Isomers of CAl4Mg and CAl4Mg? have been theoretically characterized for the first time. The most stable isomer both neutral anion contain a planar tetracoordinate carbon (ptC) atom. Unlike isovalent CAl4Be case, which contains pentacoordinate atom as global minimum geometry, replacing beryllium with magnesium makes ptC due to increased ionic radii magnesium. However, it is relatively easier con...

We consider deep linear networks with arbitrary differentiable loss. We provide a short and elementary proof of the following fact: all local minima are global minima if each hidden layer is wider than either the input or output layer.

In this paper a new technique, named Function “Stretching”, for the alleviation of the local minima problem is proposed. The main feature of this technique is the usage of a two–stage transformation of the objective function to eliminate local minima, while preserving the global ones. Experiments indicate that combined with the Particle Swarm Optimizer method, the new algorithm is capable of es...

In this paper a new technique, named Function “Stretching”, for the alleviation of the local minima problem is proposed. The main feature of this technique is the usage of a two–stage transformation of the objective function to eliminate local minima, while preserving the global ones. Experiments indicate that combined with the Particle Swarm Optimizer method, the new algorithm is capable of es...

Within the context of DNA rings, we analyze the relationship between intrinsic shape and the existence of multiple stable equilibria, either nicked or cyclized with the same link. A simple test, based on a perturbation expansion of symmetry breaking within a continuum elastic rod model, provides good predictions of the occurrence of such multiple equilibria. The reliability of these predictions...

Differential-Algebraic Constraints William R. Esposito and Christodoulos A. Floudas Department of Chemical Engineering, Princeton University, Princeton, N.J. 08544-5263,USA Differential-algebraic systems of constraints, in particular, initial value ordinary differential equations, appear in numerous optimization problems in the chemical engineering field. A difficulty in the solution of this fo...

We consider the following problem: minx∈Rn min‖E‖≤η ‖(A+E)x− b‖, where A is an m×n real matrix and b is an n-dimensional real column vector when it has multiple global minima. This problem is an errors-in-variables problem, which has an important relation to total least squares with bounded uncertainty. A computable condition for checking if the problem is degenerate as well as an efficient alg...