Quantum Parrondo's Games

Parrondo's Paradox arises when two losing games are combined to produce a winning one. A history dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general SU(2) operators to transform the game into the quantum domain. In the initial state, a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case.Comment: LateX, 10 pages, 2 figures, submitted to Physica A special issue (Gene Stanley Conference, Sicily, 2001), v2 minor correction to equations, v3 corrections to results section and table, acknowledgement adde

Illusion of Control in a Brownian Game

Both single-player Parrondo games (SPPG) and multi-player Parrondo games (MPPG) display the Parrondo Effect (PE) wherein two or more individually fair (or Llosing) games yield a net winning outcome if alternated periodically or randomly. (There is a more formal, less restrictive definition of the PE.) We illustrate that, when subject to an elementary optimization rule, the PG displays degraded rather than enhanced returns. Optimization provides only the illusion of control, when low-entropy strategies (i.e. which use more information) under-perform random strategies (with maximal entropy). This illusion is unfortuntately widespread in many human attempts to manage or predict complex systems. For the PG, the illusion is especially striking in that the optimization rule reverses an already paradoxical-seeming positive gain - the Parrondo effect proper - and turns it negative. While this phenomenon has been previously demonstrated using somewhat artificial conditions in the MPPG (L. Dinios and J.M.R. Parrondo. Europhysics Letters 63, 319 (2003); J.M.R. Parrondo et al. Advances in Condensed Matter and Statistical Mechanics, eds. E. Korutcheva and R. Cuerno, Nova Science Publishers, 2003), we demonstrate it in the natural setting of a history-dependent SPPG.Comment: 8 page with 1 tabl

Minimal Brownian Ratchet: An Exactly Solvable Model

We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force. We also indicate the off-balance behavior with biased random noise.Comment: 4 pages, 4 figures, RevTex source, General solution added. To be appeared in Phys. Rev. Let

Winning combinations of history-dependent games

The Parrondo effect describes the seemingly paradoxical situation in which two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24 (2000)]. Here we generalize this analysis to the case where both games are history-dependent, i.e. there is an intrinsic memory in the dynamics of each game. New results are presented for the cases of both random and periodic switching between the two games.Comment: (6 pages, 7 figures) Version 2: Major cosmetic changes and some minor correction

The discovery of a low mass, pre-main-sequence stellar association around gamma Velorum

We report the serendipitous discovery of a population of low mass, pre-main sequence stars (PMS) in the direction of the Wolf-Rayet/O-star binary system gamma^{2} Vel and the Vela OB2 association. We argue that gamma^{2} Vel and the low mass stars are truly associated, are approximately coeval and that both are at distances between 360-490 pc, disagreeing at the 2 sigma level with the recent Hipparcos parallax of gamma^{2} Vel, but consistent with older distance estimates. Our results clearly have implications for the physical parameters of the gamma^{2} Vel system, but also offer an exciting opportunity to investigate the influence of high mass stars on the mass function and circumstellar disc lifetimes of their lower mass PMS siblings.Comment: Monthly Notices of the Royal Astronomical Society, Letters - in pres

A review of stochastic resonance: Circuits and measurement

Copyright © 2002 IEEENoise in dynamical systems is usually considered a nuisance. However, in certain nonlinear systems, including electronic circuits and biological sensory systems, the presence of noise can enhance the detection of weak signals. The phenomenon is termed stochastic resonance and is of great interest for electronic instrumentation. We review and investigate the stochastic resonance of several bistable circuits. A new type of S characteristic circuit is demonstrated using simple nonlinear elements with an operational amplifier. Using this circuit, the effects on stochastic resonance were determined as the slope of the S shaped characteristic curve was varied.Gregory P. Harmer, Bruce R. Davis and Derek Abbot

New paradoxical games based on Brownian ratchets

Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged -- namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the current capital of the player. Here we present new games where all the rules depend only on the history of the game and not on the capital. This new history-dependent structure significantly increases the parameter space for which the effect operates.Comment: 4 pages, 3 eps figures, revte

"Illusion of control" in Minority and Parrondo Games

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Minority game and the Parrondo Games, that agents who optimize their strategy based on past information actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the "illusion of control" in set-ups a priori defined to emphasize the importance of optimization.Comment: 17 pages, four figures, 1 tabl

Brownian ratchets and Parrondo's games

Parrondo's games present an apparently paradoxical situation where individually losing games can be combined to win. In this article we analyze the case of two coin tossing games. Game B is played with two biased coins and has state-dependent rules based on the player's current capital. Game B can exhibit detailed balance or even negative drift (i.e., loss), depending on the chosen parameters. Game A is played with a single biased coin that produces a loss or negative drift in capital. However, a winning expectation is achieved by randomly mixing A and B. One possible interpretation pictures game A as a source of "noise" that is rectified by game B to produce overall positive drift-as in a Brownian ratchet. Game B has a state-dependent rule that favors a losing coin, but when this state dependence is broken up by the noise introduced by game A, a winning coin is favored. In this article we find the parameter space in which the paradoxical effect occurs and carry out a winning rate analysis. The significance of Parrondo's games is that they are physically motivated and were originally derived by considering a Brownian ratchet-the combination of the games can be therefore considered as a discrete-time Brownian ratchet. We postulate the use of games of this type as a toy model for a number of physical and biological processes and raise a number of open questions for future research. (c) 2001 American Institute of Physics.Gregory P. Harmer, Derek Abbott, Peter G. Taylor, and Juan M. R. Parrond

A Preliminary Discussion of the Kinematics of BHB and RR Lyrae Stars near the North Galactic Pole

The radial velocity dispersion of 67 RR Lyrae variable and blue horizontal branch (BHB) stars that are more than 4 kpc above the galactic plane at the North Galactic Pole is 110 km/sec and shows no trend with Z (the height above the galactic plane). Nine stars with Z < 4 kpc show a smaller velocity dispersion (40 +/-9 km/sec) as is to be expected if they mostly belong to a population with a flatter distribution. Both RR Lyrae stars and BHB stars show evidence of stream motion; the most significant is in fields RR2 and RR3 where 24 stars in the range 4.0 < Z < 11.0 kpc have a mean radial velocity of -59 +/- 16 km/sec. Three halo stars in field RR 2 appear to be part of a moving group with a common radial velocity of -90 km/sec. The streaming phenomenon therefore occurs over a range of spatial scales. The BHB and RR Lyrae stars in our sample both have a similar range of metallicity (-1.2 < [Fe/H] < -2.2). Proper motions of BHB stars in fields SA 57 (NGP) and the Anticenter field (RR 7) (both of which lie close to the meridional plane of the Galaxy) show that the stars that have Z 4 kpc have a Galactic V motion that is < -200 km/sec and which is characteristic of the halo. Thus the stars that have a flatter distribution are really halo stars and not members of the metal-weak thick-disk.Comment: Accepted for publication in the March 1996 AJ. 15 pages, AASTeX V4.0 latex format (including figures), 2 eps figures, 2 separate AASTeX V4.0 latex table