Optimal Error Estimates of the Legendre Tau Method for Second-Order Differential Equations

In this paper, we prove that the Legendre tau method has the optimal rate of convergence in L ²-norm, H ¹-norm and H ²-norm for one-dimensional second-order steady differential equations with three kinds of boundary conditions and in C([0,T];L ²(I))-norm for the corresponding evolution equation with the Dirichlet boundary condition. For the generalized Burgers equation, we develop a Legendre tau-Chebyshev collocation method, which can also be optimally convergent in C([0,T];L ²(I))-norm. Finally, we give some numerical examples.     

On the definition of the intuitionistic fuzzy subgroups

In this paper, a new kind of intuitionistic fuzzy subgroup theory, which is different from that of Ma, Zhan and Davvaz (2008) [22], [23], is presented. First, based on the concept of cut sets on intuitionistic fuzzy sets, we establish the neighborhood relations between a fuzzy point $x_a$ and an intuitionistic fuzzy set $A$. Then we give the definitions of the grades of $x_a$ belonging to $A$, $x_a$ quasi-coincident with $A$, $x_a$ belonging to and quasi-coincident with $A$ and $x_a$ belonging to or quasi-coincident with $A$, respectively. Second, by applying the 3-valued Lukasiewicz implication, we give the definition of $(\alpha ,\beta )$-intuitionistic fuzzy subgroups of a group $G$ for $\alpha ,\beta \in \{\in ,q,\in \wedge q,\in \vee q\}$, and we show that, in 16 kinds of $(\alpha ,\beta )$-intuitionistic fuzzy subgroups, the significant ones are the $(\in ,\in )$-intuitionistic fuzzy subgroup, the $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup and the $(\in \wedge q,\in )$-intuitionistic fuzzy subgroup. We also show that $A$ is a $(\in ,\in )$-intuitionistic fuzzy subgroup of $G$ if and only if, for any $a\in (0,1]$, the cut set $A_a$ of $A$ is a 3-valued fuzzy subgroup of $G$, and $A$ is a $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup (or $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup) of $G$ if and only if, for any $a\in (0,0.5]$(or for any $a\in (0.5,1]$), the cut set $A_a$ of $A$ is a 3-valued fuzzy subgroup of $G$. At last, we generalize the $(\in ,\in )$-intuitionistic fuzzy subgroup, $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup and $(\in \wedge q,\in )$-intuitionistic fuzzy subgroup to intuitionistic fuzzy subgroups with thresholds, i.e., $(s,t]$-intuitionistic fuzzy subgroups. We show that $A$ is a $(s,t]$-intuitionistic fuzzy subgroup of $G$ if and only if, for any $a\in (s,t]$, the cut set $A_a$ of $A$ is a 3-valued fuzzy subgroup of $G$. We also characterize the $(s,t]$-intuitionistic fuzzy subgroup by the neighborhood relations between a fuzzy point $x_a$ and an intuitionistic fuzzy set $A$.     

Fast and highly scalable parallel computations for fundamental matrix problems on distributed memory systems

We present fast and highly scalable parallel computations for a number of important and fundamental matrix problems on distributed memory systems (DMS). These problems include matrix multiplication, matrix chain product, and computing the powers, the inverse, the characteristic polynomial, the determinant, the rank, the Krylov matrix, and an LU- and a QR-factorization of a matrix, and solving linear systems of equations. Our highly scalable parallel computations for these problems are based on a highly scalable implementation of the fastest sequential matrix multiplication algorithm on DMS. We show that compared with the best known parallel time complexities on parallel random access machines (PRAM), the most powerful but unrealistic shared memory model of parallel computing, our parallel matrix computations achieve the same speeds on distributed memory parallel computers (DMPC), and have an extra polylog factor in the time complexities on DMS with hypercubic networks. Furthermore, our parallel matrix computations are fully scalable on DMPC and highly scalable over a wide range of system size on DMS with hypercubic networks. Such fast (in terms of parallel time complexity) and highly scalable (in terms of our definition of scalability) parallel matrix computations were rarely seen before on any distributed memory systems.     

The hybrid dynamic parallel scheduling algorithm for load balancing on Chained-Cubic Tree interconnection networks

The Chained-Cubic Tree (CCT) interconnection network topology was recently proposed as a continuation for the extended efforts in the area of interconnection networks’ performance improvement. This topology, which promises to exhibit the best properties of the hypercube and tree topologies, needs to be deeply investigated in order to evaluate its performance among other interconnection networks’ topologies. This work comes as a complementary effort, in which the load balancing technique is investigated as one of the most important aspects of performance improvement. This paper proposes a new load balancing algorithm on CCT interconnection networks. The proposed algorithm, which is called Hybrid Dynamic Parallel Scheduling Algorithm (HD-PSA), is a combination of two common load balancing strategies; dynamic load balancing and parallel scheduling. The performance of the proposed algorithm is evaluated both, analytically and experimentally, in terms of various performance metrics; including, execution time, load balancing accuracy, communication cost, number of tasks hops, and tasks locality.     

Endogenous Neighborhood Selection and the Attainment of Cooperation in a Spatial Prisoner’s Dilemma Game

There is a large literature in economics and elsewhere on the emergence and evolution of cooperation in the repeated Prisoner’s Dilemma. Recently this literature has expanded to include games in a setting where agents play only with local neighbors in a specified geography. In this paper we explore how the ability of agents to move and choose new locations and new neighbors influences the emergence of cooperation. First, we explore the dynamics of cooperation by investigating agent strategies that yield Markov transition probabilities. We show how different agent strategies yield different Markov chains which generate different asymptotic behaviors in regard to the attainment of cooperation. Second, we investigate how agent movement affects the attainment of cooperation in various networks using agent-based simulations. We show how network structure and density can affect cooperation with and without agent movement.     

Sliding Mode Control with Adaptive Fuzzy Dead-Zone Compensation of an Electro-hydraulic Servo-System

Electro-hydraulic servo-systems are widely employed in industrial applications such as robotic manipulators, active suspensions, precision machine tools and aerospace systems. They provide many advantages over electric motors, including high force to weight ratio, fast response time and compact size. However, precise control of electro-hydraulic systems, due to their inherent nonlinear characteristics, cannot be easily obtained with conventional linear controllers. Most flow control valves can also exhibit some hard nonlinearities such as dead-zone due to valve spool overlap. This work describes the development of an adaptive fuzzy sliding mode controller for an electro-hydraulic system with unknown dead-zone. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov stability theory and Barbalat’s lemma. Numerical results are presented in order to demonstrate the control system performance.     

Search intensity versus search diversity: a false trade off?

An implicit tenet of modern search heuristics is that there is a mutually exclusive balance between two desirable goals: search diversity (or distribution), i.e., search through a maximum number of distinct areas, and, search intensity, i.e., a maximum search exploitation within each specific area. We claim that the hypothesis that these goals are mutually exclusive is false in parallel systems. We argue that it is possible to devise methods that exhibit high search intensity and high search diversity during the whole algorithmic execution. It is considered how distance metrics, i.e., functions for measuring diversity (given by the minimum number of local search steps between two solutions) and coordination policies, i.e., mechanisms for directing and redirecting search processes based on the information acquired by the distance metrics, can be used together to integrate a framework for the development of advanced collective search methods that present such desiderata of search intensity and search diversity under simultaneous coexistence. The presented model also avoids the undesirable occurrence of a problem we refer to as the ‘ergometric bike phenomenon’. Finally, this work is one of the very few analysis accomplished on a level of meta-meta-heuristics, because all arguments are independent of specific problems handled (such as scheduling, planning, etc.), of specific solution methods (such as genetic algorithms, simulated annealing, tabu search, etc.) and of specific neighborhood or genetic operators (2-opt, crossover, etc.).     

Infinitesimal Perturbation Analysis in Networks of Stochastic Flow Models: General Framework and Case Study of Tandem Networks with Flow Control

This paper presents a general algorithmic framework for computing the IPA derivatives of sample performance functions defined on networks of fluid queues. The underlying network-model consists of bi-layered hybrid dynamical systems with continuous-time dynamics at the lower layer and discrete-event dynamics at the upper layer. The linearized system, computed from the sample path via a discrete-event process, yields fairly simple algorithms for the IPA derivatives. As an application-example, the paper discusses loss and workload performance functions in a tandem network with congestion control, subjected to signal delays.     

A Biologically-Inspired Micro Aerial Vehicle

This paper introduces a novel framework for the design, modeling and control of a Micro Aerial Vehicle (MAV). The vehicle’s conceptual design is based on biologically-inspired principles and emulates a dragonfly (Odonata–Anisoptera). We have taken inspiration from the flight mechanism features of the dragonfly and have developed indigenous designs in creating a novel version of a Flapping Wing MAV (FWMAV). The MAV design incorporates a complex mechanical construction and a sophisticated multi-layered, hybrid, linear/non-linear controller to achieve extended flight times and improved agility compared to other rotary wing and FWMAV Vertical Take Off and Landing (VTOL) designs. The first MAV prototype will have a ballpark weight including sensor payload of around 30 g. The targeted lifting capability is about twice the weight. The MAV features state of the art sensing and instrumentation payload, which includes integrated high-power on-board processors, 6DoF inertial sensors, 3DoF compasses, GPS, embedded camera and long-range telemetry capability. A 3-layer control mechanism has been developed to harness the dynamics and attain complete navigational control of the MAV. The inner-layer is composed of a ‘quad hybrid-energy controller’ and two higher layers are at present, implementing a linear controller; the latter will be replaced eventually with a dynamic adaptive non-linear controller. The advantages of the proposed design compared to other similar ones include higher energy efficiency and extended flight endurance. The design features elastic storage and re-use of propulsion energy favoring energy conservation during flight. The design/modeling of the MAV and its kinematics & dynamics have been tested under simulation to achieve desired performance. The potential applications for such a high endurance vehicle are numerous, including air-deployable mass surveillance and reconnaissance in cluster and swarm formations. The efficacy of the design is demonstrated through a simulation environment. The dynamics are verified through simulations and a general linear controller coupled with an energy based non-linear controller is shown to operate the vehicle in a stable regime. In accordance with specified objectives a prototype is being developed for flight-testing and demonstration purposes.