The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling

In a recent paper we developed a new algorithm for the moment-constrained maximum entropy problem in a multidimensional setting, using a multidimensional orthogonal polynomial basis in the dual space of Lagrange multipliers to achieve numerical stability and rapid convergence of the Newton iterations. Here we introduce two new improvements for the existing algorithm, adding significant computational speedup in situations with many moment constraints, where the original algorithm is known to converge slowly. The first improvement is the use of the BFGS iterations to progress between successive polynomial reorthogonalizations rather than single Newton steps, typically reducing the total number of computationally expensive polynomial reorthogonalizations for the same maximum entropy problem. The second improvement is a constraint rescaling, aimed to reduce relative difference in the order of magnitude between different moment constraints, improving numerical stability of iterations due to reduced sensitivity of different constraints to changes in Lagrange multipliers. We observe that these two improvements can yield an average wall clock time speedup of 5–6 times compared to the original algorithm.     

Classification of Random Image Fields Using Synthetic Discriminant Functions: Spectral Statistical Approach and Its Computer-Optical Realization

The problem of classification of images that have a perfectly random nature is considered. We propose a new approach to solve this problem that is based on the use of the synthetic discriminant functions being synthesized to separate linearly the power spectra of random image fields to be classified. In the stage of both discriminant function synthesis and classification, the statistical technique of power spectrum estimation is employed. The realization of the proposed approach by means of a hybrid computer-optical technique is discussed, and its efficiency is illustrated by two examples of real-world texture classification.     

Polynomial estimation of probability densities

We propose a new quality criterion and an iterative algorithm for polynomial estimation of probability densities of a random quantity. The properties of the optimal estimate are studied and the conditions and rate of its convergence are found. Antiaircraft Command High School of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 11, pp. 1416–1432, November, 1997.     

Threshold Laws for Four-Particle Fragmentation: Mass Effects

Hyperfine Interactions - The threshold laws for break-up of an atomic particle into N charged fragments reflect dynamics of long-range Coulomb correlation. Progress in experimental technique makes...     

Highly anisotropic orbitally dependent superexchange in cyano-bridged clusters containing Mn(III) and Mn(II) ions.

We study the orbitally dependent magnetic exchange in cyanide-based clusters as a source of the barrier for reversal magnetization. We consider the Mn(III)-CN-Mn(II) dimer and linear Mn(II)-NC-Mn(III)-CN-Mn(II) trimer containing octahedrally coordinated Mn(III) and Mn(II) ions with special emphasis on the magnetic manifestations of the orbital degeneracy of the Mn(III) ion. The kinetic exchange mechanism involves the electron transfer from the single occupied t(2) orbitals of the Mn(II) ion [6A1(t2(3)e2) ground state] to the singly occupied t(2) orbitals of the Mn(III) ion [3T1(t2(4)) ground state] resulting in the charge-transfer 5T2(t2(2)e2)Mn(III) - 2T2(t2(5))Mn(II) state of the pair. The deduced effective exchange Hamiltonian that takes into account orbital degeneracy leads to an essentially non-Heisenberg energy pattern. The energy levels are shown to be dependent on both spin and orbital quantum numbers, thus providing direct information about the magnetic anisotropy of the system. Along with the magnetic exchange, the model includes an axial component of the crystal field and spin-orbit coupling operating within the ground 3T1(t2(4)) cubic term of the Mn(III) ion. We have shown that under certain conditions both named interactions lead to the occurrence of the barrier for the reversal of magnetization, which significantly increases when passing from the dimer to the trimer. This provides a possible way for raising the magnetic barrier in the family of cyano-bridged manganese clusters.     

Hydroxyl radical formation by O-O bond homolysis in peroxynitrous acid

Peroxynitrite decay in weakly alkaline media occurs by two concurrent sets of pathways which are distinguished by their reaction products. One set leads to net isomerization to NO(3)(-) and the other set to net decomposition to O(2) plus NO(2)(-). At sufficiently high peroxynitrite concentrations, the decay half-time becomes concentration-independent and approaches a limiting value predicted by a mechanism in which reaction is initiated by unimolecular homolysis of the peroxo O-O bond, i.e., the following reaction: ONOOH --> (*)OH + (*)NO(2). This dynamical behavior excludes alternative postulated mechanisms that ascribe decomposition to bond rearrangement within bimolecular adducts. Nitrate and nitrite product distributions measured at very low peroxynitrite concentrations also correspond to predictions of the homolysis model, contrary to a recent report from another laboratory. Additionally, (1) the rate constant for the reaction ONOO(-) --> (*)NO + (*)O(2)(-), which is critical to the kinetic model, has been confirmed, (2) the apparent volume of activation for ONOOH decay (DeltaV() = 9.7 +/- 1.4 cm(3)/mol) has been shown to be independent of the concentration of added nitrite and identical to most other reported values, and (3) complex patterns of inhibition of O(2) formation by radical scavengers, which are impossible to rationalize by alternative proposed reaction schemes, are shown to be quantitatively in accord with the homolysis model. These observations resolve major disputes over experimental data existing in the literature; despite extensive investigation of these reactions, no verifiable experimental evidence has been advanced that contradicts the homolysis model.     

New Approximations and Tests of Linear Fluctuation-Response for Chaotic Nonlinear Forced-Dissipative Dynamical Systems

We develop and test two novel computational approaches for predicting the mean linear response of a chaotic dynamical system to small change in external forcing via the fluctuation–dissipation theorem. Unlike the earlier work in developing fluctuation–dissipation theorem-type computational strategies for chaotic nonlinear systems with forcing and dissipation, the new methods are based on the theory of Sinai–Ruelle–Bowen probability measures, which commonly describe the equilibrium state of such dynamical systems. The new methods take into account the fact that the dynamics of chaotic nonlinear forced-dissipative systems often reside on chaotic fractal attractors, where the classical quasi-Gaussian formula of the fluctuation–dissipation theorem often fails to produce satisfactory response prediction, especially in dynamical regimes with weak and moderate degrees of chaos. A simple new low-dimensional chaotic nonlinear forced-dissipative model is used to study the response of both linear and nonlinear functions to small external forcing in a range of dynamical regimes with an adjustable degree of chaos. We demonstrate that the two new methods are remarkably superior to the classical fluctuation–dissipation formula with quasi-Gaussian approximation in weakly and moderately chaotic dynamical regimes, for both linear and nonlinear response functions. One straightforward algorithm gives excellent results for short-time response while the other algorithm, based on systematic rational approximation, improves the intermediate and long time response predictions.     

Deuterium Rotating Frame NMR Relaxation Measurements in the Solid State under Static Conditions for Quantification of Dynamics

The feasibility of static deuterium rotating frame NMR relaxation measurements for characterization of slow timescale motions in powder systems is demonstrated. Using a model compound dimethyl sulfone-d₆, we show that these measurements yield conformational exchange rates and activation energy values in accordance with results obtained with other techniques. Furthermore, we demonstrate that the full Liouvillian approach as opposed to the Redfield approximation is necessary to analyze the experimental data.     

Comparative Hydrophobic Core Dynamics Between Wild-Type Amyloid-β Fibrils,Glutamate-3 Truncation,and Serine-8 Phosphorylation

Post-translational modifications (PTMs) of amyloid-β (Aβ) species are implicated in the modulation of overall toxicities and aggregation propensities. We investigated the internal dynamics in the hydrophobic core of the truncated ΔE3 mutant fibrils of Aβ_1–40 and compared them with prior and new data for wild-type fibrils as well as with phosphorylated S8 fibrils. Deuteron static solid-state NMR techniques, spanning line-shape analysis, longitudinal relaxation, and chemical exchange saturation transfer methods, were employed to assess the rotameric jumps of several methyl-bearing and aromatic groups in the core of the fibrils. Taken together, the results indicate the rather significant influence of the PTMs on the hydrophobic core dynamics, which propagates far beyond the local site of the chemical modification. The phosphorylated S8 fibrils display an overall rigidifying of the core based on the higher activation barriers of motions than the wild-type fibrils, whereas the ΔE3 fibrils induce a broader variety of changes, some of which are thermodynamic in nature rather than the kinetic ones.