A note on Keen's model: The limits of Schumpeter's "Creative Destruction"

This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Moderation. It emerges that Keen's model has just two possible long term solutions: stable growth or terminal collapse. While collapse can come about immediately from economies that are nonviable by virtue of unsuitable parameters or initial conditions, in general the collapse is preceded by an interval of exponential growth. In first approximation, the duration of that exponential growth is half a period of a sinusoidal oscillation. The period is determined by reciprocal of the imaginary part of one root of a certain quintic polynomial. The real part of the same root determines the rate of growth of the economy. The coefficients of that polynomial depend in a complicated way upon the numerous parameters in the problem and so, therefore, the pattern of roots. For a favorable choice of parameters, the salient root is purely real. This is the circumstance that admits the second possible long term solution, that of indefinite stable growth, i.e. an infinite period.Comment: 25 pages, 12 figures, JEL classification: B50, C62, C63, E12, E4

A universal rank-order transform to extract signals from noisy data

We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise "etalon" used to characterize arbitrary stationary stochastic processes. The method readily distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the logistic map from white noise. Ranking within randomness differs fundamentally from that in deterministic chaos and signals, thus forming the basis for signal detection. To further illustrate the breadth of applications, we apply this ordinate method to the canonical nonlinear parameter estimation problem of two-species radioactive decay, outperforming special-purpose least square software. It is demonstrated that the method excels when extracting trends in heavy-tailed noise and, unlike the Thiele-Sen estimator, is not limited to linear regression. Lastly, a simple expression is given that yields a close approximation for signal extraction of an underlying generally nonlinear signal.Comment: 26 pages, 18 figure

Universal rank-order transform to extract signals from noisy data

We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric and objective, and the required data processing is parsimonious. The main ingredients include a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise “etalon” used to characterize arbitrary stationary stochastic processes. The method readily distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the logistic map from white noise. Ranking within randomness differs fundamentally from that in deterministic chaos and signals, thus forming the basis for signal detection. To further illustrate the breadth of applications, we apply this ordinate method to the canonical nonlinear parameter estimation problem of two-species radioactive decay, outperforming special-purpose least squares software. We demonstrate that the method excels when extracting trends in heavy-tailed noise and, unlike the Thiele-Sen estimator, is not limited to linear regression. A simple expression is given that yields a close approximation for signal extraction of an underlying, generally nonlinear signal

Multiple solutions and advection-dominated flows in the wind-driven circulation. Part I: Slip

We consider steady solutions of the barotropic quasigeostrophic vorticity equation for a single subtropical gyre with dissipation in the form of lateral friction. Solutions are governed by two parameters: inertial boundary-layer width; and viscous boundary-layer width. Numerical computations for slip conditions indicate a wedge-shaped region in this two-dimensional parameter space, where three solutions coexist. One of these is a viscous solution with weak recirculation; one a solution of intermediate recirculation; and one a strongly nonlinear recirculation gyre. Parametric scalings based on elementary solutions are numerically corroborated as the first and third of these solutions are continued away from the vicinity of the wedge. The multiplicity of solutions is anticipated by a severely truncated Fourier modal representation paralleling Veronis (1963). The Veronis work was originally applied to predict the possibility of multiple solutions in Stommel\u27s (1948) bottom friction model of the circulation. Paradoxically, it appears the solutions are, in that case, unique

The evolution of a magnetic field subject to Taylor′s constraint using a projection operator

In the rapidly rotating, low-viscosity limit of the magnetohydrodynamic equations as relevant to the conditions in planetary cores, any generated magnetic field likely evolves while simultaneously satisfying a particular continuous family of invariants, termed Taylor′s constraint. It is known that, analytically, any magnetic field will evolve subject to these constraints through the action of a time-dependent coaxially cylindrical geostrophic flow. However, severe numerical problems limit the accuracy of this procedure, leading to rapid violation of the constraints. By judicious choice of a certain truncated Galerkin representation of the magnetic field, Taylor′s constraint reduces to a finite set of conditions of size O(N), significantly less than the O(N3) degrees of freedom, where N denotes the spectral truncation in both solid angle and radius. Each constraint is homogeneous and quadratic in the magnetic field and, taken together, the constraints define the finite-dimensional Taylor manifolδ whose tangent plane can be evaluated. The key result of this paper is a description of a stable numerical method in which the evolution of a magnetic field in a spherical geometry is constrained to the manifold by projecting its rate of change onto the local tangent hyperplane. The tangent plane is evaluated by contracting the vector of spectral coefficients with the Taylor tensor, a large but very sparse 3-D array that we define. We demonstrate by example the numerical difficulties in finding the geostrophic flow numerically and how the projection method can correct for inaccuracies. Further, we show that, in a simplified system using projection, the normalized measure of Taylorization, t, may be maintained smaller than O(10-10) (where t= 0 is an exact Taylor state) over 1/10 of a dipole decay time, eight orders of magnitude smaller than analogous measures applied to recent low Ekman-number geodynamo model

Changes in the movement and calling behavior of minke whales (Balaenoptera acutorostrata) in response to navy training

This research was funded by the U.S. Office of Naval Research under grant number N000141612859. The passive acoustic data were recorded under support by COMPACFLT for the Navy Marine Species Monitoring Program. The call association tracking algorithm was developed under a separate U.S. Office of Naval Research project (2011–2015 Advanced Detection, Classification and Localization, grant number: N0001414IP20037).Many marine mammals rely on sound for foraging, maintaining group cohesion, navigation, finding mates, and avoiding predators. These behaviors are potentially disrupted by anthropogenic noise. Behavioral responses to sonar have been observed in a number of baleen whale species but relatively little is known about the responses of minke whales (Balaenoptera acutorostrata). Previous analyses demonstrated a spatial redistribution of localizations derived from passive acoustic detections in response to sonar activity, but the lack of a mechanism for associating localizations prevented discriminating between movement and cessation of calling as possible explanations for this redistribution. Here we extend previous analyses by including an association mechanism, allowing us to differentiate between movement responses and calling responses, and to provide direct evidence of horizontal avoidance responses by individual minke whales to sonar during U.S. Navy training activities. We fitted hidden Markov models to 627 tracks that were reconstructed from 3 years of minke whale (B. acutorostrata) vocalizations recorded before, during, and after naval training events at the U.S. Navy's Pacific Missile Range Facility, Kauai, Hawaii. The fitted models were used to identify different movement behaviors and to investigate the effect of sonar activity on these behaviors. Movement was faster and more directed during sonar exposure than in baseline phases. The mean direction of movement differed during sonar exposure, and was consistent with movement away from sonar-producing ships. Animals were also more likely to cease calling during sonar. There was substantial individual variation in response. Our findings add large-sample support to previous demonstrations of horizontal avoidance responses by individual minke whales to sonar in controlled exposure experiments, and demonstrate the complex nature of behavioral responses to sonar activity: some, but not all, whales exhibited behavioral changes, which took the form of horizontal avoidance or ceasing to call.Publisher PDFPeer reviewe

Macrodynamics of ± \u3c sup\u3e 2 \u3c/sup\u3e dynamos

Two distributions of the ±-effect in a sphere are considered. The inviscid limit is approached both by direct numerical solution and by solution of a simpler nonlinear eigenvalue problem deriving from asymptotic boundary layer analysis for the case of stress-free boundaries. The inviscid limit in both cases is dominated by the need to satisfy the Taylor constraint which states that the integral of the Lorentz force over cylindrical (geostrophic) contours in a homogeneous fluid must tend to zero. For a small supercritical range in ±, this condition can only be met by magnetic fields which vanish as the viscosity goes to zero. In this range, the agreement of the two approaches is excellent. In a portion of this range, the method of finite amplitude perturbation expansion is useful, and serves as a guide for understanding the numerical results. For larger a, evidence from the nonlinear eigenvalue problem suggests both that the Taylor state exists, and that the transition from small to large amplitude can require a finite amplitude (oscillatory) instability in accord with the findings of Soward and Jones (1983). However, solutions of the full equations have not been found which are independent of viscosity at larger values of ±. © 1985, Taylor & Francis Group, LLC. All rights reserved