• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.457-467
• /
• 2013

There exist many deterministic models for signaling pathways in systems biology. However the models do not consider the stochastic properties of the pathways, which means the models fit well with experimental data in certain situations but poorly in others. Incorporating stochasticity into deterministic models is one way to handle this problem. In this paper the way is used to produce stochastic models based on the deterministic differential equations for the published extracellular signal-regulated kinase (ERK) pathway. We consider strong convergence and stability of the numerical approximations for the stochastic models.

• Structural Engineering and Mechanics
• /
• v.34 no.1
• /
• pp.15-38
• /
• 2010

In order to predict the shear strengths of reinforced concrete beams, many deterministic models have been developed based on rules of mechanics and on experimental test results. While the constant and variable angle truss models are known to provide reliable bases and to give reasonable predictions for the shear strengths of members with shear reinforcement, in the case of members without shear reinforcement, even advanced models with complicated procedures may show lack of accuracy or lead to fairly different predictions from other similar models. For this reason, many research efforts have been made for more accurate predictions, which resulted in important recent publications. This paper develops probabilistic shear strength models for reinforced concrete beams without shear reinforcement based on deterministic shear strength models, understanding of shear transfer mechanisms and influential parameters, and experimental test results reported in the literature. Using a Bayesian parameter estimation method, the biases of base deterministic models are identified as algebraic functions of input parameters and the errors of the developed models remaining after the bias-correction are quantified in a stochastic manner. The proposed probabilistic models predict the shear strengths with improved accuracy and help incorporate the model uncertainties into vulnerability estimations and risk-quantified designs.

• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.45-67
• /
• 2021

In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

• Korean Journal of Mathematics
• /
• v.22 no.3
• /
• pp.529-552
• /
• 2014

As we know, some indices and data are strong influence to the price movement of some assets now, but not to another assets and in future. Thus we define some asset models for several time intervals; intraday, weekly, monthly, and yearly asset models. We define these asset models by using Brownian motion with volatility and Poisson process, and several deterministic functions(index function, twitter data function and big-jump simple function etc). In our asset models, these deterministic functions are the positive or negative levels of auxiliary indices, of analyzed data, and for imminent and extreme state(for example, financial shock or the highest popularity in the market). These functions determined by indices, twitter data and shocking news are a kind of one of speciality of our asset models. For reasonableness of our asset models, we introduce several real data, figurers and tables, and simulations. Perhaps from our asset models, for short-term or long-term investment, we can classify and reference many kinds of usual auxiliary indices, information and data.

• Proceedings of the IEEK Conference
• /
• 1999.11a
• /
• pp.569-572
• /
• 1999

In this paper we present a color image segmentation algorithm based on statistical models. A novel deterministic annealing Expectation Maximization(EM) formula is derived to estimate the parameters of the Gaussian Mixture Model(GMM) which represents the multi-colored objects statistically. The experimental results show that the proposed deterministic annealing EM is a global optimal solution for the ML parameter estimation and the image field is segmented efficiently by using the parameter estimates.

• Information and Communications Magazine
• /
• v.24 no.9
• /
• pp.77-85
• /
• 2007

최근 컴퓨터 발전에 따라 이동통신용 채널모델로 deterministic방법이 활발히 연구되고 있다. 이 방법은 기존의 stochastic방법과 달리 주어진 환경의 전파전파현상을 물리 이론을 바탕으로 정확하게 예측하는 것을 목적으로 한다. 그러므로 차세대 주파수 환경 분석과 같은 다양하고 새로운 분야에 적용가능하고 연구의 진전에 따라 모델의 정확도 및 신뢰도가 점점 높아지고 있다. 그러므로 본보에서는 현재까지의 연구 결과를 정리하고 방법의 장단점을 논한다.

• Journal of the Korean Statistical Society
• /
• v.30 no.4
• /
• pp.597-612
• /
• 2001

We have developed a \

• Journal of Intelligence and Information Systems
• /
• v.4 no.1
• /
• pp.133-147
• /
• 1998

Recently, many researchers have been involved in finding deterministic equations which can accurately predict future event, based on chaotic theory, or fractal theory. The theory says that some events which seem very random but internally deterministic can be accurately predicted by fractal equations. In contrast to the conventional methods, such as AR model, MA, model, or ARIMA model, the fractal equation attempts to discover a deterministic order inherent in time series data set. In discovering deterministic order, researchers have found that neural networks are much more effective than the conventional statistical models. Even though prediction accuracy of the network can be different depending on the topological structure and modification of the algorithms, many researchers asserted that the neural network systems outperforms other systems, because of non-linear behaviour of the network models, mechanisms of massive parallel processing, generalization capability based on adaptive learning. However, recent survey shows that prediction accuracy of the forecasting models can be determined by the model structure and data structures. In the experiments based on actual economic data sets, it was found that the prediction accuracy of the neural network model is similar to the performance level of the conventional forecasting model. Especially, for the data set which is deterministically chaotic, the AR model, a conventional statistical model, was not significantly different from the MLP model, a neural network model. This result shows that the forecasting model. This result shows that the forecasting model a, pp.opriate to a prediction task should be selected based on characteristics of the time series data set. Analysis of the characteristics of the data set was performed by fractal analysis, measurement of Hurst index, and measurement of Lyapunov exponents. As a conclusion, a significant difference was not found in forecasting future events for the time series data which is deterministically chaotic, between a conventional forecasting model and a typical neural network model.

• Journal of Korean Society of Transportation
• /
• v.8 no.1
• /
• pp.55-71
• /
• 1990

The behavioral mechanism underlying the traffic assignment model is a choice, or decision-making process of traveling paths between origins and destinations. The deterministic approach to traffic assignment assumes that travelers choose shortest path from their origin-destination pair. Although this assumption seems reasonable, it presumes that all travelers have perfect information regarding travel time, that they make consistently correct decision, and that they all behave in identical fashion. Stochastic user equilibrium assignment relaxes these presumptions by including a random component in traveler's perception of travel time. The objective of this study is to compare "A Model of Deterministic User Equilibrium Assignment" with "Models of Stochastic User Equilibrium Assignment" in the theoretical and practical aspects. Specifically, SUE models are developed to logit and probit based models according to discrete choice functions. The models were applied to sioux Falls net ork consisting of 24 zones, 24 nodes and 76 links. The distribution of perceived travel time was obtained by using the relationship between speed and traffic flow.

• Atmosphere
• /
• v.30 no.4
• /
• pp.405-420
• /
• 2020

In this study, we investigate the predictability of intraseasonal monthly temperature and precipitation variations using hindcast datasets from eight global circulation models participating in the operational multi-model ensemble (MME) seasonal prediction system of the Asia-Pacific Economic Cooperation Climate Center for the 1983~2010 period. These intraseasonal monthly variations are defined by categorical deterministic analysis. The monthly temperature and precipitation are categorized into above normal (AN), near normal (NN), and below normal (BN) based on the σ-value ± 0.43 after standardization. The nine patterns of intraseasonal monthly variation are defined by considering the changing pattern of the monthly categories for the three consecutive months. A deterministic and a probabilistic analysis are used to define intraseasonal monthly variation for the multi-model consisting of numerous ensemble members. The results show that a pattern (pattern 7), which has the same monthly categories in three consecutive months, is the most frequently occurring pattern in observation regardless of the seasons and variables. Meanwhile, the patterns (e.g., patterns 8 and 9) that have consistently increasing or decreasing trends in three consecutive months, such as BN-NN-AN or AN-NN-BN, occur rarely in observation. The MME and eight individual models generally capture pattern 7 well but rarely capture patterns 8 and 9.