Implicit Dynamics Research Articles

Zhang neural network, Getz–Marsden dynamic system, and discrete-time algorithms for time-varying matrix inversion with application to robots' kinematic control

In this paper, we present, develop and investigate a special kind of recurrent neural network termed Zhang neural network (ZNN) for time-varying matrix inversion. Comparing with the dynamic system proposed by Getz and Marsden (G-M) for time-varying matrix inversion, we show that such a G-M dynamic system depicted in an explicit dynamics can also be derived from the presented ZNN model depicted in an implicit dynamics. In other words, a novel result on the relationship between the ZNN model and others' model/method (i.e., the G-M dynamic system) is found for time-varying matrix inversion. In addition, we propose and investigate the discrete-time algorithms (depicted by systems of difference equations) of the aforementioned ZNN and G-M models in two situations, i.e., the time-derivative of the time-varying matrix to be inverted being known or unknown. Simulative and numerical results demonstrate the superior performance of the ZNN models for time-varying matrix inversion, as well as the efficacy of the G-M dynamic system (which has to be started with initial conditions sufficiently close to the desired initial inverse). Furthermore, the ZNN models and G-M dynamic system are applied to the kinematic control of a two-link planar manipulator via online solution of time-varying matrix inversion.

Ion fluxes through nanopores and transmembrane channels

We introduce an implicit solvent Molecular Dynamics approach for calculating ionic fluxes through narrow nanopores and transmembrane channels. The method relies on a dual-control-volume grand-canonical molecular dynamics (DCV-GCMD) simulation and the analytical solution for the electrostatic potential inside a cylindrical nanopore recently obtained by Levin [Europhys. Lett. 76, 163 (2006)]. The theory is used to calculate the ionic fluxes through an artificial transmembrane channel which mimics the antibacterial gramicidin A channel. Both current-voltage and current-concentration relations are calculated under various experimental conditions. We show that our results are comparable to the characteristics associated to the gramicidin A pore, especially the existence of two binding sites inside the pore and the observed saturation in the current-concentration profiles.

A new variant of the Zhang neural network for solving online time-varying linear inequalities

Since March 2001, a special class of recurrent neural networks termed the Zhang neural network (ZNN) has been proposed by Zhang and co-workers for solving online a rich repertoire of time-varying problems. By extending Zhang et al. 's design formula (or say, the ZNN design formula), a (new) variant of the ZNN design formula is proposed and investigated in this paper, which is also based on a matrix/vector-valued indefinite error function. In addition, by employing such a novel design formula, a new variant of the ZNN (NVZNN) is proposed, developed and investigated for online solution of time-varying linear inequalities (LIs). The resultant NVZNN models are depicted in implicit dynamics and methodologically exploit the time-derivative information of time-varying coefficients. Computer simulation results further demonstrate the novelty, efficacy and superiority of the proposed NVZNN models for solving online time-varying LIs.

Superior performance of using hyperbolic sine activation functions in ZNN illustrated via time-varying matrix square roots finding

A special class of recurrent neural network (RNN), termed Zhang neural network (ZNN) depicted in the implicit dynamics, has recently been proposed for online solution of time-varying matrix square roots. Such a ZNN model can be constructed by using monotonically-increasing odd activation functions to obtain the theoretical time-varying matrix square roots in an error-free manner. Different choices of activation function arrays may lead to different performance of the ZNN model. Generally speaking, ZNN model using hyperbolic sine activation functions may achieve better performance, as compared with those using other activation functions. In this paper, to pursue the superior convergence and robustness properties, hyperbolic sine activation functions are applied to the ZNN model for online solution of time-varying matrix square roots. Theoretical analysis and computer-simulation results further demonstrate the superior performance of the ZNN model using hyperbolic sine activation functions in the context of large model-implementation errors, in comparison with that using linear activation functions.

Efficient Dynamic Protonation and Constant pH Simulations with Explicit Solvent: Calculation of Apparent pKa Values in Proteins

The pKa's of the ionizable amino acids are crucial for the function of many proteins as they are key factors that determine their electrostatic potential and its spatial distribution, often controlling and optimizing enzymatic catalysis. Further, during conformational motions pKa's and protonation states particularly of histidines may change. In established force field simulation, however, this effect is typically not included, and protonation states must therefore be either guessed or derived from experiment. There have been a number of approaches to include protonation effects within simulations, mainly based on continuum electrostatics or implicit solvent molecular dynamics [1--3]. However, these methods lack the effect of the hydrogen bonding and the entropy contribution that comes from the solvent. Here we present the implementation and application of a dynamic protonation atomistic simulation method with explicit solvent, which also allows for explicit solvent constant pH MD simulations, previously developed also in our group [4]. This method is used here to calculate the pKa's of the ionzable groups in proteins. In order to validate it, we selected a number of prototypic proteins and calculated titration curves and pKa values from constant pH simulations at a range of different pH values. The results compare favorably with measured values, and explain atomistically the strong deviations of some of the calculated pKa values from the solution ones. 1. Lee, M. S., Salsbury, F. R., Jr., and Brooks, C. L., III (2004), Proteins 56, 738–752. 2. Khandogin J, Brooks C. L., 3rd., Biophys J. 2005 Jul;89(1):141-57. Epub 2005 Apr, 29. 3. Mongan, J., Case, D. A., McCammon, J. A. J., Comput. Chem. 2004, 25, 2038–2048 4. Donnini S, Tegeler F, Groenhof G, Grubmüller H., J. Chem Theory and Comp 7: 1962–1978 (2011).

Superior robustness of power-sum activation functions in Zhang neural networks for time-varying quadratic programs perturbed with large implementation errors

A special class of recurrent neural network termed Zhang neural network (ZNN) depicted in the implicit dynamics has recently been introduced for online solution of time-varying convex quadratic programming (QP) problems. Global exponential convergence of such a ZNN model is achieved theoretically in an error-free situation. This paper investigates the performance analysis of the perturbed ZNN model using a special type of activation functions (namely, power-sum activation functions) when solving the time-varying QP problems. Robustness analysis and simulation results demonstrate the superior characteristics of using power-sum activation functions in the context of large ZNN-implementation errors, compared with the case of using linear activation functions. Furthermore, the application to inverse kinematic control of a redundant robot arm also verifies the feasibility and effectiveness of the ZNN model for time-varying QP problems solving.

Zhang neural network versus gradient-based neural network for time-varying linear matrix equation solving

A type of recurrent neural networks called Zhang neural network (ZNN) is presented and investigated to provide an online solution to the time-varying linear matrix equation, A ( t ) X ( t ) B ( t ) + X ( t ) = C ( t ) by using a novel design method. In contrast to the gradient-based neural network (GNN), the novel design of ZNN is based on a matrix-valued indefinite error function, instead of a scalar-valued norm-based energy function. Therefore, a ZNN model depicted in implicit dynamics can globally and exponentially converge to the time-varying theoretical solution of the given linear matrix equation. Computer simulation results further demonstrate the superior performance of the ZNN model in solving the time-varying linear matrix equation compared with the conventional GNN model.

Pathogenicity characterization with implicit and explicit molecular dynamics simulation

The contribution of water molecules in molecular dynamics simulation (MDS) is unquestionably high, particularly for enzymatic interaction which occurred in the cytoplasmic environment. The addition of water molecules to the system will surely influence different direct interaction between active site residues and substrate. We try to theoretically investigate to what extent the pathogenicity characterization will varies in different neuraminidase-sialic acid complex systems. The heating dynamics simulations were produced with and without TIP3P water molecules. The periodic boundary system was made for explicitly added TIP3P water molecules and generalized born molecular volume (GBMV) energy contribution was added for implicit solvent system. Both complexes, neuraminidasesialic acid of A/Tokyo/3/67 and A/Pennsylvania/10218/ 84, which have a different pathogenicity levels were minimized and simulated. The result shows more residues produced hydrogen bonds with substrate when water molecules were not added to the system. The binding free energies also show differences. Overall, even the values of energy differences, but an implicit solvent provides the similar result (HPAI complex has higher activity than LPAI for both systems) in characterization of pathogenic virus neuraminidase activity.

Annual Festivals in the Hebrew Bible II: Perspective from Ritual Studies

From the perspective of biblical studies Pentateuch’s annual festivals (Passover, First Sheaf, Unleavened Bread, Weeks, Blowing of the Shofar, Day of Atonement and Tabernacles) are usually regarded as a more or less artificial collection of heterogeneous cultic occasions. Application of ritual studies findings and methods, however, reveals that there are multiple syntagmatic links between these festivals and that their explicit and implicit dynamics also disclose something of their pre-biblical origins and significance.

Zhang neural network solving for time-varying full-rank matrix Moore–Penrose inverse

Zhang neural networks (ZNN), a special kind of recurrent neural networks (RNN) with implicit dynamics, have recently been introduced to generalize to the solution of online time-varying problems. In comparison with conventional gradient-based neural networks, such RNN models are elegantly designed by defining matrix-valued indefinite error functions. In this paper, we generalize, investigate and analyze ZNN models for online time-varying full-rank matrix Moore–Penrose inversion. The computer-simulation results and application to inverse kinematic control of redundant robot arms demonstrate the feasibility and effectiveness of ZNN models for online time-varying full-rank matrix Moore–Penrose inversion.

Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation

Different from gradient-based neural dynamics, a special kind of recurrent neural dynamics has recently been proposed by Zhang et al. for solving online time-varying problems. Such a recurrent neural dynamics is designed based on an indefinite error-monitoring function instead of a usually norm- or square-based energy function. In addition, Zhang neural dynamics (ZND) are depicted generally in implicit dynamics, whereas gradient-based neural dynamics (GND) are associated with explicit dynamics. In this paper, we generalize the ZND design method to solving online nonlinear time-varying equations in the form of f (x, t) = 0. For comparative purposes, the GND model is also employed for such time-varying equations’ solving. Computer-simulation results via power-sigmoid activation functions substantiate the theoretical analysis and efficacy of the ZND model for solving online nonlinear time-varying equations.

The wildlife picture index, monitoring and conservation

The wildlife picture index, monitoring and conservation

International Arrivals in the Canary Islands: Persistence, Long Memory, Seasonality and other Implicit Dynamics

This study models international monthly arrivals in the Canary Islands using different time-series approaches that enable an examination of the degree of persistence of the series. The author focuses on long memory processes at the long-run or zero frequency, at the seasonal frequencies and at both simultaneously. A forecasting experiment is also conducted and the results indicate that the model with two differencing parameters seems to be the most adequate specification for this series, being non-stationary with respect to the two components and mean reverting with respect to the seasonal structure.

Structure and Dynamics of End-to-End Loop Formation of the Penta-Peptide Cys-Ala-Gly-Gln-Trp in Implicit Solvents

To investigate the effects of implicit solvents on peptide structure and dynamics, we performed extensive molecular dynamics simulations on the penta-peptide Cys-Ala-Gly-Gln-Trp. Two different implicit solvent models based on the CHARMM22 all-atom force field were used. Structural properties of the peptide such as distributions of end-to-end distances and dihedral angles obtained from molecular dynamics simulations with implicit solvent models were in a good agreement with those obtained from a previous explicit solvent simulation using the same force field. Representative structures observed in explicit solvent were sampled by implicit solvent models but with different relative probabilities. However, we observed significant differences in dynamical properties in explicit and implicit solvent models when we used traditional methods for the temperature control, such as Nose-Hoover or Berendsen thermostats. The explicitly solvated peptide displayed the slowest dynamics in both end-to-end contact formation and intrinsic diffusive motion of end-to-end distances. A closer agreement between implicit and explicit solvated peptide dynamics was observed when Langevin dynamics with a friction coefficient of 10 ps(-1) was used to maintain the temperature of the systems.

Simulation and verification of Zhang neural network for online time-varying matrix inversion

Differing from gradient-based neural networks (GNN), a special kind of recurrent neural network has recently been proposed by Zhang et al. for real-time inversion of time-varying matrices. The design of such a recurrent neural network is based on a matrix-valued error function instead of a scalar-valued norm-based energy-function. In addition, it is depicted in an implicit dynamics instead of an explicit dynamics. This paper investigates the simulation and verification of such a Zhang neural network (ZNN). Four important simulation techniques are employed to simulate this system: (1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector differential equation (VDE) [i.e., finally, there is a standard ordinary-differential-equation (ODE) formulation]. (2) MATLAB routine “ode45” with a mass-matrix property is introduced to simulate the transformed initial-value implicit ODE system. (3) Matrix derivatives are obtained using the routine “diff” and symbolic math toolbox. (4) Various implementation errors and different types of activation functions are investigated, further demonstrating the advantages of the ZNN model. Three illustrative computer-simulation examples substantiate the theoretical results and efficacy of the ZNN model for online time-varying matrix inversion.

From Zhang Neural Network to Newton Iteration for Matrix Inversion

Different from gradient-based neural networks, a special kind of recurrent neural network (RNN) has recently been proposed by Zhang for online matrix inversion. Such an RNN is designed based on a matrix-valued error function instead of a scalar-valued error function. In addition, it was depicted in an implicit dynamics instead of an explicit dynamics. In this paper, we develop and investigate a discrete-time model of Zhang neural network (termed as such and abbreviated as ZNN for presentation convenience), which is depicted by a system of difference equations. Comparing with Newton iteration for matrix inversion, we find that the discrete-time ZNN model incorporates Newton iteration as its special case. Noticing this relation, we perform numerical comparisons on different situations of using ZNN and Newton iteration for matrix inversion. Different kinds of activation functions and different step-size values are examined for superior convergence and better stability of ZNN. Numerical examples demonstrate the efficacy of both ZNN and Newton iteration for online matrix inversion.

Interference control during recognition of facial affect enhances the processing of expression specific properties — An event-related fMRI study

Though we can almost pre-attentively categorize the valence of facial expressions, we experience emotional ambiguity when confronted with facial expressions in a context with incongruent emotional information. We simultaneously presented interfering background colors during forced-choice categorizations of negative (fear), neutral and positive (happy) expressions. Conflicting information induced strong and differential interference effects on a behavioral level which was mirrored in comparable activations on a neuronal level. Besides a common fronto-parietal attention network which was activated during interference resolution, we found differential interference effects for facial expressions. Incongruent trials with neutral expressions induced a distinct activation pattern in ventral visual regions particularly involved in deeper analysis for both the task-relevant facial expressions (fusiform (FFA) and occipital face area (OFA)) and the task-irrelevant color (V4). Compared to neutral expressions, incongruent trials including either negative or positive expressions elicited attenuated interference effects. Unlike incongruent trials with positive facial expressions which showed only sparse activation in frontal cortex, interference resolution during processing of negative facial expressions resulted in specific activations in regions (V3a, MT +, STS) which might be involved in processing of implicit dynamics of negative expressions. Thus, functional activations in visual processing regions might specifically be related to processing demands of different expressions.

The influence of polymer architecture on the assembly of poly(ethylene oxide) grafted C60 fullerene clusters in aqueous solution: a molecular dynamics simulation study

The effect of polymer architecture on the aggregation behavior of C60 fullerenes tethered with a single chain of poly(ethylene oxide) (PEO) in aqueous solution has been investigated using coarse-grained, implicit solvent molecular dynamics simulations. The PEO-grafted fullerenes were comprised of a single tether of 60 repeat units represented as a linear polymer, a three-arm star (20 repeat units/arm) or a six-arm star (10 repeat units/arm). Additionally, the influence of arm length on self-assembly of the PEO-fullerene conjugates was investigated for the three-arm stars. Self-assembly is driven by favorable fullerene-fullerene and fullerene-PEO interactions. Our simulations reveal that it should be possible to control the size and geometry of the self-assembled fullerene aggregates in water through variation of PEO architecture and PEO molecular weight. We found that aggregate size and shape could be understood qualitatively in terms of the packing parameter concept that has been employed for diblock polymer and surfactant self-assembly. Higher molecular weight PEO (longer arms) and more compact PEO (more arms for the same molecular weight) resulted in greater steric repulsion between fullerenes, engendering greater aggregate surface curvature and hence the formation of smaller, more spherically shaped aggregates. Finally, weak attractive interactions between PEO and the fullerenes were found to play an important role in determining aggregate shape, size and the dynamics of self-assembly.

Targeting the early steps of Aβ16–22 protofibril disassembly by N‐methylated inhibitors: A numerical study

Aggregation of the Abeta1-40/Abeta1-42 peptides is a key factor in Alzheimer's disease. Though the inhibitory effect of N-methylated Abeta16-22 (mAbeta16-22) peptides is well characterized in vitro, there is little information on how they disassemble full-length Abeta fibrils or block fibril formation. Here, we report coarse-grained implicit solvent molecular dynamics (MD) and replica exchange molecular dynamics (REMD) simulations on Abeta16-22 and mAbeta16-22 monomers, and then a preformed six-chain Abeta16-22 bilayer with either four copies of Abeta16-22 or four copies of mAbeta16-22. Our simulations show that the effect of N-methylation on mAbeta16-22 monomer is to reduce the density of compact forms. While 100 ns MD trajectories do not reveal any significant differences between the two ten-chain systems, the REMD simulations totaling 1 micros help understand the first steps of Abeta16-22 protofibril disassembly by N-methylated inhibitors. Notably, we find that mAbeta16-22 preferentially interacts with Abeta16-22 by blocking both beta-sheet extension and lateral association of layers, but also by intercalation of the inhibitors allowing sequestration of Abeta16-22 peptides. This third binding mode is particularly appealing for blocking Abeta fibrillogenesis.

Damping Characterization Using Hysteresis on Static Nonrolling and Dynamic Rolling Behavior of Farm Tires

Abstract This paper presents the characterization of damping behavior as characterized by hysteresis for farm equipment tires and time domain numerical simulation of off-road tire rolling using finite element techniques. The hysteretic behavior is characterized by the load-displacement curves from static nonrolling vertical loading tests. Using a highly simplified finite element model based solely on tire catalog information and general constructional information, a hysteresis material model is used to simulate the hysteretic load-displacement behavior of farm tires. By choosing appropriate parameters for the hysteresis model, the static nonrolling finite element analyses results correlate very well to the experimental results. The fitted hysteresis material model is then used to simulate the dynamic rolling of a tire dropping off a curb. The bouncing vertical acceleration is of great interest to off-road tires. First, implicit dynamics is used to simulate the rolling using the calibrated hysteresis model. Very good correlations between the simulation results and vehicle test results are obtained. For better off-road rolling performance, the hysteresis model is recalibrated to reduce the vertical acceleration of the tire after the first bounce following the drop-off. The hysteresis model is replicated in explicit dynamics using an Abaqus/Explicit VUMAT subroutine to simulate the dynamic tire rolling behavior. By introducing additional damping and creep dissipation, the vertical acceleration is attenuated in excess of 50% after the first bounce following the drop-off to improve riding comfort. This hysteresis characterization has been shown to give good agreement with test data on nonrolling tests and dynamic drop-off tests. All modeling and solutions were performed using commercially available Abaqus software.