New Set Of Variables Research Articles

A New Formulation for Feedforward Neural Networks

Feedforward neural network is one of the most commonly used function approximation techniques and has been applied to a wide variety of problems arising from various disciplines. However, neural networks are black-box models having multiple challenges/difficulties associated with training and generalization. This paper initially looks into the internal behavior of neural networks and develops a detailed interpretation of the neural network functional geometry. Based on this geometrical interpretation, a new set of variables describing neural networks is proposed as a more effective and geometrically interpretable alternative to the traditional set of network weights and biases. Then, this paper develops a new formulation for neural networks with respect to the newly defined variables; this reformulated neural network (ReNN) is equivalent to the common feedforward neural network but has a less complex error response surface. To demonstrate the learning ability of ReNN, in this paper, two training methods involving a derivative-based (a variation of backpropagation) and a derivative-free optimization algorithms are employed. Moreover, a new measure of regularization on the basis of the developed geometrical interpretation is proposed to evaluate and improve the generalization ability of neural networks. The value of the proposed geometrical interpretation, the ReNN approach, and the new regularization measure are demonstrated across multiple test problems. Results show that ReNN can be trained more effectively and efficiently compared to the common neural networks and the proposed regularization measure is an effective indicator of how a network would perform in terms of generalization.

Fluxomers: a new approach for 13C metabolic flux analysis

BackgroundThe ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.ResultsThis article addresses the mathematical and computational formulation of 13C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.ConclusionsSubstantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.

Conservative solutions to a nonlinear variational sine-Gordon equation

This paper is concerned with a nonlinear variational sine-Gordon equation u t t − c ( u ) [ c ( u ) u x ] x + λ 2 2 s i n ( 2 u ) = 0 which describes the motion of long waves on a neutral dipole chain in the continuum limit and a few other physical phenomena. We establish the global existence of an energy-conservative weak solution to its Cauchy problem for initial data of finite energy. To deal with the possible blowup of solutions, we introduce a new set of variables depending on the energy, whereby all singularities are resolved.

Gaudin models solver based on the correspondence between Bethe ansatz and ordinary differential equations

We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a new set of variables, the canceling divergences which occur for certain values of the coupling strength no longer appear explicitly. The problem is thus reduced to a set of quadratic algebraic equations. The required inverse transformation can then be realized using only linear operations and a standard polynomial root finding algorithm. The method is applied to Richardson's fermionic pairing model, the central spin model and generalized Dicke model.

Changing Patterns and Determinants of Interprovincial Migration in China 1985–2000

ABSTRACTMost migration analyses focus on inter‐regional migration in one particular period. Recently, efforts have also been made to compare migration intensity and patterns across countries. Instead of comparison over space, this paper is concerned with the temporal dimension. Can the same model, using the same set of variables, explain migration patterns in two different periods? Is there any change in the determinants of interprovincial migration in China? This paper attempts to answer these questions using migration data from the 1990 and 2000 censuses of China. It was found that coastal regions such as Guangdong, Zhejiang, Tianjin, and Fujian joined Shanghai and Beijing as the top destinations of migration over time. ‘Pull’ factors in the growing regions play an important role in the expanding migration in China. The same set of variables was used to explain the migration in 1985–1990 and 1995–2000. The same model can explain 51.6% of the variation of migration in 1995–2000, greater than 41.6% in 1985–1990. Nevertheless, absolute parameters in the model were bigger in 1995–2000 than in 1985–1990 to reflect the increasing scale of migration. A better model for 1995–2000 is also established using a new set of variables. Two income variables have a positive impact on migration, confirming the importance of income in internal migration in China. Copyright © 2011 John Wiley & Sons, Ltd.

지도학습기법을 이용한 비선형 다변량 공정의 비정상 상태 탐지

Principal Component Analysis (PCA) reduces the dimensionality of the process by creating a new set of variables, Principal components (PCs), which attempt to reflect the true underlying process dimension. However, for highly nonlinear processes, this form of monitoring may not be efficient since the process dimensionality can't be represented by a small number of PCs. Examples include the process of semiconductors, pharmaceuticals and chemicals. Nonlinear correlated process variables can be reduced to a set of nonlinear principal components, through the application of Kernel Principal Component Analysis (KPCA). Support Vector Data Description (SVDD) which has roots in a supervised learning theory is a training algorithm based on structural risk minimization. Its control limit does not depend on the distribution, but adapts to the real data. So, in this paper proposes a non-linear process monitoring technique based on supervised learning methods and KPCA. Through simulated examples, it has been shown that the proposed monitoring chart is more effective than <TEX>$T^2$</TEX> chart for nonlinear processes.

A PDE for non-intersecting Brownian motions and applications

Consider N = n 1 + n 2 + ⋯ + n p non-intersecting Brownian motions on the real line, starting from the origin at t = 0 , with n i particles forced to reach p distinct target points β i at time t = 1 , with β 1 < β 2 < ⋯ < β p . This can be viewed as a diffusion process in a sector of R N . This work shows that the transition probability, that is the probability for the particles to pass through windows E ˜ k at times t k , satisfies, in a new set of variables, a non-linear PDE which can be expressed as a near-Wronskian; that is a determinant of a matrix of size p + 1 , with each row being a derivative of the previous, except for the last column. It is an interesting open question to understand those equations from a more probabilistic point of view. As an application of these equations, let the number of particles forced to the extreme points β 1 and β p tend to infinity; keep the number of particles forced to intermediate points fixed (inliers), but let the target points themselves go to infinity according to a proper scale. A new critical process appears at the point of bifurcation, where the bulk of the particles forced to − n depart from those going to n . These statistical fluctuations near that point of bifurcation are specified by a kernel, which is a rational perturbation of the Pearcey kernel. This work also shows that such equations are an essential tool in obtaining certain asymptotic results. Finally, the paper contains a conjecture.

Parabolic equation solutions with increased capabilities for layered poro‐elastic media.

Parabolic equation solutions have recently been improved to increase accuracy for range‐dependent problems involving sloping fluid‐solid interfaces. One improvement is a formulation using a new set of variables that includes a term proportional to the normal stress at a horizontal interface [J. Acoust. Soc. Am. 127, 1962 (2010)]. These variables lead to horizontal interface conditions with only first‐order derivatives, which is valuable for implementing techniques such as energy conservation or single scattering that handle range dependence. This improvement is extended to problems that involve layered poro‐elastic media that occur in shallow water environments. An analogous formulation is derived for the field variables in a poro‐elastic layer. The horizontal interface conditions have similar characteristics as in the elastic case. Solutions are obtained for layered environments and are benchmarked to confirm accuracy. [Work supported by the ONR.]

A New Set of Variables in the Three-Body Problem

Abstract We propose a set of variables of the general three-body problem both for two-dimensional and three-dimensional cases. The variables are ($\lambda, \theta, \Lambda, \Theta, k, \omega$), or equivalently ($\lambda, \theta, L, \dot{I},k,\omega)$ for the two-dimensional problem, and ($\lambda, \theta, L, \dot{I}, k, \omega, \phi, \psi$) for the three-dimensional problem. Here, ($\lambda, \theta$) and ($\Lambda, \Theta)$ specify the positions in the shape spheres in the configuration and momentum spaces, $k$ is the virial ratio, $L$ is the total angular momentum, $\dot{I}$ is the time derivative of the moment of inertia, and $\omega, \phi$, and $\psi$ are the Euler angles to bring the momentum triangle from the nominal position to a given position. This set of variables defines a shape space of the three-body problem. This is also used as an initial-condition space. The initial condition of the so-called free-fall three-body problem is ($\lambda, \theta, k =$ 0, $L =$ 0, $\dot{I} =$ 0, $\omega =$ 0). We show that the hyper-surface $\dot{I} =$ 0 is a global surface of section.

NONLINEAR STABILITY ANALYSIS OF THE EMDEN–FOWLER EQUATION

In this paper, we qualitatively study radial solutions of the semilinear elliptic equation Δu+un = 0 with u(0) = 1 and u′(0) = 0 on the positive real line, called the Emden–Fowler or Lane–Emden equation. This equation is of great importance in Newtonian astrophysics and the constant n is called the polytropic index. By introducing a set of new variables, the Emden–Fowler equation can be written as an autonomous system of two ordinary differential equations which can be analyzed using linear and nonlinear stability analysis. We perform the study of stability by using linear stability analysis, the Jacobi stability analysis (Kosambi–Cartan–Chern-theory) and the Lyapunov function method. Depending on the values of n these different methods yield different results. We identify a parameter range for n where all three methods imply stability.

COMBINING FEATURE SELECTION WITH EXTRACTION: UNSUPERVISED FEATURE SELECTION BASED ON PRINCIPAL COMPONENT ANALYSIS

Principal components analysis (PCA) is a popular linear feature extractor, and widely used in signal processing, face recognition, etc. However, axes of the lower-dimensional space, i.e., principal components, are a set of new variables carrying no clear physical meanings. Thus we propose unsupervised feature selection algorithms based on eigenvectors analysis to identify critical original features for principal component. The presented algorithms are based on k-nearest neighbor rule to find the predominant row components and eight new measures are proposed to compute the correlation between row components in transformation matrix. Experiments are conducted on benchmark data sets and facial image data sets for gender classification to show their superiorities.

Existence of solutions for a model of multiphase flow in porous media applied to gas migration in underground nuclear waste repository

We prove existence of solutions for a new model of two compressible and partially miscible phase flow in porous media, applied to gas migration in underground nuclear waste repository. This model, modelling fully and partially water saturated situations, consists of a coupled system of quasilinear parabolic partial differential equations. We seek a new set of variables in order to obtain a system which belongs to the class of equations considered by Alt and Luckhaus such that it would be possible to use their existence theorem.

Optimal Estimators for Systems With Finite Consecutive Packet Dropouts

This paper is concerned with the optimal estimation problem for discrete-time stochastic linear systems with finite consecutive packet dropouts. By introducing a set of new variables, a state augmented system with a lower order is obtained. Based on the new model, the optimal estimators including filter, predictor and smoother are readily solved in the least-mean-square sense via the innovation analysis approach. The solutions depend on the recursion of a Riccati equation and a Lyapunov equation. The steady-state estimators have also been investigated. A sufficient condition for the convergence of the optimal estimators has been given. A simulation shows the effectiveness of the proposed algorithms.

Challenging Assumptions about the Achievement Gap: Part Two

Assumptions About Achievement Gap: Part Two As an educational researcher, it's gratifying to wonder about some problem of practice, undertake a systematic investigation, and discover that your speculation or gut feeling about issue proved right. This has been case in our study of gaps. Although today we are university professors with responsibilities for teaching and scholarship, other career experiences as teachers and school administrators also shaped our perspective on education. We questioned much of research literature about between minority and majority students. Our personal observations and experiences with diverse populations of students told us that was not a matter of race or ethnicity, but rather a question of personal challenges faced by individual students. We believe that key to policy development related to overcoming is more likely to be found by understanding differences within groups rather than between groups. In our first study, reported in Challenging Assumptions About Achievement Gap (Phi Delta Kappan, April 2005), we presented our findings from an examination of student among black, Hispanic (or Latino), and white students (Ramirez and Carpenter 2005; Carpenter, Ramirez, and Severn 2006). That research determined that singular definition of achievement gap (that is, difference between white and minority students) misrepresents complex and multi-layered dynamics at work in academic of black, Hispanic, and white students. Instead of dominant and singular understanding of the gap, we demonstrated that there are multiple gaps related to student and that more significant gaps were not between groups, but within groups. We concluded that casting as a white/minority dichotomy was a risky misconception that potentially promotes poor policy solutions. That research was based on an analysis of data from National Educational Longitudinal Study of 1988 (National Center for Education Statistics 2007). We recently expanded our research beyond typical measure of student performance on tests to high school dropout status. Once again, we looked at data from black, Hispanic, and white student cohorts using National Educational Longitudinal Study of 1988. As in our earlier research, we examined differences in dropout status both between and within racial/ethnic groups, paying particular attention to differences or similarities in significant predictors for each group. Moreover, we explored whether predictor variables for three groups in our earlier study would also predict dropout behavior in same manner. We found that patterns of significant predictors for dropout status were not same as in earlier study, and in process we uncovered a new set of variables associated with dropping out. Yet, new set of significant predictors for dropout status did demonstrate some consistency with our earlier research. We found certain common patterns among white and Hispanic students, but we found no statistically significant differences in dropout status based on race/ethnicity. Thus, once again we found that within-group differences may be more significant than between-group differences (Carpenter and Ramirez 2007). WHAT WE RESEARCHED The overall thrust of our research has been to challenge conventional wisdom about gap, which is typically characterized as a difference in learning between white and minority students. In our first study of gaps, we looked at academic and found not one but many gaps, and most significant of these gaps existed within racial and ethnic groups themselves. That study tested a large index of predictor variables for each racial/ethnic group and identified these as most significant: * Socioeconomic status (for all three groups); * Participation in an English language acquisition program (for all three groups); * Time spent on homework (for black and white students); * Number of units of algebra taken (for Hispanic and white students); and * Level of parent involvement (for all three groups). …

A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository

We prove existence of solutions for a new model of two compressible and partially miscible phase flow in porous media, applied to gas migration in an underground nuclear waste repository. This model, modeling fully and partially water saturated situations, consist of a coupled system of quasilinear parabolic partial differential equations. We seek a new set of variables in order to obtain a system which belongs to the class of equations considered by Alt and Luckhaus such that it would be possible to use their existence theorem. A simulation of a numerical test case is performed in order to numerically demonstrate the ability of this model to take in account the appearance of one phase. To cite this article: F. Smaï, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

On the stabilizing effect of convection in three‐dimensional incompressible flows

AbstractWe investigate the stabilizing effect of convection in three‐dimensional incompressible Euler and Navier‐Stokes equations. The convection term is the main source of nonlinearity for these equations. It is often considered destabilizing although it conserves energy due to the incompressibility condition. In this paper, we show that the convection term together with the incompressibility condition actually has a surprising stabilizing effect. We demonstrate this by constructing a new three‐dimensional model that is derived for axisymmetric flows with swirl using a set of new variables. This model preserves almost all the properties of the full three‐dimensional Euler or Navier‐Stokes equations except for the convection term, which is neglected in our model. If we added the convection term back to our model, we would recover the full Navier‐Stokes equations. We will present numerical evidence that seems to support that the three‐dimensional model may develop a potential finite time singularity. We will also analyze the mechanism that leads to these singular events in the new three‐dimensional model and how the convection term in the full Euler and Navier‐Stokes equations destroys such a mechanism, thus preventing the singularity from forming in a finite time. © 2008 Wiley Periodicals, Inc.

Automatic Freeway Incident Detection Based on Fundamental Diagrams of Traffic Flow

Algorithms for automatic incident detection (AID) detect traffic incidents on the basis of traffic flow measurements. There are two important steps in an AID algorithm: traffic flow feature generation and incident decision making. In the past decade, the research on freeway AID algorithms has been focused on using artificial intelligence to optimize the decision making of AID algorithms. In this paper, the primary focus is on finding a new set of variables for the feature generation. The new variables, uncongested and congested regime shifts (URS and CRS), are generated by conducting coordinate transformation on loop-detected flow and occupancy measurements. A novel AID algorithm, the fundamental diagrams–based automatic incident detection (FD AID) algorithm, is then developed by implementing the incident-related traffic flow knowledge using those variables. Preliminary results show superior performance of the FD algorithm compared with legacy algorithms.

On the Partial Regularity of a 3D Model of the Navier-Stokes Equations

We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected in the model. If we add the convection term back to our model, we would recover the full Navier-Stokes equations. In [11], we presented numerical evidence which seems to support that the 3D model develops finite time singularities while the corresponding solution of the 3D Navier-Stokes equations remains smooth. This suggests that the convection term play an essential role in stabilizing the nonlinear vortex stretching term. In this paper, we prove that for any suitable weak solution of the 3D model in an open set in space-time, the one-dimensional Hausdorff measure of the associated singular set is zero. The partial regularity result of this paper is an analogue of the Caffarelli-Kohn-Nirenberg theory for the 3D Navier-Stokes equations.

GAUSSIAN ELEMENT FORMULATION OF SHORT-AXIS-MODE ROTATION OF A RIGID BODY

Equations of the short-axis-mode rotation of a rigid body under a general torque field are derived in terms of a new set of variables. The transformation between the new variables and the non-canonical Andoyer variables is explicitly given in closed form. The right-hand sides of the new equations are the sum of two main terms for two angle variables and six perturbative terms. All the perturbative terms are expressed as linear combinations of torque vector components. In the case of torque-free motions, the two angle variables become linear functions of time and the remaining four variables become constants of motion. As a result, the new variables consist of a set of rotational elements in a broad sense. This formulation is a counterpart, in rotational dynamics, of the Gaussian formulation of the Keplerian orbital elements for elliptic orbits.

Understanding purchasing behaviors in a virtual economy: Consumer behavior involving virtual currency in Web 2.0 communities

This study analyzes consumer purchasing behavior in Web 2.0, expanding the technology acceptance model (TAM), focusing on which variables influence the intention to transact with virtual currency. Individuals’ responses to questions about attitude and intention to transact in Web 2.0 were collected and analyzed with various factors modified from the TAM. The results of the proposed model show that subjective norm is a key behavioral antecedent to using virtual currency. In the extended model, the moderating effects of subjective norm on the relations among the variables were found to be significant. The new set of variables is virtual environment-specific, acting as factors enhancing attitudes and behavioral intentions in Web 2.0 transactions.