Search results for: probability density function (pdf)

Authors: Mary Chriselda A

Abstract:

This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Weichao Yu, Kai Wen, Weihe Huang, Yang Yang, Jing Gong

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Metal-loss corrosion is a major threat to the safety and integrity of gas pipelines as it may result in the burst failures which can cause severe consequences that may include enormous economic losses as well as the personnel casualties. Therefore, it is important to ensure the corroding pipeline integrity and efficiency, considering the value of wall thickness, which plays an important role in the failure probability of corroding pipeline. Actually, the wall thickness is controlled during pipe purchase stage. For example, the API_SPEC_5L standard regulates the allowable tolerance of the wall thickness from the specified value during the pipe purchase. The allowable wall thickness tolerance will be used to determine the wall thickness distribution characteristic such as the mean value, standard deviation and distribution. Taking the uncertainties of the input variables in the burst limit-state function into account, the reliability approach rather than the deterministic approach will be used to evaluate the failure probability. Moreover, the cost of pipe purchase will be influenced by the allowable wall thickness tolerance. More strict control of the wall thickness usually corresponds to a higher pipe purchase cost. Therefore changing the wall thickness tolerance will vary both the probability of a burst failure and the cost of the pipe. This paper describes an approach to optimize the wall thickness tolerance considering both the safety and economy of corroding pipelines. In this paper, the corrosion burst limit-state function in Annex O of CSAZ662-7 is employed to evaluate the failure probability using the Monte Carlo simulation technique. By changing the allowable wall thickness tolerance, the parameters of the wall thickness distribution in the limit-state function will be changed. Using the reliability approach, the corresponding variations in the burst failure probability will be shown. On the other hand, changing the wall thickness tolerance will lead to a change in cost in pipe purchase. Using the variation of the failure probability and pipe cost caused by changing wall thickness tolerance specification, the optimal allowable tolerance can be obtained, and used to define pipe purchase specifications.

Keywords: allowable tolerance, corroding pipeline segment, operation cost, production cost, reliability approach

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Authors: Ahmet Kaya

Abstract:

Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

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Authors: D. Sigirli

Abstract:

The Receiver Operating Characteristic (ROC) curve is a commonly used statistical tool for evaluating the diagnostic performance of screening and diagnostic test with continuous or ordinal scale results which aims to predict the presence or absence probability of a condition, usually a disease. When the test results were measured as numeric values, sensitivity and specificity can be computed across all possible threshold values which discriminate the subjects as diseased and non-diseased. There are infinite numbers of possible decision thresholds along the continuum of the test results. The ROC curve presents the trade-off between sensitivity and the 1-specificity as the threshold changes. The empirical ROC curve which is a non-parametric estimator of the ROC curve is robust and it represents data accurately. However, especially for small sample sizes, it has a problem of variability and as it is a step function there can be different false positive rates for a true positive rate value and vice versa. Besides, the estimated ROC curve being in a jagged form, since the true ROC curve is a smooth curve, it underestimates the true ROC curve. Since the true ROC curve is assumed to be smooth, several smoothing methods have been explored to smooth a ROC curve. These include using kernel estimates, using log-concave densities, to fit parameters for the specified density function to the data with the maximum-likelihood fitting of univariate distributions or to create a probability distribution by fitting the specified distribution to the data nd using smooth versions of the empirical distribution functions. In the present paper, we aimed to propose a smooth ROC curve estimation based on the boundary corrected kernel function and to compare the performances of ROC curve smoothing methods for the diagnostic test results coming from different distributions in different sample sizes. We performed simulation study to compare the performances of different methods for different scenarios with 1000 repetitions. It is seen that the performance of the proposed method was typically better than that of the empirical ROC curve and only slightly worse compared to the binormal model when in fact the underlying samples were generated from the normal distribution.

Keywords: empirical estimator, kernel function, smoothing, receiver operating characteristic curve

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Authors: Naoyuki Sugihashi, Toshiharu Kishi

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The probability of occurrence of thermal cracks in mass concrete in Japan is evaluated by the cracking probability diagram that represents the relationship between the thermal cracking index and the probability of occurrence of cracks in the actual structure. In this paper, we propose a method to directly calculate the cracking probability, following a probabilistic theory by modeling the variance of tensile stress and tensile strength. In this method, the relationship between the variance of tensile stress and tensile strength, the thermal cracking index, and the cracking probability are formulated and presented. In addition, standard deviation of tensile stress and tensile strength was identified, and the method of calculating cracking probability in a general construction controlled environment was also demonstrated.

Keywords: thermal crack control, mass concrete, thermal cracking probability, durability of concrete, calculating method of cracking probability

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Authors: Oscar Javier Herrera, Manuel Angel Camacho

Abstract:

This paper addresses a cutting edge method of business demand forecasting, based on an empirical probability function when the historical behavior of the data is random. Additionally, it presents error determination based on the numerical method technique ‘propagation of errors’. The methodology was conducted characterization and process diagnostics demand planning as part of the production management, then new ways to predict its value through techniques of probability and to calculate their mistake investigated, it was tools used numerical methods. All this based on the behavior of the data. This analysis was determined considering the specific business circumstances of a company in the sector of communications, located in the city of Bogota, Colombia. In conclusion, using this application it was possible to obtain the adequate stock of the products required by the company to provide its services, helping the company reduce its service time, increase the client satisfaction rate, reduce stock which has not been in rotation for a long time, code its inventory, and plan reorder points for the replenishment of stock.

Keywords: demand forecasting, empirical distribution, propagation of error, Bogota

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Authors: Jihad S. Daba, J. P. Dubois

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Understanding the statistics of non-isotropic scattering multipath channels that fade randomly with respect to time, frequency, and space in a mobile environment is very crucial for the accurate detection of received signals in wireless and cellular communication systems. In this paper, we derive stochastic models for the probability density function (PDF) of the shift in the carrier frequency caused by the Doppler Effect on the received illuminating signal in the presence of a dominant line of sight. Our derivation is based on a generalized Clarke’s and a two-wave partially developed scattering models, where the statistical distribution of the frequency shift is shown to be consistent with the power spectral density of the Doppler shifted signal.

Keywords: Doppler shift, filtered Poisson process, generalized Clark’s model, non-isotropic scattering, partially developed scattering, Rician distribution

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Authors: Jihad H. Asad

Abstract:

An expression for the Green’s function (GF) of anisotropic face cantered cubic (IFCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.

Keywords: lattice Green's function, elliptic integral, physics, cubic lattice

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Authors: Kennedy Efosa Ehimwenma, Sujatha Krishnamoorthy, Safiya Al‑Sharji

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The probability computation of events is in the interval of [0, 1], which are values that are determined by the number of outcomes of events in a sample space S. The probability Pr(A) that an event A will never occur is 0. The probability Pr(B) that event B will certainly occur is 1. This makes both events A and B a certainty. Furthermore, the sum of probabilities Pr(E₁) + Pr(E₂) + … + Pr(Eₙ) of a finite set of events in a given sample space S equals 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. This paper first discusses Bayes, the complement of probability, and the difference of probability for occurrences of learning-events before applying them in the prediction of learning objects in student learning. Given the sum of 1; to make a recommendation for student learning, this paper proposes that the difference of argMaxPr(S) and the probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates i) the probability of skill-set events that have occurred that would lead to higher-level learning; ii) the probability of the events that have not occurred that requires subject-matter relearning; iii) accuracy of the decision tree in the prediction of student performance into class labels and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning.

Keywords: complement of probability, Bayes’ rule, prediction, pre-assessments, computational education, information theory

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Authors: Po-Wen Chen, Jin-Yu Wu, Md. Manirul Ali, Yang Peng, Chen-Te Chang, Der-Jun Jan

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Dynamics of cathode spot has become a major part of vacuum arc discharge with its high academic interest and wide application potential. In this article, using a three-dimensional statistical model, we simulate the distribution of the ignition probability of a new cathode spot occurring in different magnetic pressure on old cathode spot surface and at different arcing time. This model for the ignition probability of a new cathode spot was proposed in two typical situations, one by the pure isotropic random walk in the absence of an external magnetic field, other by the retrograde motion in external magnetic field, in parallel with the cathode surface. We mainly focus on developed relationship between the ignition probability density distribution of a new cathode spot and the external magnetic field.

Keywords: cathode spot, vacuum arc discharge, transverse magnetic field, random walk

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Authors: S. Benkraouda, Z. Djelloul-Khedda, B. Yagoubi

Abstract:

we present a method for early detection of forest fires from a thermal infrared satellite image, using the image matrix of the probability of belonging. The principle of the method is to compare a theoretical mathematical model to an experimental model. We considered that each line of the image matrix, as an embodiment of a non-stationary random process. Since the distribution of pixels in the satellite image is statistically dependent, we divided these lines into small stationary and ergodic intervals to characterize the image by an adequate mathematical model. A standard deviation was chosen to generate random variables, so each interval behaves naturally like white Gaussian noise. The latter has been selected as the mathematical model that represents a set of very majority pixels, which we can be considered as the image background. Before modeling the image, we made a few pretreatments, then the parameters of the theoretical Gaussian model were extracted from the modeled image, these settings will be used to calculate the probability of each interval of the modeled image to belong to the theoretical Gaussian model. The high intensities pixels are regarded as foreign elements to it, so they will have a low probability, and the pixels that belong to the background image will have a high probability. Finally, we did present the reverse of the matrix of probabilities of these intervals for a better fire detection.

Keywords: forest fire, forest fire detection, satellite image, normal distribution, theoretical gaussian model, thermal infrared matrix image

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Authors: Ahmet Kaya

Abstract:

Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

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Authors: Bohli Afef

Abstract:

The fifth-generation (5G) wireless systems is featured by extreme densities of cell stations to overcome the higher future demand. Hence, interference management is a crucial challenge in 5G ultra-dense cellular networks. In contrast to the classical inter-cell interference coordination approach, which is no longer fit for the high density of cell-tiers, this paper proposes a novel virtual coordination based on the dynamic common cognitive monitor channel protocol to deal with the inter-cell interference issue. A tractable and flexible model for the coverage probability of a typical user is developed through the use of the stochastic geometry model. The analyses of the performance of the suggested protocol are illustrated both analytically and numerically in terms of coverage probability.

Keywords: ultra dense heterogeneous networks, dynamic common channel protocol, cognitive radio, stochastic geometry, coverage probability

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Authors: Mahdieh Khanmohammadi, Sune Darkner, Nicoletta Nava, Jens Randel Nyengaard, Jon Sporring

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We study the effect of stress on nervous system and we use two experimental groups of rats: sham rats and rats subjected to acute foot-shock stress. We investigate the synaptic vesicles density as a function of distance to the active zone in serial section transmission electron microscope images in 2 and 3 dimensions. By estimating the density in 2D and 3D we compare two groups of rats.

Keywords: stress, 3-dimensional synaptic vesicle density, image registration, bioinformatics

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Authors: Xiao Zhang, HuanJun Jiang

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In order to overcome the problem of low precision caused by a single typical component, which is chosen to represent the overall fragility in the standard analysis, the continuous beam bridge is considered as a ternary system consisting of pier, abutment bearing, and pier bearing. After the main components undergo the seismic fragility analysis, the copula function in multivariate form is introduced. Based on the computation of the main components' fragility curves and the evaluation of the correlation between the main components, a method to solve the seismic vulnerability of ternary component systems is established.

Keywords: copula function, seismic fragility analysis, damage index, joint probability distribution function

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Authors: Toby Li, Julian Zhu

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In this paper, a model based on a simplified geometry is introduced to give a very conservative collision probability prediction for the Starlink satellite in its most densely clustered region. Under the model in this paper, the probability of collision for Starlink satellite where it clustered most densely is found to be 8.484 ∗ 10^−4. It is found that the predicted collision probability increased nonlinearly with the increased safety distance set. This simple model provides evidence that the continuous development of maneuver avoidance systems is necessary for the future of the orbital safety of satellites under the harsher Lower Earth Orbit environment.

Keywords: Starlink, collision probability, debris, geometry model

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Authors: Elzbieta Babula, Juhyun Park

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Tversky and Kahneman’s cumulative prospect theory assumes symmetric probability cumulation with regard to the reference point within decision weights. Theoretically, this model should be invariant under the change of the direction of probability cumulation. In the present study, this phenomenon is being investigated by creating a reference model that allows verifying the parameter interactions in the cumulative prospect theory specifications. The simultaneous parametric fitting of utility and weighting functions is applied to binary choice data from the experiment. The results show that the flexibility of the probability weighting function is a crucial characteristic allowing to prevent parameter interactions while estimating cumulative prospect theory.

Keywords: binary choice experiment, cumulative prospect theory, decision weights, parameter interactions

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Authors: Eslam Mohammed Abdelkader, Mohamed Marzouk, Tarek Zayed

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Infrastructure systems are crucial to every aspect of life on Earth. Existing Infrastructure is subjected to degradation while the demands are growing for a better infrastructure system in response to the high standards of safety, health, population growth, and environmental protection. Bridges play a crucial role in urban transportation networks. Moreover, they are subjected to high level of deterioration because of the variable traffic loading, extreme weather conditions, cycles of freeze and thaw, etc. The development of Bridge Management Systems (BMSs) has become a fundamental imperative nowadays especially in the large transportation networks due to the huge variance between the need for maintenance actions, and the available funds to perform such actions. Deterioration models represent a very important aspect for the effective use of BMSs. This paper presents a probabilistic time-based model that is capable of predicting the condition ratings of the concrete bridge decks along its service life. The deterioration process of the concrete bridge decks is modeled using semi-Markov process. One of the main challenges of the Markov Chain Decision Process (MCDP) is the construction of the transition probability matrix. Yet, the proposed model overcomes this issue by modeling the sojourn times based on some probability density functions. The sojourn times of each condition state are fitted to probability density functions based on some goodness of fit tests such as Kolmogorov-Smirnov test, Anderson Darling, and chi-squared test. The parameters of the probability density functions are obtained using maximum likelihood estimation (MLE). The condition ratings obtained from the Ministry of Transportation in Quebec (MTQ) are utilized as a database to construct the deterioration model. Finally, a comparison is conducted between the Markov Chain and semi-Markov chain to select the most feasible prediction model.

Keywords: bridge management system, bridge decks, deterioration model, Semi-Markov chain, sojourn times, maximum likelihood estimation

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Authors: Hoang Van Ngoc, Nguyen Thu Huong, Nguyen Quang Bau

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Using the quantum kinetic equation for electrons interacting with acoustic phonon, the density of the constant current associated with the drag of charge carriers in cylindrical quantum wire by a linearly polarized electromagnetic wave, a DC electric field and a laser radiation field is calculated. The density of the constant current is studied as a function of the frequency of electromagnetic wave, as well as the frequency of laser field and the basic elements of quantum wire with a parabolic potential. The analytic expression of the constant current density is numerically evaluated and plotted for a specific quantum wires GaAs/AlGaAs to show the dependence of the constant current density on above parameters. All these results of quantum wire compared with bulk semiconductors and superlattices to show the difference.

Keywords: The photon-drag effect, the constant current density, quantum wire, parabolic potential

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Authors: Hao Chen, Bo Guo, Ping Jiang

Abstract:

Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: A. Elsariti, T. Evans

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An understanding of the interaction between acoustic waves and cancellous bone is needed in order to realize the full clinical potential of ultrasonic bone measurements. Scattering is likely to be of central importance but has received little attention to date. Few theoretical approaches have been described to explain scattering of ultrasound from bone. In this study, a scattering model based on velocity and density fluctuations in a binary mixture (marrow fat and cortical matrix) was used to estimate the ultrasonic attenuation in cancellous bone as a function of volume fraction. Predicted attenuation and backscatter coefficient were obtained for a range of porosities and scatterer size. At 600 kHZ and for different scatterer size the effect of velocity and density fluctuations in the predicted attenuation was approximately 60% higher than velocity fluctuations.

Keywords: ultrasound scattering, sound speed, density fluctuations, attenuation coefficient

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Authors: Sabika Rafiq, Rubaida Mehmood, Sajid Hussain, Atia Iqbal

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Background and objectives: The pathogenesis of liver function abnormalities and cardiac dysfunction in hyperthyroid patients after I131 treatment is still unclear. This study aimed to determine the effects of radioiodine I131 on liver function parameters, lactate dehydrogenase (LDH) and low-density lipoproteins (LDL) before and after I131 therapy hyperthyroidism patients. Material & Methods: A total of 52 patients of hyperthyroidism recommended for I131were involved in this study with ages ranging from 12–65 years (mean age=38.6±14.8 & BMI=11.5±3.7). The significance of the differences between the results of 1st, 2nd and 3rd-time serum analysis was assessed by unpaired student’s t-test. Associations between the parameters were assessed by Spearman correlation analysis. Results: Significant variations were observed for thyroid profile free FT3 (p=0.04), FT4 (p=0.01), TSH (p=0.005) during the follow-up treatment. Before taking I131 (serum analyzed at 1st time), negative correlation of FT3 with AST (r=-0.458, p=0.032) and LDL (r=-0.454, p=0.039) were observed. During 2nd time (after stopping carbimazole), no correlation was assessed. Two months after the administration of I131 drops, a significant negative association of FT3 (r=-0.62, p=0.04) and FT4(r=-0.61, p=0.02) with ALB were observed. FT3(r=-0.82, p=0.00) & FT4 (r=-0.71, p=0.00) also showed negative correlation with LDL after I131 therapy. Whereas TSH showed significant positive association with ALB (r=0.61, p=0.01) and LDL (r=0.70, p=0.00) respectively. Conclusion: Current findings suggested that the association of TFTs with biochemical parameters in patients with goiter recommended for iodine therapy is an important diagnostic and therapeutic tool. The significant changes increased in transaminases and low-density lipoprotein levels after taking I131drops are alarming signs for heart and liver function abnormalities and warrant physicians' attention on an urgent basis.

Keywords: hyperthyroidism, carbimazole, radioiodine I131, liver functions, low-density lipoprotein

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Authors: Oh Hyeon Jeon, WooYoung Jung

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In this study, seepage analysis was performed by the level difference between upstream and downstream of weir structure for safety evaluation of weir structure against flooding. Monte Carlo Simulation method was employed by considering the probability distribution of the adjacent ground parameter, i.e., permeability coefficient of weir structure. Moreover, by using a commercially available finite element program (ABAQUS), modeling of the weir structure is carried out. Based on this model, the characteristic of water seepage during flooding was determined at each water level with consideration of the uncertainty of their corresponding permeability coefficient. Subsequently, fragility function could be constructed based on this response from numerical analysis; this fragility function results could be used to determine the weakness of weir structure subjected to flooding disaster. They can also be used as a reference data that can comprehensively predict the probability of failur,e and the degree of damage of a weir structure.

Keywords: weir structure, seepage, flood disaster fragility, probabilistic risk assessment, Monte-Carlo simulation, permeability coefficient

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Authors: Zhuoran Shan, Li Wan, Xianchun Zhang

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With an increasing trend of regionalization and polycentricity in Chinese contemporary big cities, “sub-region life circle” turns to be an effective method on rational organization of urban function and spatial structure. By the method of questionnaire, network big data, route inversion on internet map, GIS spatial analysis and logistic regression, this article makes research on characteristic and formation mechanism of “sub-region life circle” based on human high-probability daily activity in Chinese big cities. Firstly, it shows that “sub-region life circle” has been a new general spatial sphere of residents' high-probability daily activity and mobility in China. Unlike the former analysis of the whole metropolitan or the micro community, “sub-region life circle” has its own characteristic on geographical sphere, functional element, spatial morphology and land distribution. Secondly, according to the analysis result with Binary Logistic Regression Model, the research also shows that seven factors including land-use mixed degree and bus station density impact the formation of “sub-region life circle” most, and then analyzes the index critical value of each factor. Finally, to establish a smarter “sub-region life circle”, this paper indicates that several strategies including jobs-housing fit, service cohesion and space reconstruction are the keys for its spatial organization optimization. This study expands the further understanding of cities' inner sub-region spatial structure based on human daily activity, and contributes to the theory of “life circle” in urban's meso-scale.

Keywords: sub-region life circle, characteristic, formation mechanism, human activity, spatial structure

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Authors: Yuan-Lin Chen

Abstract:

This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

Keywords: approaching index, forward collision probability, time to collision, time headway

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Authors: Yasser Rammah, Wolf-Christian Mueller

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Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: Muhammad Imran Ahmad, Ruzelita Ngadiran, Mohd Nazrin Md Isa, Nor Ashidi Mat Isa, Mohd ZaizuIlyas, Raja Abdullah Raja Ahmad, Said Amirul Anwar Ab Hamid, Muzammil Jusoh

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This paper presents two technique, local feature extraction using image spectrum and low frequency spectrum modelling using GMM to capture the underlying statistical information to improve the performance of face recognition system. Local spectrum features are extracted using overlap sub block window that are mapping on the face image. For each of this block, spatial domain is transformed to frequency domain using DFT. A low frequency coefficient is preserved by discarding high frequency coefficients by applying rectangular mask on the spectrum of the facial image. Low frequency information is non Gaussian in the feature space and by using combination of several Gaussian function that has different statistical properties, the best feature representation can be model using probability density function. The recognition process is performed using maximum likelihood value computed using pre-calculate GMM components. The method is tested using FERET data sets and is able to achieved 92% recognition rates.

Keywords: local features modelling, face recognition system, Gaussian mixture models, Feret

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Authors: Bernardo C. P. Albuquerque, Darym J. F. Campos

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Increasing our ability to solve complex engineering problems is directly related to the processing capacity of computers. By means of such equipments, one is able to fast and accurately run numerical algorithms. Besides the increasing interest in numerical simulations, probabilistic approaches are also of great importance. This way, statistical tools have shown their relevance to the modelling of practical engineering problems. In general, statistical approaches to such problems consider that the random variables involved follow a normal distribution. This assumption tends to provide incorrect results when skew data is present since normal distributions are symmetric about their means. Thus, in order to visualize and quantify this aspect, 9 statistical distributions (symmetric and skew) have been considered to model a hypothetical slope stability problem. The data modeled is the friction angle of a superficial soil in Brasilia, Brazil. Despite the apparent universality, the normal distribution did not qualify as the best fit. In the present effort, data obtained in consolidated-drained triaxial tests and saturated direct shear tests have been modeled and used to analytically derive the probability density function (PDF) of the safety factor of a hypothetical slope based on Mohr-Coulomb rupture criterion. Therefore, based on this analysis, it is possible to explicitly derive the failure probability considering the friction angle as a random variable. Furthermore, it is possible to compare the stability analysis when the friction angle is modelled as a Dagum distribution (distribution that presented the best fit to the histogram) and as a Normal distribution. This comparison leads to relevant differences when analyzed in light of the risk management.

Keywords: statistical slope stability analysis, skew distributions, probability of failure, functions of random variables

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Authors: Jiahau Guo, Yihe Zhang

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This paper proposes solutions for pricing options on stocks paying discrete dividends in markets with daily price limits. We first extend the intraday density function of Guo and Chang (2020) to a multi-day one and use the framework of Haug et al. (2003) to value European options on stocks paying discrete dividends. Next, we adopt the fast Fourier transform (FFT) to derive accurate and efficient formulae for American options and further employ the three-point Richardson extrapolation to accelerate the computation. Finally, the accuracy of our proposed methods is verified by simulations.

Keywords: daily price limit, discrete dividend, early exercise, fast Fourier transform, multi-day density function, Richardson extrapolation

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Authors: Yun-Pang Flötteröd, Jakob Erdmann

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The human behaviors during evacuations are quite complex. One of the critical behaviors which affect the efficiency of evacuation is route choice. Therefore, the respective simulation modeling work needs to function properly. In this paper, Simulation of Urban Mobility’s (SUMO) current dynamic route modeling during evacuation, i.e. the rerouting functions, is examined with a real case study. The result consistency of the simulation and the reality is checked as well. Four influence factors (1) time to get information, (2) probability to cancel a trip, (3) probability to use navigation equipment, and (4) rerouting and information updating period are considered to analyze possible traffic impacts during the evacuation and to examine the rerouting functions in SUMO. Furthermore, some behavioral characters of the case study are analyzed with use of the corresponding detector data and applied in the simulation. The experiment results show that the dynamic route modeling in SUMO can deal with the proposed scenarios properly. Some issues and function needs related to route choice are discussed and further improvements are suggested.

Keywords: evacuation, microscopic traffic simulation, rerouting, SUMO

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