Concept Of Transition Probabilities Research Articles

Modelling Unidirectional Crowd Motion in a Corridor with Statistical Characteristics of Pedestrian Movements

Lattice gas model is a kind of mature and convenient pedestrian simulation model. The original lattice gas model adopts discontinuous step length and finite moving directions to simulate crowd motion, which will lead to some unreasonable movements; besides, the transition probability used in this model is often manually designed and lacks the verification of realistic pedestrian trajectories. Based on an open pedestrian trajectory dataset, we first derived the relationship between local density and the distribution of pedestrian movements’ length and then proposed an extended lattice gas model considering the statistical characteristics of pedestrian movements, which extends the concept of transition probability in the original lattice gas model to distribution of pedestrian movements’ length in two perpendicular directions. The proposed model is applied to a scenario which is the same as the experiments of the open dataset, and the numerical results demonstrate that the proposed model can reproduce the fundamental diagrams and the transition probability of the experimental dataset well. This study is helpful to understand the statistical characteristics of pedestrian movements and can improve the applicability and accuracy of the lattice gas model.

Attitudes towards climate policies in a macrodynamic model of the economy

In a recent article published in this journal, Guarini and Porcile (2016) expanded the Balance-of-Payments Constraint (BoPC) growth model suggesting a way to make it possible to address some of the challenges posed by greenhouse gas emissions. Building on their set up, we formalise into the model a mechanism that explains how people with different environmental attitudes or sentiments influence each other and contribute to the design of environmental policies. We detail the concept of transition probabilities for the agent's switching from pro- to anti-environmental positions and vice-versa and discuss the macroeconomic results that follow. Numerical simulations allow us to investigate in more detail the implications of the validity of Porter's hypothesis as well as to discuss the feasibility of decoupling conditions. A policy implication of our analysis is that we should encourage the dissemination of pro-environmental attitudes among the public because this could lead to a more desirable equilibrium. As important as enhancing public knowledge of climate change is to keep alive the debate at the collective level so as to influence the probability of switching sides.

Developing Performance Prediction Models for Pavement Management Systems in Local Governments in Absence of Age Data

Pavement Management Systems (PMS) use a strategic and data-driven approach to optimize budget allocation to various maintenance and rehabilitation (M&R) projects. Performance prediction models are used in PMS to determine the optimum timing for M&R interventions on every pavement section. Many local roadway agencies use empirical regression models which are based on past condition and age data. Often, these agencies are faced with limited resources for data collection and a high staff turnover rate, which all result in inadequate or unreliable construction history and pavement age data. This paper recommends a simple practical approach for local governments to develop performance prediction models in the absence of reliable pavement age data. Also, best practices for data pre-processing and validation of the model prediction capability are synthesized. Instead of using regression models based on condition and age, the pavement deterioration rate at each condition level is estimated. Similar to the Markovian transition probability concept, it is assumed that deterioration rates for every family of pavements are independent of time and only dependent on the current condition level. For every pair of subsequent condition measurements on a section, the difference in condition score is normalized by the difference in measurement time. These deterioration rates are then classified into bins based on the initial condition level for every pair of measurements. The average deterioration rate for all data records in each bin is then used to build a deterioration curve. This approach is demonstrated in this paper using real but anonymous agency data.

Application of Quantile Graphs to the Automated Analysis of EEG Signals

Epilepsy is classified as a chronic neurological disorder of the brain and affects approximately 2% of the world population. This disorder leads to a reduction in people’s productivity and imposes restrictions on their daily lives. Studies of epilepsy often rely on electroencephalogram (EEG) signals to provide information on the behavior of the brain during seizures. Recently, a map from a time series to a network has been proposed and that is based on the concept of transition probabilities; the series results in a so-called “quantile graph” (QG). Here, this map, which is also called the QG method, is applied for the automatic detection of normal, pre-ictal (preceding a seizure), and ictal (occurring during a seizure) conditions from recorded EEG signals. Our main goal is to illustrate how the differences in dynamics in the EEG signals are reflected in the topology of the corresponding QGs. Based on various network metrics, namely, the clustering coefficient, the shortest path length, the mean jump length, the modularity and the betweenness centrality, our results show that the QG method is able to detect differences in dynamical properties of brain electrical activity from different extracranial and intracranial recording regions and from different physiological and pathological brain states.

Neurophysical substrates of arousal and attention

The study of arousal and attention could be of prominent importance for elucidating both fundamental and practical aspects of the mind-brain puzzle. Defined as "general activation of mind" (Kahnemann in Attention and effort. Prentice-Hall, New Jersey, 1973), or "general operation of consciousness" (Thacher and John in Functional neuroscience: foundations of cognitive processing. Erlbaum, Hillsdale, 1977), arousal can be considered as a starting point of fundamental research on consciousness. Similar role could be assigned to attention, which can be defined by substituting the attributes "general" with "focused". Concerning the practical applications, the empirically established correlation between neuronal oscillations and arousal/attention levels is widely used in research and clinics, including neurofeedback, brain-computer communication, etc. However, the neurophysical mechanism underlying this correlation is still not clear enough. In this paper, after reviewing some present classical and quantum approaches, a transition probability concept of arousal based on field-dipole quantum interactions and information entropy is elaborated. The obtained analytical expressions and numerical values correspond to classical empirical results for arousal and attention, including the characteristic frequency dependence and intervals. Simultaneously, the fundamental (substrate) role of EEG spectrum has been enlightened, whereby the attention appears to be a bridge between arousal and the content of consciousness. Finally, some clinical implications, including the brain-rate parameter as an indicator of arousal and attention levels, are provided.

Thermal Equilibrium Between Radiation and Matter

In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the conditions of thermodynamic equilibrium of electromagnetic radiation and the energy balance of thermal radiation by the matter, between any of its two energy-states, not only result in Planck's radiation law and the Bohr frequency condition, but they remarkably yield the law of the statistical thermal equilibrium of matter: the Maxwell–Boltzmann distribution. Since the transition probabilities of the modern quantum theory of radiation coincide with their definition in Einstein's theory of blackbody radiation, the presented deduction of the Maxwell–Boltzmann distribution is equally valid within the bounds of modern quantum theory. Consequently, within the framework of the fundamental assumptions, the Maxwell–Boltzmann distribution of energy-states is not only a sufficient, but a necessary condition for thermal equilibrium between the matter and radiation.

Examination of the statistical rate theory expression for liquid evaporation rates

Recent measurements of the temperature at the interface of an evaporating liquid have been found to be in conflict with the predictions of classical kinetic theory. Under 20 different experimental conditions for water evaporation, the temperature in the vapor at the interface was measured to be greater than that in the liquid at the interface and this relation between the interfacial temperatures is the opposite to that predicted from classical kinetic theory. When these same data were used to examine the statistical rate theory (SRT) expression for the liquid evaporation rate, almost complete agreement was found. This theoretical approach is based on the transition probability concept, as defined in quantum mechanics, a hypothesis that assumes the rate of exchange between the possible quantum mechanical states of an isolated system that are within the energy uncertainty has the same value, and the Boltzmann definition of entropy. To determine whether the SRT expression for the evaporation rate also describes the liquid-vapor phase transition for liquids other than water, two hydrocarbons have been examined. The agreement between the predictions from SRT and the measurements is equally as good. These results raise the question of whether a quantum mechanical description is essential to describe the condition existing at the interface of an evaporating liquid.

Expression for predicting liquid evaporation flux: Statistical rate theory approach

Recent measurements of the conditions existing at the interface of an evaporating liquid have found that the temperature approximately one mean free path from the interface in the vapor was higher than the temperature of the liquid at the interface. The measured temperature discontinuity at the interface is in the opposite direction of that predicted by several recent studies based on classical kinetic theory. A theoretical approach based on the transition probability concept of quantum mechanics, called statistical rate theory (SRT), is used herein to develop an expression for predicting the evaporation flux. The expression obtained is free of any fitting parameters. When applied to predict the conditions at which a particular value of the evaporation flux is expected and the result compared with the measurements at 15 different experimental conditions, it is found that the SRT expression accurately predicts the conditions.

The Model of Hysteretic Behavior of SMA Based on the High Order Approximation of Differential Equation Method

Due to thermomechanical hysteresis in solids undergoing martensitic type of structure transformations the macroscopic strain and volume fraction of martensite are not a single-valued function of stress and temperature, but they become functions of the process of their change. Some of the phenomenological approaches describing main thermomechanical properties of shape-memory alloys (SMA) connected with hysteresis were recently developed. A special type of differential equations (DE) describing evolution of the inelastic macroscopic strain and volume fraction of martensite as functions of the temperature have been proposed in out recent papers. Simplest applications of these equations to a strain evolution during the multiple temperature cycling in a small temperature interval live been also discussed. Some other problems associated with the irreversible processes caused by hysteresis will be discussed in the present paper. In particular, a new interpretation of DE method based on the transition probability concept and high order approximation inciuding the return point effect is considered.

A Two‐Step Probabilistic Model of Storage Reservoir with Correlated Inputs

Fragmentation of Moran's model and decomposition of its transition matrix into a release rule and an input component are used to simplify the problem formulation for reservoirs with complex operating rules and to derive the Lloyd model directly from that of Moran by introducing two successive transitions of one variable instead of a single bivariate transition. Combined with Gould's concept of transition probabilities, the suggested model is used to take into account the correlation between monthly flows simultaneously with that between annual flows.