Fluctuation and Noise Letters

The two-envelope problem has intrigued mathematicians for decades, and is a question of choice between two states in the presence of uncertainty. The problem so far, is considered open and there has been no agreed approach or framework for its analysis. In this paper we outline an elementary approach based on Cover's switching function that, in essence, makes a biased random choice where the bias is conditioned on the observed value of one of the states. We argue that the resulting symmetry breaking introduced by this process results in a gain counter to naive expectation. Finally, we discuss a number of open questions and new lines of enquiry that this discovery opens up.

The influence of spontaneous emission channel and generalized Pauli channel on quantum Monty Hall Game is analyzed. The scheme of Flittney and Abbott is reformulated using the formalism of density matrices. Optimal classical strategies for given quantum strategies are found. The whole presented scheme illustrates how quantum noise may change the odds of a zero-sum game.

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of stick-slip friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.

We have found a security risk in the Liu's cypher based on random signals and feedback, when it utilizes a large class of noises for communication in its most secure state, the steady state. For the vulnerability to exist, the noise must have a spectrum which can be transformed to white-like noise by linear filtering. For the cracking, we utilize the natural properties of power density spectra and autocorrelation functions. We introduce and demonstrate the method for Lorentzian spectra. Some of the implications of the results concern the transient operation during changing bits, where the modulation products of noise cannot be band-limited therefore the cypher is vulnerable. We propose the application of line filters to provide a proper spectral shape and to improve the security.

Previous investigation of the length of coding sequence lengths (CDS) in the bacterial circular chromosome revealed short range correlation in the series of these data. We have further analyzed the averaged periodograms of these series and we found that the organization of CDS can be well described by first-order autoregressive processes. This involves interaction between the neighboring terms. The autoregressive analysis may have great potential in modeling various physical and biological processes like light emission of galaxies, protein organization, cell flickering, cognitive processes and perhaps others.

We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider become very much involved even for a small number of players, which has hindered a precise analysis in previous works. We here present a systematic way to reach the solution for a general number of players, and show that this game is an example of conflict between the group and the individual interests.

Canonical-dissipative oscillatory systems subjected to fluctuations are considered. It is shown how to estimate key parameters of such systems using the first and second moments of energy fluctuations and the short-time mean square displacement of velocity fluctuations. The key parameters describe the strength of the deterministic attractive forces that drive the oscillator dynamics towards a limit cycle and the strength of the random perturbations that drive the oscillator dynamics away from the limit cycle. A test statistics is proposed to assess the validity of the canonical-dissipative modeling approach.

We study stochastically forced multiple limit cycles of nonlinear dynamical systems in a period-doubling bifurcation zone. Noise-induced transitions between separate parts of the cycle are considered. A phenomenon of a decreasing of the stochastic cycle multiplicity with a noise intensity growth is investigated. We call it by a backward stochastic bifurcation (BSB). In this paper, for the BSB analysis we suggest a stochastic sensitivity function technique. As a result, a method for the estimation of critical values of noise intensity corresponding to BSB is proposed. The constructive possibilities of this general method for the detailed BSB analysis of the multiple stochastic cycles of the forced Roessler system are demonstrated.

It is commonly known in economics that markets follow both positive and/or negative trends, crashes and bubble effects. In general a strong positive trend is followed by a crash. Famous examples of these effects were seen in the recent crash on the NASDAQ (April 2000) and prior to the crash on the Hong Kong market, which was associated with the Asian crisis in the early 1994. In this paper we use real market data input into a minority game with a variable payoff function and a nonlinear super exponential model for bubbles, to explore financial bubbles. By changing the payoff function in the minority game we study how one can get the price function to follow the dynamics of a real market.

In 1996, Parrondo's games were first constructed using a simple coin tossing scenario, demonstrating the paradoxical situation where individually losing games combine to win. Parrondo's principle has become paradigmatic for situations where losing strategies or deleterious effects can combine to win. Intriguingly, there are deep connections between the Parrondo effect and a range of physical phenomena, as it turns out that Parrondo's original games are a discrete-time and discrete-space version of a flashing Brownian ratchet. This has been formally established via discretization of the Fokker–Planck equation. Over the past decade, many examples ranging from physics to population genetics have been reported in the literature pointing to the generality of Parrondo's principle. In general terms, the Parrondo effect occurs where there is a nonlinear interaction of random behavior with an asymmetry, and can be mathematically understood in terms of a convex linear combination. Many effects, where randomness plays a constructive role, such as stochastic resonance, volatility pumping, the Brazil nut paradox, etc., can be viewed as being in the class of Parrondian phenomena. We will briefly review the history of Parrondo's paradox, recent developments, and connections to related phenomena.