A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning

Journal of Optimization Theory and Applications - We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with...     

Synthesis and Properties of Azoles and Their Derivatives. Part 70. Nitroallylic Systems in [2 + 3] Cycloaddition Reactions with Nitrones: A DFT Computational Study

The analysis of electrophilicity indexes and the results of potential energy surface (PES) simulations for the reaction pathways proved that the [2 + 3] cycloadditions of nitroallylic systems with nitrones should be considered nonpolar reactions. Our simulations proved that the reactions always proceed via a one‐step mechanism through a prereaction complex. Although the symmetry of respective transition states is quite varied, their polarity is low and does not change when a polar medium is introduced to the reaction environment. When the polarity of the reaction medium increases, the kinetic pathway preference does not change. The regiochemistry of the cycloadditions tested may, however, be controlled to some extent by steric effects.     

Space-Time Directional Lyapunov Exponents for Cellular Automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.     

Effective dimensionality approach to the RKKY interaction in multilayer systems

We consider RKKY interaction in a quasi 2D system with nonparabolic dispersion. In our paper we calculate the RKKY range function assuming the in-layer confinement via effective dimensionality approach. We show, that indirect magnetic exchange in our system can be modelled by the effective spectral dimension which equals one.     

Regularization of Discrete Ill-Posed Problems

The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is proved under the assumption of the suitable relation between the discretization level and the data error. As an example the method of truncated singular value decomposition with regularization is considered. This revised version was published online in July 2006 with corrections to the Cover Date.