Technology scoring model for reflecting evaluator’s perception within confidence limits

The main purpose of this study is to propose a new technology scoring model for reflecting the total perception scoring phenomenon which happens often in many evaluation settings. A base model used is a logistic regression for non-default prediction of a firm. The point estimator used to predict the probability for non-default based on this model does not consider the risk involved in the estimation error. We propose to update the point estimator within its confidence interval using the evaluator’s perception. The proposed approach takes into account not only the risk involved in the estimation error of the point estimator but also the total perception scoring phenomenon. Empirical evidence of a better prediction ability of the proposed model is displayed in terms of the area under the ROC curves. Additionally, we showed that the proposed model can take advantage when it is applied to smaller data size. It is expected that the proposed approach can be applied to various technology related decision-makings such as R&D investment, alliance, transfer, and loan.     

Prediction of confidence limits for reliability indexes with linear dependence on parameters

We construct the confidence limits for a reliability index when the reliability-determining stochastic process is linear in random parameters.Translated from Statisticheskie Metody, pp. 134–141, 1982.     

Boundary element method in Biot's linear consolidation

A boundary element method is formulated for the general theory of Biot's linear consolidation. Results for typical examples show good agreement with finite element solutions. As the cpu time in two dimensions is unsatisfactory an alternative method of calculating the stresses is suggested.     

Estimating a linear functional relationship under linear constraints for errors

Maximum likelihood estimates for parameters in a linear functional relationship are derived when the errors are also linearly related for each observation. This is approximately the case, for example, when both variables are smooth functions of time and their values are recorded as an experimental unit reaches a certain state. This kind of model specification was needed to describe how the timing of growth cessation of trees depends on night length and temperature sum. If the slope in the constraint equation for errors varies, then an iterative estimation procedure is needed. The estimation method is extended for a two-phase linear model.     

Kuratowski's and Wagner's theorems for matroids

In an earlier paper we proved the following theorem, which provides a strengthening of Tutte's well-known characterization of regular (totally unimodular) matroids: A binary matroid is regular if it does not have the Fano matroid or its dual as a series-minor (parallel-minor). In this paper we prove two theorems (Theorems 5.1 and 6.1) which provide the same kind of strengthening for Tutte's characterization of the graphic matroids (i.e., bond-matroids). One interesting aspect of these theorems is the introduction of the matroids of “type R”. It turns out that these matroids are, in at least two different senses, the smallest regular matroids which are neither graphic nor cographic (Theorems 6.2 and 6.3).     

On the solvability of Bellman's functional equations for Markov renewal programming

The functional equations of undiscounted, stationary, infinite horizon Markov renewal programming are shown to possess a solution, by an elementary application of the Leray-Schauder fixed point theorem.     

Mersenne's solution for Galileo's problem of the rotating earth

More than twenty years before Huygens and Newton developed formulas for centrifugal acceleration, Mersenne contrived a statisfactory solution for Galileo's problem of the extrusion of bodies from the earth as a result of its daily rotation. Mersenne was able to overcome an error in Galileo's approach without the use either of an explicit notion of infinitesimals or of any clear concept of force. His solution depends on comparing the lengths of two lines, a technique that several historians have claimed to be inadequate for this problem.     

Estimation of the slope in a linear functional relationship

Summary Two nonparametric estimators of the slope of a regression line with error on both variables are considered, each of them being defined as the zero-crossing of a stochastic process whose sample paths are monotone. Their asymptotic behaviour is derived from the local asymptotic behaviour of the underlying processes. One of the estimators is a nonparametric version of Wald's (1940) estimator.This research was supported by the Swiss National Science Foundation     

Reducibility of first order linear operators on tori via Moser's theorem

In this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus

${?}_{t}u+\zeta ?{?}_{x}u+a(\omega t,x)?{?}_{x}u=0,x\in {\mathbb{T}}^d,\zeta \in {\mathbb{R}}^d,\omega \in {\mathbb{R}}^{\nu }.$

As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on ${\mathbb{T}}^{\nu +d}$ to a constant diophantine flow. For this purpose we generalize Moser's straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.     

Note on the Markus-Yamabe conjecture for gradient dynamical systems

Let be a C¹ vector field which has a singular point O and its linearization is asymptotically stable at every point of Rn. We say that the vector field v satisfies the Markus-Yamabe conjecture if the critical point O is a global attractor of the dynamical system . In this note we prove that if v is a gradient vector field, i.e. v=∇f (f∈C²), then the basin of attraction of the critical point O is the whole Rn, thus implying the Markus-Yamabe conjecture for this class of vector fields. An analogous result for discrete dynamical systems of the form xm+1=∇f(xm) is proved.     

A conjugate Rosen’s gradient projection method with global line search for piecewise linear concave optimization

The Kelley cutting plane method is one of the methods commonly used to optimize the dual function in the Lagrangian relaxation scheme. Usually the Kelley cutting plane method uses the simplex method as the optimization engine. It is well known that the simplex method leaves the current vertex, follows an ascending edge and stops at the nearest vertex. What would happen if one would continue the line search up to the best point instead? As a possible answer, we propose the face simplex method, which freely explores the polyhedral surface by following the Rosen’s gradient projection combined with a global line search on the whole surface. Furthermore, to avoid the zig-zagging of the gradient projection, we propose a conjugate gradient version of the face simplex method. For our preliminary numerical tests we have implemented this method in Matlab. This implementation clearly outperforms basic Matlab implementations of the simplex method. In the case of state-of-the-art simplex implementations in C or similar, our Matlab implementation is only competitive for the case of many cutting planes.     

Stillman's question for exterior algebras and Herzog's conjecture on Betti numbers of syzygy modules

Let K be a field of characteristic 0 and consider exterior algebras of finite dimensional K-vector spaces. In this short paper we exhibit principal quadric ideals in a family whose Castelnuovo–Mumford regularity is unbounded. This negatively answers the analogue of Stillman's Question for exterior algebras posed by I. Peeva. We show that, via the Bernstein–Gel'fand–Gel'fand correspondence, these examples also yields counterexamples to a conjecture of J. Herzog on the Betti numbers in the linear strand of syzygy modules over polynomial rings.     

The efficiency of adjusted least squares in the linear functional relationship

A linear functional errors-in-variables model with unknown slope parameter and Gaussian errors is considered. The measurement error variance is supposed to be known, while the variance of errors in the equation is unknown. In this model a risk bound of asymptotic minimax type for arbitrary estimators is established. The bound lies above that one which was found previously in the case of both variances known. The bound is attained by an adjusted least-squares estimators.     

On some analogs of Sturm's and Kneser's theorems for nonlinear systems

Analogs of certain conjugate point properties in the calculus of variations are developed for optimal control problems. The main result in this direction is concerned with the characterization of a parameterized family of extremals going through the first backward conjugate point, t_c. A corollary of this result is that for the linear quadratic problem (LQP) there exists at least a one-parameter family of extremals going though the conjugate point which gives the same cost as the candidate extremal, i.e., the extremal control is optimal but nonunique on [t_c, t_f]. An analysis of the effect on the conjugate point of employing penalty functions for terminal equality constraints in the LQP is presented, also. It is shown that the sequence of approximate conjugate points is always conservative, and it converges to the conjugate point of the constrained problem. Furthermore, it is proved that the addition of terminal constraints has the effect of causing the conjugate point to move backward (or remain the same).     

Some test statistics for the structural coefficients of the multivariate linear functional relationship model

Summary For the testing problem concerning the coefficients of the multivariate linear functional relationship model, the distribution of a statistic previously proposed by A. P. Basu depends on the unknown covariance matrixV of errors, so limiting its applicability. This article proposes new test statistics with sampling distributions which are independent of the unknown parameters for the cases whereV is either unknown or known only up to a proportionality factor. The exact distributions of the test statistics are also discussed.