Many Faces of Entropy or Bayesian Statistical Mechanics

Some 80-90 years ago, George A. Linhart, unlike A. Einstein, P. Debye, M. Planck and W. Nernst, has managed to derive a very simple, but ultimately general mathematical formula for heat capacity vs. temperature from the fundamental thermodynamical principles, using what we would nowadays dub a "Bayesian approach to probability". Moreover, he has successfully applied his result to fit the experimental data for diverse substances in their solid state in a rather broad temperature range. Nevertheless, Linhart's work was undeservedly forgotten, although it does represent a valid and fresh standpoint on thermodynamics and statistical physics, which may have a significant implication for academic and applied science.Comment: submitte

An Interdisciplinary Survey on Origin-destination Flows Modeling: Theory and Techniques

Origin-destination~(OD) flow modeling is an extensively researched subject across multiple disciplines, such as the investigation of travel demand in transportation and spatial interaction modeling in geography. However, researchers from different fields tend to employ their own unique research paradigms and lack interdisciplinary communication, preventing the cross-fertilization of knowledge and the development of novel solutions to challenges. This article presents a systematic interdisciplinary survey that comprehensively and holistically scrutinizes OD flows from utilizing fundamental theory to studying the mechanism of population mobility and solving practical problems with engineering techniques, such as computational models. Specifically, regional economics, urban geography, and sociophysics are adept at employing theoretical research methods to explore the underlying mechanisms of OD flows. They have developed three influential theoretical models: the gravity model, the intervening opportunities model, and the radiation model. These models specifically focus on examining the fundamental influences of distance, opportunities, and population on OD flows, respectively. In the meantime, fields such as transportation, urban planning, and computer science primarily focus on addressing four practical problems: OD prediction, OD construction, OD estimation, and OD forecasting. Advanced computational models, such as deep learning models, have gradually been introduced to address these problems more effectively. Finally, based on the existing research, this survey summarizes current challenges and outlines future directions for this topic. Through this survey, we aim to break down the barriers between disciplines in OD flow-related research, fostering interdisciplinary perspectives and modes of thinking.Comment: 49 pages, 6 figure

Pedestrian Mobility Mining with Movement Patterns

In street-based mobility mining, pedestrian volume estimation receives increasing attention, as it provides important applications such as billboard evaluation, attraction ranking and emergency support systems. In practice, empirical measurements are sparse due to budget limitations and constrained mounting options. Therefore, estimation of pedestrian quantity is required to perform pedestrian mobility analysis at unobserved locations. Accurate pedestrian mobility analysis is difficult to achieve due to the non-random path selection of individual pedestrians (resulting from motivated movement behaviour), causing the pedestrian volumes to distribute non-uniformly among the traffic network. Existing approaches (pedestrian simulations and data mining methods) are hard to adjust to sensor measurements or require more expensive input data (e.g. high fidelity floor plans or total number of pedestrians in the site) and are thus unfeasible. In order to achieve a mobility model that encodes pedestrian volumes accurately, we propose two methods under the regression framework which overcome the limitations of existing methods. Namely, these two methods incorporate not just topological information and episodic sensor readings, but also prior knowledge on movement preferences and movement patterns. The first one is based on Least Squares Regression (LSR). The advantage of this method is the easy inclusion of route choice heuristics and robustness towards contradicting measurements. The second method is Gaussian Process Regression (GPR). The advantages of this method are the possibilities to include expert knowledge on pedestrian movement and to estimate the uncertainty in predicting the unknown frequencies. Furthermore the kernel matrix of the pedestrian frequencies returned by the method supports sensor placement decisions. Major benefits of the regression approach are (1) seamless integration of expert data and (2) simple reproduction of sensor measurements. Further advantages are (3) invariance of the results against traffic network homeomorphism and (4) the computational complexity depends not on the number of modeled pedestrians but on the traffic network complexity. We compare our novel approaches to state-of-the-art pedestrian simulation (Generalized Centrifugal Force Model) as well as existing Data Mining methods for traffic volume estimation (Spatial k-Nearest Neighbour) and commonly used graph kernels for the Gaussian Process Regression (Squared Exponential, Regularized Laplacian and Diffusion Kernel) in terms of prediction performance (measured with mean absolute error). Our methods showed significantly lower error rates. Since pattern knowledge is not easy to obtain, we present algorithms for pattern acquisition and analysis from Episodic Movement Data. The proposed analysis of Episodic Movement Data involve spatio-temporal aggregation of visits and flows, cluster analyses and dependency models. For pedestrian mobility data collection we further developed and successfully applied the recently evolved Bluetooth tracking technology. The introduced methods are combined to a system for pedestrian mobility analysis which comprises three layers. The Sensor Layer (1) monitors geo-coded sensor recordings on people’s presence and hands this episodic movement data in as input to the next layer. By use of standardized Open Geographic Consortium (OGC) compliant interfaces for data collection, we support seamless integration of various sensor technologies depending on the application requirements. The Query Layer (2) interacts with the user, who could ask for analyses within a given region and a certain time interval. Results are returned to the user in OGC conform Geography Markup Language (GML) format. The user query triggers the (3) Analysis Layer which utilizes the mobility model for pedestrian volume estimation. The proposed approach is promising for location performance evaluation and attractor identification. Thus, it was successfully applied to numerous industrial applications: Zurich central train station, the zoo of Duisburg (Germany) and a football stadium (Stade des Costières Nîmes, France)

EPR Paradox,Locality and Completeness of Quantum Theory

The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time -series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The probability distribution is not an attribute of a dice but it is a characteristic of a whole random experiment : '' rolling a dice''. and statistical long range correlations between two random variables X and Y are not a proof of any causal relation between these variable. Moreover any probabilistic model used to describe a random experiment is consistent only with a specific protocol telling how the random experiment has to be performed.In this sense the quantum theory is a statistical and contextual theory of phenomena. In this paper we discuss these important topics in some detail. Besides we discuss in historical perspective various prerequisites used in the proofs of Bell and CHSH inequalities concluding that the violation of these inequalities in spin polarization correlation experiments is neither a proof of the completeness of QT nor of its nonlocality. The question whether QT is predictably complete is still open and it should be answered by a careful and unconventional analysis of the experimental data. It is sufficient to analyze more in detail the existing experimental data by using various non-parametric purity tests and other specific statistical tools invented to study the fine structure of the time-series. The correct understanding of statistical and contextual character of QT has far reaching consequences for the quantum information and quantum computing.Comment: 16 pages, 59 references,the contribution to the conference QTRF-4 held in Vaxjo, Sweden, 11-16 june 2007. To be published in the Proceeding