The circuit optimization process is formulated as a dynamic controllable system. A special control vector is defined to redistribute the compute expense between a network analysis and a parametric optimization. This redistribution permits the minimization a computer time. The problem of a minimal-time circuit optimization can be formulated in this case as a classical problem of the optimal cont...

This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining t...

In this article, we explore the concept of minimization of information loss (MIL) as a a target for neural network learning. We relate MIL to supervised and unsupervised learning procedures such as the Bayesian maximum a-posteriori (MAP) discriminator, minimization of distortion measures such as mean squared error (MSE) and cross-entropy (CE), and principal component analysis (PCA). To deal wit...

The design process for analog network design is formulated on the basis of the optimum control theory. A special control vector is defined to redistribute the compute expensive between a network analysis and a parametric optimization. This redistribution permits the minimization of a computer time. The problem of the minimal-time network design can be formulated in this case as a classical prob...

Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle highdimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the large-scale data with high dimensionality. Meanwhile, the squared L2-norm based objective makes it sensitive to data outliers. In recent research, the L1-norm maximi...

We have recently made explicit the precise connection between the optimization of orthonormal filter banks (FBs) and the principal component property: The principal component filter bank (PCFB) is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This explains PCFB optimality for compression, progressive transmission, and various hitherto unno...

Principal component analysis (PCA), a well-established technique for data analysis and processing, provides a convenient form of dimensionality reduction that is effective for cleaning small Gaussian noises presented in the data. However, the applicability of standard principal component analysis in real scenarios is limited by its sensitivity to large errors. In this paper, we tackle the chall...

*Correspondence: Claudius Gros, Institute forTheoretical Physics, Goethe University Frankfurt, Max-von-Laue-Strasse 1, Postfach 111932, Frankfurt, Germany e-mail: [email protected] Generating functionals may guide the evolution of a dynamical system and constitute a possible route for handling the complexity of neural networks as relevant for computational intelligence. We propose and...

We have recently made explicit the precise connection between the optimization of orthonor-mal lter banks (FB's) and the principal component property: The principal component lter bank (PCFB) is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This explains PCFB optimality for compression, progressive transmission and various hitherto unnotic...

This paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. The equations of evolution satisfying the conservation law are geodesics under the diffeomorphism metric and therefore termed geodesically controlled diffeomorphic active shapes (GDAS). Our principal application in this paper is...