### Concept: Nonlinear system

#### 171

##### Visualization of system dynamics using phasegrams

- OPEN
- Journal of the Royal Society, Interface / the Royal Society
- Published over 5 years ago
- Discuss

A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

#### 170

##### Nonlinear vibration behavior of graphene resonators and their applications in sensitive mass detection.

- OPEN
- Nanoscale research letters
- Published over 6 years ago
- Discuss

Graphene has received significant attention due to its excellent mechanical properties, which has resulted in the emergence of graphene-based nano-electro-mechanical system such as nanoresonators. The nonlinear vibration of a graphene resonator and its application to mass sensing (based on nonlinear oscillation) have been poorly studied, although a graphene resonator is able to easily reach the nonlinear vibration. In this work, we have studied the nonlinear vibration of a graphene resonator driven by a geometric nonlinear effect due to an edge-clamped boundary condition using a continuum elastic model such as a plate model. We have shown that an in-plane tension can play a role in modulating the nonlinearity of a resonance for a graphene. It has been found that the detection sensitivity of a graphene resonator can be improved by using nonlinear vibration induced by an actuation force-driven geometric nonlinear effect. It is also shown that an in-plane tension can control the detection sensitivity of a graphene resonator that operates both harmonic and nonlinear oscillation regimes. Our study suggests the design principles of a graphene resonator as a mass sensor for developing a novel detection scheme using graphene-based nonlinear oscillators.

#### 28

##### A simple model of mechanotransduction in primate glabrous skin

- Journal of neurophysiology
- Published about 6 years ago
- Discuss

Tactile stimulation of the hand evokes highly precise and repeatable patterns of activity in mechanoreceptive afferents; the strength (i.e., firing rate, Muniak et al. 2007) and timing (Johansson and Birznieks 2004; Mackevicius et al. 2012; Saal et al. 2009) of these responses have been shown to convey stimulus information. To achieve an understanding of the mechanisms underlying the representation of tactile stimuli in the nerve, we developed a two-stage computational model consisting of a nonlinear mechanical transduction stage followed by a generalized integrate-and-fire mechanism. The model improves upon a recently published counterpart (Kim et al. 2010) in two important ways. First, complexity is dramatically reduced (at least one order of magnitude fewer parameters). Second, the model comprises a saturating non-linearity and therefore can be applied to a much wider range of stimuli. We show that both the rate and timing of afferent responses are predicted with remarkable precision, and observed adaptation patterns and threshold behavior are well captured. We conclude that the responses of mechanoreceptive afferents can be understood using a very parsimonious mechanistic model, which can then be used to accurately simulate the responses of afferent populations.

#### 26

##### Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling

- OPEN
- Proceedings of the National Academy of Sciences of the United States of America
- Published almost 4 years ago
- Discuss

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner-recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts.

#### 26

##### Adaptive control of nonlinear uncertain active suspension systems with prescribed performance

- ISA transactions
- Published over 4 years ago
- Discuss

This paper proposes adaptive control designs for vehicle active suspension systems with unknown nonlinear dynamics (e.g., nonlinear spring and piece-wise linear damper dynamics). An adaptive control is first proposed to stabilize the vertical vehicle displacement and thus to improve the ride comfort and to guarantee other suspension requirements (e.g., road holding and suspension space limitation) concerning the vehicle safety and mechanical constraints. An augmented neural network is developed to online compensate for the unknown nonlinearities, and a novel adaptive law is developed to estimate both NN weights and uncertain model parameters (e.g., sprung mass), where the parameter estimation error is used as a leakage term superimposed on the classical adaptations. To further improve the control performance and simplify the parameter tuning, a prescribed performance function (PPF) characterizing the error convergence rate, maximum overshoot and steady-state error is used to propose another adaptive control. The stability for the closed-loop system is proved and particular performance requirements are analyzed. Simulations are included to illustrate the effectiveness of the proposed control schemes.

#### 25

Cerebrospinal fluid (CSF) studies consistently show that CSF levels of amyloid-beta 1-42 (Aβ42) are reduced and tau levels increased prior to the onset of cognitive decline related to Alzheimer’s disease (AD). However, the preclinical prediction accuracy for low CSF Aβ42 levels, a surrogate for brain Aβ42 deposits, is not high. Moreover, the pathology data suggests a course initiated by tauopathy contradicting the contemporary clinical view of an Aβ initiated cascade. CSF Aβ42 and tau data from 3 normal aging cohorts (45-90 years) were combined to test both cross-sectional (n = 766) and longitudinal (n = 651) hypotheses: 1) that the relationship between CSF levels of Aβ42 and tau are not linear over the adult life-span; and 2) that non-linear models improve the prediction of cognitive decline. Supporting the hypotheses, the results showed that a u-shaped quadratic fit (Aβ2) best describes the relationship for CSF Aβ42 with CSF tau levels. Furthermore we found that the relationship between Aβ42 and tau changes with age-between 45 and 70 years there is a positive linear association, whereas between 71 and 90 years there is a negative linear association between Aβ42 and tau. The quadratic effect appears to be unique to Aβ42, as Aβ38 and Aβ40 showed only positive linear relationships with age and CSF tau. Importantly, we observed the prediction of cognitive decline was improved by considering both high and low levels of Aβ42. Overall, these data suggest an earlier preclinical stage than currently appreciated, marked by CSF elevations in tau and accompanied by either elevations or reductions in Aβ42. Future studies are needed to examine potential mechanisms such as failing CSF clearance as a common factor elevating CSF Aβxx analyte levels prior to Aβ42 deposition in brain.

#### 25

##### Spatial (Mis-)Interpretation of Pointing Gestures to Distal Referents

- Journal of experimental psychology. Human perception and performance
- Published over 3 years ago
- Discuss

Pointing gestures are a vital aspect of human communication. Nevertheless, observers consistently fail to determine the exact location to which another person points when that location lies in the distance. Here we explore the reasons for this misunderstanding. Humans usually point by extending the arm and finger. We show that observer’s interpret these gestures by nonlinear extrapolation of the pointer’s arm-finger line. The nonlinearity can be adequately described as the Bayesian-optimal integration of a linear extrapolation of the arm-finger line and observers' prior assumptions about likely referent positions. Surprisingly, the spatial rule describing the interpretation of pointing gestures differed from the rules describing the production of these gestures. In the latter case, the eye, index finger, and referent were aligned. We show that the differences in the production and interpretation of pointing gestures accounts for the systematic spatial misunderstanding of pointing gestures to distant referents. No evidence was found for the hypotheses that action-related processes are involved in the perception of pointing gestures. How participants interpreted pointing gestures was independent of how they produce these gestures and whether they had practiced pointing movements before. By contrast, both the production and interpretation seem to be primarily determined by salient visual cues. (PsycINFO Database Record

#### 23

##### The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport

- OPEN
- Scientific reports
- Published about 2 years ago
- Discuss

We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.

#### 20

##### Association between Homocysteine Levels and All-cause Mortality: A Dose-Response Meta-Analysis of Prospective Studies

- OPEN
- Scientific reports
- Published over 1 year ago
- Discuss

Plasma homocysteine (Hcy) levels may be associated with all-cause mortality risk. However, the results of this association are conflicting and the dose-response relationship between them has not been clearly defined. In this meta-analysis, we conducted a systematic literature search of the PubMed, Embase, Web of Science and Cochrane Library for the relevant articles dated up to February 2017. Pooled relative risks (RRs) and corresponding 95% confidence intervals (CIs) were calculated to evaluate the estimates, and the dose-response relationship was estimated using a restricted cubic spline model. Eleven prospective studies (4,110 deaths among 27,737 individuals) were included. The summary RR of all-cause mortality for the highest Hcy category vs. the lowest Hcy category was 1.80 (95% CI: 1.51, 2.14) with the random effects model. In dose-response meta-analysis, Hcy levels were significantly associated with all-cause mortality risk in a linear fashion (p nonlinearity = 0.255), and the risk of all-cause mortality increased by 33.6% for each 5 µmol/L increase in Hcy levels (RR = 1.336, 95% CI: 1.254-1.422, p < 0.001). Findings from this dose-response meta-analysis suggest that Hcy levels are linearly and positively associated with risk of all-cause mortality.

#### 11

##### Exact broadband excitation of two-level systems by mapping spins to springs

- OPEN
- Nature communications
- Published over 1 year ago
- Discuss

Designing accurate and high-fidelity broadband pulses is an essential component in conducting quantum experiments across fields from protein spectroscopy to quantum optics. However, constructing exact and analytic broadband pulses remains unsolved due to the nonlinearity and complexity of the underlying spin system dynamics. Here, we present a nontrivial dynamic connection between nonlinear spin and linear spring systems and show the surprising result that such nonlinear and complex pulse design problems are equivalent to designing controls to steer linear harmonic oscillators under optimal forcing. We derive analytic broadband π/2 and π pulses that perform exact, or asymptotically exact, excitation and inversion over a defined bandwidth, and also with bounded amplitude. This development opens up avenues for pulse sequence design and lays a foundation for understanding the control of two-level systems.Coherent control of two-level systems is crucial for achieving fidelity in spectroscopy and quantum computing, but inherent nonlinearities and parameter variation have, to date, required an approximate, numerical approach. Here, Li et al. show how to map a spin ensemble to a spring model so analytic pulses can be designed using linear methods.