Statistical predictions for the dynamics of a low-speed system: newtonian versus special-relativistic mechanics

The newtonian and special-relativistic statistical predictions for the mean, standard deviation and probability density function of the position and momentum are compared for the periodically-delta-kicked particle at low speed. Contrary to expectation, we find that the statistical predictions, which are calculated from the same parameters and initial gaussian ensemble of trajectories, do not always agree if the initial ensemble is sufficiently well-localized in phase space. Moreover, the breakdown of agreement is very fast if the trajectories in the ensemble are chaotic, but very slow if the trajectories in the ensemble are non-chaotic. The breakdown of agreement implies that special-relativistic mechanics must be used, instead of the standard practice of using newtonian mechanics, to correctly calculate the statistical predictions for the dynamics of a low-speed system.     

Newtonian versus Special-Relativistic Statistical Predictions for Low-Speed Scattering

The statistical predictions of Newtonian and special-relativistic mechanics, which are calculated from an initially Gaussian ensemble of trajectories, are compared for a low-speed scattering system. The comparisons are focused on the mean dwell time, transmission and reflection coefficients, and the position and momentum means and standard deviations. We find that the statistical predictions of the two theories do not always agree as conventionally expected. The predictions are close if the scattering is non-chaotic but they are radically different if the scattering is chaotic and the initial ensemble is well localized in phase space. Our result indicates that for low-speed chaotic scattering, special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to obtain empirically-correct statistical predictions from an initially well-localized Gaussian ensemble.     

Whole-body mechanics and kinematics of terrestrial locomotion in the Elegant-crested Tinamou Eudromia elegans

Whereas humans and certain birds experience an abrupt change in locomotor dynamics when shifting from walks to runs, a smooth walk–run transition characterizes many ground-dwelling birds. This study defines the biomechanical distinction between walks and runs in the Elegant-crested Tinamou Eudromia elegans using ground reaction forces. Three birds were filmed at 250 Hz from a lateral view as they moved over a force plate built into a trackway. Centre of mass mechanics and kinematic variables were analysed in 81 steady-speed trials that represented a speed range from 0.66 to 2.78 m/s. E. elegans undergoes two speed-related changes in locomotor mechanics. The first is a shift from walking strides that utilize vaulting mechanics to low-speed runs that exhibit bouncing mechanics; this transition occurs at Froude numbers between 0.4 and 0.6. Such low-speed runs exhibit duty factors exceeding 0.5 and, hence, lack an aerial phase between steps. The second transition, from grounded running to aerial running, occurs when duty factors decrease below 0.5. Grounded running in birds may enhance vision by stabilizing visual stimuli over the retina. The eventual incorporation of an aerial phase during running enables increased locomotor speeds primarily through longer stride lengths.     

A bit of sex stabilizes host-parasite dynamics

To date, only a few studies have focused on the effects of sex on population dynamics. Previous models have typically found that sexual reproduction dampens population fluctuations. Although asexual and sexual reproduction are just the two endpoints along a continuum of varying rates of sex, previous work has ignored the effects of intermediate degrees of sex on population dynamics. Here we study the effects of partial sexual reproduction (i.e. sex occurs only every few generations or with small probability in each generation) on the coupled population dynamics of a Nicholson-Bailey host-parasite model. We show that complex dynamics are simplified for high host population growth rates if the frequency of sex is sufficiently high in both host and parasite: sex decreases fluctuations in population density, and leads to non-chaotic dynamics for population growth rates that would result in chaotic dynamics in the absence of sexual reproduction. However, the simplification does not increase gradually with an increasing frequency of sex but appears abruptly at low-to-intermediate frequencies of sex. For some parameter settings, intermediate frequencies of sexual reproduction can simplify the dynamics more than lower or higher frequencies. Thus, in agreement with earlier results, sexual reproduction typically stabilizes complex population dynamics in our models. Additionally, our results suggest that low-to-intermediate frequencies of sex may often be as (or even more) stabilizing as high frequencies.     

Respiratory influences on non-linear dynamics of heart rate variability in humans

 The goal of our study was to determine whether evidence for chaos in heart rate variability (HRV) can be observed when the respiratory input to the autonomic controller of heart rate is forced by the deterministic pattern associated with periodic breathing. We simultaneously recorded, in supine healthy volunteers, RR intervals and breathing volumes for 20 to 30 min (1024 data point series) during three protocols: rest (control), fixed breathing (15 breath/min) and voluntary periodic breathing (3 breaths with 2 s inspiration and 2 s expiration followed by an 8 s breath hold). On both the RR interval and breathing volume series we applied the non-linear prediction method (Sugihara and May algorithm) to the original time series and to distribution-conserved isospectral surrogate data. Our results showed that, in contrast to the control test, during both fixed and voluntary periodic breathing the variability of breathing volumes was clearly deterministic non-chaotic. During all the three protocols, the RR-interval series’ non-linear predictability was consistent with one of a chaotic series. However, at rest, no clear difference was observed between the RR-interval series and their surrogates, which means that no clear chaos was observed. During fixed breathing a difference appeared, and this difference seemed clearer during voluntary periodic breathing. We concluded that HRV dynamics were chaotic when respiration was forced with a deterministic non-chaotic pattern and that normal spontaneous respiratory influences might mask the normally chaotic pattern in HRV. Received: 7 August 1995 / Accepted in revised form: 20 March 1997     

Structural perturbations to population skeletons: transient dynamics, coexistence of attractors and the rarity of chaos

BACKGROUND: Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic) fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons). The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction) through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data. METHODOLOGY/PRINCIPAL FINDINGS: We present a proportional feedback mechanism that is independent of model formulation and capable of perturbing population skeletons in an evolutionary way, as opposed to requiring constant feedbacks. We observe the same repertoire of patterns, from equilibrium states to non-chaotic aperiodic oscillations to chaotic behaviour, across different population models, in agreement with observations in real population data. Model outputs also indicate the existence of multiple attractors in some parameter regimes and this coexistence is found to depend on initial population densities or the duration of transient dynamics. Our results suggest that such a feedback mechanism may enable a better understanding of the regulatory processes in natural populations.     

Modeling spatial trajectories in dynamics testing using basis splines: application to tracking human volunteers in low-speed frontal impacts

Designing motor vehicle safety systems requires knowledge of whole body kinematics during dynamic loading for occupants of varying size and age, often obtained from sled tests with postmortem human subjects and human volunteers. Recently, we reported pediatric and adult responses in low-speed (<4 g) automotive-like impacts, noting reductions in maximum excursion with increasing age. Since the time-based trajectory shape is also relevant for restraint design, this study quantified the time-series trajectories using basis splines and developed a statistical model for predicting trajectories as a function of body dimension or age. Previously collected trajectories of the head, spine, and pelvis were modeled using cubic basis splines with eight control points. A principal component analysis was conducted on the control points and related to erect seated height using a linear regression model. The resulting statistical model quantified how trajectories became shorter and flatter with increasing body size, corresponding to the validation data-set. Trajectories were then predicted for erect seated heights corresponding to pediatric and adult anthropomorphic test devices (ATDs), thus generating performance criteria for the ATDs based on human response. This statistical model can be used to predict trajectories for a subject of specified anthropometry and utilized in subject-specific computational models of occupant response.     

An approach to improve Wang-Smith chaotic simulated annealing

Previous research shows that Wang-Smith chaotic simulated annealing, which employs a gradually decreasing time-step, has only a scaling effect to computational energy of the Hopfield model without changing its shape. This makes the net has sensitive dependence on the value of damping factor. Considering Chen-Aihara chaotic simulated annealing with decaying self-coupling has a shape effect to computational energy of the Hopfield model, a novel approach to improve Wang-Smith chaotic simulated annealing, which reaps the benefits of Wang-Smith model and Chen-Aihara model, is proposed in this paper. With the aid of this method the improved model can affect on computational energy of the Hopfield model from scaling and shape. By adjusting the time-step, the improved neural network can also pass from a chaotic to a non-chaotic state. From numerical simulation experiments, we know that the improved model can escape from local minima more efficiently than original Wang-Smith model.     

Invasion of an intermediate predator: the dynamics of fish populations in the mathematical model of a trophic chain (as applied to the Syamozero lake)

We present a mathematical model of the dynamics of a spatially heterogeneous predator-prey population system. A prototype of the model system is the Syamozero lake fish community. We study the impact of the invader, an intermediate predator, on the dynamics of the fish community. We show that the invasion can lead to the appearance of chaotic oscillations in the population density. We show also that different dynamical regimes resulting from the invasion, i.e., stationary, non-chaotic oscillatory and chaotic ones, can coexist. The "choice" of a specific regime therewith depends on the initial invader density. Our analysis of solutions of the mathematical models shows that the successful invasion of the alien species takes place solely in the absence of the competition between the invaders and the native species.     

The Calculation of 3D Solubility Parameters Using Molecular Models

Abstract

In this paper we describe the use of molecular mechanics models to examine detailed intermolecular interactions within the liquid state of a common nonionic surfactant system, nonyl phenol ethoxylate (NPE). Using constant energy molecular dynamics simulations we have studied the relative strengths of dispersive interactions versus polar interactions and have estimated three dimensional solubility parameters for NPE systems as a function of temperature and ethylene oxide content. The predictions at 300 K are in good agreement with three dimensional solubility parameters predicted using group contribution tables. Models of the amorphous liquid state were represented by single molecular structures of NPE in a periodic cell. The solubility parameters predicted with these models were in good agreement with those values derived from models having eight NPE molecules packed into a cell with the exception of the electrostatic interactions, which are the most sensitive to system size effects.     

具有共生作用两种群离散耦合Logistic模型混沌控制

针对具有共生作用的离散耦合Logistic模型,首先采用Lyapunov指数方法验证了混沌现象的存在.然后详细地分析了系统随参数变化的分岔图,发现了系统中存在更复杂的现象.最后应用混沌跟踪控制方法控制系统的混沌现象,使得种群稳定到正不动点轨道上,消除了种群中存在的混沌现象.仿真结果验证了控制方法的有效性.     

Aerobic microbial growth in semisolid matrices: Heat and mass transfer limitation

A conceptual model of aerobic microbial growth in semisolid matrices was developed as a first step in the prediction of the rate of breakdown of semisolid cellulosic material. The conceptual model was described by a series of equations simplified by the assumption of steady-state microbial activity, and heat and mass transfer limitation. Temperature and oxygen distribution in compost piles were measured experimentally at the Butler County Mushroom Farm, Butler County, Pennsylvania, to test the validity of these assumptions. The compost piles consisted of ground corn husks, straw, and race horse manure. The data fit with the model was excellent with deviations between model predictions (as solved by an analog computer) and actual temperature measurements never exceeding 3°C. The effects of compost pile geometry, external temperature, compost density, external oxygen concentration, and insulation at the bottom of the pile were then predicted using a digital computer to solve the model. The predictions show that the maximum breakdown rate occurs for an optimum height (which depends upon the system), insulating the base increases the breakdown rate, increasing the external temperature increases the initial breakdown rate but decreases the pseudo-steady-state breakdown rate and the uniformity, and any increase in the external oxygen concentration increases the breakdown rate but decreases the uniformity.     

Statistical mechanics unifies different ecological patterns

Recently there has been growing interest in the use of maximum relative entropy (MaxREnt) as a tool for statistical inference in ecology. In contrast, here we propose MaxREnt as a tool for applying statistical mechanics to ecology. We use MaxREnt to explain and predict species abundance patterns in ecological communities in terms of the most probable behaviour under given environmental constraints, in the same way that statistical mechanics explains and predicts the behaviour of thermodynamic systems. We show that MaxREnt unifies a number of different ecological patterns: (i) at relatively local scales a unimodal biodiversity-productivity relationship is predicted in good agreement with published data on grassland communities, (ii) the predicted relative frequency of rare vs. abundant species is very similar to the empirical lognormal distribution, (iii) both neutral and non-neutral species abundance patterns are explained, (iv) on larger scales a monotonic biodiversity-productivity relationship is predicted in agreement with the species-energy law, (v) energetic equivalence and power law self-thinning behaviour are predicted in resource-rich communities. We identify mathematical similarities between these ecological patterns and the behaviour of thermodynamic systems, and conclude that the explanation of ecological patterns is not unique to ecology but rather reflects the generic statistical behaviour of complex systems with many degrees of freedom under very general types of environmental constraints.     

Why do evolutionary systems stick to the edge of chaos

Summary  The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly different initial conditions, a regular system converges to the same final trajectory, whereas a chaotic system follows two distinct trajectories exponentially diverging from each other. In spite of these differences, regular and chaotic systems share a common property: both arrive exponentially fast to their final destiny, becoming trapped there. In both cases one has finite transient times. This is not a profitable property in what concerns evolutionary strategies, where the eternal search for new forms, better than the current one, is imperative. That is why evolutionary dynamic systems tend to tune themselves in very particular situations in between regular and chaotic regimes. These particular situations present eternal transients, and the system actually never reaches its final destiny, preserving diversity. This feature allows the system to visit other regions of the space of possibilities, not only the tiny region covered by its final attractor.     

Molecular dynamics and binding specificity analysis of the bovine immunodeficiency virus BIV Tat-TAR complex

We have performed molecular dynamics (MD) simulations, with particle-mesh Ewald, explicit waters, and counterions, and binding specificity analyses using combined molecular mechanics and continuum solvent (MM-PBSA) on the bovine immunodeficiency virus (BIV) Tat peptide-TAR RNA complex. The solution structure for the complex was solved independently by Patel and co-workers and Puglisi and co-workers. We investigated the differences in both structures and trajectories, particularly in the formation of the U-A-U base triple, the dynamic flexibility of the Tat peptide, and the interactions at the binding interface. We observed a decrease in RMSD in comparing the final average RNA structures and initial RNA structures of both trajectories, which suggests the convergence of the RNA structures to a MD equilibrated RNA structure. We also calculated the relative binding of different Tat peptide mutants to TAR RNA and found qualitative agreement with experimental studies.     

Protein kinase C epsilon in cell division: Control of abscission

Cell division requires the separation and partitioning of sister chromatids to opposite ends of the cell before an actomyosin ring contracts the membrane in between during cytokinesis. The final irreversible step occurs during abscission when the ring breaks down and the membrane is sealed in its place. The physical mechanics of contraction depend on RhoA which is stimulated by a centralspindlin complex around the cell equator. However exactly how these events are reversed to allow actomyosin breakdown and abscission were not well understood. Here we will discuss new findings which implicate Protein Kinase C epsilon (PKCε) as a regulator of RhoA signalling required for abscission.     

Protein structure prediction force fields: Parametrization with quasi-newtonian dynamics

We present an unusual method for parametrizing low-resolution force fields of the type used for protein structure prediction. Force field parameters were-determined by assigning each a fictitious mass and using a quasi-molecular dynamics algorithm in parameter space. The quasi-energy term favored folded native structures and specifically penalized folded nonnative structures. The force field was generated after optimizing less than 70 adjustable parameters, but shows a strong ability to discriminate between native structures and compact misfolded-alternatives. The functional form of the force field was chosen as in molecular mechanics and is not table-driven. It is continuous with continuous derivatives and is thus suitable for use with algorithms such as energy minimization or newtonian dynamics. Proteins 27:367–384, 1997. © 1997 Wiley-Liss, Inc.