Nonlinear Rule Research Articles

Investigating four neighbourhood cellular automata as better cryptographic primitives

Three-neighbourhood Cellular Automata (CA) are widely studied and accepted as suitable cryptographic primitive. Rule 30, a 3-neighbourhood nonlinear CA rule, was proposed as an ideal candidate for cryptographic primitive by Wolfram. However, rule 30 was shown to be weak against Meier-Staffelbach attack [11]. The cryptographic properties like diffusion and randomness increase with increase in neighbourhood radius and thus opens the avenue of exploring the cryptographic properties of 4-neighbourhood CA. This work explores whether 4-neighbourhood CA can be a better cryptographic primitive. We construct a class of cryptographically suitable 4-neighbourhood nonlinear CA rules that resembles rule 30 and study its cryptographic properties. Four-neighbourhood nonlinear CA are shown to be resistant against Meier-Staffelbach attack on rule 30, justifying the applicability of 4-neighbourhood CA as better cryptographic primitives.

Nonlinear dynamics characteristics and influence factors analysis of servo hydraulic cylinder

Aiming at problems of vibration, impact, and noise, the nonlinear dynamic characteristics of servo hydraulic cylinder are studied by using combination of theoretical derivation and simulation experiment methods. The nonlinear effect rules of spring force and friction force are analyzed based on nonlinear dynamic theory; it can be derived that the coupling effect rules of nonlinear spring force and friction force can be described by Duffing–Van Der Pol equation. The dynamic simulation model of servo hydraulic cylinder is established by using SimHydraulics software. The numerical simulation and experiment results showed that nonlinear vibration of servo hydraulic cylinder is mainly caused by exciting force, spring force, and friction force; the system has different motion states when the parameters take different values, which lays a good foundation for the optimal designs and precise control of hydraulic cylinder.

Day-to-day rerouting modeling and analysis with absolute and relative bounded rationalities

ABSTRACTIn contrast to a large number of studies in the route choice behavior with absolute bounded rationality, little concern is laid on that with relative bounded rationality which is hypothetically suggested in this paper and can also be an indispensable component of the bounded rationality. This study is conducted to investigate travelers’ day-to-day rerouting behaviors with the above two bounded rationalities. Along this line, an absolute and a relative boundedly rational swapping process (abbreviated as ABRSP and RBRSP, respectively) model are proposed in the frame of nonlinear pairwise swapping rule. It is found that both ABRSP and RBRSP show satisfactory properties. The numerical results suggest that ABRSP and RBRSP share some general similarity in macroscopic convergence, while still showing obvious distinctions in swapping process, and RBRSP cannot be approximated or substituted by ABRSP or its extensions. Therefore, the suggested relative bounded rationality, even if it is hypothetical, still deserves to be taken seriously.

Analytic solutions throughout a period doubling route to chaos.

We show examples of dynamical systems that can be solved analytically at any point along a period doubling route to chaos. Each system consists of a linear part oscillating about a set point and a nonlinear rule for regularly updating that set point. Previously it has been shown that such systems can be solved analytically even when the oscillations are chaotic. However, these solvable systems show few bifurcations, transitioning directly from a steady state to chaos. Here we show that a simple change to the rule for updating the set point allows for a greater variety of nonlinear dynamical phenomena, such as period doubling, while maintaining solvability. Two specific examples are given. The first is an oscillator whose set points are determined by a logistic map. We present analytic solutions describing an entire period doubling route to chaos. The second example is an electronic circuit. We show experimental data confirming both solvability and a period doubling route to chaos. These results suggest that analytic solutions may be a more useful tool in studying nonlinear dynamics than was previously recognized.

Are Central Banks In CEE Countries Concerned About The Burden Of Public Debt?

The aim of this study is to analyze the monetary policy rules in the Czech Republic, Hungary and Poland, with public debt as an additional explanatory variable. We estimate linear rules by the GMM estimation and non-linear rules, using the Markov-switching model. Our findings suggest that in the Czech Republic and Poland the monetary authorities respond to growing public debt by lowering interest rates, while in Hungary the opposite may be observed. Moreover, we distinguish between passive and active monetary policy regimes and find that the degree of interest rate smoothing is lower and the response of the central banks to inflation and/or output gap is stronger in an active regime. In the passive regime, the output gap seems to be statistically insignificant.

Residual Weighted Learning for Estimating Individualized Treatment Rules

ABSTRACTPersonalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has some problems in performance. (1) The estimated ITR of OWL is affected by a simple shift of the outcome. (2) The rule from OWL tries to keep treatment assignments that subjects actually received. (3) There is no variable selection mechanism with OWL. All of them weaken the finite sample performance of OWL. In this article, we propose a general framework, called residual weighted learning (RWL), to alleviate these problems, and hence to improve finite sample performance. Unlike OWL which weights misclassification errors by clinical outcomes, RWL weights these errors by residuals of the outcome from a regression fit on clinical covariates excluding treatment assignment. We use the smoothed ramp loss function in RWL and provide a difference of convex (d.c.) algorithm to solve the corresponding nonconvex optimization problem. By estimating residuals with linear models or generalized linear models, RWL can effectively deal with different types of outcomes, such as continuous, binary, and count outcomes. We also propose variable selection methods for linear and nonlinear rules, respectively, to further improve the performance. We show that the resulting estimator of the treatment rule is consistent. We further obtain a rate of convergence for the difference between the expected outcome using the estimated ITR and that of the optimal treatment rule. The performance of the proposed RWL methods is illustrated in simulation studies and in an analysis of cystic fibrosis clinical trial data. Supplementary materials for this article are available online.

Monetary Policy and Asset Price Bubbles: A Nonlinear Policy Rule

Abstract The recent debate about asset price bubbles and monetary policy in view of “leaning against the wind” is controversial in economic literature. In this paper we argue that depending on the circumstances there is space for the central bank to lean against financial imbalances. With an optimal bounded control problem in continuous time we have developed an augmented nonlinear Taylor Rule. The main advantage of our formulation is its much greater analytical tractability, which produces distinct results. Even under the assumption of nonlinearities the central bank is in a position to move the interest rate above a threshold value to provide financial stability. Geldpolitik und Vermogenspreisblasen: Eine nichtlineare Politikregel Zusammenfassung Die jungste Debatte um das Konzept des Gegensteuerns („leaning against the wind“) im Angesicht von Vermogenspreisblasen ist hochst kontrovers in der okonomischen Literatur. In der vorliegenden Arbeit wird argumentiert, dass die Notenbank unter bestimmten Beding...

Asymmetric preferences and monetary policy deviations

This paper examines the linkages between monetary policy equilibria and asymmetric preferences. Much has been written on the relationship between discretionary monetary policy and policy under commitment from a timeless perspective. Additionally, there is a relatively robust literature that suggests monetary policy in the U.S. responds asymmetrically to fluctuations in the output gap. Here, asymmetric optimal policy is analyzed under both commitment and discretion in a simple dynamic New-Keynesian model. The timeless perspective equilibrium leads to a policy rule with inertia (consistent with the literature), but in this case implies asymmetry over time. This result is not found under discretion. Both model variants and those imposing linearity are estimated for five developed economies. Policy deviations are simulated for the linear and nonlinear rules. Results imply that the asymmetric commitment policy produces the lowest average deviations from observed policy, and also the policy deviations with the smallest variance, for all five countries. A linear Taylor rule produces statistically larger average deviations than both asymmetric commitment and asymmetric discretionary policy.

Non-linear cellular automata based edge detector for optical character images

Design of parallel algorithms for edge detection is extremely important for image analysis and understanding. Cellular automata are the most common and simple models of parallel computation and over the last decade, numerous cellular automata techniques have already been proposed. This paper presents a novel method for edge detection of optical character images based on a variant of cellular automata, called non-linear cellular automata. The method consists of three stages and each stage is simple to understand and implement. A standard binarization technique is applied to a grayscale image and boundary conditions are added to the resultant image. Finally, non-linear cellular automata rules are designed and applied simultaneously to all pixels of the image. The suggested scheme has been validated on optical characters (handwritten as well as printed) of different languages. Furthermore, results are compared with standard edge detection techniques in terms of different performance parameters like entropy, kappa values, true positives, false negatives, etc. It is observed that the suggested scheme is superior to other standard schemes. Hence, the scheme has the potential application for character recognition.

Nonlinear monetary policy and macroeconomic stabilization in emerging market economies: Evidence from China

This paper provides a new approach to investigate monetary policy nonlinearities within a micro-founded DSGE model by incorporating a transition function into the traditional Taylor rule. The model is estimated using the Bayesian method for the Chinese economy over the period 1998–2013. The empirical results show that the central bank of China actually adopts a nonlinear Taylor rule and pursues an inflation target zone of [1%, 5%] rather than sticking to a rigid target. Further results from impulse responses and welfare comparisons suggest that economic stabilization is an important motive in the conduct of monetary policy in China and the adoption of a nonlinear rule seems to serve this goal better than the traditional linear rule.

A regime-switching approach to estimating the nonlinear quantity-based monetary policy rule in China

ABSTRACTThis article focuses on the quantity-based monetary policy rule in China. The article applies a Markov regime-switching approach to estimate the nonlinear policy rule using quarterly data from 1997Q1 to 2015Q2. Overall, the performance of the estimated two-state rule is significantly better than the performance of the linear rule. The regime-switching estimation suggests that the quantity-based policy tool displays a countercyclical response to the inflation gap but a pro-cyclical response to the output gap during recessions. In addition, this article provides notable evidence of the fact that China’s central bank has been targeting inflation over the gradual course of financial liberalization.

Fault rheology in an aseismic fold‐thrust belt (Shahdad, eastern Iran)

AbstractGeodetic observations of aseismic deformation in a thrust belt near Shahdad in eastern Iran have been used to place constraints on the rheology of creeping faults in a thin‐skinned thrust belt (<5 km thickness). Creep on shallow and high‐angle thrust ramps at the range front occurs at a steady rate, in response to the topographic gradient across the thrust belt. Parts of these thrust ramps, and the low‐angle basal thrust they connect to at depth in a ramp‐and‐flat geometry, underwent accelerated creep following the nearby Mw 6.6 Fandoqa earthquake in 1998. Estimates of the rate of fault slip and the driving stresses in these two contrasting times reveal a nonlinear relationship between the stresses and sliding velocity. The degree of nonlinearity rules out bulk shear of a weak layer in the sedimentary section (e.g., evaporites) as the deformation mechanism. Instead, we suggest that the motions are accommodated by slip on faults governed by a friction law with a highly nonlinear relationship between shear stress and slip rate (e.g., as predicted by “rate and state” models). The high‐angle thrust ramps are responsible for building aspects of the geological and geomorphological signs of active shortening visible at the surface, but the folding preserved in the geology must be accomplished by other methods, possibly during the rapid transient postseismic deformation following nearby earthquakes.

Cost-efficient contingent claims with market frictions

In complete frictionless securities markets under uncertainty, it is well-known that in the absence of arbitrage opportunities, there exists a unique linear positive pricing rule, which induces a state-price density (e.g., Harrison and Kreps (1979)). Dybvig (1988) showed that the cheapest way to acquire a certain distribution of a consumption bundle (or security) is when this bundle is anti-comonotonic with the state-price density, i.e., arranged in reverse order of the state-price density. In this paper, we look at extending Dybvig's ideas to complete markets with imperfections represented by a nonlinear pricing rule (e.g., due to bid-ask spreads). We consider an investor in a securities market where the pricing rule is "law-invariant" with respect to a capacity (e.g., Choquet pricing as in Araujo et al. (2011), Chateauneuf et al. (1996), Chateauneuf and Cornet (2015), or Cerreia-Vioglio et al. (2015)). The investor holds a security with a random payoff X and his problem is that of buying the cheapest contingent claim Y on X, subject to some constraints on the performance of the contingent claim and on its level of risk exposure. The cheapest such claim is called "cost-efficient". If the capacity satisfies standard continuity and a property called "strong diffuseness" introduced in Ghossoub (2015), we show the existence and monotonicity of cost-efficient claims, in the sense that a cost-efficient claim is anti-comonotonic with the underlying security's payoff X. Strong diffuseness is satisfied by a large collection of capacities, including all distortions of diffuse probability measures. As an illustration, we consider the case of a Choquet pricing functional with respect to a capacity and the case of a Choquet pricing functional with respect to a distorted probability measure. Finally, we consider a simple example in which we derive an explicit analytical form for a cost-efficient claim.

Random Walks in Daily Foreign Exchange Rates? The Case of Lebanon (2010-2015)

In most of the academic literature on asset prices, like equities or foreign exchange, the words weak-form efficiency and random walk are used interchangeably. This paper makes a distinction between these two concepts. Weak-form efficiency holds when price increments are independent and random. A random walk is more stringent: it requires that the probability distribution of price increments be identical and normal, in addition of being independent. As expected the null hypothesis of a random walk is rejected with force while the null of weak-form efficiency is not. This implies that linear filter rules, chartism, and technical analysis cannot produce abnormal profits. But this implies also that non-linear filter rules, chartism, and technical analysis can be profitable. This explains the reality of finding departments of technical analysis in most Lebanese banks. If the market experience of Lebanon is generalized to other countries this would explain why international banks also have such departments.

Nonlinear Fuzzy Linguistics for the Determination of Nitrogen Monoxide, Nitrogen Dioxide, and Sulfur Dioxide by Molecular Absorption Spectroscopy

The nonlinearity and high dimensionality of spectra data affect the precision and the complexity of molecular absorption spectroscopy models. This article proposes a nonlinear fuzzy linguistic method for spectral quantitative analysis. A nonlinear fuzzy linguistic rule is presented. In the rule antecedent, a set operation was used to express the input variables by the fuzzy linguistic terms. A flexible polynomial equation of the input variables was the rule consequent. The fuzzy linguistic terms, the membership functions, and the nonlinear linguistic rules were initialized automatically by Gaussian kernel fuzzy clustering analysis, and the related parameters of nonlinear fuzzy linguistic rules were tuned by the iterative optimization for minimizing the root-mean square error. The principal components of the absorption measurements were extracted as input variables to reduce the complexity of the model. Experimental measurements employed a spectral dataset of flue gas for quantitative determination of the components that included sulfur dioxide, nitric oxide, and nitrogen dioxide. The experimental results verify the effectiveness of the theoretical approach.

Nonlinear Behavior of the Main Beams of Butterfly-Shaped Arch Bridges and Its Influencing Factors

Given the unique pattern of butterfly-shaped arch bridges, the nonlinear behavior rules of the main girders are difficult to determined compared with those of ordinary arch bridges. The traditional design method that does not fully consider nonlinear influences is unsuitable for such investigation. The nonlinear behavior of the main girders was analyzed by considering various nonlinear factors using a self-compiled program. The influences and rules of different design parameters such as depression angle, rise/span ratio, steel ratio, and so on, were studied. The following results were obtained. (1) The beam-column effect of arch rib elements has unfavorable influences on the main beam moment, but the beam-column effect of the main beam elements can effectively prevent such unfavorable effects. (2) The nonlinear behavior rules of the main beam moment are more complicated than the rules of deformation. (3) The distance of the eccentric load has a significant effect on the influence coefficients of the boundary beams at the unloading side. (4) The influence coefficients of the mid-span deformation and moment increase as the depression angle increases. (5) The influence of the steel ratio and the angle between the cable plane and the arch plane on the nonlinear behavior of the main beams can be neglected.

Robust observer-based controller design for Takagi–Sugeno systems with nonlinear consequent parts

This paper considers the design of robust observer-based controller for a class of continuous-time nonlinear systems with disturbances. The system is presented by Takagi–Sugeno (TS) model with nonlinear consequents. The proposed TS structure reduces the number of rules in the Sugeno model by using local nonlinear rules. It is assumed that the nonlinearities satisfy a sector condition as well as an incremental quadratic constraint. These constraints are fuzzified to reduce the conservativeness. The proposed controller guarantees H∞ performance of the system by using Linear Matrix Inequality (LMI) formulation. Moreover, the proposed observer benefits from a nonlinear injection term to add more degrees of freedom to the LMIs. Numerical examples illustrate effectiveness of the proposed method as compared to the existing methods in literature in terms of performance and enlarging the class of system.

Finite Element Analysis of High Tensile Strength Steel Sheet by Using Complex Step Derivative Approximations

The framework for the complex step derivative approximations (hereafter CDSA) to calculate the consistent tangent moduli is studied. The present methods is one of the most effective methods to implement any material constitutive equations to the commercial finite element codes and does not suffer from calculation conditions and errors. In order to confirm the efficiency of CDSA, we developed the user subroutine code based on the CDSA using associative J2 flow rules with general nonlinear isotropic hardening rules that is commonly and widely utilized in commercial finite element codes. In this study, the user material subroutine ‘Hypela2’ of MSC.Marc (ver.2013.0.0) was utilized. The finite element calculation result by the proposal method shows a good agreement with the corresponding result by the MSC.Marc default setting. Also we apply the Yoshida-Uemori back stress model to the CDSA and evaluate this new technique to predict the deformation behavior of high tensile strength steel sheet.

Vortices as Degenerate Metrics

We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian–Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as degenerate Hermitian metrics that satisfy a certain curvature equation. Using this viewpoint, we rephrase standard results about vortices and make new observations. We note the existence of a conceptually simple, non-linear rule for superposing vortex solutions, and we describe the natural behaviour of the L 2-metric on the moduli space upon restriction to a class of submanifolds.

On observer-based controller design for Sugeno systems with unmeasurable premise variables

This paper considers the design of observer-based controller for a class of continuous-time nonlinear systems presented by Takagi–Sugeno (T–S) model with unmeasurable premise variables. This T–S structure can represent a larger class of nonlinear systems as compared to the measurable premise variable case but its analysis is more complicated. To reduce the design complexity, a common output model for subsystems is employed by the use of local nonlinear rules. As a result, the proposed T–S structure reduces the number of rules in the Sugeno model as well as the analysis complexity. The proposed controller guarantees exponential convergence of states based on the fuzzy Lyapunov function analysis and Linear Matrix Inequality (LMI) formulation. Simulation results illustrate effectiveness of the proposed method.