Discontinuous solutions to hyperbolic systems under operator splitting

Two-dimensional systems of linear hyperbolic equations are studied with regard to their behavior under a solution strategy that in alternate time-steps solves exactly the component one-dimensional operators. The initial data is a step function across an oblique discontinuity. The manner in which this discontinuity breaks up under repeated applications of the split operator is analyzed, and it is shown that the split solution will fail to match the true solution in any case where the two operators do not share all their eigenvectors. The special case of the fluid flow equations is analyzed in more detail, and it is shown that arbitrary initial data gives rise to pseudo acoustic waves and a non-physical stationary wave. The implications of these findings for the design of high-resolution computing schemes are discussed

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries

Empirical modelling principles to support learning in a cultural context

Much research on pedagogy stresses the need for a broad perspective on learning. Such a perspective might take account (for instance) of the experience that informs knowledge and understanding [Tur91], the situation in which the learning activity takes place [Lav88], and the influence of multiple intelligences [Gar83]. Educational technology appears to hold great promise in this connection. Computer-related technologies such as new media, the internet, virtual reality and brain-mediated communication afford access to a range of learning resources that grows ever wider in its scope and supports ever more sophisticated interactions. Whether educational technology is fulfilling its potential in broadening the horizons for learning activity is more controversial. Though some see the successful development of radically new educational resources as merely a matter of time, investment and engineering, there are also many critics of the trends in computer-based learning who see little evidence of the greater degree of human engagement to which new technologies aspire [Tal95]. This paper reviews the potential application to educational technology of principles and tools for computer-based modelling that have been developed under the auspices of the Empirical Modelling (EM) project at Warwick [EMweb]. This theme was first addressed at length in a previous paper [Bey97], and is here revisited in the light of new practical developments in EM both in respect of tools and of model-building that has been targetted at education at various levels. Our central thesis is that the problems of educational technology stem from the limitations of current conceptual frameworks and tool support for the essential cognitive model building activity, and that tackling these problems requires a radical shift in philosophical perspective on the nature and role of empirical knowledge that has significant practical implications. The paper is in two main sections. The first discusses the limitations of the classical computer science perspective where educational technology to support situated learning is concerned, and relates the learning activities that are most closely associated with a cultural context to the empiricist perspective on learning introduced in [Bey97]. The second outlines the principles of EM and describes and illustrates features of its practical application that are particularly well-suited to learning in a cultural setting

Studies of Stability and Robustness for Artificial Neural Networks and Boosted Decision Trees

In this paper, we compare the performance, stability and robustness of Artificial Neural Networks (ANN) and Boosted Decision Trees (BDT) using MiniBooNE Monte Carlo samples. These methods attempt to classify events given a number of identification variables. The BDT algorithm has been discussed by us in previous publications. Testing is done in this paper by smearing and shifting the input variables of testing samples. Based on these studies, BDT has better particle identification performance than ANN. The degradation of the classifications obtained by shifting or smearing variables of testing results is smaller for BDT than for ANN.Comment: 23 pages, 13 figure

Monotone decompositions of inverse limit spaces based on finite graphs

AbstractA Θn,L graph is defined to be a compact, connected, locally connected metric space which is not separated into more than n components by any subcontinuum and no subcontinuum is separated into more than L components by any of its subcontinua. If X is a Θn,L graph and f is a continuous surjection of X onto X, then the inverse limit space (X,f) is a Θn continuum (not necessarily locally connected). Furthermore (X,f) admits a unique minimal monotone, upper semicontinuous decomposition D such that the quotient space (X,f)/D is a Θn,L graph if and only if (X,f) contains no indecomposable subcontinua with nonempty interior

Studies of Boosted Decision Trees for MiniBooNE Particle Identification

Boosted decision trees are applied to particle identification in the MiniBooNE experiment operated at Fermi National Accelerator Laboratory (Fermilab) for neutrino oscillations. Numerous attempts are made to tune the boosted decision trees, to compare performance of various boosting algorithms, and to select input variables for optimal performance.Comment: 28 pages, 22 figures, submitted to Nucl. Inst & Meth.

Introduction to MiniBooNE and Vu charged-current quasi-elastic results

"The MiniBooNE experiment is described together with the procedures used to obtain a result for Vm - Ve oscillations. (The oscillation results are described in the companion talk of M. Sorel.) Results are given here for the charged-current quasi-elastic (CCQE) cross section, Vmn - m[?]p. It is found that the simple relativistic Fermi gas nuclear model with Fermi momentum, PF = 220 MeV/c and binding energy EB = 34 MeV is insufficient to describe the reaction for any values of the axial vector mass MA. It was found necessary to add a new empirical Pauli blocking parameter, k. With this new term, the best values found were MA = 1.23 +- 0.20 GeV and k = 1.019 +- 0.011."http://deepblue.lib.umich.edu/bitstream/2027.42/64213/1/jpconf8_110_082018.pd

A randomized controlled trial of PEEK versus titanium interference screws for anterior cruciate ligament reconstruction with 2-year follow-up

Purpose: To compare the clinical performance of ACL reconstruction with PEEK and titanium interference screws at 2 years and to evaluate a novel method of measuring tunnel volume. Study Design: Randomized controlled trial; Level of evidence, 1. Methods: A total of 133 patients underwent arthroscopic ACL reconstruction with 4-strand hamstring autografts and were randomized to have titanium or PEEK interference screws for femoral and tibial tunnel fixation. At 2 years, subjective Lysholm and International Knee Documentation Committee scores were assessed and clinical examination performed. At 12 months, MRI was performed to assess graft incorporation and cyst formation, and a novel technique was employed to measure tunnel volumes. Results: There were no significant differences in graft rerupture rate, contralateral ACL rupture rate, subjective outcomes, or objective outcomes. In the titanium and PEEK groups, MRI demonstrated high overall rates of graft integration (96%-100% and 90%-93%, respectively) and ligamentization (89% and 84%) and low rates of synovitis (22% and 10%) and cyst formation (0%-18% and 13%-15%). There was a higher proportion of patients with incomplete graft integration within the femoral tunnel in the PEEK group as compared with the titanium group (10% vs 0%, P = .03); however, the authors suggest that metal artifact precluded proper assessment of the graft in the titanium group by MRI. Tunnel volumes also appeared to be equivalent in the 2 groups and were measured with a novel technique that was highly reproducible in the PEEK group secondary to the absence of flare. Conclusion: Two-year clinical analysis of PEEK interference screws for femoral and tibial fixation of ACL reconstructions showed equivalent clinical performance to titanium interference screws. Given the excellent mechanical characteristics, biological compatibility, and absence of metal artifact on MRI, PEEK has become our material of choice for interference screw fixation in ACL reconstruction

Computers for learning : an empirical modelling perspective

In this thesis, we explore the extent to which computers can provide support for domain learning. Computer support for domain learning is prominent in two main areas: in education, through model building and the use of educational software; and in the workplace, where models such as spreadsheets and prototypes are constructed. We shall argue that computerbased learning has only realised a fraction of its full potential due to the limited scope for combining domain learning with conventional computer programming. In this thesis, we identify some of the limitations in the current support that computers offer for learning, and propose Empirical Modelling (EM) as a way of overcoming them. We shall argue that, if computers are to be successfully used for learning, they must support the widest possible range of learning activities. We introduce an Experiential Framework for Learning (EFL) within which to characterise learning activities that range from the private to the public, from the empirical to the theoretical, and from the concrete to the abstract. The term ‘experiential’ reflects a view of knowledge as rooted in personal experience. We discuss the merits of computer-based modelling methods with reference to a broad constructionist perspective on learning that encompasses bricolage and situated learning. We conclude that traditional programming practice is not well-suited to supporting bricolage and situated learning since the principles of program development inhibit the essential cognitive model building activity that informs domain learning. In contrast, the EM approach to model construction directly targets the semantic relation between the computer model and its domain referent and exploits principles that are closely related to the modeller’s emerging understanding or construal. In this way, EM serves as a uniform modelling approach to support and integrate learning activities across the entire spectrum of the EFL. This quality makes EM a particularly suitable approach for computer-based model construction to support domain learning. In the concluding chapters of the thesis, we demonstrate the qualities of EM for educational technology with reference to practical case studies. These include: a range of EM models that have advantages over conventional educational software due to their particularly open-ended and adaptable nature and that serve to illustrate a variety of ways in which learning activities across the EFL can be supported and scaffolded

The 'optimum' upwind advection on a triangular mesh

For advection schemes based on fluctuation splitting, a design criterion of optimizing the time step leads to linear schemes that coincide with those designed for least truncation error. A further stage of optimizing the time step using a nonlinear positivity criterion, leads to considerable further gains in resolution