Orca: A Visualization Toolkit for High-Dimensional Data

Abstract

This article describes constructing interactive and dynamic linked data views using the Java programming language. The data views are designed for data that have a multivariate component. The approach to displaying data comes from earlier research on building statistical graphics based on data pipelines, in which different aspects of data processing and graphical rendering are organized conceptually into segments of a pipeline. The software design takes advantage of the object-oriented nature of the Java language to open up the data pipeline, allowing developers to have greater control over their visualization applications. Importantly, new types of data views coded to adhere to a few simple design requirements can easily be integrated with existing pipe sections. This allows access to sophisticated linking and dynamic interaction across all (new and existing) view types. Pipe segments can be accessed from data analysis packages such as Omegahat or R, providing a tight coupling of visual and numerical methods.     

Mixed methods with dynamic finite-element spaces for miscible displacement in porous media

Miscible displacement in porous media is modeled by a nonlinear coupled system of two partial differential equations. We approximate the pressure equation, which is elliptic, and the concentration equation, which is parabolic but normally convection-dominated, by the mixed methods with dynamic finite-element spaces, i.e., different number of elements and different basis functions are adopted at different time levels; and the approximate concentration is projected onto the next finite-element space in weighted L²-norm for starting a new time step. This allows us to make local grid refinements or unrefinements and basis function improvements. Two fully discrete schemes are presented and analysed. Error estimates show that these methods have optimal convergent rate in some sense. The efficiency and capability of the dynamic finite-element method are commented for accurately solving time-dependent problems with localized phenomena, such as fronts, shocks, and boundary layers.     

A Bayesian approach for the alignment of high-resolution NMR spectra

Metabolic analysis with high-resolution nuclear magnetic resonance (NMR) enables simultaneous investigation of numerous chemical species in response to biochemical changes in subjects. When the analysis involves comparing two or more NMR spectra, it is essential to properly align them because small variations across different spectra influence the alignment and thus, interfere with direct comparisons between samples. We propose a new alignment method within the Bayesian modeling framework. The proposed method allows us to estimate the amplitude and phase shifts simultaneously and to obtain robust results in the existence of noise. Effectiveness of our proposed method is demonstrated through real NMR spectra in human plasma and a comparison study with dynamic time warping and correlated optimized warping, two widely used alignment methods in spectral data.     

The role of prior mathematical experience in predicting mathematics performance in higher education

Evidence of deficiencies in basic mathematical skills of beginning undergraduates has been documented worldwide. Many different theories have been set out as to why these declines in mathematical competency levels have occurred over time. One such theory is the widening access to higher education which has resulted in a less mathematically prepared profile of beginning undergraduates than ever before. In response to this situation, the present study details the examination of a range of methods through which a student's mathematical performance in higher education could be predicted at the beginning of their third-level studies. Several statistical prediction methods were examined and the most effective method in predicting students’ mathematical performance was discriminant analysis. The discriminant analysis correctly classified 71.3% of students in terms of mathematics performance. An ability to carry out such a prediction in turn allows for appropriate mathematics remediation to be offered to students predicted to fail third-level mathematics. The results of the prediction of mathematical performance, which was carried out using a database consisting of over 1000 beginning undergraduates over a 3-year period, are detailed in this article along with the implications of such findings to educational policy and practice.     

Semi-analytical hybrid approach for the simulation of layered waveguide with a partially debonded piezoelectric structure

This paper presents an efficient semi-analytical hybrid approach for simulating the dynamic interaction of perfectly bonded or damaged piezoelectric structures with a layered elastic waveguide. In the proposed approach, the frequency domain spectral element method is utilized for the discretization of the finite-sized surface mounted piezoelectric structure, and the semi-analytical boundary integral method is employed for the evaluation of wave phenomena in the host laminate structure. While the spectral element method allows cost-effective simulation of dynamics of a complex-shaped transducer (e.g. curvilinear or with wrapped electrodes), the analytically-based technique reliably describes wave excitation and propagation in multi-layered structures. The coupling of these methods is achieved through the rigorous fulfillment of the boundary conditions at the area of waveguide-transducer contact. Three various combinations of approximation polynomials and surface-load interpolation functions are applied in order to obtain the solution in a frequency domain. The time-domain solution is evaluated employing the inverse Laplace transform. Convergence of the method is confirmed for different bonding conditions. The paper demonstrates the efficiency of the proposed method for the multi-parameter analysis of the dependence of the resonance characteristics on the debonding parameters and contact conditions. The approach can be used for such a crucial task as diagnosing failures of piezoelectric devices incorporated into a structural health monitoring system based on guided waves.     

Determination of Inner and Outer Bounds of Reachable Sets Through Subpavings

The computation of the reachable set of states of a given dynamic system is an important step to verify its safety during operation. There are different methods of computing reachable sets, namely interval integration, capture basin, methods involving the minimum time to reach function, and level set methods. This work deals with interval integration to compute subpavings to over or under approximate reachable sets of low dimensional systems. The main advantage of this method is that, compared to guaranteed integration, it allows to control the amount of over-estimation at the cost of increased computational effort. An algorithm to over and under estimate sets through subpavings, which potentially reduces the computational load when the test function or the contractor is computationally heavy, is implemented and tested. This algorithm is used to compute inner and outer approximations of reachable sets. The test function and the contractors used in this work to obtain the subpavings involve guaranteed integration, provided either by the Euler method or by another guaranteed integration method. The methods developed were applied to compute inner and outer approximations of reachable sets for the double integrator example. From the results it was observed that using contractors instead of test functions yields much tighter results. It was also confirmed that for a given minimum box size there is an optimum time step such that with a greater or smaller time step worse results are obtained.     

Comparison of coupled and decoupled modal approaches in seismic analysis of concrete gravity dams in time domain

Different methods are available for dynamic analysis of concrete dams. Among these, modal approach is highly popular due to the efficiency of the method. This becomes more significant if the response is to be calculated for several earthquake ground motion records as required in most practical cases. In this study, two different modal approaches have been considered for dynamic analysis of concrete gravity dam–reservoir systems. These are coupled modal method and decoupled modal technique. The former approach utilizes the coupled modes of the system. It is well known that calculation of these modes involves some complications due to its corresponding unsymmetrical eigenproblem. However, the response at each step can be obtained very efficiently in this method. The latter technique, relies on the decoupled modes of the system, which are easily obtained by standard eigenvalue solvers. The equation of motion is also solved with reasonable efficiency in this approach. In the latter part of this paper, analysis of a typical dam–reservoir system is performed by both methods mentioned above. These analyses are compared from accuracy and efficiency point of view.     

基于社会网络结构的创新扩散动力机制及其仿真研究

随着社会资本的大量涌入,创新扩散逐渐受到社会网络关系的影响。在分析了创新扩散机理的基础上,构建了基于不同拓扑结构的创新扩散演化动力模型。将信息获取、领导者创新能力及机会利益作为创新扩散的动力因子。通过利用复杂网络的演化博弈仿真分析,揭示了小世界、无标度等不同网络拓扑结构下,创新技术的扩散情况。仿真结果表明:在网络结构相同的情况下,信息获取对创新扩散的影响较大;在动力因子设定相同的情况下,网络主体连接越规则,创新扩散越充分。     

A new nonlinear dynamic analysis method of rotor system supported by oil-film journal bearings

The strong nonlinear behavior usually exists in rotor systems supported by oil-film journal bearings. In this paper, the partial derivative method is extended to the second-order approximate extent to predict the nonlinear dynamic stiffness and damping coefficients of finite-long journal bearings. And the nonlinear oil-film forces approximately represented by dynamic coefficients are used to analyze nonlinear dynamic performance of a symmetrical flexible rotor-bearing system via the journal orbit, phase portrait and Poincaré map. The effects of mass eccentricity on dynamic behaviors of rotor system are mainly investigated. Moreover, the computational method of nonlinear dynamic coefficients of infinite-short bearing is presented. The nonlinear oil-film forces model of finite-long bearing is validated by comparing the numerical results with those obtained by an infinite-short bearing-rotor system model. The results show that the representation method of nonlinear oil-film forces by dynamic coefficients has universal applicability and allows one easily to conduct the nonlinear dynamic analysis of rotor systems.     

Multilevel Functional Principal Component Analysis for High-Dimensional Data

We propose fast and scalable statistical methods for the analysis of hundreds or thousands of high-dimensional vectors observed at multiple visits. The proposed inferential methods do not require loading the entire dataset at once in the computer memory and instead use only sequential access to data. This allows deployment of our methodology on low-resource computers where computations can be done in minutes on extremely large datasets. Our methods are motivated by and applied to a study where hundreds of subjects were scanned using Magnetic Resonance Imaging (MRI) at two visits roughly five years apart. The original data possess over ten billion measurements. The approach can be applied to any type of study where data can be unfolded into a long vector including densely observed functions and images. Supplemental materials are provided with source code for simulations, some technical details and proofs, and additional imaging results of the brain study.     

Smoothed Particle Hydrodynamics modelling of poroelastic media

Numerical modelling of poroelastic properties in porous media allows widely varied investigations at low costs and relatively short times. The study of porous media is of high interest at different scales, in this case we focus our analysis at meso- and macroscale which is highly relevant e.g. in geothermal explorations. We model a biphasic poroelastic media assuming incompressible fluid and solid grains and a large solid-fluid density ratio. Meshfree methods are nowadays more widely used due to the advantages that present in the simulation of large deformations. In this case we choose to employ the Smoothed Particle Hydrodynamics method (SPH), a Lagrangian method where the domain is discretized in particles. The solution is computed in parallel, which allows to simulate large domains more representative of the scale of our study cases. We validate our implementation with a classical consolidation problem and compare the simulated diffusion process with Terzaghi's analytical solution. Future work includes simulation of fractures initiation and propagation in the porous media at reservoir scale. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Decision Analysis and Real Options: A Discrete Time Approach to Real Option Valuation

In this paper we seek to enhance the real options methodology developed by Copeland and Antikarov (2001) with traditional decision analysis tools to propose a discrete time method that allows the problem to be specified and solved with off the shelf decision analysis software. This method uses dynamic programming with an innovative algorithm to model the project’s stochastic process and real options with decision trees. The method is computationally intense, but simpler and more intuitive than traditional methods, thus allowing for greater flexibility in the modeling of the problem.     

Splitting and composition methods for explicit time dependence in separable dynamical systems

We consider splitting methods for the numerical integration of separable non-autonomous differential equations. In recent years, splitting methods have been extensively used as geometric numerical integrators showing excellent performances (both qualitatively and quantitatively) when applied on many problems. They are designed for autonomous separable systems, and a substantial number of methods tailored for different structures of the equations have recently appeared. Splitting methods have also been used for separable non-autonomous problems either by solving each non-autonomous part separately or after each vector field is frozen properly. We show that both procedures correspond to introducing the time as two new coordinates. We generalize these results by considering the time as one or more further coordinates which can be integrated following either of the previous two techniques. We show that the performance as well as the order of the final method can strongly depend on the particular choice. We present a simple analysis which, in many relevant cases, allows one to choose the most appropriate split to retain the high performance the methods show on the autonomous problems. This technique is applied to different problems and its performance is illustrated for several numerical examples.     

Mixed quadratic-cubic autocatalytic reaction–diffusion equations: Semi-analytical solutions

Semi-analytical solutions for autocatalytic reactions with mixed quadratic and cubic terms are considered. The kinetic model is combined with diffusion and considered in a one-dimensional reactor. The spatial structure of the reactant and autocatalyst concentrations are approximated by trial functions and averaging is used to obtain a lower-order ordinary differential equation model, as an approximation to the governing partial differential equations. This allows semi-analytical results to be obtained for the reaction–diffusion cell, using theoretical methods developed for ordinary differential equations. Singularity theory is used to investigate the static multiplicity of the system and obtain a parameter map, in which the different types of steady-state bifurcation diagrams occur. Hopf bifurcations are also found by a local stability analysis of the semi-analytical model. The transitions in the number and types of bifurcation diagrams and the changes to the parameter regions, in which Hopf bifurcations occur, as the relative importance of the cubic and quadratic terms vary, is explored in great detail. A key outcome of the study is that the static and dynamic stability of the mixed system exhibits more complexity than either the cubic or quadratic autocatalytic systems alone. In addition it is found that varying the diffusivity ratio, of the reactant and autocatalyst, causes dramatic changes to the dynamic stability. The semi-analytical results are show to be highly accurate, in comparison to numerical solutions of the governing partial differential equations.     

Improvement of separability of time series in singular spectrum analysis using the method of independent component analysis

The separation of signal components is an important problem of time-series analysis. For example, the solution of this problem allows one to extract a trend and to separate harmonic signals with different frequencies. In the paper, the modification of the singular spectrum analysis (SSA) method is considered for improving the separability of time-series components. The new method is called SSA-AMUSE, since it is based on the AMUSE method, which is used to apply independent component analysis to signal separation. The suggested modification weakens the conditions of the so-called strong separability and, thus, improves the quality of the separation of time-series components by comparing similar methods. The paper contains proof of the algorithm, as well as the conditions of separability for the considered modification. Besides the exact separability, the asymptotic separability is also considered. The separability conditions are applied to the case of two harmonic time series. It appears that separability by SSA-AMUSE does not depend on the amplitudes of the separated harmonics, while the Basic SSA method requires different amplitudes. A numerical example demonstrates the advantage of the SSA-AMUSE method compared with a similar modification.     

Dynamic Programming in One-Day Cricket-Optimal Scoring Rates

Using a dynamic programming formulation, an analysis is presented of the innings of the team which bats first (here referred to as the first innings) and the innings of the team which bats second (here referred to as the second innings). This allows a calculation, at any stage of the innings, of the optimal scoring rate, along with an estimate of the total number of runs to be scored (in the first innings) or the chance of winning (in the second innings). The analysis is used to shed some light on possible batting tactics (in terms of the best run rate at any stage of the innings), to quantify the effects of selecting extra batsmen in a side, and to suggest a method for the development of alternative measures of player performance. Results suggest that scoring rates should be more uniform than at present, and that the team batting second has an advantage. Possible extensions to the model are discussed.     

Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk

The dynamics of a circular cylindrical shell carrying a rigid disk on the top and clamped at the base is investigated. The Sanders–Koiter theory is considered to develop a nonlinear analytical model for moderately large shell vibration. A reduced order dynamical system is obtained using Lagrange equations: radial and in-plane displacement fields are expanded by using trial functions that respect the geometric boundary conditions.The theoretical model is compared with experiments and with a finite element model developed with commercial software: comparisons are carried out on linear dynamics.The dynamic stability of the system is studied, when a periodic vertical motion of the base is imposed. Both a perturbation approach and a direct numerical technique are used. The perturbation method allows to obtain instability boundaries by means of elementary formulae; the numerical approach allows to perform a complete analysis of the linear and nonlinear response.     

基于分位点自回归模型的动态持续期风险估计

两笔交易之间的持续期可以用来度量资产的流动性,本文借鉴VaR的思想,提出了持续期风险DaR的定义,可以用来度量资产的流动性风险,并给出了两种DaR的静态估计方法。同时根据持续期数据的序列相关的特点,应用分位点自回归方法得到了DaR的一种有效的动态估计方法。最后对我国股票市场的单只股票的分笔交易数据进行了实证分析,结果表明由分位点自回归方法得出的DaR结果预测效果最好。     

On regularization methods based on dynamic programming techniques

In this article, we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of these methods is to obtain stable approximations to the solution of linear inverse ill-posed problems. We follow two different approaches and derive a continuous and a discrete regularization method. Regularization properties for both methods are proved as well as rates of convergence. A numerical benchmark problem concerning integral operators with convolution kernels is used to illustrate the theoretical results.