Optimal portfolio for nonstationary security market

A new interpretation of the classical portfolio problem is suggested. It is based on the optimization on the conditional expectation of a utility function where the conditional expectation is calculated taking into account all information available at the moment of decision making. This approach allows to show that the risk is a sequence of forecasting errors. Main classes of forecasting algorithms are described and compared. A similarity between some variants of solutions to the modified portfolio problem and the traditional technical analysis recommendations is shown. The scheme is essentially important for nonstationary nonequilibrium security market. Some results of its practical application to the Russian bond market are presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal nonlinear passage through a quantum critical point

We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power law in time. The optimal power is proportional to the logarithm of the total passage time multiplied by universal critical exponents characterizing the phase transition. We support our results by the general scaling analysis and by explicit calculations for the transverse-field Ising model.     

Increasing rewriting speed of optical rewritable e-paper by selecting proper liquid crystals

Effect of interaction between liquid crystal (LC) and photoalignment material on speed of optical rewriting process is investigated. The theoretical analysis shows that smaller frank elastic constant K₂₂ of liquid crystal corresponds to larger twist angle, which gives rise to larger rewriting speed. Six different LC cells with the same boundary conditions (one substrate is covered with rubbed polyimide (PI) and other with photo sensitive rewritable sulfuric dye 1(SD1)) are tested experimentally under the same illumination intensity (450 nm, 80 mW/cm²). The results demonstrate that with suitable liquid crystal, LC optical rewriting speed for e-paper application can be obviously improved. For two well known LC materials E7 (K₂₂ is larger) and 5CB (K₂₂ is smaller), they require 11 s and 6 s corresponding to change alignment direction for generating image information.     

Phase transition in a system of one-dimensional bosons with strong disorder

We study one-dimensional disordered bosons at large commensurate filling. Using a real space renormalization group approach, we find a new random fixed point which controls a phase transition from a superfluid to an incompressible Mott glass. The transition can be tuned by changing the disorder distribution even with vanishing interactions. We derive the properties of the transition, which suggest that it is in the Kosterlitz-Thouless universality class.     

Influence of capture centers of luminophore mixtures on their efficiency in energy-saving luminescent daylight lamps

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 5, pp. 798–802, May, 1991.     

Temperature dependences of thermal expansion and exchange magnetostriction of holmium and dysprosium single crystals

Information on the character of the temperature relationships of linear expansion coefficients (α_a, α_c) and exchange magnetostrictions (λ_a, λ_a) of single crystal Ho and Dy, based on temperature dependence of thec- anda-axis lattice constants, were accurately determined by X-ray diffraction from 4,2 to 300 K. In the helical phases we observed a large anisotropy of expansion coefficients (α_a>0, α_c<0) and their variations at 24,5, 45 and 96 in Ho and 156 K in Dy. These anomalies were caused by the commensurate transitions. The Curie transition in Ho is found to be of the 1-st order.     

Randomized first order algorithms with applications to ℓ 1-minimization

In this paper we propose randomized first-order algorithms for solving bilinear saddle points problems. Our developments are motivated by the need for sublinear time algorithms to solve large-scale parametric bilinear saddle point problems where cheap online assessment of the solution quality is crucial. We present the theoretical efficiency estimates of our algorithms and discuss a number of applications, primarily to the problem of ? ₁ minimization arising in sparsity-oriented signal processing. We demonstrate, both theoretically and by numerical examples, that when seeking for medium-accuracy solutions of large-scale ? ₁ minimization problems, our randomized algorithms outperform significantly (and progressively as the sizes of the problem grow) the state-of-the art deterministic methods.     

Optimal Mathematical Models for Nonlinear Dynamical Systems

We propose a new method for the optimal causal representation of nonlinear systems. The proposed approach is based on the best constrained approximation of mappings in probability spaces by operators constructed from matrices of special form so that the approximant preserves the causality property. It is supposed that the observable input is contaminated with noise. The approximant minimises the mean-square difference between a desired output signal and the output signal of the approximating model. The method provides a numerically realisable mathematical model of the system. An analysis is given of the error associated with this representation.     

Verifiable conditions of <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1</Subscript>-recovery for sparse signals with sign restrictions

We propose necessary and sufficient conditions for a sensing matrix to be “s-semigood” – to allow for exact ℓ ₁-recovery of sparse signals with at most s nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect ℓ ₁-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse ℓ ₁-recovery and thus efficiently computable upper bounds on those s for which a given sensing matrix is s-semigood. We examine the properties of proposed verifiable sufficient conditions, describe their limits of performance and provide numerical examples comparing them with other verifiable conditions from the literature.