Presence Of Dynamical Noise Research Articles

Machine Learning Link Inference of Noisy Delay-Coupled Networks with Optoelectronic Experimental Tests

We devise a machine learning technique to solve the general problem of inferring network links that have time-delays. The goal is to do this purely from time-series data of the network nodal states. This task has applications in fields ranging from applied physics and engineering to neuroscience and biology. To achieve this, we first train a type of machine learning system known as reservoir computing to mimic the dynamics of the unknown network. We formulate and test a technique that uses the trained parameters of the reservoir system output layer to deduce an estimate of the unknown network structure. Our technique, by its nature, is non-invasive, but is motivated by the widely-used invasive network inference method whereby the responses to active perturbations applied to the network are observed and employed to infer network links (e.g., knocking down genes to infer gene regulatory networks). We test this technique on experimental and simulated data from delay-coupled opto-electronic oscillator networks. We show that the technique often yields very good results particularly if the system does not exhibit synchrony. We also find that the presence of dynamical noise can strikingly enhance the accuracy and ability of our technique, especially in networks that exhibit synchrony.

Quench-induced dynamical topology under dynamical noise

Equilibrium topological phases are robust against weak static disorder but may break down in the strong disorder regime. Here we explore the stability of the quench-induced emergent dynamical topology in the presence of dynamical noise. We develop an analytic theory and show that for weak noise, the quantum dynamics induced by quenching an initial trivial phase to Chern insulating regime exhibits robust emergent topology on certain momentum subspaces called band inversion surfaces (BISs). The dynamical topology is protected by the minimal oscillation frequency over the BISs, mimicking a bulk gap of the dynamical phase. Singularities emerge in the quench dynamics, with the minimal oscillation frequency vanishing on the BISs if increasing noise to critical strength, manifesting a dynamical topological transition, beyond which the emergent topology breaks down. Two types of dynamical transitions are predicted. Interestingly, we predict a sweet spot in the critical transition when noise couples to all three spin components in the same strength, in which case the dynamical topology survives at arbitrarily strong noise regime. This work unveils novel features of the dynamical topology under dynamical noise, which can be probed with control in experiment.

Quantum spatial search on graphs subject to dynamical noise

We address quantum spatial search on graphs and its implementation by continuous-time quantum walks in the presence of dynamical noise. In particular, we focus on search on the complete graph and on the star graph of order $N$, proving that also the latter is optimal in the computational limit $N \gg 1$, being nearly optimal also for small $N$. The noise is modeled by independent sources of random telegraph noise (RTN), dynamically perturbing the links of the graph. We observe two different behaviours depending on the switching rate of RTN: fast noise only slightly degrades performance, whereas slow noise is more detrimental and, in general, lowers the success probability. In particular, we still find a quadratic speed-up for the average running time of the algorithm, while for the star graph with external target node we observe a transition to classical scaling. We also address how the effects of noise depend on the order of the graphs, and discuss the role of the graph topology. Overall, our results suggest that realizations of quantum spatial search are possible with current technology, and also indicate the star graph as the perfect candidate for the implementation by noisy quantum walks, owing to its simple topology and nearly optimal performance also for just few nodes.

Statistical test of quasiperiodicity in the presence of dynamical noise

Statistical test of quasiperiodicity in the presence of dynamical noise

Kalman-Takens filtering in the presence of dynamical noise

The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model is known, a hybrid Kalman-Takens method has been recently introduced, in order to exploit the advantages of optimal filtering in a nonparametric setting. This procedure replaces the parametric model with dynamics reconstructed from delay coordinates, while using the Kalman update formulation to assimilate new observations. We find that this hybrid approach results in comparable efficiency to parametric methods in identifying underlying dynamics, even in the presence of dynamical noise. By combining the Kalman-Takens method with an adaptive filtering procedure we are able to estimate the statistics of the observational and dynamical noise. This solves a long standing problem of separating dynamical and observational noise in time series data, which is especially challenging when no dynamical model is specified.

Optimal efficiency of quantum transport in a disordered trimer.

Disordered quantum networks, such as those describing light-harvesting complexes, are often characterized by the presence of peripheral ringlike structures, where the excitation is initialized, and inner structures and reaction centers (RCs), where the excitation is trapped and transferred. The peripheral rings often display distinguished coherent features: Their eigenstates can be separated, with respect to the transfer of excitation, into two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In the absence of disorder, superradiant states have an enhanced coupling strength to the RC, while the subradiant ones are basically decoupled from it. Static on-site disorder induces a coupling between subradiant and superradiant states, thus creating an indirect coupling to the RC. The problem of finding the optimal transfer conditions, as a function of both the RC energy and the disorder strength, is very complex even in the simplest network, namely, a three-level system. In this paper we analyze such trimeric structure, choosing as the initial condition an excitation on a subradiant state, rather than the more common choice of an excitation localized on a single site. We show that, while the optimal disorder is of the order of the superradiant coupling, the optimal detuning between the initial state and the RC energy strongly depends on system parameters: When the superradiant coupling is much larger than the energy gap between the superradiant and the subradiant levels, optimal transfer occurs if the RC energy is at resonance with the subradiant initial state, whereas we find an optimal RC energy at resonance with a virtual dressed state when the superradiant coupling is smaller than or comparable to the gap. The presence of dynamical noise, which induces dephasing and decoherence, affects the resonance structure of energy transfer producing an additional incoherent resonance peak, which corresponds to the RC energy being equal to the energy of the superradiant state.

Maps serving the combined coupling for use in environmental models and their behaviour in the presence of dynamical noise

Many physical, biological as well as the environmental problems, can be described by the dynamics of driven coupled oscillators. In order to study their behaviour as a function of coupling strength and nonlinearity, we considered dynamics of two maps serving the combined coupling (diffusive and linear) in the above fields. Firstly, we have considered a logistic difference equation on extended domain that is a part of the maps, that is discussed using its bifurcation diagram, Lyapunov exponent, sample as well as the permutation entropy. Secondly we have performed the dynamical analysis of the coupled maps using Lyapunov exponent and cross sample entropy in dependence on two coupling parameters. Further, we investigated how dynamical noise can affects the structure of their bifurcation diagrams. It was done (i) by the noise entering in two specific ways, that disturbs either the logistic parameter on extended domain or (ii) by an additive “shock” to the state variables. Finally, we demonstrated the effect of forcing by parametric noise, introduced in all maps’ parameter, on Lyapunov exponent of coupled maps.

Influence of dynamical noise on time series generated by nonlinear maps

We consider periodic and chaotic dynamics of discrete nonlinear maps in the presence of dynamical noise. We show that dynamical noise corrupting dynamics of a nonlinear map may be considered as a measurement “pseudonoise” with the distribution determined by the Jacobian of the map. The formula for the distribution of the measurement “pseudonoise” for one-dimensional quadratic maps has also been obtained in an explicit form. We expect that our results apply to an arbitrary distribution of low-level dynamical noise and hope that these results could help to find a universal method of discriminating dynamical from measurement noise.

Practical criterion for delay estimation using random perturbations

Many systems contain an internal time delay, which significantly influences their dynamical properties. Methods to estimate this delay from times series in the presence of dynamical noise are not systematically studied. Addressing this problem, we demonstrate that it is sufficient to analyze the system's response to short-correlated external disturbances or internal noise. Following this idea, it is shown for linear and nonlinear systems, as well as for periodic dynamics, that the delay can be estimated by analyzing the correlation function. This method covers the case of strong noise and multiple delays.

Discriminating additive from dynamical noise for chaotic time series

We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only for one variable of the system, while the noise corrupting the second variable is still Gaussian distributed independent of distribution of dynamical noise. Based on these results and using scaling properties of the correlation entropy, we propose a simple method of discriminating additive from dynamical noise. This approach is also useful for estimation of noise level for chaotic time series. We show that the proposed method works well in a wide range of noise levels, providing that one kind of noise predominates and we analyze the variable of the system for which the contamination follows Cauchy-like distribution in the presence of dynamical noise.

Efficiency of the human visual system in discrimination of dynamic patterns

The efficiency of the human visual system during the observation of motionless test objects with additive dynamic Gaussian quasi-white noise was studied. It was found that the relationship between the duration of presentation of the object and the efficiency in presence of dynamic noise has a maximum at 20 ms. The presence of this maximum is explained by the simultaneous effects of two factors: (1) the limited duration of accumulation of visual memory and (2) the time necessary to develop decision-making thresholds during recognition. It was also shown that absence of prior information about the position of the target object reduces the efficiency more than absence of prior information about the time of its appearance.

Discriminating dynamical from additive noise in the Van der Pol oscillator

We address the distinction between dynamical and additive noise (AN) in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low levels of the latter and high levels of the former indicate the presence of dynamical noise (DN) only, while low values of the two are observed as soon as AN contaminates the signal. The method is presented through numerical tests on the well-known Van der Pol oscillator, including the chaotic case driven with a harmonic force. However, we give arguments according to which we expect a general validity for continuous-time systems.

Delay embedding in the presence of dynamical noise

We present a new embedding theorem for time series, in the spirit of Takens's theorem, but requiring multivariate signals. Our result is part of a growing body of work that extends the domain of geometric time series analysis to some genuinely stochastic systems-including such natural examples where φ is some fixed map and the ηi are i.i.d. random displacements

The effects of spatiotemporal integration on maximum displacement thresholds for the detection of coherent motion

In a series of nine experiments, observers were required to identify the shapes of moving targets, and to discriminate regions of motion from regions of uncorrelated noise. Maximum displacement thresholds ( D max) for performing these tasks were obtained under a wide variety of conditions. The stimulus parameters manipulated included the number of distinct frames in the motion sequences, the stimulus onset asynchrony between each frame, the size of the moving dots, and the shape, area and eccentricity of the target regions. For two-frame displays presented in alternation, the area of the target region was the only one of these variables to have any significant effect on D max. For longer length sequences, in contrast, D max varied dramatically among the the different conditions over a range of 10 min arc to 10 deg. In an effort to isolate the specific processes of spatiotemporal integration, we also examined how performance is affected by having overlapping transparent motions in opposite directions, or by the presence of dynamic noise or limited dot lifetimes within the moving target regions. The overall pattern of results suggest that D max is primarily determined by the ability of the visual system to isolate motion signals from the noise produced by spurious false target correlations. As a general rule, D max will increase as a result of any stimulus manipulation that increases the number of local signal correlations detected relative to those arising from noise, and vice versa.