Multi-value cellular automata model for mixed bicycle flow

In this paper, we investigate mixed bicycle flow using the multi-value cellular automata (CA) model. Two types of bicycles with different maximum speed are considered in the system. The system of mixed bicycles is investigated under both deterministic and stochastic regimes. It is shown under the deterministic case that there appear multiple states both in congested flow and free flow regions. Analytical analysis is carried out and is in good agreement with the simulation results. Under the stochastic case, the multiple states effect disappears only when both slow and fast bicycles are randomized. Spacetime plots are presented to show the evolution of mixed bicycle flow.     

Kinetic market models with single commodity having price fluctuations

We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.     

A generalized spin model of financial markets

We reformulate the Cont-Bouchaud model of financial markets in terms of classical “super-spins” where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to model the tendency of agencies getting influenced by the opinion of other managers. We also introduce a fictitious temperature (to model other random influences), and time-dependent local fields to model a slowly changing optimistic or pessimistic bias of traders. We point out close similarities between the price variations in our model with N super-spins and total displacements in an N-step Levy flight. We demonstrate the phenomena of natural and artificially created bubbles and subsequent crashes as well as the occurrence of “fat tails” in the distributions of stock price variations. Received 13 October 1998     

Optimal trading from minimizing the period of bankruptcy risk

Assuming that financial markets behave similar to random walk processes we derive a trading strategy with variable investment which is based on the equivalence of the period of bankruptcy risk and the risk to profit ratio. We define a state dependent predictability measure which can be attributed to the deterministic and stochastic components of the price dynamics. The influence of predictability variations and especially of short term inefficiency structures on the optimal amount of investment is analyzed in the given context and a method for adaptation of a trading system to the proposed objective function is presented. Finally we show the performance of our trading strategy on the DAX and S&P 500 as examples for real world data using different types of prediction models in comparison. Received 15 September 2000 and Received in final form 2 October 2000     

Delay, feedback and quenching in financial markets

An asset whose price exhibits geometric Brownian motion is analysed. The basic Brownian motion model is modified to account for the effects of market delay and investor feedback. A Langevin equation model is appropriate. When the feedback coupling is sufficiently strong, the market dynamics switches from a slow random walk behaviour to a rapid unstable behaviour with a fast time scale characteristic of the market delay. The unstable runaway behaviour is subsequently quenched by investors deserting a collapsing market or saturating a booming one. This quenching effect is sufficient to ensure long term bounding of the asset price. A form of market sabotage is demonstrated in which investors can push the market from a stable to an unstable regime. Received 24 February 2000     

Langevin dynamics of financial systems: A second-order analysis

We address the issue of stock market fluctuations within Langevin Dynamics (LD) and the thermodynamics definitions of multifractality in order to study its second-order characterization given by the analogous specific heat C_q, where q is an analogous temperature relating the moments of the generating partition function for the financial data signals. Due to non-linear and additive noise terms within the LD, we found that C_q can display a shoulder to the right of its main peak as also found in the S&P500 historical data which may resemble a classical phase transition at a critical point. Received 6 November 2000 and Received in final form 26 March 2001     

Liquid markets and market liquids

We characterize the collective phenomena of a liquid market. By interpreting the behavior of a no-arbitrage N asset market in terms of a particle system scenario, (thermo)dynamical-like properties can be extracted from the asset kinetics. In this scheme the mechanisms of the particle interaction can be widely investigated. We test the verisimilitude of our construction on two-decade stock market daily data (DAX30) and show the result obtained for the interaction potential among asset pairs. Received 1st September 2000     

A cellular automata model for social-learning processes in a classroom context

A model for teaching-learning processes that take place in the classroom is proposed and simulated numerically. Recent ideas taken from the fields of sociology, educational psychology, statistical physics and computational science are key ingredients of the model. Results of simulations are consistent with well-established empirical results obtained in classrooms by means of different evaluation tools. It is shown that students engaged in collaborative groupwork reach higher achievements than those attending traditional lectures only. However, in many cases, this difference is subtle and consequently very difficult to be detected using tests. The influence of the number of students forming the collaborative groups on the average knowledge achieved is also studied and discussed. Received 22 October 2001     

Evidence for the exponential distribution of income in the USA

Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8 = 0.375 calculated for two-earners families. Received 21 August 2000     

Bulk effects in the coherent inelastic scattering of ultracold neutrons

With the use of a theory developed earlier, bulk effects in ultracold neutron coherent inelastic scattering are considered both for solid and liquid target samples related to energy and momentum exchange with phonon and diffusion-like modes. For the neutron in a material trap, differential and integral probabilities for the energy transfer per bounce are presented in a simple analytic form which exhibits parameter dependence. As an example, the theoretical values for the ultracold-neutron loss rate from a storage bottle with Fomblin-coated walls and stainless-steel walls are evaluated. A possible contribution from incoherent inelastic scattering is discussed.     

Optimal investment horizons

In stochastic finance, one traditionally considers the return as a competitive measure of an asset, i.e., the profit generated by that asset after some fixed time span Δt, say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established that the distribution of returns exhibits “fat tails” indicating that large returns occur more frequently than what is expected from standard Gaussian stochastic processes [1-3]. Instead of estimating this “fat tail” distribution of returns, we propose here an alternative approach, which is outlined by addressing the following question: What is the smallest time interval needed for an asset to cross a fixed return level of say 10%? For a particular asset, we refer to this time as the investment horizon and the corresponding distribution as the investment horizon distribution. This latter distribution complements that of returns and provides new and possibly crucial information for portfolio design and risk-management, as well as for pricing of more exotic options. By considering historical financial data, exemplified by the Dow Jones Industrial Average, we obtain a novel set of probability distributions for the investment horizons which can be used to estimate the optimal investment horizon for a stock or a future contract. Received 20 February 2002 Published online 25 June 2002     

Competing species dynamics: Qualitative advantage versus geography

A simple cellular automata model for a two-group war over the same “territory” is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria. Received: 21 April 1998 / Revised and Accepted: 22 April 1998     

Anomalous scaling of stock price dynamics within ARCH-models

We show that autoregressive-conditional-heteroskedasticity (ARCH) models can encompass the observed anomalous scaling properties of stock price dynamics remarkably well. We find that with a suitable choice of parameters, simple ARCH models can reproduce the non-standard scaling behavior of the central part of the probability distribution functions of stock prices at different time horizons, as empirically found for the Standard & Poors 500 (S&P 500) index data, but fail to reproduce the shape of the S&P 500 distribution, in particular at the smallest time horizon (1 min). A linear version of ARCH processes, denoted here as LARCH models, still preserving the anomalies observed, permits to fit the 1 min S&P 500 distribution more accurately. Received 12 October 2000 and Received in final form 5 February 2001     

Influence of corruption on economic growth rate and foreign investment

We analyze the dependence of the Gross Domestic Product (GDP) per capita growth rates on changes in the Corruption Perceptions Index (CPI). For the period 1999–2004 for all countries in the world, we find on average that an increase of CPI by one unit leads to an increase of the annual GDP per capita growth rate by 1.7%. By regressing only the European countries with transition economies, we find that an increase of CPI by one unit generates an increase of the annual GDP per capita growth rate by 2.4%. We also analyze the relation between foreign direct investments received by different countries and CPI, and we find a statistically significant power-law functional dependence between foreign direct investment per capita and the country corruption level measured by the CPI. We introduce a new measure to quantify the relative corruption between countries based on their respective wealth as measured by GDP per capita.     

Quantitative relations between corruption and economic factors

We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investment per capita. These relations hold for diverse countries, and also remain stable over different time periods. We also observe a negative correlation between level of corruption and long-term economic growth. We find similar results for two independent indices of corruption, suggesting that the relation between corruption and wealth does not depend on the specific measure of corruption. The functional relations we report have implications when assessing the relative level of corruption for two countries with comparable wealth, and for quantifying the impact of corruption on economic growth and foreign investment.     

How do output growth-rate distributions look like? Some cross-country,time-series evidence

This paper investigates the statistical properties of within-country gross domestic product (GDP) and industrial production (IP) growth-rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether also within-country, time-series GDP and IP growth rates can be approximated by tent-shaped distributions. We fit output growth rates with the exponential-power (Subbotin) family of densities, which includes as particular cases both Gaussian and Laplace distributions. We find that, for a large number of OECD (Organization for Economic Cooperation and Development) countries including the US, both GDP and IP growth rates are Laplace distributed. Moreover, we show that fat-tailed distributions robustly emerge even after controlling for outliers, autocorrelation and heteroscedasticity.     

The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash

The Nasdaq Composite fell another % on Friday the 14'th of April 2000 signaling the end of a remarkable speculative high-tech bubble starting in spring 1997. The closing of the Nasdaq Composite at 3321 corresponds to a total loss of over 35% since its all-time high of 5133 on the 10'th of March 2000. Similarities to the speculative bubble preceding the infamous crash of October 1929 are quite striking: the belief in what was coined a “New Economy” both in 1929 and presently made share-prices of companies with three digits price-earning ratios soar. Furthermore, we show that the largest draw downs of the Nasdaq are outliers with a confidence level better than 99% and that these two speculative bubbles, as well as others, both nicely fit into the quantitative framework proposed by the authors in a series of recent papers. Received 3 May 2000