Dilations and constrained algebras

It is well known that unital contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f whose first derivative vanishes at 0. We prove that there are unital contractive representations of A which are not completely contractive, and furthermore provide a Kaiser and Varopoulos inspired example for A and present a characterization of those contractive representations of A which are completely contractive. In the positive direction, for the algebra of rational functions with poles off the distinguished variety V in the bidisk determined by (z-w)(z+w)=0, unital contractive representations are completely contractive.Comment: New to version 2 is a proof of rational dilation for the distinguished variety in the bidisk determined by (z-w)(z+w)=

Coordinating on Reducing Advertising: Carbonated Soft Drinks Industry and Combating Obesity

Replaced with revised version of paper 06/08/11.television advertising, carbonated soft drink, oligopoly advertising, pulse advertising, Food Consumption/Nutrition/Food Safety, Health Economics and Policy, Industrial Organization, Marketing, I18, L13, M37,

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the R\"ossler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures -- thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length and network diameter are highly sensitive to the interior crisis captured in this particular data set

Phase space reconstruction methods in applied economics and econometrics

Market responses to unpredictable events such as preference change, food contamination, or changes in technology and information are not always known. Phase space reconstruction, a tool designed to analyze nonlinear time series, is investigated for use as an econometric tool to detect nonlinear dynamics economic time series. It is applied to examine consumer responses to unpredictable events, changes in dynamic livestock cycles, and nonlinear structure in regression residuals. The empirical application of phase space reconstruction analyzing economic behavior demonstrates an intuitive, appealing, and straightforward demonstration as to the use of this diagnostic tool. The first essay investigates how to reconstruct dynamic consumer reactions from market events using phase space reconstruction. This approach can provide important and unique empirical insights into consumer reactions to product recall or contaminant events. We apply phase space reconstruction analysis to U.S. meat demand, demonstrating distinct differences between intertemporal shorter run impacts from food safety incidents (e.g., E. Coli and BSE) relative to longer run health effects (e.g., cholesterol). Moreover, we show that consumers have reacted to food safety events differently depending on the particular food contaminate associated with that event. In the second essay, phase space reconstruction is investigated as a diagnostic tool for determining the structure of detected nonlinear processes in regression residuals. Empirical evidence supporting this approach is provided using simulations from an Ikeda mapping and the S&P 500. Results in the form of phase portraits (e.g., scatter plots of reconstructed dynamical systems) provide qualitative information to discern structural components from apparent randomness and provide insights categorizing structural components into functional classes to enhance econometric/time series modeling efforts. The third essay applies the technique of phase space reconstruction to investigate U.S. livestock cycles. Results are presented for both pork and cattle cycles, providing empirical evidence that the cycles themselves have slowly diminished. By comparing the two livestock cycles important insights can be made. The phase space analysis suggests that the biological constraint has become a less significant factor in livestock cycles while technology and information are relatively more significant

Phase Space Reconstruction and Nonlinear Equilibrium Dynamics in the United States Beef Market

This paper investigates dynamic interactions in the US beef market using phase space reconstruction, which has been developed to analyze nonlinear dynamical systems. This approach provides important and unique empirical insights into consumers behavior in the beef market. Our results from a phase space reconstruction analysis demonstrate distinct differences between intertemporal short run impacts from food safety outbreaks (e.g., E. Coli) and longer run health effects (e.g., cholesterol). Adjustments due to factors such as cholesterol are permanent changes and do not affect the manner by which people consume, while consumers react to food safety scares by adjusting consumption for a short period of time and then returning to their normal steady state cycle of consumption.nonlinear time series, phase space reconstruction, food safety, health effects, Livestock Production/Industries, Marketing,