The problem of the uniqueness of solutions during the evaluation of primary energy spectra in the knee region using an extensive air shower (EAS) data set and the EAS inverse approach is investigated. It is shown that the unfolding of primary energy spectra in the knee region leads to mutually compensative pseudo solutions. These solutions may be the reason for the observed disagreements in the...

An alternative approach, between much others, for mathematical representation of dynamics systems with complex or chaotic behaviour, is a radial basis function neural network using k-means for clustering and optimized by pseudo-inverse and particle swarm optimisation. This paper presents the implementation and study to identify a dynamic system, with nonlinear and chaotic behaviour, called Röss...

A bstract We point out that neutrinos can have enhanced couplings to photons, if light (pseudo)scalar mediators are present, resulting in a potentially measurable neutrino polarizability. show the expected suppression from small masses be compensated by mediator mass, generating dimension 7 Rayleigh operators at low scales. explore rich phenomenology of such models, computing detail constraints...

A new BAM model is presented that uses a chaotic output function operating in chaotic mode during recall. Our results show that the model develops well-defined attractor basins, with the result that our chaotic BAM is more tolerant to noise than a regular fixed point BAM. This is concluded from simulations that showed the superior performance of the new model when compared to the original BAM a...

An experiment is described to obtain estimates of the spectral sensitivities of a digital image capture device by photographing a wide range of input color signals. Given the red, green, and blue signals from the device and the spectral power distributions of the color signals, we apply the methods of simple linear regression, rankdeficient pseudo-inverse, and Wiener estimation. Nominal data an...

In this paper we study the problem of the occurrence of cycles in autoassociative neural networks. We call these cycles dynamic attractors, show when and why they occur and how they can be identi-ed. Of particular interest is the pseudo-inverse network with reduced self-connection. We prove that it has dynamic attractors, which occur with a probability proportional to the number of prototypes a...

| We show how to automatically acquire a Euclidean shape representations of objects from noisy image sequences under weak perspective. The proposed method is linear and incre-mental, requiring no more than pseudo-inverse. A nonlinear but numerically sound preprocessing stage is added to improve the accuracy of the results even further. Experiments show that attention to noise and computational ...

Ivan Selesnick March 7, 2013 NYU-Poly These notes address (approximate) solutions to linear equations by least squares. We deal with the ‘easy’ case wherein the system matrix is full rank. If the system matrix is rank deficient, then other methods are needed, e.g., QR decomposition, singular value decomposition, or the pseudo-inverse, [2, 3]. In these notes, least squares is illustrated by appl...

We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of J.F. Colombeau and establish the inverse Cauchy-Schwarz inequality in this context. As an application, we prove a dominant energy condition for some energy tensors as put forward in Hawking and Ellis’s book “The large scale structure of space-time”. Our work is based on a new character...