Algebraic methods for control system analysis and design Final report, Apr. 1967 - Apr. 1969

Algebraic methods for analysis and design of control system

Defense mechanisms of empathetic players in the spatial ultimatum game

Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share an amount of money, unfair offers are rare and their acceptance rate small. While empathy and spatiality may lead to the evolution of fairness, thus far considered continuous strategies have precluded the observation of solutions that would be driven by pattern formation. Here we introduce a spatial ultimatum game with discrete strategies, and we show that this simple alteration opens the gate to fascinatingly rich dynamical behavior. Besides mixed stationary states, we report the occurrence of traveling waves and cyclic dominance, where one strategy in the cycle can be an alliance of two strategies. The highly webbed phase diagram, entailing continuous and discontinuous phase transitions, reveals hidden complexity in the pursuit of human fair play.Comment: 4 two-column pages, 5 figures; accepted for publication in Physical Review Letter

Algebraic methods for dynamic systems

Algebraic methods for application to dynamic control system

Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.Comment: 8 pages, 8 figure

The cost of anchoring on credit-card minimum repayments

About three quarters of credit card accounts attract interest charges. In the US, credit card debt is $951.7 billion of a total of$2,539.7 billion of consumer credit. In the UK, credit card debt is £55.1 billion of £174.4 billion of consumer credit. The 2005 US Bankruptcy Abuse Prevention and Consumer Protection Act and the 2003 UK Treasury Select Committee's report require lenders to collect a minimum payment of at least the interest accrued each month. Thus people are protected from the effects of compounding interest. But including minimum payment information has an unintended negative effect, because minimum payments act as psychological anchors

Steady-state decoupling and design of linear multivariable systems

A constructive criterion for decoupling the steady states of a linear time-invariant multivariable system is presented. This criterion consists of a set of inequalities which, when satisfied, will cause the steady states of a system to be decoupled. Stability analysis and a new design technique for such systems are given. A new and simple connection between single-loop and multivariable cases is found. These results are then applied to the compensation design for NASA STOL C-8A aircraft. Both steady-state decoupling and stability are justified through computer simulations

Reference Distorted Prices

I show that when consumers (mis)perceive prices relative to reference prices, budgets turn out to be soft, prices tend to be lower and the average quality of goods sold decreases. These observations provide explanations for decentralized purchase decisions, for people being happy with a purchase even when they have paid their evaluation, and for why trade might affect high quality local firms 'unfairly'

‘Better off, as judged by themselves’:A reply to Cass Sunstein

This paper is a reply to Sunstein’s comment on my paper ‘Do people really want to be nudged towards healthy lifestyles?’ The central claim of that paper was that, in their book Nudge, Thaler and Sunstein switch between two different interpretations of the ‘better off, as judged by themselves’ criterion, and that consistent use of one or other interpretation would have blunted the persuasive power of the book. In this reply, I defend that claim against Sunstein’s counter-arguments

After the Standard Model: New Resonances at the LHC

Experiments will soon start taking data at CERN's Large Hadron Collider (LHC) with high expectations for discovery of new physics phenomena. Indeed, the LHC's unprecedented center-of-mass energy will allow the experiments to probe an energy regime where the standard model is known to break down. In this article, the experiments' capability to observe new resonances in various channels is reviewed.Comment: Preprint version of a Brief Review for Modern Physics Letters A. Changes w.r.t. the fully corrected version are smal