Avoiding spurious submovement decompositions: a globally optimal algorithm

Evidence for the existence of discrete submovements underlying continuous human movement has motivated many attempts to extract them. Although they produce visually convincing results, all of the methodologies that have been employed are prone to produce spurious decompositions. Examples of potential failures are given. A branch-and-bound algorithm for submovement extraction, capable of global nonlinear minimization (and hence capable of avoiding spurious decompositions), is developed and demonstrated.     

Statistical analysis of structural compensatory growth: how can we reduce the rate of false detection?

Compensatory growth (CG) is a key issue in work aiming at a full understanding of the adaptive significance of growth plasticity and its carryover effects on life-history. The number of studies addressing evolutionary explanations for CG has increased rapidly during the last few years, but there has not been a parallel gain in our understanding of the methodological difficulties associated with the analysis of CG. We point out two features of growth that can have serious consequences for detecting CG: (1) size dependence of growth rates, which causes nonlinearity of growth trajectories, and; (2) temporal overlapping of structural growth and replenishment of energy reserves after a period of famine. We show that the currently used methods can be prone to spurious detection of CG (Type I error) under conditions of nonlinear growth, and therefore lead to the accumulation of a significant amount of false “empirical support.” True and simulated growth data provided consistent results suggesting that a substantial fraction of the existing evidence for CG may be spurious. A small curvature in the growth trajectory can lead to spurious “detection” of CG when control and manipulated trajectories are compared over the same time interval (the “simultaneous” approach). We present a novel, robust method (the “asynchronous” approach) based on the accurate selection of control trajectories and comparison of control and treatment growth rates at different times. This method enables a reliable test to be performed for compensation under asymptotic growth. While the general results of our simulations do not support the application of conventional methods to the general case of nonlinear growth trajectories under the simultaneous approach, simple methods may prove valid if the experimental design allows for asynchronous comparisons. We advocate an alternative approach to deal with “safe” detection of CG that overcomes the problems associated with the occurrence of nonlinear and asymptotic growth, and provide recommendations for improving CG study designs. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The combinatorial distance geometry method for the calculation of molecular conformation. II. Sample problems and computational statistics

The performance of a branch and bound algorithm for molecular energy minimization is evaluated on a variety of test problems. Although not at present efficient enough for use in most practical situations, we show that it has distinct advantages over more conventional methods of global minimization. In addition, this study illustrates the technique on which the present algorithm is based, and the problems which must be overcome in developing an efficient algorithm based on similar principles.     

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers''-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers''-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.     

Characterization of Information-Based Learning Benefits with Submovement Dynamics and Muscular Rhythmicity

For skill advancement, motor variability must be optimized based on target information during practice sessions. This study investigated structural changes in kinematic variability by characterizing submovement dynamics and muscular oscillations after practice with visuomotor tracking under different target conditions. Thirty-six participants were randomly assigned to one of three groups (simple, complex, and random). Each group practiced tracking visual targets with trajectories of varying complexity. The velocity trajectory of tracking was decomposed into 1) a primary contraction spectrally identical to the target rate and 2) an intermittent submovement profile. The learning benefits and submovement dynamics were conditional upon experimental manipulation of the target information. Only the simple and complex groups improved their skills with practice. The size of the submovements was most greatly reduced by practice with the least target information (simple > complex > random). Submovement complexity changed in parallel with learning benefits, with the most remarkable increase in practice under a moderate amount of target information (complex > simple > random). In the simple and complex protocols, skill improvements were associated with a significant decline in alpha (8–12 Hz) muscular oscillation but a potentiation of gamma (35–50 Hz) muscular oscillation. However, the random group showed no significant change in tracking skill or submovement dynamics, except that alpha muscular oscillation was reduced. In conclusion, submovement and gamma muscular oscillation are biological markers of learning benefits. Effective learning with an appropriate amount of target information reduces the size of submovements. In accordance with the challenge point hypothesis, changes in submovement complexity in response to target information had an inverted-U function, pertaining to an abundant trajectory-tuning strategy with target exactness.     

Assignment of MS-based metabolomic datasets via compound interaction pair mapping

Assignment of physical meaning to mass spectrometry (MS) data peaks is an important scientific challenge for metabolomics investigators. Improvements in instrumental mass accuracy reduce the number of spurious database matches, however, this alone is insufficient for accurate, unique high-throughput assignment. We present a method for clustering MS instrumental artifacts and a stochastic local search algorithm for the automated assignment of large, complex MS-based metabolomic datasets. Artifact peaks and their associated source peaks are grouped into “instrumental clusters.” Instrumental clusters, peaks grouped together by shared peak shape in the temporal domain, serve as a guide for the number of assignments necessary to completely explain a given dataset. We refine mass only assignments through the intersection of peak correlation pairs with a database of biochemically relevant interaction pairs. Further refinement is achieved through a stochastic local search optimization algorithm that selects individual assignments for each instrumental cluster. The algorithm works by choosing the peak assignment that maximally explains the connectivity of a given cluster. We demonstrate that this methodology provides a significant advantage over standard methods for the assignment of metabolites in a UPLC-MS diabetes dataset. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Identification of Rhodococcuserythropolis isolates capable of degrading the fungicide carbendazim

Continuous enrichment cultures were used to identify bacterial isolates capable of degrading the fungicide carbendazim. The bacteria originated from sites that had been repeatedly treated with the structurally related parent fungicide, benomyl, over a period of several years. Six isolates were identified as carbendazim degraders on the basis of their ability to produce diffusion-clearing zones on a minimal salts solid medium spray-coated with a 0.1% solution of carbendazim, their ability to grow in a minimal salts broth supplemented with carbendazim as the sole carbon source, and their ability to reduce carbendazim levels in liquid cultures. All six isolates were identified as Rhodococcus erythropolis or a closely related species by analyses of nutritional utilization and whole-cell fatty acid methyl ester profiles. A chemically induced mutant of R. erythropolis isolate B2E was identified that was no longer capable of degrading carbendazim, as determined by negative results in all three assays. Further characterization of these strains provides an opportunity for their development in bioremediation of the compound. Received: 22 July 1996 / Received revision: 16 December 1996 / Accepted: 10 January 1997     

Listing all sorting reversals in quadratic time

We describe an average-case O(n ²) algorithm to list all reversals on a signed permutation π that, when applied to π, produce a permutation that is closer to the identity. This algorithm is optimal in the sense that, the time it takes to write the list is Ω(n ²) in the worst case.     

The train fueling cost minimization problem with fuzzy fuel prices

The train fueling cost minimization problem is to find a scheduling and fueling strategy such that the fueling cost is minimized and no train runs out of fuel. Since fuel prices vary by location and time from month to month, we estimate them by fuzzy variables in this paper. Furthermore, we propose a fuzzy fueling cost minimization model by minimizing the expected fueling cost under the traversing time constraint, maximal allowable speed constraint, tank capacity constraint, and so on. In order to solve the model, we decompose it into a nonlinear scheduling strategy model and a linear fueling strategy model. Based on the Karush–Kuhn–Tucker conditions, we design an iterative algorithm to solve the scheduling strategy model, and furthermore design a numerical algorithm to solve the fuzzy fueling cost minimization model. Finally, some numerical examples are presented for showing the efficiency of the proposed approach on saving fueling cost.     

A new criterion for the global stability of simultaneous cell replication and maturation processes

 We analyze a population model of cells that are capable of simultaneous and independent proliferation and maturation. This model is described by a first order partial differential equation with a time delay and a retardation of the maturation variable, both due to cell replication. We provide a general criterion for global stability in such equations. Received: 26 August 1996 / Revised version: 22 March 1997     

Conformational analysis of methyl 6-O-[(R)- and (S)-1-carboxyethyl]-α-D-galactopyranoside by MM and Langevin dynamics simulations

The conformational space of methyl 6-O-[(R)- and (S)- 1-carboxyethyl]-α-D-galactopyranoside has been investigated. A grid search employing energy minimization at each grid point over the three major degrees of freedom, namely φ, ψ and ω, identified low energy regions. The R-isomer shows five low energy conformers within ca. 1 kcal mol−1 of the global energy minimum. The S-isomer has two conformers within a few tenths of a kcal mol−1 of the global energy minimum. Langevin dynamics simulations have been have been performed at 300 K for 30 ns of each isomer. The φ dihedral angle has as its major conformer (g−1) for the R-isomer whereas it is the (g+) conformer for the S-isomer. For the ψ dihedral angle the (t) conformer has the highest population for both isomers. The dihedral angle ω has the (g+) conformer most highly populated, both for the R- and S-isomer. The above five and two conformational states for the R- and S-isomers, respectively, make up 90% in each case of the populated states during the Langevin dynamics (LD) simulations. Rate constants for the ω dihedral angle have been calculated based on a number correlation function. Three bond homo- and heteronuclear, i.e. proton and carbon-13, coupling constants have been calculated from the dynamics trajectories for comparison to experimental values. The heteronuclear coupling constant H2′,C6 has been measured for the S-isomer and found to be 3.3 Hz. The J value calculated from the LD simulations, namely 2.6 Hz, is in fair agreement with experiment. A comparison to the X-ray structure of the R-isomer shows that the conformation of the crystalline compound occupies the low energy region most highly populated as a single R-conformer (30%) during the LD simulations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Computer vision analysis of somatic embryos of sweet potato [Ipomoea batatas (L.) Lam.] for assessing their ability to convert to plants

Apical and axial shoot tips of sweet potato were cultured to produce somatic embryos that mature and develop into plants in basal nutrient medium. However, the lack of high regeneration efficiency is an impediment to the use of somatic embryos to produce synthetic seeds. Conversion experiments with mature embryos over a 20-day period revealed that 80–90% of the embryos formed roots but only 40–50% formed shoots. Using computer vision and canonical or Fisher discriminant function (CDA) analysis along with conversion results, it was possible to correctly classify competent embryos 40–50% of the time based on size features, 50–60% of the time based on shape features, and 55–60% of the time based on color features. Non-competent embryos were correctly classified 65–75%, 55–60%, and 70–75% of the time based on size, shape, and color, respectively. These results can be used effectively to identify and select competent embryos for improved regeneration efficiency. Received: 2 January 1997 / Revision received: 21 January 1998 / Accepted: 12 February 1998     

Factors affecting Caco-2 intestinal epithelial cell interleukin-6 secretion

Summary Intestinal epithelial cells (IEC) have previously been shown to produce several cytokines including interleukin-6 (IL-6). However, many factors which may regulate IL-6 secretion by human IEC still remain a mystery due in part to the lack of appropriate model cell lines and the difficulty of culturing human IEC over long periods of time. We have determined that the human colonic carcinoma cell line Caco-2 is capable of secreting IL-6 when stimulated by the inflammatory cytokines IL-1β or tumor necrosis factor-α (TNF-α), and stimulation of these cells with IL-1β plus TNF-α induced a synergistic enhancement of IL-6 secretion. The inflammatory cytokine-induced enhancement in IL-6 secretion was greatest when the cells were cultured in a 10% CO₂ atmosphere as compared to cells grown in 5% CO₂, suggesting that environmental CO₂ levels may affect IEC cytokine secretion. Finally, long-term culture of the Caco-2 cells to induce cellular differentiation had no effect on the capacity of these cells to produce IL-6, indicating that the regulation of IL-6 secretion was not affected by differentiation. Taken together, these studies provide important information on the factors which regulate IL-6 secretion by human IEC as they may contribute to the cytokine network during a mucosal inflammation. The results also suggest that the Caco-2 cell line is an appropriate model for further studies on the regulation of cytokine secretion by human IEC.     

Control of multistability in ring circuits of oscillators

The essential dynamics of some biological central pattern generators (CPGs) can be captured by a model consisting of N neurons connected in a ring. These circuits, like many oscillatory nonlinear circuits of sufficient complexity, are capable of multistability, that is, of generating different firing patterns distinguished by the phasic relationships between the firing in each circuit element (neuron). Moreover, a shift in firing pattern can be induced by a transient perturbation. A systematic approach, based on phase-response curve (PRC) theory, was used to determine the optimum timing for perturbations that induce a shift in the firing pattern. The first step was to visualize the solution space of the ring circuit, including the attractive basins for each stable firing pattern; this was possible using the relative phase of N−1 oscillators, with respect to an arbitrarily selected reference oscillator, as coordinate axes. The trajectories in this phase space were determined using an iterative mapping based only on the PRCs of the uncoupled component oscillators; this algorithm was called a circuit emulator. For an accurate mapping of the attractive basin of each pattern exhibited by the ring circuit, the emulator had to take into account the effect of a perturbation or input on the timing of two bursts following the onset of the perturbation, rather than just one. The visualization of the attractive basins for rings of two, three, and four oscillators enabled the accurate prediction of the amounts of phase resetting applied to up to N−1 oscillators within a cycle that would induce a transition from any pattern to any another pattern. Finally, the timing and synaptic characterization of an input called the switch signal was adjusted to produce the desired amount of phase resetting. Received: 29 May 1998 / Accepted in revised form: 18 September 1998     

Complex nonlinear dynamics of the Hodgkin-Huxley equations induced by time scale changes

 The Hodgkin–Huxley equations with a slight modification are investigated, in which the inactivation process (h) of sodium channels or the activation process of potassium channels (n) is slowed down. We show that the equations produce a variety of action potential waveforms ranging from a plateau potential, such as in heart muscle cells, to chaotic bursting firings. When h is slowed down – differently from the case of n variable being slow – chaotic bursting oscillations are observed for a wide range of parameter values although both variables cause a decrease in the membrane potential. The underlying nonlinear dynamics of various action potentials are analyzed using bifurcation theory and a so-called slow–fast decomposition analysis. It is shown that a simple topological property of the equilibrium curves of slow and fast subsystems is essential to the production of chaotic oscillations, and this is the cause of the large difference in global firing characteristics between the h-slow and n-slow cases. Received: 9 August 2000 / Accepted in revised form: 10 January 2001     

Nonlinear process modeling of fructosyltransferase (FTase) using bootstrap re-sampling neural network model

Recently, the increased demand of fructooligosaccharides (FOS) as a functional food has alarmed researchers to screen and identify new strains capable of producing fructosyltransferase (FTase). FTase is the enzyme that converts the substrate (sucrose) to glucose and fructose. The characterization of complex sugar such as table sugar, brown sugar, molasses, etc. will be carried out and the sugar that contained the highest sucrose concentration will be selected as a substrate. Eight species of macro-fungi will be screened for its ability to produce FTase and only one strain with the highest FTase activity will be selected for further studies. In this work, neural networks (NN) have been chosen to model the process based on their excellent ‘resume’ in coping with nonlinear process. Bootstrap re-sampling method has been utilized in re-sampling the data in this work. This method has successfully modeled the process as shown in the results.     

On the correlation dimension of optokinetic nystagmus eye movements: computational parameters, filtering, nonstationarity, and surrogate data

 We discuss the estimation of the correlation dimension of optokinetic nystagmus (OKN), a type of reflexive eye movement. Parameters of the time-delay reconstruction of the attractor are investigated, including the number of data points, the time delay, the window duration, and the duration of the signal being analyzed. Adequate values are recommended. Digital low-pass filtering causes the dimension to increase as the filter cutoff frequency decreases, in accord with a previously published prediction. The stationarity of the correlation dimension is examined; the dimension appears to decrease over the course of 120 s of continuous stimulation. Implications for the reliable estimation of the dimension are considered. Several surrogate data sets are constructed, based on both early (0–30 s) and late (100–130 s) OKN segments. Most of the surrogate data sets randomize some aspect of the original OKN, while maintaining other aspects. Dimensions are found for all surrogates and for the original OKN. Evidence is found that is consistent with some amount of deterministic and nonlinear dynamics in OKN. When this structure is randomized in the surrogate, the dimension changes or the dimension algorithm ceases to converge to a finite value. Implications for further analysis and modeling of OKN are discussed. Received: 30 August 1996/Accepted in revised form: 13 November 1996     

A nonlinear regularization approach to early vision

We propose a new class of approaches to smooth visual data while preserving significant transitions of these data as clues for segmentation. Formally, the given visual data are represented as a noisy (image) function , and we present a class of continuously formulated global minimization problems to smooth . The resulting function can be characterized as the minimizer of a specific nonquadratic functional or, equivalently, as the result of an associated nonlinear diffusion process. Our approach generalizes the well-known quadratic regularization principle while retaining its attractive properties: For any given , the solution to the proposed minimization problem is unique and depends continuously on the data . Furthermore, convergence of approximate solutions obtained by finite element discretization holds true. We show that the nodal variables of any chosen finite element subspace can be interpreted as computational units whose activation dynamics due to the nonlinear smoothing process evolve like a globally asymptotically stable network. A corresponding analogue implementation is thus feasible and would provide a real time processing stage for the transition preserving smoothing of visual data. Using artificial as well as real data we illustrate our approach by numerical examples. We demonstrate that solutions to our approach improve those obtained by quadratic minimization and show the influence of global parameters which allow for a continuous, scale-dependent, and selective control of the smoothing process. Received: 23 February 1994 / Accepted in revised form: 28 July 1994     

A flexible approach for understanding protein stability

A distance constraint model (DCM) is presented that identifies flexible regions within protein structure consistent with specified thermodynamic condition. The DCM is based on a rigorous free energy decomposition scheme representing structure as fluctuating constraint topologies. Entropy non-additivity is problematic for naive decompositions, limiting the success of heat capacity predictions. The DCM resolves non-additivity by summing over independent entropic components determined by an efficient network-rigidity algorithm. A minimal 3-parameter DCM is demonstrated to accurately reproduce experimental heat capacity curves. Free energy landscapes and quantitative stability-flexibility relationships are obtained in terms of global flexibility. Several connections to experiment are made.     

Two equilibration pools of chlorophylls in the Photosystem I core antenna of <Emphasis Type="Italic">Chlamydomonas reinhardtii</Emphasis>

Summary Femtosecond transient absorption spectroscopy was applied for a comparative study of excitation decay in several different Photosystem I (PSI) core preparations from the green alga Chlamydomonas reinhardtii. For PSI cores with a fully interconnected network of chlorophylls, the excitation energy was equilibrated over a pool of chlorophylls absorbing at ∼683 nm, independent of excitation wavelength [Gibasiewicz et al. J Phys Chem B 105:11498–11506, 2001; J Phys Chem B 106:6322–6330, 2002]. In preparations with impaired connectivity between chlorophylls, we have found that the spectrum of chlorophylls connected to the reaction center (i.e., with ∼20 ps decay time) over which the excitation is equilibrated becomes excitation-wavelength-dependent. Excitation at 670 nm is finally equilibrated over chlorophylls absorbing at ∼675 nm, whereas excitation at 695 nm or 700 nm is equilibrated over chlorophylls absorbing at ∼683 nm. This indicates that in the vicinity of the reaction center there are two spectrally different and spatially separated pools of chlorophylls that are equally capable of effective excitation energy transfer to the reaction center. We propose that they are related to the two groups of central PSI core chlorophylls lying on the opposite sides of reaction center.