattern according to the properties of the fabric. With this model, the outline of 2D patterns can be revised by distributing the strain energy with different results according to different fabric properties. Finally, this research uses some common design cases to illustrate and verify the feasibility of this methodology.