Comon’s well-known scheme for independent component analysis (ICA) is based on the maximal diagonalization, in a least-squares sense, of a higher-order cumulant tensor. In a previous papr, we proved that for fourth-order cumulants, the computation of an elementary Jacobi rotation is equivalent to the computation of the best rank-1 approximation of a fourth-order tensor. In this paper, we show t...

Abstract The magnetization process of the S = 1 antiferromagnetic chain with single-ion anisotropy D and biquadratic interaction is investigated using numerical diagonalization. Both interactions stabilize 2-magnon Tomonaga-Luttinger liquid (TLL) phase in process. Based on several excitation gaps calculated by diagonalization, some diagrams are presented. These reveal that spin nematic dominant...

Joint diagonalization of several correlation matrices is a powerful tool for blind signal separation. This paper addresses the blind signal separation problem for the case where the source signals are non-stationary and / or non-white, and the sensors are possibly noisy. We present cost functions for jointly diagonalizing several correlation matrices. The corresponding gradients are derived and...

This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method [1891]. It renders the proof of the so–called fixed point theorem transparent. We also point out various historical details and make some observations on circularity and some comparisons with natural language. The sketch does not include the messy details of the arithmetization o...

We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the N -site fermion model are used to compute the entropy density: our results are consistent with the numerical solution of N =∞ saddle point equations, and the presence of a non-zero entropy density in the limit of vanishing...

Since the stage of diagonalization of Jacobi–type methods is difficult to monitor in a parallel environment, it is usually proposed to execute a predetermined number of sweeps (iterations) on a parallel processor array. A possibility for monitoring the stage of diagonalization is essential in order to avoid the execution of a significant number of unnecessary sweeps. Based on a Lemma used for a...

Functional magnetic resonance imaging group studies rely on the ability to establish correspondence across individuals. This enables location specific comparison of functional brain characteristics. Registration is often based on morphology and does not take variability of functional localization into account. This can lead to a loss of specificity, or confounds when studying diseases. In this ...