Objective Function Features Providing Barriers to Rapid Global Optimization

The purposes of this discussion paper are twofold. First, features of an objective function landscape which provide barriers to rapid finding of the global optimum are described. Second, stochastic algorithms are discussed and their performance examined, both theoretically and computationally, as the features change. The paper lays a foundation for the later findings paper.     

Entropic Penalties in Finite Games

The main objects here are finite-strategy games in which entropic terms are subtracted from the payoffs. After such subtraction each Nash equilibrium solves an explicit, unconstrained, nonlinear system of smooth equations. That system, while characteristic of perturbed best responses, is amenable in computation. It also facilitates analysis of fictitious play, learning by reinforcement, and evolutionary dynamics.     

Robust$${\cal {H}}_{\infty}$$ Stabilization of Stochastic Hybrid Systems with Wiener Process

This paper deals with the class of uncertain continuous-time linear stochastic hybrid systems with Wiener process. The uncertainties that we are considering are of the norm-bounded type. The robust stochastic stabilization problem is treated. LMIs based sufficient conditions are developed to design the state feedback controller that robustly and stochastically stabilizes the studied class of systems and at the same time rejects a disturbance of desired level. The minimum disturbance rejection is also determined. A numerical example is provided to show the validity of the proposed results.     

Weighted BMO and discrete time hedging within the Black-Scholes model

The paper combines two objects rather different at first glance: spaces of stochastic processes having weighted bounded mean oscillation (weighted BMO) and the approximation of certain stochastic integrals, driven by the geometric Brownian motion, by integrals over piece-wise constant integrands. The consideration of the approximation error with respect to weighted BMO implies L_p and uniform distributional estimates for the approximation error by a John-Nirenberg type theorem. The general results about weighted BMO are given in the first part of the paper and applied to our approximation problem in the second one.     

Stochastic nonlinear beam equations

An extensible beam equation with a stochastic force of a white noise type is studied, Lyapunov functions techniques being used to prove existence of global mild solutions and asymptotic stability of the zero solution.This research was supported in part by the GA R Grants no. 201/98/1454, 201/01/1197 and by a Royal Society grant     

On the relationship between differentiability conditions and existence of a strong gradient

It is proved that for any n 2 there exists continuous function f : ⁿ which is differentiable almost everywhere, but has no strong gradient almost everywhere.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 93–98.Original Russian Text Copyright © 2005 by G. G. Oniani.This revised version was published online in April 2005 with a corrected issue number.     

Quadrupole interaction of tantalum impurities in bismuth metal

The time differential perturbed angular correlation technique has been used in the measurement of the electric quadrupole interaction of Ta impuritiy in bismuth metal. The interaction frequencies at 293, 400 and 500 K have been observed to be 288±1.5, 266.9±3 and 244.5±4.3 MHz respectively. The electric field gradient at 293 K is 4.75±0.3 × 10¹⁷ V/cm² with the temperature coefficientB=2.2±0.2 × 10⁻⁵ (K)^−3/2.     

Amphiphilic Peptide–Polymer Conjugates with Side‐Conjugation

Polymers conjugated to the exterior of a protein mediate its interactions with surroundings, enhance its processability and can be used to direct its macroscopic assemblies. Most studies to date have focused on peptide–polymer conjugates based on hydrophilic polymers. Engineering amphiphilicity into protein motifs by covalently linking hydrophobic polymers has the potential to interface peptides and proteins with synthetic polymers, organic solvents, and lipids to fabricate functional hybrid materials. Here, we synthesized amphiphilic peptide–polymer conjugates in which a hydrophobic polymer is conjugated to the exterior of a heme‐binding four‐helix bundle and systematically investigated the effects of the hydrophobicity of the conjugated polymer on the peptide structure and the integrity of the heme‐binding pocket. In aqueous solution with surfactants present, the side‐conjugated hydrophobic polymers unfold peptides and may induce an α‐helix to β‐sheet conformational transition. These effects decrease as the polymer becomes less hydrophobic and directly correlate with the polymer hydrophobicity. Upon adding organic solvent to solubilize the hydrophobic polymers, however, the deleterious effects of hydrophobic polymers on the peptide structures can be eliminated. Present studies demonstrate that protein structure is sensitive to the local environment. It is feasible to dissolve amphiphilic peptide–polymer conjugates in organic solvents to enhance their solution processability while maintaining the protein structures.