Baud-rate blind equalization algorithms may converge to undesirable stable equi-libria due to diierent reasons. One is the use of FIR lter as an equalizer. It is proved in this paper that this kind of local minima exist for all blind equalization algorithms. The local minima generated by this mechanism are thus called unavoidable local minima. The other one is due to the cost function adopted b...

Recently, we reported a series of global minima whose structures consist carbon rings decorated with heavier group 14 elements. Interestingly, these feature planar tetracoordinate carbons (ptCs) and result from the replacement five or six protons (H+) cyclopentadienyl anion (C5H5−) pentalene dianion (C8H62−) by three four E2+ dications (E = Si–Pb), respectively. The silicon derivatives are Si3C...

The marginal entropy hðZÞ of a weighted sum of two variables Z 1⁄4 aX þ bY ; expressed as a function of its weights, is a usual cost function for blind source separation (BSS), and more precisely for independent component analysis (ICA). Even if some theoretical investigations were done about the relevance from the BSS point of view of the global minimum of hðZÞ; very little is known about poss...

Many machine learning and data science tasks require solving non-convex optimization problems. When the loss function is a sum of multiple terms, popular method stochastic gradient descent. Viewed as process for sampling landscape, descent known to prefer flat minima. Though this desired certain problems such in deep learning, it causes issues when goal find global minimum, especially if minimu...

The spectrum of nitrous oxide dimer was investigated by constructing new potential energy surfaces using coupled-cluster theory and solving the rovibrational Schrödinger equation with a Lanczos algorithm. Two four-dimensional (rigid monomer) global ab initio potential energy surfaces (PESs) were made using an interpolating moving least-squares (IMLS) fitting procedure specialized to describe th...

The ignoring delete lists relaxation is of paramount importance for both satisficing and optimal planning. In earlier work [Hoffmann, JAIR’05], it was observed that the optimal relaxation heuristic h has amazing qualities in many classical planning benchmarks, in particular pertaining to the complete absence of local minima. The proofs of this are hand-made, raising the question whether such pr...