Design and Implementation of a Novel Spherical Mobile Robot

In this paper, the design, modeling and implementation of a novel spherical mobile robot is presented. The robot composes of a spherical outer shell made of a transparent thermoplastic material, two pendulums, two DC motors with gearboxes, two equipments for linear motion and two control units. It possesses four distinct motional modes including: driving, steering, jumping and zero-radius turning. In driving and steering modes, the robot moves along straight and circular trajectories, respectively. The robot performs these motional modes using movable internal masses. In the jumping mode, it can jump over obstacles and in the zero-radius turning mode, the robot can turn with zero-radius to improve the motion flexibility. Furthermore, the attempts to establish the dynamic models of some motional modes are made and finally, the accuracy of the obtained dynamic models is verified by simulation and experimental results.     

The Random Members of a Π 1 0 ${\Pi }_{1}^{0}$ Class

Theory of Computing Systems - We examine several notions of randomness for elements in a given ${\Pi }_{1}^{0}$ class $\mathcal {P}$ . Such an effectively closed subset $\mathcal {P}$ of 2 ω...     

Performance and Comparison of Cell-Centered and Node-Centered Unstructured Finite Volume Discretizations for Shallow Water Free Surface Flows

Finite volume (FV) methods for solving the two-dimensional (2D) nonlinear shallow water equations (NSWE) with source terms on unstructured, mostly triangular, meshes are known for some time now. There are mainly two basic formulations of the FV method: node-centered (NCFV) and cell-centered (CCFV). In the NCFV formulation the finite volumes, used to satisfy the integral form of the equations, are elements of the mesh dual to the computational mesh, while for the CCFV approach the finite volumes are the mesh elements themselves. For both formulations, details are given of the development and application of a second-order well-balanced Godunov-type scheme, developed for the simulation of unsteady 2D flows over arbitrary topography with wetting and drying. The popular approximate Riemann solver of Roe is utilized to compute the numerical fluxes, while second-order spatial accuracy is achieved with a MUSCL-type reconstruction technique. The Green-Gauss (G-G) formulation for gradient computations is implemented for both formulations, in order to maintain a common framework. Two different stencils for the G-G gradient computations in the CCFV formulation are implemented and tested. An edge-based limiting procedure is applied for the control of the total variation of the reconstructed field. This limiting procedure is proved to be effective for the NCFV scheme but inadequate for the CCFV approach. As such, a simple but very effective modification to the reconstruction procedure is introduced that takes into account geometrical characteristics of the computational mesh. In addition, consistent well-balanced second-order discretizations for the topography source term treatment and the wet/dry front treatment are presented for both FV formulations, ensuring absolute mass conservation, along with a stable friction term treatment.     

On the Quantum Query Complexity of Local Search in Two and Three Dimensions

The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been determined asymptotically for all fixed d≥5, but the lower dimensional cases present special difficulties, and considerable gaps exist in our knowledge. In the present paper we present near-optimal lower bounds, showing that the quantum query complexity for the 2-dimensional grid [n]² is Ω(n ^1/2?δ ), and that for the 3-dimensional grid [n]³ is Ω(n ^1?δ ), for any fixed δ>0.A general lower bound approach for this problem, initiated by Aaronson (based on Ambainis’ adversary method for quantum lower bounds), uses random walks with low collision probabilities. This approach encounters obstacles in deriving tight lower bounds in low dimensions due to the lack of degrees of freedom in such spaces. We solve this problem by the novel construction and analysis of random walks with non-uniform step lengths. The proof employs in a nontrivial way sophisticated results of Sárközy and Szemerédi, Bose and Chowla, and Halász from combinatorial number theory, as well as less familiar probability tools like Esseen’s Inequality.     

On a reduction of the interval coloring problem to a series of bandwidth coloring problems

Given a graph G=(V,E) with strictly positive integer weights ω _i on the vertices i∈V, an interval coloring of G is a function I that assigns an interval I(i) of ω _i consecutive integers (called colors) to each vertex i∈V so that I(i)∩I(j)=∅ for all edges {i,j}∈E. The interval coloring problem is to determine an interval coloring that uses as few colors as possible. Assuming that a strictly positive integer weight δ _ij is associated with each edge {i,j}∈E, a bandwidth coloring of G is a function c that assigns an integer (called a color) to each vertex i∈V so that |c(i)−c(j)|≥δ _ij for all edges {i,j}∈E. The bandwidth coloring problem is to determine a bandwidth coloring with minimum difference between the largest and the smallest colors used. We prove that an optimal solution of the interval coloring problem can be obtained by solving a series of bandwidth coloring problems. Computational experiments demonstrate that such a reduction can help to solve larger instances or to obtain better upper bounds on the optimal solution value of the interval coloring problem.     

Manhattan Room Layout Reconstruction from a Single $$360^{circ }$$ 360 ∘ Image: A Comparative Study of State-of-the-Art Methods

International Journal of Computer Vision - Recent approaches for predicting layouts from 360 $$^{circ }$$ panoramas produce excellent results. These approaches build on a common framework...     

On the Characterization and Fault Identification of Sequentially t-Diagnosable System Under PMC Model

Sequential diagnosis is a very useful strategy for system-level fault identification because of its lower cost of hardware.In this paper,the characterization of sequentially t-diagnosable system is given,and a universal algorithm to seek faulty units in the system is developed.     

Evaluation of gang scheduling performance and cost in a cloud computing system

Cloud Computing refers to the notion of outsourcing on-site available services, computational facilities, or data storage to an off-site, location-transparent centralized facility or “Cloud.” Gang Scheduling is an efficient job scheduling algorithm for time sharing, already applied in parallel and distributed systems. This paper studies the performance of a distributed Cloud Computing model, based on the Amazon Elastic Compute Cloud (EC2) architecture that implements a Gang Scheduling scheme. Our model utilizes the concept of Virtual Machines (or VMs) which act as the computational units of the system. Initially, the system includes no VMs, but depending on the computational needs of the jobs being serviced new VMs can be leased and later released dynamically. A simulation of the aforementioned model is used to study, analyze, and evaluate both the performance and the overall cost of two major gang scheduling algorithms. Results reveal that Gang Scheduling can be effectively applied in a Cloud Computing environment both performance-wise and cost-wise.     

On resol vability of Steine r systems S( v = 2m, 4, 3) of rank r ≤ v − m + 1 o ve r $$\mathbb{F}_2 $$

Two new constructions of Steiner quadruple systems S(v, 4, 3) are given. Both preserve resolvability of the original Steiner system and make it possible to control the rank of the resulting system. It is proved that any Steiner system S(v = 2 ^m , 4, 3) of rank r ≤ v ? m + 1 over F₂ is resolvable and that all systems of this rank can be constructed in this way. Thus, we find the number of all different Steiner systems of rank r = v ? m + 1.     

Topological and Variational Properties of a Model for the Reconstruction of Three-Dimensional Transparent Images with Self-Occlusions

We introduce and study a two-dimensional variational model for the reconstruction of a smooth generic solid shape E, which may handle the self-occlusions and that can be considered as an improvement of the 2.1D sketch of Nitzberg and Mumford (Proceedings of the Third International Conference on Computer Vision, Osaka, 1990). We characterize from the topological viewpoint the apparent contour of E, namely, we characterize those planar graphs that are apparent contours of some shape E. This is the classical problem of recovering a three-dimensional layered shape from its apparent contour, which is of interest in theoretical computer vision. We make use of the so-called Huffman labeling (Machine Intelligence, vol. 6, Am. Elsevier, New York, 1971), see also the papers of Williams (Ph.D. Dissertation, 1994 and Int. J. Comput. Vis. 23:93–108, 1997) and the paper of Karpenko and Hughes (Preprint, 2006) for related results. Moreover, we show that if E and F are two shapes having the same apparent contour, then E and F differ by a global homeomorphism which is strictly increasing on each fiber along the direction of the eye of the observer. These two topological theorems allow to find the domain of the functional ℱ describing the model. Compactness, semicontinuity and relaxation properties of ℱ are then studied, as well as connections of our model with the problem of completion of hidden contours.

On the choice of boundary conditions for mode shapes in flexible multibody systems

The modal representation of the deformation field is a widespread and efficient approach in the analysis of flexible multibody systems. However, it requires a pre-processing in advance to the actual multibody survey that includes the imposition of boundary conditions for the evaluation of the mode functions as an essential user input. Quite often the appropriateness of these boundary conditions is a point of discussion. Therefore the present paper reviews the theoretical background and the implications of this task. Then, a consistent and comprehensive proposal is made how these boundary conditions may be chosen. The suggestion is justified by theoretical considerations and compared to alternative approaches from the literature in a simulation study with three representative examples. It may be concluded that several approaches lead to reasonable results for a sufficient number of mode functions. However, the proposed approach turned out to be the most efficient one and provides a consistent framework.     

Comparison and analysis of eight scheduling heuristics for the optimization of energy consumption and makespan in large-scale distributed systems

In this paper, we study the problem of scheduling tasks on a distributed system, with the aim to simultaneously minimize energy consumption and makespan subject to the deadline constraints and the tasks’ memory requirements. A total of eight heuristics are introduced to solve the task scheduling problem. The set of heuristics include six greedy algorithms and two naturally inspired genetic algorithms. The heuristics are extensively simulated and compared using an simulation test-bed that utilizes a wide range of task heterogeneity and a variety of problem sizes. When evaluating the heuristics, we analyze the energy consumption, makespan, and execution time of each heuristic. The main benefit of this study is to allow readers to select an appropriate heuristic for a given scenario.     

The space of EDF deadlines: the exact region and a convex approximation

It is well known that the performance of computer controlled systems is heavily affected by delays and jitter occurring in the control loops, which are mainly caused by the interference introduced by other concurrent activities. A common approach adopted to reduce delay and jitter in periodic task systems is to decrease relative deadlines as much as possible, but without jeopardizing the schedulability of the task set. In this paper, we formally characterize the region of admissible deadlines so that the system designer can appropriately select the desired values to maximize a given performance index defined over the task set. Finally we also provide a sufficient region of feasible deadlines which is proved to be convex.

On a Method of Paired Representation: Enhancement and Decomposition by Series Direction Images

In the paired representation, a two-dimensional (2-D) image is represented uniquely by a complete set of 1-D signals, so-called splitting-signals, that carry the spectral information of the image at frequency-points of specific subsets that divide the whole domain of frequencies. Image processing can thus be reduced to processing of splitting-signals and such process requires a modification of only a few spectral components of the image, for each signal. For instance, the α-rooting method of image enhancement can be fulfilled through processing one or a few splitting-signals. Such process can even be accomplished without computing the 2-D Fourier transforms of the original and enhanced images. To show that, we present an effective formula for inverse 2-D N×N-point paired transform, where N is a power of 2. The representation of the image and 2-D DFT by paired splitting-signals leads to the new concepts of direction and series images, that define the resolution and periodic structures of the image components, which can be packed in the form of the “resolution map” of the size of the image. Simple method of image enhancement by series images is described.

A framework for development and evaluation of a dynamic subchannel allocation scheme in an OFDMA system

This paper presents a framework for allocating radio resources to the Access Points (APs) introducing an Access Point Controller (APC). Radio resources can be either time slots or subchannels. The APC assigns subchannels to the APs using a dynamic subchannel allocation scheme. The developed framework evaluates the dynamic subchannel allocation scheme for a downlink multicellular Orthogonal Frequency Division Multiple Access (OFDMA) system. In the considered system, each AP and the associated Mobile Terminals (MTs) are not operating on a frequency channel with fixed bandwidth, rather the channel bandwidth for each AP is dynamically adapted according to the traffic load. The subchannels assignment procedure is based on quality estimations due to the interference measurements and the current traffic load. The traffic load estimation is realized with the measurement of the utilization of the assigned radio resources. The reuse partitioning for the radio resources is done by estimating mutual Signal to Interference Ratio (SIR) of the APs. The developed dynamic subchannel allocation ensures Quality of Service (QoS), better traffic adaptability, and higher spectrum efficiency with less computational complexity.

Sense and sidedness in the graphics pipeline via a passage through a separable space

Computer graphics is ostensibly based on projective geometry. The graphics pipeline—the sequence of functions applied to 3D geometric primitives to determine a 2D image—is described in the graphics literature as taking the primitives from Euclidean to projective space, and then back to Euclidean space. This is a weak foundation for computer graphics. An instructor is at a loss: one day entering the classroom and invoking the established and venerable theory of projective geometry while asserting that projective spaces are not separable, and then entering the classroom the following week to tell the students that the standard graphics pipeline performs clipping not in Euclidean, but in projective space—precisely the operation (deciding sidedness, which depends on separability) that was deemed nonsensical. But there is no need to present Blinn and Newell’s algorithm (Comput. Graph. 12, 245–251, 1978; Commun. ACM 17, 32–42, 1974)—the crucial clipping step in the graphics pipeline and, perhaps, the most original knowledge a student learns in a fourth-year computer graphics class—as a clever trick that just works. Jorge Stolfi described in 1991 oriented projective geometry. By declaring the two vectors and distinct, Blinn and Newell were already unknowingly working in oriented projective space. This paper presents the graphics pipeline on this stronger foundation.

On a Petrov–Galerkin method for the electrical and thermal behaviour of semiconductor devices in two dimensions

We consider the equations governing the electrical and thermal behaviour of a semiconductor device in two dimensions. A non-standard Petrov-Galerkin method is used to obtain a discretisation of the equations for stationary problems. The resulting scheme is a generalization to the two-dimensional case and to the full set of equations of the well-known Scharfetter-Gummel scheme, which is the most successful discretisation for one-dimensional problems. The dependent variables used are the carrier densities, the electrostatic potential and the absolute temperature.     

On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods

We examine four nodal versions of tensor product discontinuous Galerkin spectral element approximations to systems of conservation laws for quadrilateral or hexahedral meshes. They arise from the two choices of Gauss or Gauss-Lobatto quadrature and integrate by parts once (I) or twice (II) formulations of the discontinuous Galerkin method. We show that the two formulations are in fact algebraically equivalent with either Gauss or Gauss-Lobatto quadratures when global polynomial interpolations are used to approximate the solutions and fluxes within the elements. Numerical experiments confirm the equivalence of the approximations and indicate that using Gauss quadrature with integration by parts once is the most efficient of the four approximations.     

On improving resource utilization and system throughput of master slave job scheduling in heterogeneous systems

The rapid advances of network technologies shed light on many aspects of the practicability of large scale ubiquitous computing. Grid technology has been recognized as an efficient solution to coordinate large-scale shared resources and execute complex applications in heterogeneous network environments. The problem of resource management and task allocation has always been one of the main challenges. In this paper, we present an efficient task allocation strategy for distributing tasks onto computing nodes in the underlying heterogeneous networks. The contribution of the proposed technique is to minimize average turnaround time by dispatching tasks to processors with smallest communication ratio. System throughput could be also enhanced by dispersing processor idle time. The proposed technique can be applied to heterogeneous cluster systems as well as computational grid environments, in which the communication costs vary in different clusters. Experimental results show that the proposed scheme outperforms other previous algorithms in terms of throughput and turnaround time.