Boolesche zweidimensionale Lagrange-Interpolation

In this paper the Boolean method for approximation of multivariate functions developed by Gordon [4], [5] is systematically applied to bivariate Lagrange interpolation. Interpolation methods are considered whose interpolation projectors can be characterized by K-times (K ∈ ?) Boolean sums of tensor product Lagrange interpolation projectors. Using certain properties of Boolean Lagrange interpolation projectors we derive explicit representation formulas for the interpolants. After showing that the classical Biermann interpolation on a triangular mesh is a special case of Boolean Lagrange interpolation a method for the construction of Serendipity elements of arbitrary order is presented. This method provides a systematic generalization of the construction of special Serendipity elements proposed by Gordon-Hall [6]. Furthermore, we derive an explicit remainder representation formula for Boolean Lagrange interpolation. Finally, a list of generalized Serendipity elements of order N-1 (2≦N≦8) is presented.     

A comparison of lagrangian and serendipity mindlin plate elements for free vibration analysis

The performance of five Lagrangian and Serendipity (4,8,9,12 and 16 noded) isoparametric elements in the free vibration finite analysis of Mindlin plates is evaluated. The results are compared with well established analytical and numerical solutions based on Mindlin's thick plate theory and three dimensional elasticity solutions.     

基于Cosserat理论的平面等参元

为解释材料在微尺度下的尺度效应,基于Cosserat理论,从势能泛函驻值条件出发提出构造8节点Serendipity平面等参元,并建立平面有限元法．每个节点拥有3个独立节点自由度,分别为2个方向的线位移和1个逆时针方向的角位移．用该方法分析含中心小孔的无限平板在单轴拉伸情况下的应力集中问题．数值计算结果与Cosserat理论的解析解非常符合,表明应力集中因数k受泊松比μ,常数c及a／l值的影响很大;由于偶应力的存在,小孔周围的应力分布明显小于经典弹性力学理论的预测．通过对材料常数c的调节可以将该方法推广应用于基于Mindlin偶应力理论的数值分析中．     

Complete lagrange family for the cube in finite element interpolations

Noting a vagueness in the Serendipity definition, the complete Lagrange family for the cube and the mixed complete Lagrange family are introduced. The unisolvent Lagrange interpolations over rectangular finite elements are then presented definitively in hierarchy-ranking expressions so that the polynominal completeness is realized with appropriately necessary minimum nodes. The corresponding interpolation bases in the conventional form can easily be derived through the basis transformation without matrix inversion.     

Finite element analysis of geometrically nonlinear plate behaviour using a mindlin formulation

The paper presents a finite element analysis of the geometrically nonlinear behaviour of plates using a Mindlin formulation with the assumption of small rotations. A comparison of the performance of Linear, Serendipity, Lagrangian and Heterosis elements is given for square, skew, circular and elliptical plates subjected to distributed and point loading. All results are presented numerically. Generally the higher order elements give good results although no particular element emerges as being “best”.     

Serendipity: “Expect also the Unexpected”

Serendipity is defined as the art of discovering an unsought finding. Over a thousand examples have been collected and examined, including material from unpublished work by the American sociologist, Robert Merton. It is suggested that serendipity play a supporting but essential role in discoveries in science, technology, the arts and daily life. The phenomenon deserves more serious attention as it may offer prospects of unsought benefits in all these fields of endeavour.     

A Kirchhoff-mode method for C0 bilinear and serendipity plate elements

A new formulation for the C⁰ quadrilateral and Serendipity plate elements is presented. It is an extension of the mode-decomposition approach that has been successfully applied in evaluating the C⁰ triangular linear plate element. In contrast to the triangular element, the concept of an equivalent discrete Kirchhoff configuration is utilized. The elements are applied to several examples and the performance of these elements is shown to be quite good.     

Social serendipity: mobilizing social software

Many mobile devices incorporate low-power wireless connectivity protocols, such as Bluetooth, that can be used to identify an individual to other people nearby. We have developed an architecture that leverages this functionality in mobile phones - originally designed for communication at a distance - to connect people across the room. Serendipity is an application of the architecture. It combines the existing communications infrastructure with online introduction systems' functionality to facilitate interactions between physically proximate people through a centralized server. A new mobile-phone-based system uses Bluetooth hardware addresses and a database of user profiles to cue informal, face-to-face interactions between nearby users who don't know each other, but probably should.     

A hybrid-stress quadratic serendipity displacement mindlin plate bending element

A hybrid-stress plate bending element is developed for thin and moderately thick plates based on a Serendipity-type quadratic displacement assumption. The through-thickness displacement behavior is consistent with Mindlin plate theory, and all components of stress are included. By proper choice of the transverse shear stress distributions, the element stiffness possesses correct rank, and results show no signs of locking in the thin plate limit; these and other considerations discussed herein suggest that the stress assumption used is optimum for the 8-node element. Results are compared with 8-node Serendipity and 9-node Lagrange assumed-displacement elements. The present element demonstrates high accuracy for all problems considered and has no apparent deficiencies.     

Serendipity: Integrated Environment Support for Process Modelling, Enactment and Work Coordination

Large cooperative work systems require work coordination, context awareness and process modelling and enactment mechanisms to be effective. Support for process modelling and work coordination in such systems also needs to support informal aspects of work which are difficult to codify. Computer-Supported Cooperative Work (CSCW) facilities, such as inter-person communication and collaborative editing, also need to be well-integrated into both process-modelling tools and tools used to perform work. Serendipity is an environment which provides high-level, visual process modelling and event-handling languages, and diverse CSCW capabilities, and which can be integrated with a range of tools to coordinate cooperative work. This paper describes Serendipity's visual languages, support environment, architecture, and implementation, together with experience using the environment and integrating it with other environments.     

Geometric validity (positive jacobian) of high-order Lagrange finite elements,theory and practical guidance

Finite elements of degree two or more are needed to solve various P.D.E. problems. This paper discusses a method to validate such meshes for the case of the usual Lagrange elements of various degrees. The first section of this paper comes back to Bézier curve and Bézier patches of arbitrary degree. The way in which a Bézier patch and a finite element are related is recalled. The usual Lagrange finite elements of various degrees are discussed, including simplices (triangle and tetrahedron), quads, prisms (pentahedron), pyramids and hexes together with some low-degree Serendipity elements. A validity condition, the positivity of the jacobian, is exhibited for these elements. Elements of various degrees are envisaged also including some “linear” elements (therefore straight-sided elements of degree 1) because the jacobian (polynomial) of some of them is not totally trivial.     

Serendipity in Recommender Systems: A Systematic Literature Review

A recommender system is employed to accurately recommend items,which are expected to attract the user's attention.The over-emphasis on the accuracy of the recommendations can cause information over-specialization and make recommendations boring and even predictable.Novelty and diversity are two partly useful solutions to these problems.However,novel and diverse recommendations cannot merely ensure that users are attracted since such recommendations may not be relevant to the user's interests.Hence,it is necessary to consider other criteria,such as unexpectedness and relevance.Serendipity is a criterion for making appealing and useful recommendations.The usefulness of serendipitous recommendations is the main superiority of this criterion over novelty and diversity.The bulk of studies of recommender systems have focused on serendipity in recent years.Thus,a systematic literature review is conducted in this paper on previous studies of serendipity-oriented recommender systems.Accordingly,this paper focuses on the contextual convergence of serendipity definitions,datasets,serendipitous recommendation methods,and their evaluation techniques.Finally,the trends and existing potentials of the serendipity-oriented recommender systems are discussed for future studies.The results of the systematic literature review present that the quality and the quantity of articles in the serendipity-oriented recommender systems are progressing.     

Supporting serendipity: Using ambient intelligence to augment user exploration for data mining and web browsing

Serendipity is the making of fortunate discoveries by accident, and is one of the cornerstones of scientific progress. In today's world of digital data and media, there is now a vast quantity of material that we could potentially encounter, and so there is an increased opportunity of being able to discover interesting things. However, the availability of material does not imply that we will be able to actually find it; the sheer quantity of data mitigates against us being able to discover the interesting nuggets.This paper explores approaches we have taken to support users in their search for interesting and relevant information. The primary concept is the principle that it is more useful to augment user skills in information foraging than it is to try and replace them. We have taken a variety of artificial intelligence, statistical, and visualisation techniques, and combined them with careful design approaches to provide supportive systems that monitor user actions, garner additional information from their surrounding environment and use this enhanced understanding to offer supplemental information that aids the user in their interaction with the system.We present two different systems that have been designed and developed according to these principles. The first system is a data mining system that allows interactive exploration of the data, allowing the user to pose different questions and understand information at different levels of detail. The second supports information foraging of a different sort, aiming to augment users browsing habits in order to help them surf the internet more effectively. Both use ambient intelligence techniques to provide a richer context for the interaction and to help guide it in more effective ways: both have the user as the focal point of the interaction, in control of an iterative exploratory process, working in indirect collaboration with the artificial intelligence components.Each of these systems contains some important concepts of their own: the data mining system has a symbolic genetic algorithm which can be tuned in novel ways to aid knowledge discovery, and which reports results in a user-comprehensible format. The visualisation system supports high-dimensional data, dynamically organised in a three-dimensional space and grouped by similarity. The notions of similarity are further discussed in the internet browsing system, in which an approach to measuring similarity between web pages and a user's interests is presented. We present details of both systems and evaluate their effectiveness.     

Mapping nested loop algorithms into multidimensional systolicarrays

Consideration is given to transforming depth p-nested for loop algorithms into q-dimensional systolic VLSI arrays where 1⩽q⩽p-1. Previously, there existed complete characterizations of correct transformation only for the cases where q=p-1 or q=1. This gap is filled by giving formal necessary and sufficient conditions for correct transformation of a p-nested loop algorithm into a q-dimensional systolic array for any q, 1⩽q⩽p-1. Practical methods are presented. The techniques developed are applied to the automatic design of special purpose and programmable systolic arrays. The results also contribute toward automatic compilation onto more general purpose programmable arrays. Synthesis of linear and planar systolic array implementations for a three-dimensional cube-graph algorithm and a reindexed Warshall-Floyd path-finding algorithm are used to illustrate the method     

Protection switching schemes and mapping strategies for fail-operational hard real-time NoCs

Communication infrastructures designed for mixed-critical MPSoCs must provide isolation of traffic, hard real-time guarantees, and fault-tolerance. In previous work, we proposed the combination of protection-switching with a hybrid Time-Division-Multiplexed (TDM) and packet-switched Network-on-Chip (NoC) to achieve all three goals. In this paper, we present an FPGA implementation of such a NoC with all its features. We give synthesis results for the hybrid NoC, including the network interface, and show that our router uses over 32% fewer LUTs and registers than a competitive state-of-the-art router for mixed-critical MPSoC. We then explore different channel and task mapping strategies for critical applications which use protection switching and evaluate the effect these mappings have on the best-effort (BE) traffic in the system. Results show, that spreading out the critical traffic rather than naively dividing the system in critical and non-critical application domains is advantageous or even necessary in many cases and can allow for up to 13% more BE traffic. We give a comprehensive trade-off analysis of three protection switching schemes—1:n, 1:1, and 1+1—and show that 1+1 protection has less than half the worst case latency for critical traffic that 1:n and 1:1 protection have. At the same time, 1+1 protection, on average, only causes a 1.18% earlier saturation rate for BE traffic, which we consider to be affordable. We conclude that 1+1 protection is ideally suited for use in mixed-critical systems with high safety requirements.     

Properties of optimal hop-by-hop allocation policies in networkswith multiple transmitters and linear equal holding costs

Flow control between one receiving node and its adjacent transmitting nodes in a computer network is modeled as a Markov decision problem. By deriving several qualitative properties of an optimal allocation policy, it is shown that finding dynamic optimal allocations for only T states suffices to completely describe an optimal allocation policy. When the number of transmitters M=2, for all but one of the T states there are only two allocations that are candidates for optimality. It is desirable to extend this property to M>2. However, it appears that the technique used for M =2 does not generalize to M>2     

The application of scheduled H∞controllers to a VSTOL aircraft

The authors apply H_∞-designed controllers to a generic VSTOL (vertical and short takeoff and landing) aircraft model GVAM. The design study motivates the use of H _∞ techniques, and addresses some of the implementation issues which arise for multivariable and H_∞-designed controllers. An approach for gain scheduling H_∞ controllers on the basis of the normalized comprime factor robust stabilization problem formulation used for the H_∞ design is developed. It utilizes the observer structure unique to this particular robustness optimization. A weighting selection procedure, has been developed for the associated loop-shaping technique used to specify performance. Multivariable controllers pose additional problems in the event of actuator saturations, and a desaturation scheme which accounts for this is applied to the GVAM. A comprehensive control law was developed and evaluated using the Royal Aerospace Establishment piloted simulation facility     

Efficient routing schemes for multiple broadcasts in hypercubes

The authors analyze the problem in which each node of the binary hypercube independently generates packets according to a Poisson process with rate λ; each of the packets is to be broadcast to all other nodes. Assuming unit packet length and no other communications taking place, it is observed that the system can be stable in steady-state only if the load factor ρ≡λ (2^d-1)/d satisfies ρ<1 where d is the dimensionality (diameter) of the hypercube. Moreover, the authors establish some lower bounds for the steady-state average delay D per packet and devise and analyze two distributed routing schemes that are efficient in the sense that stability is maintained for all ρ<ρ* where ρ* does not depend on the dimensionality d of the network, while the average delay D per packet satisfies D⩽Kd(1+ρ) for small values of ρ (with constant K). The performance evaluation is rigorous for one scheme, while for the other the authors resort to approximations and simulations     

An efficient digital search algorithm by using a double-arraystructure

An efficient digital search algorithm that is based on an internal array structure called a double array, which combines the fast access of a matrix form with the compactness of a list form, is presented. Each arc of a digital search tree, called a DS-tree, can be computed from the double array in 0(1) time; that is to say, the worst-case time complexity for retrieving a key becomes 0(k) for the length k of that key. The double array is modified to make the size compact while maintaining fast access, and algorithms for retrieval, insertion, and deletion are presented. If the size of the double array is n+cm, where n is the number of nodes of the DS-tree, m is the number of input symbols, and c is a constant particular to each double array, then it is theoretically proved that the worst-case times of deletion and insertion are proportional to cm and cm², respectively, and are independent of n. Experimental results of building the double array incrementally for various sets of keys show that c has an extremely small value, ranging from 0.17 to 1.13     

A unified task-based dependability model for hypercube computers

A unified analytical model for computing the task-based dependability (TDB) of hypercube architectures is presented. A hypercube is deemed operational as long as a task can be executed on the system. The technique can compute both reliability and availability for two types of task requirements-I-connected model and subcube model. The I-connected TBD assumes that a connected group of at least I working nodes is required for task execution. The subcube TBD needs at least an m-cube in an n-cube, m⩽ n, for task execution. The dependability is computed by multiplying the probability that x nodes (x⩾I or x⩾2^m) are working in an n-cube at time t by the conditional probability that the hypercube can satisfy any one of the two task requirements from x working nodes. Recursive models are proposed for the two types of task requirements to find the connection probability. The subcube requirement is extended to find multiple subcubes for analyzing multitask dependability. The analytical results are validated through extensive simulation