Statistical approach to partial equilibrium analysis

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and demand can be derived directly from these distributions. The characteristics of excess demand function are analyzed and the necessary conditions for the existence and uniqueness of equilibrium point of the market are specified. The rationing rates of buyers and sellers are introduced to describe the ratio of realized exchange to willing exchange, and their dependence on the market price is studied in the cases of shortage and surplus. The realized market surplus, which is the criterion of market efficiency, can be written as a function of the distributions of willing exchange and the rationing rates. With this approach we can strictly prove that a market is efficient in the state of equilibrium.     

Statistical mechanical approach to lossy data compression: Theory and practice

The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the perceptron-based code saturates the theoretically achievable limit in most cases although exactly performing the compression is computationally difficult. To resolve this difficulty, we provide a computationally tractable approximation algorithm using belief propagation (BP), which is a current standard algorithm of probabilistic inference. Introducing several approximations and heuristics, the BP-based algorithm exhibits performance that is close to the achievable limit in a practical time scale in optimal cases.     

Statistical analysis of solar neutrino data

We calculate with Monte Carlo the goodness of fit and the confidence level of the standard allowed regions for the neutrino oscillation parameters obtained from the fit of the total rates measured in solar neutrino experiments. We show that they are significantly overestimated in the standard method. We also calculate exact allowed regions with correct frequentist coverage. We show that the exact VO, LMA and LOW regions are much larger than the standard ones and merge together giving an allowed band at large mixing angles for all Δm² 10⁻¹⁰ eV².     

Statistical approach to multiple-q modulated structures: average Patterson analysis

Using a statistical approach, the average unit cells have been constructed for modulated structures with different types of modulation, from simple sinusoidal to square-wave functions. The obtained unit cells fully describe diffraction intensities of the main reflections and their satellites. A universal distribution, valid for different lengths of the modulation vector, has been found. Average Patterson functions have been constructed and used to distinguish between different types of modulation.     

Statistical analysis and accuracy of PIV data

In an assessment of PIV measurement accuracy under practical experimental circumstances, grid-generated turbulence in its early decay (x/M=13.6–15.2,Re _λ≈25) has been studied. Since a real-time processor was used, it was practical to acquire a statistically significant sample size of 3000 vector maps so that accurate turbulence statistics could be calculated. Results include moments of velocity components and spatial structures in terms of auto-correlations, turbulence scales and spectra. Data fall within limits of standard error estimates. This study demonstrates the need for large sample sizes, particularly for higher order statistics.     

Statistical approach to the measurement of velocity field

Present paper describes the principle and applications of a velocity measurement using statistical analysis of visualized flow images. The authors have developed a new algorithm for the measurement using the passing probability of a particle. It is known that this kind methods gives the total flow speed at each pixel unit. In this study, the method is extended by forming the governing equation using the Lagrange’s differentiation. The process is similar to the so-called spatio-temporal derivative method. The extension of the equation enables to measure the velocity components with the help of the statistical technique. The idea is based on the fact that the temporal derivative of luminance function is proportional to the vector product of the flow velocity and the gradient of luminance function in space which gives the velocity component normal to the edge of particle image. This is easy to apply on the three-dimensional flow field.     

Statistical approach to the kinetics of nonuniform fluids

We present a new formalism in Fourier space for the study of spatially nonuniform fluids in nonequilibrium states which generalizes previous work on uniform fluids. Starting from the Liouville equation we obtain a hierarchy of equations for the reduced distribution functions which gives their rate of change at any given order of the system mean density as a sum of a finite number of terms. Using a finite-ranged repulsive interaction potential we derive, as a first application of the formalism, the Boltzmann integrodifferential equation for an infinite system which is initially in a “weakly” inhomogeneous state. This is accomplished introducing an initial statistical assumption, namely initial molecular chaos; this condition is seen to hold during the time evolution described by the resulting kinetic equation.     

Statistical mechanics of learning: a variational approach for real data

Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators for generalization errors that are based on training data alone.     

Statistical approach to the antiferromagnetic ground state problem

The statistical approach is adopted in an attempt to find the antiferromagnetic ground state. As a result an eigenstate of the Heisenberg hamiltonian is found which is not the true ground state, but which could serve as a useful starting point for other methods.The author is grateful to ing. P. Novák for valuable discussions.     

Statistical analysis of floating-car data: an empirical study

We present the results of statistical analysis of the empirical floating-car data. Our investigations are based on analyzing the time series of four basic quantities namely velocity, velocity difference, spatial gap and the acceleration associated to some instrumented cars. We obtain the statistical characteristics, including the mean, variance and relative variance of these time series by taking direct time averages. We also try to identify the moving phases of the instrumented vehicle according to the statistical properties of its velocity time series. Moreover, by exploring the two-point joint probabilities, we propose a new approach for modelling vehicular dynamics based on the floating car data.     

Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory

We propose a simple cellular automaton for traffic flow within the fundamental diagram, which could reproduce aspects of the three-phase theory. This so-called average space gap model (ASGM) is based on the Nagel–Schreckenberg model with additional slow-to-start and anticipation rules. The anticipation rule takes into account the average space gap of multiple leading vehicles and conveys to the model its three-phase property. Due to the anticipation rule, ASGM can show the transition from free flow to synchronized flow. Due to the slow-to-start rule, ASGM can show the spontaneous wide moving jam emerges in the synchronized flow. Simulations are carried out for periodic and open boundary conditions. Under periodic boundary condition, the fundamental diagram, and the properties of synchronized flow are studied. Under open boundary condition, different congested patterns induced by an on-ramp are analyzed. We found that the ASGM produces the same spatiotemporal dynamics as many of the more complex three-phase models. Due to its simplicity and its close relation to conventional slow-to-start models, this model can shed light on the relation between ‘two-phase’ and three-phase models.     

Statistical analysis of 5 s index data of the Budapest Stock Exchange

A statistical analysis of the Budapest Stock Index (BUX) is presented. The high time resolution (5 s sampling) makes it possible to extract information on market functioning which does not emerge from daily data. The main results are as follows: from a statistical point of view the large drop in October 1997 was a “normal” event. Strong autocorrelation has been detected in the volatility and market activity data. Detrended fluctuation analysis reveals “superdiffusive” scaling without persistence. Finally, we report on a simple method for mapping local trends to represent sequences in order to obtain pattern statistics.     

Difference approach to the analysis of resistivity recovery data for irradiated short-range ordered alloys

Electrical resistivity recovery (RR) data for irradiated concentrated alloys typically consist of two inseparable parts, one resulting from defect annihilation and the other from short-range order (SRO) effects. These parts exhibit different behaviour and often follow opposite trends. Therefore, in this case, analysis of RR data within the conventional method is too complicated. A new approach to data analysis of such a two-component RR is proposed. The approach involves a new quantity, the difference RR (DRR), which is composed of RR dependences of two similar samples irradiated to different defect concentrations. It is shown that the SRO formation proper and the stages corresponding to the onset of long-range migration of Frenkel pair defects, formed in each part of RR, can be clearly related to certain features of the DRR plots. This interrelationship allows detecting and identifying these stages in each part of RR separately. The validity of the approach is illustrated by analysis of the available pairwise RR data for Fe–16Cr–20Ni and Fe–4Cr alloys. It makes it possible to detect the small contribution from the SRO formation to RR in Fe–4Cr, which we failed to observe previously. It is shown that stage III of Fe–4Cr, which has a negligible contribution to the part of RR induced by defect annihilation, is clearly observed in the part induced by SRO formation.     

Statistical approach to investigating transport through single molecules

We present a statistical approach that combines comprehensive current-voltage data acquisition during the controlled manipulation of a molecular junction with subsequent statistical analysis. Thereby the most probable transport characteristics can be determined. The excellent sensitivity of this impartial approach to even subnanometer-long molecules is illustrated by benzene-1,4-dithiol and 4,4"-bis(acetylthiol)-2,2',5',2"-tetramethyl-[1,1';4',1"] terphenyl results.     

Cellular automaton model in the fundamental diagram approach reproducing the synchronized outflow of wide moving jams

Velocity effect and critical velocity are incorporated into the average space gap cellular automaton model [J.F. Tian, et al., Phys. A 391 (2012) 3129], which was able to reproduce many spatiotemporal dynamics reported by the three-phase theory except the synchronized outflow of wide moving jams. The physics of traffic breakdown has been explained. Various congested patterns induced by the on-ramp are reproduced. It is shown that the occurrence of synchronized outflow, free outflow of wide moving jams is closely related with drivers time delay in acceleration at the downstream jam front and the critical velocity, respectively.     

Statistical approach of the irreversible entropy variation

The constructal theory is based on the thought that flow architecture is a consequence of a principle of maximization of flow access, in time, and in flow configuration that is free to be realised. The principle of maxima for the variation of the entropy due to irreversibility represents a general principle of investigation for the stability of open systems, by which it is possible to predict some macroscopic shapes, originated by the spatial organisation, in Nature, both in living and in non-living objects. Its statistical meaning has recently been introduced. Here a statistical and dynamical interpretation for the entropy due to irreversibility is proposed as a foundation of the constructal theory.     

Statistical approach to bulk inclusion initialized damage in films

In experiments, we have found an abnormal relationship between probability of laser induced damage and number density of surface inclusion. From results of X-ray diffraction (XRD) and laser induced damage, we have drawn a conclusion that bulk inclusion plays a key role in damage process. Combining thermo-mechanical damage process and statistics of inclusion density distribution, we have deduced an equation which reflects the relationship between probability of laser induced damage, number density of inclusion, power density of laser pulse, and thickness of films. This model reveals that relationship between critical sizes of the dangerous inclusions (dangerous inclusions refer to the inclusions which can initialize film damage), embedded depth of inclusions, thermal diffusion length and tensile strength of films. This model develops the former work which is the statistics about surface inclusion.