Extreme Nonlinearity Research Articles

Interpolation Errors in Thermistor Calibration Equations

Thermistors are widely used temperature sensors capable of measurement uncertainties approaching those of standard platinum resistance thermometers. However, the extreme nonlinearity of thermistors means that complicated calibration equations are required to minimize the effects of interpolation errors and achieve low uncertainties. This study investigates the magnitude of interpolation errors as a function of temperature range and the number of terms in the calibration equation. Approximation theory is used to derive an expression for the interpolation error and indicates that the temperature range and the number of terms in the calibration equation are the key influence variables. Numerical experiments based on published resistance–temperature data confirm these conclusions and additionally give guidelines on the maximum and minimum interpolation error likely to occur for a given temperature range and number of terms in the calibration equation.

Subcycle Extreme Nonlinearities in GaP Induced by an Ultrastrong Terahertz Field

We report on the experimental observation of extreme laser spectral broadening and a change in optical transmission in gallium phosphite induced by 25 MV/cm terahertz (THz) single-cycle internal field. Such intense THz radiation leads to twofold transient modifications of the optical properties in the electro-optical crystal. First, the electric field provokes extensive cross-phase modulation via the χ^{(2)} and χ^{(3)} nonlinearities on a copropagating 50fs near infrared laser pulse which turns into 500% spectral broadening. Second, we observe an instantaneous change of the optical transmission occurring at the THz field which is alleged to interband Zener tunneling and charge carrier density modification by impact ionization turning the semiconductor in a metal-like transient state. The presented scheme displays a pathway to coherently control the optical properties of semiconductors on an ultrafast time scale by a strong THz field.

Efficient numerical solution to vacuum decay with many fields

Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.

Rare shocks vs. non-linearities: What drives extreme events in the economy? Some empirical evidence

A small-scale vector autoregression (VAR) is used to shed some light on the roles of extreme shocks and non-linearities during stress events observed in the economy. The model focuses on the link between credit/financial markets and the real economy and is estimated on US quarterly data for the period 1984–2013. Extreme shocks are accounted for by assuming t-distributed reduced-form shocks. Non-linearity is allowed by the possibility of regime switch in the shock propagation mechanism. Strong evidence for fat tails in error distributions is found. Moreover, the results suggest that accounting for extreme shocks rather than explicit modeling of non-linearity contributes to the explanatory power of the model. Finally, it is shown that the accuracy of density forecasts improves if non-linearities and shock distributions with fat tails are considered.

Kink pair production and dislocation motion

The motion of extended defects called dislocations controls the mechanical properties of crystalline materials such as strength and ductility. Under moderate applied loads, this motion proceeds via the thermal nucleation of kink pairs. The nucleation rate is known to be a highly nonlinear function of the applied load, and its calculation has long been a theoretical challenge. In this article, a stochastic path integral approach is used to derive a simple, general, and exact formula for the rate. The predictions are in excellent agreement with experimental and computational investigations, and unambiguously explain the origin of the observed extreme nonlinearity. The results can also be applied to other systems modelled by an elastic string interacting with a periodic potential, such as Josephson junctions in superconductors.

Turbulent Transitions in Optical Wave Propagation.

We report the direct observation of the onset of turbulence in propagating one-dimensional optical waves. The transition occurs as the disordered hosting material passes from being linear to one with extreme nonlinearity. As the response grows, increased wave interaction causes a modulational unstable quasihomogeneous flow to be superseded by a chaotic and spatially incoherent one. Statistical analysis of high-resolution wave behavior in the turbulent regime unveils the emergence of concomitant rogue waves. The transition, observed in a photorefractive ferroelectric crystal, introduces a new and rich experimental setting for the study of optical wave turbulence and information transport in conditions dominated by large fluctuations and extreme nonlinearity.

Detection of micro gap weld joint by using magneto-optical imaging and Kalman filtering compensated with RBF neural network

An approach for seam tracking of micro gap weld whose width is less than 0.1mm based on magneto optical (MO) imaging technique during butt-joint laser welding of steel plates is investigated. Kalman filtering(KF) technology with radial basis function(RBF) neural network for weld detection by an MO sensor was applied to track the weld center position. Because the laser welding system process noises and the MO sensor measurement noises were colored noises, the estimation accuracy of traditional KF for seam tracking was degraded by the system model with extreme nonlinearities and could not be solved by the linear state-space model. Also, the statistics characteristics of noises could not be accurately obtained in actual welding. Thus, a RBF neural network was applied to the KF technique to compensate for the weld tracking errors. The neural network can restrain divergence filter and improve the system robustness. In comparison of traditional KF algorithm, the RBF with KF was not only more effectively in improving the weld tracking accuracy but also reduced noise disturbance. Experimental results showed that magneto optical imaging technique could be applied to detect micro gap weld accurately, which provides a novel approach for micro gap seam tracking.

Modeling and Estimation of Energy‐Based Hyperelastic Objects

AbstractIn this paper, we present a method to model hyperelasticity that is well suited for representing the nonlinearity of real‐world objects, as well as for estimating it from deformation examples. Previous approaches suffer several limitations, such as lack of integrability of elastic forces, failure to enforce energy convexity, lack of robustness of parameter estimation, or difficulty to model cross‐modal effects. Our method avoids these problems by relying on a general energy‐based definition of elastic properties. The accuracy of the resulting elastic model is maximized by defining an additive model of separable energy terms, which allow progressive parameter estimation. In addition, our method supports efficient modeling of extreme nonlinearities thanks to energy‐limiting constraints. We combine our energy‐based model with an optimization method to estimate model parameters from force‐deformation examples, and we show successful modeling of diverse deformable objects, including cloth, human finger skin, and internal human anatomy in a medical imaging application.

On the dynamic dependence and asymmetric co-movement between the US and Central and Eastern European transition markets

In this paper, we attempt to evaluate the time-varying and asymmetric co-movement of CEE equity markets with the US stock markets around the subprime crisis and the resulting global financial crisis. The econometric approach adopted is based on recent development of time-varying copulas. For that, we propose a new class of time-varying copulas that allows for long memory behavior in both marginal and joint distributions. Our empirical approach relies on the flexibility and usefulness of bivariate copulas that allow to model not only the dynamic co-movement through time but also to account for any extreme interaction, nonlinearity and asymmetry in the co-movement patterns. The time-varying dependence structure can be also modeled conditionally on the economic policy uncertainty index of the crisis country. Empirical results show strong evidence of co-movement between the US and CEE equity markets and find that the co-movement exhibits large time-variations and asymmetry in the tails of the return distributions.

Fluctuation prediction of stock market index by adaptive evolutionary higher order neural networks

The stock market is complex and dynamic in nature, and has been a subject of research for modelling its random fluctuations. Higher order neural network (HONN) has the ability to expand the input representation space, perform high learning capabilities and have been utilised to solve many complex data mining problems. To capture the extreme volatility, nonlinearity and uncertainty associated with stock data, this paper compares two adaptive evolutionary optimisation-based Pi-Sigma neural networks (AE-PSNN), for prediction of closing prices of five real stock markets. For this experimental study, BSE, DJIA, NASDAQ, FTSE and TAIEX stock indices are employed for short, medium and long term predictions. The performance of the AE-PSNN models has been compared with that of a gradient descent-based PSNN (GD-PSNN) model and found to be superior in terms of prediction accuracy and prediction of change in direction.

Hybrid Perturbation-Projection Method for Solving DSGE Asset Pricing Models

This paper conduct a quantitative experiment to assess the effectiveness of a hybrid perturbation-projection (HPP) method to solve dynamic stochastic general equilibrium (DSGE) asset pricing models. We employ a macro-based asset pricing model to compare HPP method and value function iteration (VFI) method based on the same reasonable calibrations. This DSGE asset pricing model in the paper incorporates nonlinearities in both household preferences and firm production technologies. Additionally, the market for debt introduces its own type of nonlinearity; leverage can force a nonlinear wedge between asset rates. In the paper, we first show how to apply the HPP method and then assess its accuracy and speed compared with the old VFI method. Accuracy of solutions is demonstrated by comparing standard deviations of the logged values of first order conditions errors of important financial assets. Speed of the solution methods is shown by comparing the computational time. By comparing the results from applying the same DSGE asset pricing model to the competing methods, we find that the HPP method is not only feasible but also robust to the extreme nonlinearities in the asset pricing model.

Microscopic Characterization of Scalable Coherent Rydberg Superatoms

Strong interactions can amplify quantum effects such that they become important on macroscopic scales. Controlling these coherently on a single particle level is essential for the tailored preparation of strongly correlated quantum systems and opens up new prospects for quantum technologies. Rydberg atoms offer such strong interactions which lead to extreme nonlinearities in laser coupled atomic ensembles. As a result, multiple excitation of a Micrometer sized cloud can be blocked while the light-matter coupling becomes collectively enhanced. The resulting two-level system, often called "superatom", is a valuable resource for quantum information, providing a collective Qubit. Here we report on the preparation of two orders of magnitude scalable superatoms utilizing the large interaction strength provided by Rydberg atoms combined with precise control of an ensemble of ultracold atoms in an optical lattice. The latter is achieved with sub shot noise precision by local manipulation of a two-dimensional Mott insulator. We microscopically confirm the superatom picture by in-situ detection of the Rydberg excitations and observe the characteristic square root scaling of the optical coupling with the number of atoms. Furthermore, we verify the presence of entanglement in the prepared states and demonstrate the coherent manipulation of the superatom. Finally, we investigate the breakdown of the superatom picture when two Rydberg excitations are present in the system, which leads to dephasing and a loss of coherence.

The decision-making process between convention and cognition

Abstract. The main research on the cognitive foundations of the economy has claimed for many years that there is a clear separation between the theory of economic rationality and the psychology of reasoning and economic decision. More recently, the relationship between the two disciplines has become increasingly tight and cross-fertilizing. While Economics proposes normative theories about what it means to decide rationally, Psychology provides an explanation as to why individuals frequently make irrational decisions. The role of intuition in decision-making, as well as the effect of emotions, are also relevant. The issue of rationality should then be tackled by finding appropriate restrictions of the definition of the term 'rational', which in its common usage stands for 'reasonable' and/or 'acceptable to reason'. Economics and psychology can then find a common and useful ground of discussion by focusing on coherence rather than on substance. (Legrenzi and Girotto 1996). As acknowledged by the mainstream theory, the notion of Bounded Rationality (Simon 1972) is central in explaining the failures of human making processes. Therefore took this concept as our starting point in the analysis of the complexity behind the individual choices, taking into account the cross-fertilizing relationship between economics and psychology.Keywords: Coordination, Decision, Economics, Psychology, RationalityJEL Classification: B4, D81, D83IntroductionThe discovery of the existence of social preferences, understood as positive and/or negative predispositions towards the social and economic conditions of others, complicates in a decisive way the theory of economic rationality. The latter binds the only to reasons of individual utility, without any interest in the plight of others. To be changed radically by these are also the models of strategic interaction. Insights and emotions frequently violate all the principles of rationality, but certainly do not eliminate them. One has the sensation of a cognitive duplicity where rational logic and emotions are forced to cohabit. What determines the prevalence of intuition over reasoning or vice-versa? It is conceivable that the context with the factors conditioning it assumes a decisive role. But because the contexts cannot all be summarized in a theoretical model, what follows is the awareness of the extreme complexity and non-linearity of the phenomena that are often the result of the interaction of different economic agents. What arises is an extreme difficulty to develop models with a comprehensive predictive capacity and the holistic impossibility of explaining economic phenomena, abolishing the role of individual economic action and its cognitive genesis.In addition to that criticism to unlimited rationality does not rely only on the awareness of the reduced computational capacity and of calculating the conscious and intentional part of the human mind. In reality, such a limiting condition pairs with the influence of intuitive, emotional, affective, tacit factors that characterize the intuitive mind (as opposed to the conscious reasoning mind). Therefore, the choices and decisions of homo oeconomicus are moving on a strongly connected cognitive duplicity, with the prevalence of one or the other of the components that is heavily dependent, typically on the situations and contexts; but also on the different attitude compared to emotional categories such as regret (Loomes and Sugden 1982) or disappointment (Gul 1991). This leads to the necessity of building the decisional context, one that incorporates information from the environment and of the mental and behavioural model of the individual actor. The conclusion that follows that is that the decision has nothing axiomatic to it, being the final act of a previous and complex process that involves objective and subjective conditions (as, moreover, already generally contained in Simon's concept of bounded rationality, 1972). …

An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity.

Standardized tests are frequently used for selection decisions, and the validation of test scores remains an important area of research. This paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples. Existing formulas for direct range restriction require three assumptions: (1) the criterion variable is missing at random; (2) a linear relationship between independent and dependent variables; and (3) constant error variance or homoscedasticity. The results in this paper demonstrate that the standard approach for correcting restricted correlations is severely biased in cases of extreme monotone quadratic nonlinearity and heteroscedasticity. This paper offers at least three significant contributions to the existing literature. First, a method from the econometrics literature is adapted to provide more accurate estimates of unrestricted correlations. Second, derivations establish bounds on the degree of bias attributed to quadratic functions under the assumption of a monotonic relationship between test scores and criterion measurements. New results are presented on the bias associated with using the standard range restriction correction formula, and the results show that the standard correction formula yields estimates of unrestricted correlations that deviate by as much as 0.2 for high to moderate selectivity. Third, Monte Carlo simulation results demonstrate that the new procedure for correcting restricted correlations provides more accurate estimates in the presence of quadratic and heteroscedastic test score and criterion relationships.

Gigantic Optical Nonlinearity: Laser-Induced Change of Dielectric Permittivity of the Order of Unity

A possibility to tune optical properties of materials on demand is of great importance to both fundamental science and applications. We show that nanosecond laser pumping can significantly depopulate the ground state of AF455 dye nanoparticles, resulting in gigantic change of dielectric permittivity of the order of unity. Such extreme nonlinearity (χ(3) = 1.3 × 10–5 esu), evidenced by increase of the Mie scattering efficiency, places AF455 dye among the most efficient χ(3) nonlinear optical materials, extends the limits of active metamaterials and plasmonics, and paves the way to ultimate control of photonic devices and systems.

An Introduction to the General Monotone Model with Application to Two Problematic Data Sets

We argue that the mismatch between data and analytical methods, along with common practices for dealing with “messy” data, can lead to inaccurate conclusions. Specifically, using previously published data on racial bias and culture of honor, we show that manifest effects, and therefore theoretical conclusions, are highly dependent on how researchers decide to handle extreme scores and nonlinearities when data are analyzed with traditional approaches. Within LS approaches, statistical effects appeared or disappeared on the basis of the inclusion or exclusion of as little as 1.5% (3 of 198) of the data, and highly predictive variables were masked by nonlinearities. We then demonstrate a new statistical modeling technique called the general monotone model (GeMM) and show that it has a number of desirable properties that may make it more appropriate for modeling messy data: It is more robust to extreme scores, less affected by outlier analyses, and more robust to violations of linearity on both the response and predictor variables compared with a variety of well-established statistical algorithms and frequently possesses greater statistical power. We argue that using procedures that make fewer assumptions about the data, such as GeMM, can lessen the need for researchers to use data-editing strategies (e.g., to apply transformations or to engage outlier analyses) on their data to satisfy often unrealistic statistical assumptions, leading to more consistent and accurate conclusions about data than traditional approaches of data analysis.

Maximum Likelihood SNR Estimation of Linearly-Modulated Signals Over Time-Varying Flat-Fading SIMO Channels

In this paper, we tackle for the first time the problem of maximum likelihood (ML) estimation of the signal-to-noise ratio (SNR) parameter over time-varying single-input multiple-output (SIMO) channels. Both the data-aided (DA) and the non-data-aided (NDA) schemes are investigated. Unlike classical techniques where the channel is assumed to be slowly time-varying and, therefore, considered as constant over the entire observation period, we address the more challenging problem of instantaneous (i.e., short-term or local) SNR estimation over fast time-varying channels. The channel variations are tracked locally using a polynomial-in-time expansion. First, we derive in closed-form expressions the DA ML estimator and its bias. The latter is subsequently subtracted in order to obtain a new unbiased DA estimator whose variance and the corresponding Cram\'er-Rao lower bound (CRLB) are also derived in closed form. Due to the extreme nonlinearity of the log-likelihood function (LLF) in the NDA case, we resort to the expectation-maximization (EM) technique to iteratively obtain the exact NDA ML SNR estimates within very few iterations. Most remarkably, the new EM-based NDA estimator is applicable to any linearly-modulated signal and provides sufficiently accurate soft estimates (i.e., soft detection) for each of the unknown transmitted symbols. Therefore, hard detection can be easily embedded in the iteration loop in order to improve its performance at low to moderate SNR levels. We show by extensive computer simulations that the new estimators are able to accurately estimate the instantaneous per-antenna SNRs as they coincide with the DA CRLB over a wide range of practical SNRs.

Terahertz-driven harmonics

Researchers have demonstrated high-harmonic generation using strong terahertz pulses in a bulk solid without damaging it. The mechanism underpinning such an extreme nonlinearity also generates coherent electromagnetic radiation covering the terahertz, infrared and optical regions.

Harmonic phase detector for phase locking of cryogenic terahertz oscillators

We present a simple and effective way to phase lock terahertz cryogenic oscillators. Extreme nonlinearity of a superconductor-insulator-superconductor tunnel junction allows its implementation as a cryogenic high-harmonic phase detector (HPD), which is used both for mixing a terahertz oscillator signal with a microwave reference and for generating a phase error feedback signal that is directly applied to the oscillator for its phase locking. An integration of the HPD with a cryogenic flux-flow oscillator results in synchronization bandwidth as wide as 70 MHz (significantly exceeding conventional room-temperature system bandwidth), providing phase locking of 84% emitted power for 15 MHz oscillator linewidth.

GTROTA: A code for the solution of the coupled nonlinear extended neoclassical rotation equations in tokamak plasmas using successive over-relaxation and simulated annealing

GTROTA (Georgia Tech ROTAtion) is a code that solves the extended neoclassical rotation equations for tokamak plasmas, derived from the multifluid moment equations (including electromagnetic effects) in generalized toroidal magnetic flux surface geometry. It computes the toroidal and poloidal fluid rotation velocities and the in–out and up–down density asymmetries at each radial location. The solution of these equations is accomplished iteratively, using a physically motivated decomposition, successive over-relaxation and the concept of simulated annealing. Program summaryProgram title: GTROTAv1Catalogue identifier: AEPT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPT_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 12890No. of bytes in distributed program, including test data, etc.: 1099937Distribution format: tar.gzProgramming language: Matlab.Computer: Any workstation or PC where Matlab can be run.Operating system: Any with Matlab available. Tested on Windows 7.RAM: 1024 MB to run MatlabClassification: 19.11.Nature of problem:Tokamak plasma rotation velocities and the poloidal in–out and up–down asymmetries of plasma densities are calculated from the coupled set of nonlinear equations, which show a very instable iterative dynamics. To solve for the true solution for this nonlinearly coupled system that does not converge to a single solution, physics-based determination of the true solution becomes necessary and GTROTA provides the algorithm for users to find the true solution from the nonlinear topological maps.Solution method:The code decomposes the given system into three subsystems to stabilize the iterative dynamics and uses Successive Over-Relaxation and the concept of Simulated Annealing to determine the true solution.Restrictions:The code is designed for strong rotation analysis. An updated code for slow rotation and plasma edge analysis is to be developed in the future.Unusual features:For a new rotation calculation, the code requires several test runs to determine the iterations step for the true solution.Additional comments:Due to the extreme nonlinearity of the extended rotation calculation model, the signs of the inputs must be adjusted correctly to yield correct solutions. Refer to the User’s Manual for this discussion.Running time:8 s (except test runs that depend on the complexity of the nonlinear dynamics).