1991 Mathematics Subject Classi cation: 11F11, 11E20.

The Particle Swarm Optimizer, like many other evolutionary and classical minimization methods, su ers the problem of occasional convergence to local minima, especially in multimodal and scattered landscapes. In this work we propose a modi cation of the Particle Swarm Optimizer that makes use of a new technique, named Function \Stretching", to alleviate the local minima problem. Function \Stretc...

We study local energy minima of twenty(L-alanine). The minima are generated using high-temperature Molecular Dynamics and Chain-Growth Monte Carlo simulations, with subsequent minimization. We find that the lower-energy configurations are α-helices for a wide range of dielectric constant values (ǫ = 1, 10, 80), and that there is no noticeable difference between the distribution of energy minima

Given a branching random walk, let Mn be the minimum position of any member of the n’th generation. We calculate EMn to within O(1) and prove exponential tail bounds for P {|Mn − EMn| > x}, under quite general conditions on the branching random walk. In particular, together with work of [8], our results fully characterize the possible behavior of EMn when the branching random walk has bounded b...

We propose a theory that relates difficulty of learning in deep architectures to culture and language. It is articulated around the following hypotheses: (1) learning in an individual human brain is hampered by the presence of effective local minima; (2) this optimization difficulty is particularly important when it comes to learning higher-level abstractions, i.e., concepts that cover a vast a...

Finite length CMA equalizers contain undesired minima termed Length Dependent Local Minima (LDLM). We note that for auto-regressive (AR) channels, the equalizer output is correlated with a delayed input at these minima. This property is then used to modify the CMA cost function and remove the LDLM in AR channels. Permission to publish this abstract separately is granted.

In this paper we study a class of integral functionals defined on H 0 (Ω), but non coercive on the same space, so that the standard approach of the Calculus of Variations does not work. However, the functionals are coercive on W 1,1 0 (Ω) and we will prove the existence of minima, despite the non reflexivity of W 1,1 0 (Ω), which implies that, in general, the Direct Methods fail due to lack of ...

We investigate the cosmological signatures of instantons mediating tunneling between de Sitter minima. For generic potentials the Coleman-de Luccia instanton does not necessarily exist; when it does not, the instanton which contributes to the decay rate is the trivial constant solution, known as the Hawking-Moss instanton. With the aid of a toy model we interpret this solution and describe the ...

Wepropose a theory that relates difficulty of learning in deep architectures to culture and language. It is articulated around the following hypotheses: (1) learning in an individual human brain is hampered by the presence of effective local minima; (2) this optimization difficulty is particularly important when it comes to learning higher-level abstractions, i.e., concepts that cover a vast an...