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PubMed2004

Generalized monotonically convergent algorithms for solving quantum optimal control problems.

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.

Journal Article↗
PubMed2004

Globally convergent trust-region methods for self-consistent field electronic structure calculations.

As far as more complex systems are being accessible for quantum chemical calculations, the reliability of the algorithms used becomes increasingly important. Trust-region strategies comprise a large family of optimization algorithms that incorporates both robustness and applicability for a great variety of problems. The objective of this work is to provide a basic algorithm and an adequate theoretical framework for the application of globally convergent trust-region methods to electronic structure calculations. Closed shell restricted Hartree-Fock calculations are addressed as finite-dimensional nonlinear programming problems with weighted orthogonality constraints. A Levenberg-Marquardt-like modification of a trust-region algorithm for constrained optimization is developed for solving this problem. It is proved that this algorithm is globally convergent. The subproblems that ensure global convergence are easy-to-compute projections and are dependent only on the structure of the constraints, thus being extendable to other problems. Numerical experiments are presented, which confirm the theoretical predictions. The structure of the algorithm is such that accelerations can be easily associated without affecting the convergence properties.

Journal Article↗
PubMed2005

Longitudinal polarizability of long polymeric chains: quasi-one-dimensional electrostatics as the origin of slow convergence.

The longitudinal linear polarizability alpha(N) of a stereoregular oligomer of size N is proportional to N in the large-N limit, provided the system is nonconducting in that limit. It has long been known that the convergence of alpha(N)/N to the asymptotic alpha(infinity) value is slow. We show that the leading term in the difference between alpha(N)/N and alpha(infinity) is of the order of 1/N. The difference [alpha(N)-alpha(N-1)], as well as alpha(center)(N) (when computationally accessible), also converge to alpha(infinity), but faster, the leading term being of the order of 1/N(2). We also present evidence that in these cases the power law convergence behavior is due to quasi-one-dimensional electrostatics, with one exception. Specifically, in molecular systems the difference between alpha(N)/N and alpha(infinity) has not just one but two sources of the O(1/N) term, with one being due to the aforementioned Coulomb interactions, and the second due to the short ranged exponentially decaying perturbations on chain ends. The major role of electrostatics in the convergence of the remainders is demonstrated by means of a Clausius-Mossotti-type classical model. The conclusions derived from the model are also shown to be applicable in molecular systems, by means of test-case ab initio calculations on linear stacks of H(2) molecules, and on polyacetylene chains. The implications of the modern theory of polarization for extended systems are also discussed.

Journal Article↗
PubMed2005

Convergence of replica exchange molecular dynamics.

Replica exchange molecular dynamics (REMD) method is one of the generalized-ensemble algorithms which performs random walk in energy space and helps a system to escape from local energy traps. In this work, we studied the accuracy and efficiency of REMD by examining its ability to reproduce the results of multiple extended conventional molecular dynamics (MD) simulations and to enhance conformational sampling. Two sets of REMD simulations with different initial configurations, one from the fully extended and the other from fully helical conformations, were conducted on a fast-folding 21-amino-acid peptide with a continuum solvent model. Remarkably, the two REMD simulation sets started to converge even within 1.0 ns, despite their dramatically different starting conformations. In contrast, the conventional MD within the same time and with identical starting conformations did not show obvious signs of convergence. Excellent convergence between the REMD sets for T>300 K was observed after 14.0 ns REMD simulations as measured by the average helicity and free-energy profiles. We also conducted a set of 45 MD simulations at nine different temperatures with each trajectory simulated to 100.0 and 200.0 ns. An excellent agreement between the REMD and the extended MD simulation results was observed for T>300 K, showing that REMD can accurately reproduce long-time MD results with high efficiency. The autocorrelation times of the calculated helicity demonstrate that REMD can significantly enhance the sampling efficiency by 14.3+/-6.4, 35.1+/-0.2, and 71.5+/-20.4 times at, respectively, approximately 360, approximately 300, and approximately 275 K in comparison to the regular MD. Convergence was less satisfactory at low temperatures (T<300 K) and a slow oscillatory behavior suggests that longer simulation time was needed to reach equilibrium. Other technical issues, including choice of exchange frequency, were also examined.

Algorithms↗
PubMed2001

Calculation of mitral regurgitant orifice area with use of a simplified proximal convergence method: initial clinical application.

To validate a previously proposed simplified proximal flow convergence method for calculating mitral regurgitant orifice area (ROA), a prospective study was conducted in ambulatory patients and in patients undergoing open heart surgery. Assuming a pressure difference between the left ventricle and left atrium of approximately 100 mm Hg (jet velocity [v(p)] 500 cm/s) and setting the color aliasing velocity (v(a)) to 40 cm/s, we simplified the conventional proximal convergence method formula (ROA = 2pi(r2)v(a)/v(p)) to r2/2, where r is the radius of the proximal convergence isovelocity hemisphere. For 57 ambulatory patients with a wide range of mitral regurgitant severity (1 to 4+), ROA was calculated by the conventional (x) and simplified (y) methods, demonstrating excellent accuracy (r = 0.92; P <.001; DeltaROA [y - x] = 0.004 +/- 0.08 cm2). For 24 intraoperative patients, ROA calculated by the simplified formula (y) correlated well with the pulsed Doppler-thermodilution method (x) (r = 0.84; P <.01; DeltaROA [y - x] = -0.002 +/- 0.08cm2). This simplified proximal convergence formula yields an accurate assessment of ROA for a wide range of regurgitant severity, while the time required for this measurement is shortened by half (1.5 +/- 0.5 minutes versus 3.2 +/- 0.7 minutes). This may increase the frequency of calculating ROA in the clinical laboratory.

Aged↗
PubMed2002

Quantitative assessment of regurgitant flow with total digital three-dimensional reconstruction of color Doppler flow in the convergent region: in vitro validation.

BACKGROUND: This study was designed to develop and test a total digital 3-dimensional (3D) color flow map reconstruction for proximal isovelocity surface area (PISA) measurement in the convergent region. METHODS: Asymmetric flow convergent velocity field was created in an in vitro pulsatile model of mitral regurgitation. Image files stored in the echocardiographic scanner memory were digitally transferred to a computer workstation, and custom software decoded the file format, extracted velocity information, and generated 3D flow images automatically. PISA and volume flow rate were calculated without geometric assumption. For comparison, regurgitant volume was also calculated, using continuous wave Doppler, 2-dimensional (2D), and M-mode color flow Doppler with the hemispheric approach. RESULTS: Flows from 3D digital velocity profiles showed a closed, excellent relation with actual flow rates, especially for instantaneous flow rate. Regurgitant volume calculated with the 3D method underestimated the actual flow rate by 2.6%, whereas 2D and the M-mode method show greater underestimation (44.2% and 32.1%, respectively). CONCLUSION: Our 3D reconstruction of color flow Doppler images gives more exact information of the flow convergent zone, especially in complex geometric flow fields. Its total digital velocity process allows accurate measurement of convergent surface area and improves quantitation of valvular regurgitation.

Blood Flow Velocity↗
PubMed2003

Radioulnar convergence after distal ulnar resection: mechanical performance of two commonly used soft tissue stabilizing procedures.

Resection of the distal ulna (Darrach operation) is a common method for salvaging the arthrotic distal radioulnar joint (DRUJ). However, problems have been reported with this procedure due to residual instability and radioulnar convergence. As a result, several methods of soft tissue stabilization for the unstable distal ulna have been developed. Although their clinical efficacy has been reported, biomechanical investigations of these procedures have not been reported. The purpose of our study was to evaluate the dynamic effects on radioulnar convergence and dorsal-palmar displacement of three procedures: the Darrach procedure, a pronator quadratus interposition flap and an extensor and flexor carpi ulnaris tenodesis. We tested 7 fresh-frozen cadaver upper extremities using a dynamic computer-controlled device that generated forearm rotation with physiologic loading of relevant muscles. Displacement data concerning the ulna relative to the radius through the range of forearm rotation was collected for 4 experimental conditions: intact, distal ulna resection alone, distal ulna resection with pronator quadratus interposition and distal ulna resection with extensor and flexor carpi ulnaris tenodesis. Distal ulna resection altered the kinematics, most predictably creating a convergence of the radius towards the ulna. Anteroposterior translations in each loading condition could be detected as well. The interposition of the pronator quadratus muscle or tenodesis with the extensor and flexor carpi ulnaris tendons did not reduce the radioulnar convergence created by resection of the distal ulna.

Aged↗
PubMed2004

Analysis of local convergence in NMR structure calculation for RNA by a classification system for nucleic acid structure (CSNA).

We are developing a program system, CSNA, to classify a set of structures into groups sharing similar structural characters. In the present study, CSNA was applied to the analysis of NMR structures obtained by the simulated annealing calculation to elucidate local convergences. A 34-mer RNA, U6-34, having a bulge-out region that is derived from the human U6 snRNA is used as a target molecule in the present study. Although the structure calculation was not converged with the conventional method, it was found by the CSNA analysis that the two stem regions in the molecule were converged well. Furthermore, one strand of the bulge-out region (A7-A11) was found to form a continuously stacked structure in two-thirds of calculated structures. In conclusion, CSNA can be a novel tool to elucidate the local convergence of the NMR structure calculations.

Base Sequence↗
PubMed1999

Depolarization and neurotrophins converge on the phosphatidylinositol 3-kinase-Akt pathway to synergistically regulate neuronal survival.

In this report, we have examined the mechanisms whereby neurotrophins and neural activity coordinately regulate neuronal survival, focussing on sympathetic neurons, which require target-derived NGF and neural activity for survival during development. When sympathetic neurons were maintained in suboptimal concentrations of NGF, coincident depolarization with concentrations of KCl that on their own had no survival effect, synergistically enhanced survival. Biochemical analysis revealed that depolarization was sufficient to activate a Ras-phosphatidylinositol 3-kinase-Akt pathway (Ras-PI3-kinase-Akt), and function-blocking experiments using recombinant adenovirus indicated that this pathway was essential for approximately 50% of depolarization-mediated neuronal survival. At concentrations of NGF and KCl that promoted synergistic survival, these two stimuli converged to promote increased PI3-kinase-dependent Akt phosphorylation. This convergent PI3-kinase-Akt pathway was essential for synergistic survival. In contrast, inhibition of calcium/calmodulin-dependent protein kinase II revealed that, while this molecule was essential for depolarization-induced survival, it had no role in KCl- induced Akt phosphorylation, nor was it important for synergistic survival by NGF and KCl. Thus, NGF and depolarization together mediate survival of sympathetic neurons via intracellular convergence on a Ras-PI3-kinase-Akt pathway. This convergent regulation of Akt may provide a general mechanism for coordinating the effects of growth factors and neural activity on neuronal survival throughout the nervous system.

Animals↗
PubMed1993

The convergence of object dependent resolution in maximum likelihood based tomographic image reconstruction.

Study of the maximum likelihood by EM algorithm (ML) with a reconstruction kernel equal to the intrinsic detector resolution and sieve regularization has demonstrated that any image improvements over filtered backprojection (FBP) are a function of image resolution. Comparing different reconstruction algorithms potentially requires measuring and matching the image resolution. Since there are no standard methods for describing the resolution of images from a nonlinear algorithm such as ML, we have defined measures of effective local Gaussian resolution (ELGR) and effective global Gaussian resolution (EGGR) and examined their behaviour in FBP images and in ML images using two different measurement techniques. For FBP these two resolution measures are equal and exhibit the standard convolution behaviour of linear systems. For ML, the FWHM of the ELGR monotonically increased with decreasing Gaussian object size due to slower convergence rates for smaller objects. For the simple simulated phantom used, this resolution dependence is independent of object position. With increasing object size, number of iterations and sieve size the object size dependence of the ELGR decreased. The FWHM of the EGGR converged after approximately 200 iterations, masking the fact that the ELGR for small objects was far from convergence. When FBP is compared to a nonlinear algorithm such as ML, it is recommended that at least the EGGR be matched; for ML this requires more than the number of iterations (e.g., < 100) that are typically run to minimize the mean square error or to satisfy a feasibility or similar stopping criterion. For many tasks, matching the EGGR of ML to FBP images may be insufficient and >> 200 iterations may be needed, particularly for small objects in the ML image because their ELGR has not yet converged.

Algorithms↗
PubMed2001

Designing fast converging phylogenetic methods.

Absolute fast converging phylogenetic reconstruction methods are provably guaranteed to recover the true tree with high probability from sequences that grow only polynomially in the number of leaves, once the edge lengths are bounded arbitrarily from above and below. Only a few methods have been determined to be absolute fast converging; these have all been developed in just the last few years, and most are polynomial time. In this paper, we compare pre-existing fast converging methods as well as some new polynomial time methods that we have developed. Our study, based upon simulating evolution under a wide range of model conditions, establishes that our new methods outperform both neighbor joining and the previous fast converging methods, returning very accurate large trees, when these other methods do poorly.

Computational Biology↗
PubMed1997

Sequence convergence in the peptide-binding region of primate and rodent MHC class Ib molecules.

In addition to the universally expressed and highly polymorphic class Ia genes, the major histocompatibility complex (MHC) of placental mammals includes class Ib genes that are characterized by restricted expression and low levels of sequence polymorphism. The functional importance of class Ib genes as well as their actual function has long been controversial. Phylogenetic analyses have suggested that there are no orthologous relationships among class Ib loci of mammals belonging to different orders, suggesting that these loci have evolved independently since the placental mammals diverged. Here, we present evidence of convergent evolution at the molecular sequence level in the putative peptide-binding regions (PBRs) of human and mouse class Ib genes. So far, there are few if any convincing examples of convergent evolution at the amino acid sequence level, and such evolution is believed to be likely to occur only as a result of strong positive selection. Because the present case involves the functionally important PBR and because the primate and rodent molecules are known to bind similar peptides, this study represents both a convincing case of molecular-level convergence and evidence that MHC class Ib molecules, although not orthologous, may evolve similar functions convergently.

Amino Acid Sequence↗
PubMed2001

Social convergence of disturbed eating attitudes in young adult women.

It has been suggested that a broad range of social factors influence disturbed eating attitudes, but there has been relatively little investigation of the role of peer influence. Drawing from social identity theory, this longitudinal study of a nonclinical group of women examined whether social proximity results in a convergence of eating psychopathology over time. Forty-one nonclinical women (living in 11 communal apartments) completed the Eating Disorders Inventory (EDI) at three time points (1 week after moving in, 10 weeks later, and a further 14 weeks later). The women's eating and related attitudes were compared across the three time points. Then divergence scores were calculated (showing the spread of EDI scores within each apartment) and compared across the three time points. The spread of scores within the apartments changed significantly, indicating some convergence in those attitudes that are socially valued (restrictive attitudes; body concerns) and divergence in those attitudes that are not socially valued (bulimia). There was also an increase in convergence of levels of perfectionism. The findings support the suggestion that social proximity promotes convergence of socially valued eating characteristics but divergence of socially stigmatised characteristics. Further research is suggested to establish the generalizability of these findings and to identify those who are most at risk of such social effects on eating disturbance.

Adult↗
PubMed1979

The relationship between convergence insufficiency and school achievement.

Schoolchildren (735) between the ages of 7 and 14 were examined for convergence ability. Nine percent had an objective near point of convergence of more than 10 cm and 10% had a subjective near point of convergence of more than 10 cm. The recovery point was greater than 15 cm for 9% of the subjects when measured objectively and 12% subjectively. The sample was analyzed with regard to age, sex, and IQ. There was no significant difference between children who showed convergence insufficiency and those who did not with regard to school results in their mother tongue and in their grade point average.

Accommodation, Ocular↗
PubMed1980

Accommodation, convergence, and distance perception in low illumination.

The role of oculomotor adjustments for distance perception in dim light was investigated while preserving the natural interactions between accommodation and convergence. The results show that perceived distance in the dark is biased toward an intermediate value that is correlated with the vergence adjustment assumed in darkness but unrelated to the dark focus of accommodation. A subsequent experimient showed that short-term adaptation to base-out prisms and negative lenses of corresponding strength affects perceived distance and dark convergence but has no influence on the dark focus of accommodation. These findings were interpreted as indicating that convergence is a more important distance cue than accommodation under low illumination and that the physiological resting states of convergence and accommodation are relatively independent.

Accommodation, Ocular↗
PubMed2002

Improvements on the application of convergence accelerators for the evaluation of some three-electron atomic integrals.

Convergence accelerator methods are employed to analyze some of the most difficult three-electron integrals that arise in atomic calculations. These integrals have an explicit dependence on the interelectronic coordinates, and take the form integral r(i)(1)r(j)(2)r(k)(3)r(l)(23)r(m)(31)r(n)(12) exp((-alpha(r1)-beta(r2)-gamma(r3))dr(1)dr(2)dr(3). The focus of the present investigation are the most difficult cases of the parameter set [i, j, k, l, m, n]. Several convergence accelerator techniques are studied, and a comparison presenting the relative effectiveness of each technique is reported. When the convergence accelerator approach is combined with specialized numerical quadrature methods, we find that the overall technique yields high-precision results and is fairly efficient in terms of computational resources. Difficulties associated with the standard numerical precision loss of convergence accelerator techniques are circumvented.

Journal Article↗
PubMed2002

Convergence of threshold estimates for two-dimensional percolation.

Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system with a square boundary, specifically for site percolation on a square lattice. We show that the convergence of the average-probability estimate is described by a nontrivial correction-to-scaling exponent as predicted previously, and measure the value of this exponent to be 0.90+/-0.02. For the median and cell-to-cell estimates of the percolation threshold we verify that convergence does not depend on this exponent, having instead a slightly faster convergence with a trivial analytic leading exponent.

Journal Article↗
PubMed2004

Modeling and convergence analysis of distributed coevolutionary algorithms.

A theoretical foundation is presented for modeling and convergence analysis of a class of distributed coevolutionary algorithms applied to optimization problems in which the variables are partitioned among p nodes. An evolutionary algorithm at each of the p nodes performs a local evolutionary search based on its own set of primary variables, and the secondary variable set at each node is clamped during this phase. An infrequent intercommunication between the nodes updates the secondary variables at each node. The local search and intercommunication phases alternate, resulting in a cooperative search by the p nodes. First, we specify a theoretical basis for a class of centralized evolutionary algorithms in terms of construction and evolution of sampling distributions over the feasible space. Next, this foundation is extended to develop a model for a class of distributed coevolutionary algorithms. Convergence and convergence rate analyzes are pursued for basic classes of objective functions. Our theoretical investigation reveals that for certain unimodal and multimodal objectives, we can expect these algorithms to converge at a geometrical rate. The distributed coevolutionary algorithms are of most interest from the perspective of their performance advantage compared to centralized algorithms, when they execute in a network environment with significant local access and internode communication delays. The relative performance of these algorithms is therefore evaluated in a distributed environment with realistic parameters of network behavior.

Journal Article↗