The built-up land represents an important type of overall landscape. In this paper the built-up land structure in the largest cities in the Czech Republic and selected cities in the U.S.A. is analysed using the framework of statistical physics. We ca
lculate the variance of the built-up area and the number variance of built-up landed plots in discs. In both cases the variance as a function of a disc radius follows a power law. The obtained values of power law exponents are comparable through different cities. The study is based on cadastral data from the Czech Republic and building footprints from GIS data in the U.S.A.
Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions of level
curvatures and avoided crossing gaps are calculated. The numerical results are compared with the predictions of Random Matrix Theory (RMT) for Gaussian Orthogonal Ensemble (GOE) and for coupled GOE matrices. The application of coupled GOE matrices was justified by studying localization phenomena in graphs wave functions Psi(x) using the Inverse Participation Ratio (IPR) and the amplitude distribution P(Psi(x)).
Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by
the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data.
During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the traffic obje
cts (cars or pedestrians). But the problem is not restricted on humans. It comes up again when we try to describe the statistics of distances between perching birds or moving sheep herd. Our aim is to demonstrate that the spacing distribution is generic and independent on the nature of the object considered. We show that this fact is based on the unconscious perception of space that people share with the animals. We give a simple mathematical model of this phenomenon and prove its validity on the real data that include the clearance distribution between: parked cars, perching birds, pedestrians, cars moving in a dense traffic and the distances inside a sheep herd.
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties are nontrivi
al. The level spacing distribution between its neighboring odd and even levels displays a surprising agreement with the prediction obtained for the Gaussian Orthogonal Ensemble of random matrices.
Using the methods originally developed for Random Matrix Theory we derive an exact mathematical formula for number variance (introduced in [4]) describing a rigidity of particle ensembles with power-law repulsion. The resulting relation is consequent
ly compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of an inverse temperature, which can be identified as a coefficient of a mental strain of car drivers, is then discussed in detail with the respect to the traffic density and flow.
We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results for some colored noise signals.
During the attempt to park a car in the city the drivers have to share limited resources (the available roadside). We show that this fact leads to a predictable distribution of the distances between the cars that depends on the length of the street s
egment used for the collective parking. We demonstrate in addition that the individual parking maneuver is guided by generic psychophysical perceptual correlates. Both predictions are compared with the actual parking data collected in the city of Hradec Kralove (Czech Republic).
We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss a relation of this results to the random matrix theory.
