Modified Langevin approach for a stochastic calcium puff model

In many cell types, intracellular calcium is released from internal stores through calcium release channels. Because these channels are distributed in clusters with a few tens of channels, the clusters show a strongly stochastic open and close dynamics, resulting in noisy localized Ca²⁺ signals called puffs. Using the Li-Rinzel model we compare the stochastic channel simulations for the Markov method and three different Langevin approaches. We suggest that a modified Langevin approach should be considered in order to more accurately simulate Markov channel noise for puff dynamics.     

Stochastic dynamics of the cubic map: A study of noise-induced transition phenomena

The effects of finite-amplitude, additive noise on the dynamics generated by a one-dimensional, two-parameter cubic map are considered. The underlying deterministic system exhibits bistability and hysteresis, and noise-induced processes associated with these phenomena are studied. If a bounded noise source is applied to this system, trajectories may be confined to a finite region. Mechanisms are given for the merging transitions between different parts of this region and the eventual escape from it as the noise level is increased. The noisy dynamics is also represented by an integral evolution operator, with an equilibrium density function with finite support. The operator's spectrum is determined as a function of map parameters and noise amplitude. Such noisy one-dimensional maps can provide models for the study of noise-induced phenomena described by stochastic differential equations.     

Modulated noisy biological dynamics: Three examples

Three examples of noisy biological dynamics modulated by a periodic signal are discussed. A minimal neuron model driven by stochastic noise and small periodic force show a firing statistic comparable with stochastic resonance as demonstrated in bistable systems. Similar results are obtained from responses to periodic vibrotactile stimulation on higher-order neuronal units of the somatosensory pathway. Finally, results from a bistable visual perception task exhibiting stochastic resonance are reported.     

Stochastic dynamical analysis of a kind of vibro-impact system under multiple harmonic and random excitations

There have been many contributions concerned with non-smooth dynamics. The purpose of this study is focused on the global stochastic dynamics of a kind of vibro-impact oscillator under the multiple harmonic and bounded noisy excitations. The well-known cell-to-cell mapping method is firstly developed to investigate the incursive fractal boundaries between the attracting domains of different random attractors, and a specific Poincaré map is then set up to explore the noise-contaminated dynamical transitions in the system. Lastly, the leading Lyapunov exponents and the surrogate tests are used to identify the noise-contaminated dynamics. It is shown that several random attractors will coexist in the phase space of the randomly driven system by adjusting the parameters’ values, and fractal boundaries may also arise between the attracting domains of different random attractors. Under the joint action of the harmonic excitation and the weak bounded noise excitation, the noisy period-doubling process, similar to a deterministic one, can appear in the Poincaré’s global cross-section by increasing the strength of the bounded noisy excitation. Moreover, the noisy periodic, the noisy chaotic, and the random-dominant dynamics are also distinguished from the noise-contaminated signals.     

Dynamics of macroautophagy: Modeling and oscillatory behavior

We propose a model for macroautophagy and study the resulting dynamics of autophagy in a system isolated from its extra-cellular environment. It is found that the intracellular concentrations of autophagosomes and autolysosomes display oscillations with their own natural frequencies. Such oscillatory behaviors, which are interrelated to the dynamics of intracellular ATP, amino acids, and proteins, are consistent with the very recent biological observations. Implications of this theoretical study of autophagy are discussed, with regard to the possibility of guiding molecular studies of autophagy.     

Unbiased reconstruction of the dynamics underlying a noisy chaotic time series

Refined methods for the construction of a deterministic dynamical system which can consistently reproduce observed aperiodic data are discussed. The determination of the dynamics underlying a noisy chaotic time series suffers strongly from two systematic errors: One is a consequence of the so-called "error-in-variables problem." Standard least-squares fits implicitly assume that the independent variables are noise free and that the dependent variable is noisy. We show that due to the violation of this assumption one receives considerably wrong results for moderate noise levels. A straightforward modification of the cost function solves this problem. The second problem consists in a mutual inconsistency between the images of a point under the model dynamics and the corresponding observed values. For an improved fit we therefore introduce a multistep prediction error which exploits the information stored in the time series in a better way. The performance is demonstrated by several examples, including experimental data. (c) 1996 American Institute of Physics.     

Quantum Dynamics in Noisy Backgrounds: from Sampling to Dissipation and Fluctuations

We investigate the dynamics of a quantum system coupled linearly to Gaussian white noise using functional methods. By performing the integration over the noisy field in the evolution operator, we get an equivalent non-Hermitian Hamiltonian, which evolves the quantum state with a dissipative dynamics. We also show that if the integration over the noisy field is done for the time evolution of the density matrix, a gain contribution from the fluctuations can be accessed in addition to the loss one from the non-hermitian Hamiltonian dynamics. We illustrate our study by computing analytically the effective non-Hermitian Hamiltonian, which we found to be the complex frequency harmonic oscillator, with a known evolution operator. It leads to space and time localisation, a common feature of noisy quantum systems in general applications.     

Function Package for Computing Quantum Resource Measures

In this paper, we present a function package for to calculate quantum resource measures and dynamics of open systems. Our package includes common operators and operator lists, frequently-used functions for computing quantum entanglement, quantum correlation, quantum coherence, quantum Fisher information and dynamics in noisy environments. We briefly explain the functions of the package and illustrate how to use the package with several typical examples. We expect that this package is a useful tool for future research and education.     

Detecting subthreshold events in noisy data by symbolic dynamics

We show that a symmetric threshold crossing detector can be described by a symbolic dynamics of a static three-symbol encoding which is highly efficient to detect subthreshold events in noisy nonstationary data. After computing instantaneous word statistics and running cylinder entropies, we introduce a mean-field transformation of the three-symbol dynamics considered as a Potts-spin lattice onto a distribution of two symbols. This transformed word statistics enables one to derive an estimator of the signal-to-noise ratio (SNR). Subthreshold events are then proven by a prominent peak of the SNR estimator as a function of the noise intensity.     

FAST EVOLVING MULTI-LAYER PERCEPTRONS FOR NOISY CHAOTIC TIME SERIES MODELING AND PREDICTIONS

A fast evolutionary programming (FEP) is proposed to train multi-layer perceptrons (MLP) for noisy chaotic time series modeling and predictions. This FEP, which uses a Cauchy mutation operator that results in a significantly faster convergence to the optimal solution, can help MLP to escape from local minima. A comparison against back-propagation-trained networks was performed. Numerical experimental results show that the FEP can help MLP better capturing dynamics from noisy chaotic time series than the back-propagation algorithm and produce a more consistently modeling and prediction.     

Reconstruction of non-linear time delay models from data by the use of optimal transformations

We propose a new technique for the numerical reconstruction of non-linear delay differential equations from time series by applying the method of optimal transformations, a concept of multiple non-linear regression analysis. By constructing a generalized correlation function, this method allows for testing time series for delay-induced dynamics. Also, the delay times and the governing differential equations are estimated with good numerical accuracy. We present several examples which show that this method is useful also for the analysis of short and noisy time series.     

Imaging of Ca(2)+ intracellular dynamics with a third-harmonic generation microscope

We describe the promising development of third-harmonic generation (THG) in laser scanning microscopy for study of the functional imaging of live biological cells. The dynamics of Ca(2+) in biological cells is shown. The Ca(2+) signal consists of a transient increase in the intracellular concentration. THG microscopy allows one to temporally visualize the release of Ca(2+) from internal stores and (or) calcium influx.     

White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability

White noise-induced pattern formation is studied in a network composed of Morris–Lecar neuronal models with type I excitability and with initial values higher than that of the resting potential. The appearance and disappearance of spiral waves, as well as the transitions between spiral wave patterns with different kinds of complexity characterized by the normalized spatial autocorrelation function, enable changes in the order of the network so as to exhibit a scenario with two or more locally maximal peaks, as can be clearly seen in the signal to noise ratio curves, as the noise intensity is adjusted from small to large in a wide range. A possible physical mechanism of the multiple resonances based on the dynamics of type I excitability and initial values is provided. The potential biological significance of the noise-induced spiral waves is discussed.     

Re-examining the sources of heteroskedasticity: The paradigm of noisy chaotic models

In this paper, we analyze the rich dynamic properties of the noisy chaotic model developed by Kyrtsou [C. Kyrtsou, Evidence for neglected linearity in noisy chaotic models, International Journal of Bifurcation and Chaos 15 (10) (2005)] considering homoskedastic errors, with the aim of deriving information about possible links between noisy chaotic dynamics and ARCH effects. With the joint application of the Engle [R.F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50 (1982) 987-1007] and McLeod-Li [A.I. McLeod, W.K. Li, Diagnostic checking ARMA time series models using squared-residuals autocorrelations, Journal of Time Series Analysis 4 (1983) 269-273] tests for non-linearity in the second moment, we attempt to show how highly non-linear models can exhibit heteroskedasticity when no heteroskedastic structure is assumed by construction.     

Under what kind of parametric fluctuations is spatiotemporal regularity the most robust?

It was observed that the spatiotemporal chaos in lattices of coupled chaotic maps was suppressed to a spatiotemporal fixed point when some fractions of the regular coupling connections were replaced by random links. Here we investigate the effects of different kinds of parametric fluctuations on the robustness of this spatiotemporal fixed point regime. In particular we study the spatiotemporal dynamics of the network with noisy interaction parameters, namely fluctuating fraction of random links and fluctuating coupling strengths. We consider three types of fluctuations: (i) noisy in time, but homogeneous in space; (ii) noisy in space, but fixed in time; (iii) noisy in both space and time. We find that the effect of different kinds of parametric noise on the dynamics is quite distinct: quenched spatial fluctuations are the most detrimental to spatiotemporal regularity; spatiotemporal fluctuations yield phenomena similar to that observed when parameters are held constant at the mean value, and interestingly, spatiotemporal regularity is most robust under spatially uniform temporal fluctuations, which in fact yields a larger fixed point range than that obtained under constant mean-value parameters.     

Controlling transfer of quantum correlations among bi-partitions of a composite quantum system by combining different noisy environments

The correlation dynamics are investigated for various bi-partitions of a composite quantum system consisting of two qubits and two independent and non-identical noisy environments. The two qubits have no direct interaction with each other and locally interact with their environments. Classical and quantum correlations including the entanglement are initially prepared only between the two qubits. We find that contrary to the identical noisy environment case, the quantum correlation transfer direction can be controlled by combining different noisy environments. The amplitude-damping environment determines whether there exists the entanglement transfer among bi-partitions of the system. When one qubit is coupled to an amplitude-damping environment and the other one to a bit-flip one, we find a very interesting result that all the quantum and the classical correlations, and even the entanglement, originally existing between the qubits, can be completely transferred without any loss to the qubit coupled to the bit-flit environment and the amplitude-damping environment. We also notice that it is possible to distinguish the quantum correlation from the classical correlation and the entanglement by combining different noisy environments.     

Dynamical properties of water in living cells

With the aim of studying the effect of water dynamics on the properties of biological systems, in this paper, we present a quasi-elastic neutron scattering study on three different types of living cells, differing both in their morphological and tumor properties. The measured scattering signal, which essentially originates from hydrogen atoms present in the investigated systems, has been analyzed using a global fitting strategy using an optimized theoretical model that considers various classes of hydrogen atoms and allows disentangling diffusive and rotational motions. The approach has been carefully validated by checking the reliability of the calculation of parameters and their 99% confidence intervals. We demonstrate that quasi-elastic neutron scattering is a suitable experimental technique to characterize the dynamics of intracellular water in the angstrom/picosecond space/time scale and to investigate the effect of water dynamics on cellular biodiversity.