Support vector machine via nonlinear rescaling method

In this paper we construct the linear support vector machine (SVM) based on the nonlinear rescaling (NR) methodology (see [Polyak in Math Program 54:177–222, 1992; Polyak in Math Program Ser A 92:197–235, 2002; Polyak and Teboulle in Math Program 76:265–284, 1997] and references therein). The formulation of the linear SVM based on the NR method leads to an algorithm which reduces the number of support vectors without compromising the classification performance compared to the linear soft-margin SVM formulation. The NR algorithm computes both the primal and the dual approximation at each step. The dual variables associated with the given data-set provide important information about each data point and play the key role in selecting the set of support vectors. Experimental results on ten benchmark classification problems show that the NR formulation is feasible. The quality of discrimination, in most instances, is comparable to the linear soft-margin SVM while the number of support vectors in several instances were substantially reduced.     

Kinetics of the reactions of 2,4,6-tri-t-butylphenoxyl with cumene hydroperoxide,cumylperoxyl radicals,and molecular oxygen

Reactions of 2,4,6-tri-t-butylphenoxyl (TBP) with cumene hydroperoxide (ROOH), cumylperoxyl radicals (RO₂), and molecular oxygen in benzene solution have been investigated kinetically by the ESR method. The rate constant of the reaction TBP + ROOH has been estimated in the temperature range 27°-75°C: log₁₀(k_?7/M^?1sec^?1) = (7.1 ± 0.4) - (10.9 ± 0.6 kcal mole^?1)/θ The ratio of the rate constants of reactions TBPH + RO₂ products has been determined from the experimental dependence of the rate constant of reaction TBP with ROOH on [TBPH]₀/[TBP]₀. Putting k₇ = 4.0 × 10³M^?1sec^?1, we obtain k₈ = (2.0 ± 0.2) × 10⁸M^?1sec^?1 at 30°C. The reaction of TBP with O₂ obeys the kinetic law ?d[TBP]/dt = k′[O₂][TBP]². This is in accordance with scheme TBP + O₂ ← TBP ?O₂ [I]; TBP ?O₂ + TBP · products, log₁₀ (k′/M^?2sec^?1) = (?14.5 ± 0.9) + (27.2 ± 1.4)/θ at 66°?78°C, where ° = 2.303RT.     

Conductive wiring of immobilized photosynthetic reaction center to electrode by cytochrome C

The photosynthetic reaction center (RC) found in photosynthetic bacteria is one of the most advanced photoelectronic devices developed by nature. However, after immobilization on the electrode surface, the efficiency of electron transfer (ET) between the RC and the electrode is relatively low. This inefficiency has limited the possibility of using the RC for technological applications. Here we show that photoinduced electron transfer between the immobilized RC and a gold electrode can be increased by several tens-fold by incorporation of cytochrome c into the RC-self-assembled monolayer (SAM)-electrode complex. The effect does not depend on the initial redox state of the cytochrome and seems to be the result of the formation of a complex between the RC and the cytochrome c serving as an ET wire. This observation opens the possibility for electrochemical analysis of the special pair in the RC protein that is deeply buried inside the protein globe and is barely electrically addressable from the electrode surface.     

Structural reorganizations control intermolecular conductance and charge trapping in paraquat-tetraphenylborate inverse photochemical cell

Miniaturization of electronic devices to the level of single molecules requires detailed understanding of the mechanisms of their operation. One of the questions here is the identification of the role of structural alterations in charge separation and stabilization in photoactive complexes. To address this question, we calculate optimized molecular and electronic structures, and optical and vibrational spectra of l,l'-dimethyl 4,4'-bipyridinium-bis tetraphenylborate PQ(BPh(4))(2) complex ab initio using density functional theory approach and compare them with the experimentally observed UV-Vis and Raman spectra of the molecules in solid-state films. The results indicate that the association of PQ and BPh(4) leads to the formation of an internally ionized structure that is accompanied by the structural reorganization of both PQ (the twisting of pyridinium rings) and BPh(4) (phenyl rings rotation) moieties. The quanta of light do not seem to be directly involved in the formation of this ionized structure, but provide energy for fast recombination of the separated charges between BPh(4)(-) and PQ(2+). The high efficiency of the dark charge separation and the stabilization of separated charges in the complex permit the using of PQ(BPh(4))(2) in various charge-transfer devices like molecular probes, photovoltaic devices or chemical memory units.     

Bimolecular reaction of 2,4,6-tri-tert-butylphenoxyl with hydroperoxide group in a solid polymer matrix

2,4,6-Tri-tert-butylphenoxyl (TBP) is dissolved and reacted with hydroperoxide groups of polyethylene and polypropylene in the amorphous phase. The reaction is not limited by diffusion, and unlike the case in the liquid phase, the concentration of TBP is not zero at the end of the reaction time, even though hydroperoxide groups are in excess. The biomolecular rate constant is smaller in the solid than it is in the liquid phase and depends on molecular motion. A linear relationship between the rate constant and frequency of rotation of radicals in polymers is observed.     

1.5-Q-superlinear convergence of an exterior-point method for constrained optimization

We introduce and analyze an exterior-point method (EPM) for constrained optimization problems with both inequality constraints and equations. We show that under the standard second-order optimality conditions the EPM converges to the primal–dual solution with 1.5-Q-superlinear rate. Dedicated to Professor Gil Strang on the occasion on his 70th birthday.     

Primal-dual nonlinear rescaling method with dynamic scaling parameter update

In this paper we developed a general primal-dual nonlinear rescaling method with dynamic scaling parameter update (PDNRD) for convex optimization. We proved the global convergence, established 1.5-Q-superlinear rate of convergence under the standard second order optimality conditions. The PDNRD was numerically implemented and tested on a number of nonlinear problems from COPS and CUTE sets. We present numerical results, which strongly corroborate the theory. The research of the authors supported by the NSF Grant CCF-0324999     

Numerical Experiments with an Interior-Exterior Point Method for Nonlinear Programming

The paper presents an algorithm for solving nonlinear programming problems. The algorithm is based on the combination of interior and exterior point methods. The latter is also known as the primal-dual nonlinear rescaling method. The paper shows that in certain cases when the interior point method (IPM) fails to achieve the solution with the high level of accuracy, the use of the exterior point method (EPM) can remedy this situation. The result is demonstrated by solving problems from COPS and CUTE problem sets using nonlinear programming solver LOQO that is modified to include the exterior point method subroutine.     

Primal-Dual Nonlinear Rescaling Method for Convex Optimization

In this paper, we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate the error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions, the error bounds for the primal and dual sequences converge to zero with linear rate. Moreover, for any given ratio 0 > > 1, there is a fixed scaling parameter k > 0 such that each PDNR step shrinks the primal-dual error bound by at least a factor 0 > > 1, for any k k. The PDNR solver was tested on a variety of NLP problems including the constrained optimization problems (COPS) set. The results obtained show that the PDNR solver is numerically stable and produces results with high accuracy. Moreover, for most of the problems solved, the number of Newton steps is practically independent of the problem size.