A family of non-conforming elements and the analysis of Nitsche’s method for a singularly perturbed fourth order problem

In this paper we address several issues arising from a singularly perturbed fourth order problem with small parameter ε. First, we introduce a new family of non-conforming elements. We then prove that the corresponding finite element method is robust with respect to the parameter ε and uniformly convergent to order h ^1/2. In addition, we analyze the effect of treating the Neumann boundary condition weakly by Nitsche’s method. We show that such treatment is superior when the parameter ε is smaller than the mesh size h and obtain sharper error estimates. Such error analysis is not restricted to the proposed elements and can easily be carried out to other elements as long as the Neumann boundary condition is imposed weakly. Finally, we discuss the local error estimates and the pollution effect of the boundary layers in the interior of the domain.     

Hermite approximation for free-form deformation of curves and surfaces

Free-Form Deformation Techniques (FFD) are commonly used to generate animations, where a polygonal approximation of the final object suffices for visualization purposes. However, for some CAD/CAM applications, we need an explicit expression of the object, rather than a collection of sampled points. If both object and deformation are polynomial, their composition yields a result that is also polynomial, albeit very high degree, something undesirable in real applications. To solve this problem, we transform each curve or surface composing the object, usually expressed in the Bernstein basis, to a modified Newton form. In this representation, the two-point analogue of Taylor expansions, the composition admits a simple expression in terms of discrete convolutions, and degree reduction corresponding to Hermite approximation is trivial by dropping high-degree coefficients. Furthermore, degree-reduction can be incorporated into the composition. Finally, the deformed curve or surface is converted back to the Bernstein form. This method extends to general non-polynomial deformation, such as bending and twisting, by computing a polynomial approximant of the deformation.     

Strongdeco: Expansion of analytical,strongly correlated quantum states into a many-body basis

We provide a Mathematica code for decomposing strongly correlated quantum states described by a first-quantized, analytical wave function into many-body Fock states. Within them, the single-particle occupations refer to the subset of Fock–Darwin functions with no nodes. Such states, commonly appearing in two-dimensional systems subjected to gauge fields, were first discussed in the context of quantum Hall physics and are nowadays very relevant in the field of ultracold quantum gases. As important examples, we explicitly apply our decomposition scheme to the prominent Laughlin and Pfaffian states. This allows for easily calculating the overlap between arbitrary states with these highly correlated test states, and thus provides a useful tool to classify correlated quantum systems. Furthermore, we can directly read off the angular momentum distribution of a state from its decomposition. Finally we make use of our code to calculate the normalization factors for Laughlin?s famous quasi-particle/quasi-hole excitations, from which we gain insight into the intriguing fractional behavior of these excitations.Program summaryProgram title: StrongdecoCatalogue identifier: AELA_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5475No. of bytes in distributed program, including test data, etc.: 31 071Distribution format: tar.gzProgramming language: MathematicaComputer: Any computer on which Mathematica can be installedOperating system: Linux, Windows, MacClassification: 2.9Nature of problem: Analysis of strongly correlated quantum states.Solution method: The program makes use of the tools developed in Mathematica to deal with multivariate polynomials to decompose analytical strongly correlated states of bosons and fermions into a standard many-body basis. Operations with polynomials, determinants and permanents are the basic tools.Running time: The distributed notebook takes a couple of minutes to run.     

Asynchronous privacy-preserving iterative computation on peer-to-peer networks

Privacy preserving algorithms allow several participants to compute a global function collaboratively without revealing local information to each other. Examples of applications include trust management, collaborative filtering, and ranking algorithms such as PageRank. Most solutions that can be proven to be privacy preserving theoretically are not appropriate for highly unreliable, large scale, distributed environments such as peer-to-peer (P2P) networks because they either require centralized components, or a high degree of synchronism among the participants. At the same time, in P2P networks privacy preservation is becoming a key requirement. Here, we propose an asynchronous privacy preserving communication layer for an important class of iterative computations in P2P networks, where each peer periodically computes a linear combination of data stored at its neighbors. Our algorithm tolerates realistic rates of message drop and delay, and node churn, and has a low communication overhead. We perform simulation experiments to compare our algorithm to related work. The problem we use as an example is power iteration (a method used to calculate the dominant eigenvector of a matrix), since eigenvector computation is at the core of several practical applications. We demonstrate that our novel algorithm also converges in the presence of realistic node churn, message drop rates and message delay, even when previous synchronized solutions are able to make almost no progress.     

TangiWheel: A Widget for Manipulating Collections on Tabletop Displays Supporting Hybrid Input Modality

In this paper we present TangiWheel,a collection manipulation widget for tabletop displays.Our implementation is flexible,allowing either multi-touch or interaction,or even a hybrid scheme to better suit user choice and convenience.Different TangiWheel aspects and features are compared with other existing widgets for collection manipulation.The study reveals that TangiWheel is the first proposal to support a hybrid input modality with large resemblance levels between touch and tangible interaction styles.Several experiments were conducted to evaluate the techniques used in each input scheme for a better understanding of tangible surface interfaces in complex tasks performed by a single user (e.g.,involving a typical master-slave exploration pattern).The results show that tangibles perform significantly better than fingers,despite dealing with a greater number of interactions,in situations that require a large number of acquisitions and basic manipulation tasks such as establishing location and orientation.However,when users have to perform multiple exploration and selection operations that do not require previous basic manipulation tasks,for instance when collections are fixed in the interface layout,touch input is significantly better in terms of required time and number of actions.Finally,when a more elastic collection layout or more complex additional insertion or displacement operations are needed,the hybrid and tangible approaches clearly outperform finger-based interactions.     

A co-evolutionary differential evolution algorithm for solving min–max optimization problems implemented on GPU using C-CUDA

Several areas of knowledge are being benefited with the reduction of the computing time by using the technology of graphics processing units (GPU) and the compute unified device architecture (CUDA) platform. In case of evolutionary algorithms, which are inherently parallel, this technology may be advantageous for running experiments demanding high computing time. In this paper, we provide an implementation of a co-evolutionary differential evolution (DE) algorithm in C-CUDA for solving min–max problems. The algorithm was tested on a suite of well-known benchmark optimization problems and the computing time has been compared with the same algorithm implemented in C. Results demonstrate that the computing time can significantly be reduced and scalability is improved using C-CUDA. As far as we know, this is the first implementation of a co-evolutionary DE algorithm in C-CUDA.     

Open Innovation in an Enterprise 3.0 framework: Three case studies

Nowadays, especially after the recent financial downturn, companies are looking for much more efficient and creative business processes. They need to place better solutions in the market in a less time with less cost. There is a general intuition that communication and collaboration, especially mixed with Web 2.0 approach within companies and ecosystems, can boost the innovation process with positive impacts on business indicators. Open Innovation within an Enterprise 2.0 context is a one of the most chosen paradigm for improving the innovation processes of enterprises, based on the collaborative creation and development of ideas and products. The key feature of this new paradigm is that the knowledge is exploited in a collaborative way flowing not only among internal sources, i.e. R&D departments, but also among external ones as other employees, customers, partners, etc. In this paper we show how an ontology-based analysis of plain text can provide a semantic contextualization of content support tasks, such as finding semantic distance between contents, and can help in creating relations between people with shared knowledge and interests. Along this paper we will present the results obtained by the adoption of this technology in a large corporate environment like Bankinter, a financial institution, Telefonica I+D, an international telecommunication firm and Repsol, a major oil company in Spain.     

Ontology-based semantic similarity: A new feature-based approach

Estimation of the semantic likeness between words is of great importance in many applications dealing with textual data such as natural language processing, knowledge acquisition and information retrieval. Semantic similarity measures exploit knowledge sources as the base to perform the estimations. In recent years, ontologies have grown in interest thanks to global initiatives such as the Semantic Web, offering an structured knowledge representation. Thanks to the possibilities that ontologies enable regarding semantic interpretation of terms many ontology-based similarity measures have been developed. According to the principle in which those measures base the similarity assessment and the way in which ontologies are exploited or complemented with other sources several families of measures can be identified. In this paper, we survey and classify most of the ontology-based approaches developed in order to evaluate their advantages and limitations and compare their expected performance both from theoretical and practical points of view. We also present a new ontology-based measure relying on the exploitation of taxonomical features. The evaluation and comparison of our approach’s results against those reported by related works under a common framework suggest that our measure provides a high accuracy without some of the limitations observed in other works.