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Sign language recognition (SLR) has got wide applicability. SLR system is considered to be a challenging one. This paper presents empirical analysis of different mathematical models for Pakistan SLR (PSLR). The proposed method is using the parameterization of sign signature. Each sign is represented with a mathematical function and then coefficients of these functions are used as the feature vector. This approach is based on exhaustive experimentation and analysis for getting the best suitable mathematical representation for each sign. This extensive empirical analysis, results in a very small feature vector and hence to a very efficient system. The robust proposed method has got general applicability as it just need a new training set and it can work equally good for any other dataset. Sign set used is quite complex in the sense that intersign similarity distance is very small but even then proposed methodology has given quite promising results.

There is an increasing need for high-quality software components. Reusable components and formal specifications are two complementary and promising approaches to achieve this goal. One method for enhancing the reusability of existing components is generalization that creates generic components by parameterizing specific ones. Generalization and instantiation are two methods related respectively to the development for reuse and development with reuse. Generalization, that is the abstraction of existing components, identifies commonalities across a class of entities, while instantiation customizes the general properties under different circumstances. In this paper, we present several generalization and instantiation algorithms for algebraic specifications. A major difficulty during the generalization process is determining the appropriate level of generality. Highly specific components have little chance of being reused. Meanwhile, if a component is too general, its reuse might also be hard. Therefore, we introduce a novel method based on the categorized constructors to control the level of abstraction in generic components with the goal of producing effective reusable components. Through a medium-scale example, the generalization and instantiation operations are illustrated in detail.

Parameterization approaches for non-uniform Doo-Sabin subdivision surfaces are developed in this paper using the eigenstructure of Doo-Sabin subdivision. New methods for evaluation of values and derivatives of Doo-Sabin surfaces at arbitrary parameters by means of non-iterative approaches are presented. Furthermore, generalized basis functions for non-uniform Doo-Sabin surfaces are derived. Thus, many algorithms and analysis techniques developed for parametric surfaces can be extended to Doo-Sabin surfaces.

A 1-bridge torus knot in a 3-manifold of genus ≤ 1 is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal form we give algorithms to determine the number of components and to compute the fundamental group of the complement when the normal form determines a knot. We also give a description of the double branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by using its Conway's normal form and obtain an explicit formula for the first homology of the double cover.

There are a variety of surface types (such as meshes and implicit surfaces) that lack a natural parameterization. We believe that manifolds are a natural method for representing parameterizations because of their ability to handle arbitrary topology and represent smooth surfaces. Manifolds provide a formal mechanism for creating local, overlapping parameterization and defining the functions that map between them. In this paper we present specific manifolds for several genus types (sphere, plane, n-holed tori, and cylinder) and an algorithm for establishing a bijective function between an input mesh and the manifold of the appropriate genus. This bijective function is used to define a smooth embedding of the manifold that approximates or interpolates the mesh. The smooth embedding is used to calculate analytical quantities, such as curvature and area, which can then be mapped back to the mesh.

Possible applications include texture mapping, surface fitting, arbitrary topology surface modeling, feature detection, and surface comparison.

Parameterizing a 3D triangular mesh is the process of finding an isomorphic planar mesh. It is widely used in graphics, as it is required, for instance, for surface fitting, texture mapping and re-meshing. In this paper, we present a new 3D approach to triangular mesh parameterization, which includes three steps: (1) construct a boundary polygon triangulation by mesh simplification; (2) parameterize the boundary polygon triangulation by first smoothing and then flattening it; (3) parameterize the interior vertices by parameterizing the vertex-split-cells one by one while refining the boundary polygon triangulation to the original one. The fact that all calculations are local makes it a fast approach, and the fact that a series of meshes in a multiresolution representation model could be well parameterized makes it appropriate for hierarchical surface fitting. Experiments show that the approach presented can result in a low distortion parameterization.

In this paper, we propose a new method for creating the displacement map to restore the detailed geometry from the low-level base mesh. The displacement mapping actually changes the surface geometry with the displacement information. Recent CG software can treat the displacement mapping for increasing the accuracy of the surface. We convert the displacement map to the color image that is mapped to the low-level mesh in order to utilize the displacement map by existing CG software. Because displacement information is in image format, we can compress the displacement information by any image compression technique. The load for creating the three-dimensional scene is reduced by using such a low-level mesh which has the displacement information.

We obtain the displacement information by finding the point on the input mesh corresponding to the point on the base mesh. The corresponding point is calculated by using the barycentric coordinate of the parameterized mesh. Because the mesh parameterization creates one-to-one mapping between the input mesh and the base mesh, we can avoid the problems that are caused by the traditional ray-triangle intersection method. For demonstration, we restore the detailed surface from our result by using the Blender 2.44.

It is an important way for segmentations of CT images to extract contours of objects slice-by-slice. For such a way, an important idea is analogy. That is to say, correct the contour in current slice (current contour) according to the contour in previous slice (previous contour). The key to properly correct the current contour is the ability to recognize occlusions (or say leaking parts) in the current contour. We present a curve-based curve parameterization method to recognize occlusions. The previous contour is evolved to the current contour using line projections. In the process of evolution, the parameterization is realized, which includes two types of information for every point in the evolved contour: the arc length parameter on the previous contour, and distance moved from the initial position to the present position. Using these two parameters, we are able to recognize occlusions in the current contour. Many experiments indicate that the method can recognize all of the occlusions in a given contour. Consequently, the method is robust and can be used as a part of an algorithm to automatically extract contours for CT images.

Dissipative particle dynamics (DPD) was initially used to simulate the polystyrene/nanoparticle composite microspheres (PNCM) in this paper. The coarse graining model of PNCM was established. And the DPD parameterization of the model was represented in detail. The DPD repulsion parameters were calculated from the cohesive energy density which could be calculated by amorphous modules in Materials Studio. The equilibrium configuration of the simulated PNCM shows that the nanoparticles were actually "modified" with oleic acid and the modified nanoparticles were embedded in the bulk of polystyrene. As sodium dodecyl sulfate (SDS) was located in the interface between water and polystyrene, the hydrophilic head of SDS stretched into water while the hydrophobic tailed into polystyrene. All simulated phenomena were consistent with the experimental results in preparation of polystyrene/nanoparticles composite microspheres. The effect of surface modification of nanoparticles on its dispersion in polystyrene matrix was also studied by adjusting the interaction parameters between the OA and NP beads. The final results indicated that the nanoparticles removed from the core of composite microsphere to the surface with increase of a_OA-NP. All the simulated results demonstrated that our coarse–grained model was reasonable.

Structured meshes are becoming increasingly popular as a discretization technique in industries where solution accuracy is of paramount importance. However, generating structured meshes directly on the model surface presents a challenge. Consequently, many researchers are now exploring mapping methods for structured mesh generation. In this context, parameterization algorithms are vital as they map the model surface from 3D space to a 2D parametric domain. Existing parameterization algorithms, despite their advancements, still face limitations in preserving symmetry information from the input model. To address this issue, we propose a symmetry preserving parameterization algorithm based on geometric constraint. This algorithm utilizes plane reflection symmetry transformation to identify the main symmetry plane of the model and calculate the symmetry factor. Based on the fixed points and the symmetry factor, a conformal parametric symmetry plane is obtained. Furthermore, we develop a surface structured mesh generation system to provide engineers with a tool that can rapidly generate meshes. Experimental results demonstrate that our proposed algorithm achieves higher quality results compared to other parameterization algorithms.

This paper describes a methodology translating human spatial coordination in a humanoid robots context. Once the human locomotion is captured, we highlight coordination relations describing motions. Relations and inverse kinematics are applied to a virtual humanoid, which is a tradeoff between human (anthropomorphic proportions) and robot (joints configuration). Further, we quantify all required adaptations for a real humanoid, such as scaling and equilibrium. Finally, this methodology is applied to a specific humanoid robot (called NAO) in order to illustrate and compare some preliminary results.

The weights for a finite group G with respect to a prime number p were introduced by Jon Alperin, in order to formulate his celebrated conjecture. In 1992, Everett Dade formulated a refinement of Alperin's conjecture involving ordinary irreducible characters — with their defect — and, in 2000, Geoffrey Robinson proved that the new conjecture holds for p-solvable groups. But this refinement is formulated in terms of a vanishing alternating sum, without giving any possible refinement for the weights. In this note we show that, in the case of the p-solvable finite groups, the method developed in a previous paper can be suitably refined to provide, up to the choice of a polarization ω, a natural bijection — namely compatible with the action of the group of outer automorphisms of G — between the sets of absolutely irreducible characters of G and of G-conjugacy classes of suitable inductive weights, preserving blocks and defects.

We investigate the relationship between the numbers of representations of certain integers by a primitive integral binary quadratic form $f$ of discriminant $D$ and the order of the class of $f$ in the form class group of discriminant $D$, in the case when this order is even. The explicit form of the solutions obtained is used to give a partial answer to a question regarding which multiples of $f$ can be parameterized in a particular way.

In this paper, an eco-economic model with harvesting on biological population is established, which takes the form of a differential-algebra system. The impact of the economic profit from harvesting upon the dynamics of the model is studied. By using a suitable parameterization for the differential-algebra system, we derive an equivalent parameterized system which gives the stability results for the positive equilibrium point of our model. Moreover, based on the parameterized system as well as the approaches of normal form and formal series, the conditions on the Hopf bifurcation and the stability of center are obtained. Several numerical simulations for demonstrating the theoretical results are also presented. Lastly, according to the dynamical analysis, we provide a threshold value for the economic profit, which can maintain the sustainable development of our eco-economic system.

The recent development of image analysis and visualization tools allowing explicit 3D depiction of both normal anatomy and pathology provides a powerful means to obtain morphological descriptions and characterizations. Shape analysis offers the possibility of improved sensitivity and specificity for detection and characterization of structural differences and is becoming an important tool for the analysis of medical images. It provides information about anatomical structures and disease that is not always available from a volumetric analysis. In this chapter we present our own shape analysis work directed to the study of anatomy and disease as seen on medical images. Section 2 presents a new comprehensive method to establish correspondences between morphologically different 3D objects. The correspondence mapping itself is performed in a geometry- and orientation-independent parameter space in order to establish a continuous mapping between objects. Section 3 presents a method to compute 3D skeletons robustly and show how they can be used to perform statistical analyses describing the shape changes of the human hippocampus. Section 4 presents a method to approximate individual MS lesions' 3D geometry using spherical harmonics and its application for analyzing their changes over time by quantitatively characterizing the lesion's shape and depicting patterns of shape evolution.

Let the curvature of a plane curve parametrized by arclength s be given as a function of the Cartesian co-ordinates of the points the curve is passing through in the Euclidean plane. Then, the co-ordinates of its position vector are determined by a system of equations arising from the Frenet-Serret relations that can be regarded as a dynamical system of two degrees of freedom determining the motion (trajectories) of a particle of unit mass, s playing the role of time. Here, two classes of integrable systems of the foregoing type are identified. For that purpose, we explore the variational symmetries of a generic system of this kind with respect to Lie groups of point transformations of the involved variables. As a result, a set of sufficient conditions are found which ensure that such a system possesses two functionally independent integrals of motion and, consecutively, is integrable by quadratures. In each such case, we achieve either an explicit parameterization of the corresponding trajectory curves in terms of their curvatures or, at least, a separation of the dependent variables.

The atmospheric boundary layer (ABL) is the lowest part of the atmosphere that is continuously under the influence of the underlying surfaces through mechanical (roughness and shear) and thermal effects (cooling and warming), and the overlying, more free layers. Such boundary layers and the related geophysical turbulence exist also in oceans, seas, lakes and rivers. Here we focus on those in the atmosphere; however, similar reasoning as presented here also applies to the other geophysical flows mentioned. Since most of human activities and overall life take place in the ABL, it is easy to grasp the need for an ever better understanding of the ABL: its nature, state and future evolution. In order to provide a reasonable and reliable short- or medium-range weather forecast, a decent climate scenario, or an applied micrometeorological study (for e.g. agriculture, road construction, forestry, traffic), etc., the state of the ABL and its turbulence should be properly characterized and marched forward in time in concert with the other prognostic fields. This is one of many tasks of numerical weather prediction and climate models. Many of these models have problems in handling rapid surface cooling under weak or without synoptic forcing (e.g. calm nighttime mountainous or even hilly conditions).

Overall research during the last ∼ 10 years or so, strongly suggests that the evolution of the stable ABL is still poorly understood today. There we make a contribution by assessing some recent advances in the understanding of nature, theory and modeling of the stable ABL (SABL). In particular, we address inclined very (or strongly) stratified SABL in more details. We show that a relatively thin and very SABL, as recently modeled using an improved “z-less” mixing length scale, can be successfully treated nowadays; the result is quietly extended to other types of the SABL. Finally, a new generalized “z-less” mixing length-scale is proposed. At the same time, no major improvements in modeling weak-wind strongly-stable ABL is reported yet.

The work presented here focus on humanoid walking. More precisely we deliberately divide the control architecture in two distinct parts, coordination and stability. The goal is to design robot coordination mimicking the human one, by reducing the latter’s complexity to a minimal set of relations. In our previous work, polynomial approximations were done and implemented into a kinematic simulation of an anthropomorphic humanoid model. This simulation showed smooth biomimetic walking at different speeds. This paper presents the real-world implementation of our methodology using the humanoid robot NAO. The results are promising for applying this entire work on more complex humanoid robots, other gaits, and gait transitions.

Based on the principle of heat transfer theory, mathematical model of steady-state thermal analysis of the gear is created and the boundary conditions is analyzed, furthermore, steady temperature field of a pair of meshed driving and driven gear is calculated in the finite element method. According to the calculation, distributional principle of temperature field of the standard involute cylindrical spur gear is studied. The result shows that high-temperature region of the meshing tooth surface appears in the tooth root or the tooth top and the highest temperature is locate near tooth root of the pinion, where is most likely to occur gluing. The product of relative sliding velocity and contact stress of the tooth surface at meshing point has a significant impact on the frictional heat distribution of the meshing tooth surface, thereby affects the distributional form of body temperature field of the gear.