In a triangulated category, cofibre fill-ins always exist. Neeman showed that there is at least one "good" fill-in, i.e., whose mapping cone exact. Verdier constructed fill-in of particular form in his proof the $4 \times 4$ lemma, which we call "Verdier good". We show for several classes morphisms exact triangles, notions good and agree. prove lifting criterion commutative squares terms (Verdi...

This paper presents a simple yet powerful original approach for approximating dispersivity in porous media. The key to this approach is both use of least-squares criterion and image processing technique. Two dimensional transparent models, including horizontal and vertical configurations, under different combinations of grain sizes and pore velocities, experimented. Concentration data were obta...

In this work we deal with the mathematical analysis and application of piecewise (or segmented) polynomial regression. Motivated by an application in neurobiology we allow the residual processes of our model to exhibit long memory, short memory or antipersistence. As a solid biological background is essential for understanding the application in this work, we start with an introduction to neuro...

In this paper, a revised Group Method of Data Handling (GMDH)-type neural network algorithm with a feedback loop identifying sigmoid function neural network is proposed. In this algorithm, the optimum sigmoid function neural network architecture is automatically organized so as to minimize the prediction error criterion defined as Akaike’s Information Criterion (AIC) or Prediction Sum of Square...

In factor analysis, a loading matrix is often rotated to simple target for its simplicity. For the purpose, Procrustes rotation minimizes discrepancy between and loadings using two types of approximation: 1) approximate zeros in by non-zeros loadings, 2) loadings. The central issue considered article that it equally treats approximation, while former more important simplifying matrix. Furthermo...

We propose a new optimizer in the context of multimodal image registration. The optimized criterion is the mutual information between the images to align. This criterion requires that their joint histogram be available. For its computation, we introduce differentiable and separable Parzen windows that satisfy the partition of unity. Along with a continuous model of the images based on splines, ...

We present new results on the nonlinear PCA (Principal Component Analysis) criterion in blind source separation (BSS). We derive the criterion in a form that allows easy comparisons with other BSS and Independent Component Analysis (ICA) contrast functions like cumulants, Bussgang criteria, and information theoretic contrasts. This clariies how the nonlinearity should be chosen optimally. We al...

An anisotropic refinement criterion suitable for Finite-Volume methods is presented and Navier–Stokes solutions are reported for the lid-driven cavity flow configuration at Re 1⁄4 1000 with adaptive anisotropic meshes (h-refinement). The a posteriori error estimation criterion is based on the assessment of the goodness-of-fit of the least squares regression used to perform the variables profile...

Adaptive signal processing theory was born and has lived by exclusively exploiting the mean square error criterion. When we think of the goal of least squares without restrictions of Gaussianity, one has to wonder why an information theoretic error criterion is not utilized instead. After all, the goal of adaptive filtering should be to find the linear projection that best captures the informat...

Linear system identifcation with noisy inputs is a critical problem in signal processing and control. Conventional techniques based on the Mean Squared-Error (MSE) criterion can at best provide a biased estimate of the unknown system being modeled. Recently, we proposed a new criterion called the Error Whitening Criterion (EWC) to solve the problem of linear parameter estimation in the presence...