GOSH: derivative-free global optimization using multi-dimensional space-filling curves

Global optimization is a field of mathematical programming dealing with finding global (absolute) minima of multi-dimensional multiextremal functions. Problems of this kind where the objective function is non-differentiable, satisfies the Lipschitz condition with an unknown Lipschitz constant, and is given as a “black-box” are very often encountered in engineering optimization applications. Due to the presence of multiple local minima and the absence of differentiability, traditional optimization techniques using gradients and working with problems having only one minimum cannot be applied in this case. These real-life applied problems are attacked here by employing one of the mostly abstract mathematical objects—space-filling curves. A practical derivative-free deterministic method reducing the dimensionality of the problem by using space-filling curves and working simultaneously with all possible estimates of Lipschitz and Hölder constants is proposed. A smart adaptive balancing of local and global information collected during the search is performed at each iteration. Conditions ensuring convergence of the new method to the global minima are established. Results of numerical experiments on 1000 randomly generated test functions show a clear superiority of the new method w.r.t. the popular method DIRECT and other competitors.     

Generalized Correspondence Analysis for Three-Valued Logics

Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP (which is built in the \( \{\vee ,\wedge ,\lnot \} \)-language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete analogue of LP, strong Kleene logic \( \mathbf K_3 \). In this paper, we generalize these results for the negative fragments of LP and \( \mathbf K_3 \), respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or \( \mathbf K_3 \), but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of \( \mathbf K_3 \) and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic \( \mathbf G_3 \) and its dual \( \mathbf DG_3 \) (which have different interpretations of negation than \( \mathbf K_3 \) and LP).     

Highly asymmetric soliton complexes in parabolic optical lattices

We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states can be stable. The unique topology of parabolic lattices affords new types of soliton motion: single solitons launched into the lattice with nonzero transverse momentum perform periodic oscillations along parabolic paths.     

Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index

We address vortex solitons supported by optical lattices featuring modulation of both the linear and nonlinear refractive indices. We find that when the modulation is out of phase the competition between both effects results in remarkable shape transformations of the solitons that profoundly affect their properties and stability. Nonlinear refractive index modulation is found to impose restrictions on the maximal power of off-site solitons, which are shown to be stable only below a maximum nonlinearity modulation depth.     

Weak values of electron spin in a double quantum dot

We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.     

Gd-doping of HfO2

An increase in the density of states between the oxygen 2p bands and the Fermi level is seen with increasing Gd concentrations. In addition, for the Gd-doped HfO₂ films, the Gd 4f photoexcitation peak at 5.5 eV below the valence band maximum was identified using resonant photoemission. Electrical measurements show pronounced rectification properties for lightly-doped Gd:HfO₂ films on p-Si and for heavily-doped Gd:HfO₂ films on n-Si, suggesting a crossover from n-type to p-type behavior with increasing doping level. In addition, there is an increase in the reverse bias current with neutron irradiation.     

Poly[3,3-bis(azidomethyl)oxetane]–2,4-dinitro-2,4-diazapentane

Constructing phase diagrams for the mixtures of semicrystalline polymers and low molecular mass substances by DSC can meet with difficulties in the case of slow polymer crystallization. A problem of this kind is encountered for high-energy compositions poly[3,3-bis(azidomethyl)oxetane] (PBAMO)–2,4-dinitro-2,4-diazapentane (DNAP). In this study, the experimental phase diagram PBAMO–DNAP is constructed by an optical method, which makes it possible to visualize structural transformations. The kinetic studies by DSC and XRD reveal that 30–50 days of storing a homogenized PBAMO–DNAP mixture at room temperature are needed to attain stationary values of the crystallinity degree and heat of fusion. Even after that, the DSC method cannot deliver a solubility curve of DNAP in PBAMO, which is naturally generated by the optical method. This curve separates a domain of physical gels, effectively crosslinked by polymer crystallites and swollen with the plasticizer molecules, from a two-phase domain, in which the above gel reaches osmotic equilibrium with the pure plasticizer. It is also shown that the melting temperature of DNAP drops with growing the PBAMO content in the mixture, which is consistent with a decrease in the mean size of plasticizer crystals formed in polymer pores during the previous cooling.     

Inhomogeneous nature of UV absorption bands of bulk and surface oxygen-deficient centers in silica glasses

Photochemical and photoluminescence studies of oxygen-deficient centers stabilized in the bulk and on the surface of silica glasses clearly demonstrate the inhomogeneous nature of the absorption and luminescence spectra of oxygen-deficient centers. The conclusion is drawn that the inhomogeneity of the absorption spectra is due to the dispersion of the energy of the S₀-S₁ transition, while the inhomogeneity of the luminescence spectra is due to the dispersion of the energy barrier of intersystem crossing. The inhomogeneous nature of the oxygen-deficient centers in silica glasses is assumed to be caused by a small dispersion in the geometrical parameters of different groups of centers with similar chemical properties.     

Conjugated microporous poly(phenylene butadiynylene)s

High surface area porous poly(phenylene butadiynylene) networks were obtained (BET surface area up to 842 m(2) g(-1)) by the palladium-catalyzed homocoupling of 1,3,5-triethynylbenzene and 1,4-diethynylbenzene.