• Title/Summary/Keyword: Convergence in probability

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CONVERGENCE PROPERTIES FOR THE PARTIAL SUMS OF WIDELY ORTHANT DEPENDENT RANDOM VARIABLES UNDER SOME INTEGRABLE ASSUMPTIONS AND THEIR APPLICATIONS

  • He, Yongping;Wang, Xuejun;Yao, Chi
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.6
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    • pp.1451-1473
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    • 2020
  • Widely orthant dependence (WOD, in short) is a special dependence structure. In this paper, by using the probability inequalities and moment inequalities for WOD random variables, we study the Lp convergence and complete convergence for the partial sums respectively under the conditions of RCI(α), SRCI(α) and R-h-integrability. We also give an application to nonparametric regression models based on WOD errors by using the Lp convergence that we obtained. Finally we carry out some simulations to verify the validity of our theoretical results.

Optimization of Yonsei Single-Photon Emission Computed Tomography (YSECT) Detector for Fast Inspection of Spent Nuclear Fuel in Water Storage

  • Hyung-Joo Choi;Hyojun Park;Bo-Wi Cheon;Kyunghoon Cho;Hakjae Lee;Yong Hyun Chung;Yeon Soo Yeom;Sei Hwan You;Hyun Joon Choi;Chul Hee Min
    • Journal of Radiation Protection and Research
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    • v.49 no.1
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    • pp.29-39
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    • 2024
  • Background: The gamma emission tomography (GET) device has been reported a reliable technique to inspect partial defects within spent nuclear fuel (SNF) of pin-by-pin level. However, the existing GET devices have low accuracy owing to the high attenuation and scatter probability for SNF inspection condition. The purpose of this study is to design and optimize a Yonsei single-photon emission computed tomography version 2 (YSECT.v.2) for fast inspection of SNF in water storage by acquisition of high-quality tomographic images. Materials and Methods: Using Geant4 (Geant4 Collaboration) and DETECT-2000 (Glenn F. Knoll et al.) Monte Carlo simulation, the geometrical structure of the proposed device was determined and its performance was evaluated for the 137Cs source in water. In a Geant4-based assessment, proposed device was compared with the International Atomic Energy Agency (IAEA)-authenticated device for the quality of tomographic images obtained for 12 fuel sources in a 14 × 14 Westinghouse-type fuel assembly. Results and Discussion: According to the results, the length, slit width, and septal width of the collimator were determined to be 65, 2.1, and 1.5 mm, respectively, and the material and length of the trapezoidal-shaped scintillator were determined to be gadolinium aluminum gallium garnet and 45 mm, respectively. Based on the results of performance comparison between the YSECT.v.2 and IAEA's device, the proposed device showed 200 times higher performance in gamma-detection sensitivity and similar source discrimination probability. Conclusion: In this study, we optimally designed the GET device for improving the SNF inspection accuracy and evaluated its performance. Our results show that the YSECT.v.2 device could be employed for SNF inspection.

COMPLETE f-MOMENT CONVERGENCE FOR EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

  • Lu, Chao;Wang, Rui;Wang, Xuejun;Wu, Yi
    • Journal of the Korean Mathematical Society
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    • v.57 no.6
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    • pp.1485-1508
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    • 2020
  • In this paper, we investigate the complete f-moment convergence for extended negatively dependent (END, for short) random variables under sub-linear expectations. We extend some results on complete f-moment convergence from the classical probability space to the sub-linear expectation space. As applications, we present some corollaries on complete moment convergence for END random variables under sub-linear expectations.

A data extension technique to handle incomplete data (불완전한 데이터를 처리하기 위한 데이터 확장기법)

  • Lee, Jong Chan
    • Journal of the Korea Convergence Society
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    • v.12 no.2
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    • pp.7-13
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    • 2021
  • This paper introduces an algorithm that compensates for missing values after converting them into a format that can represent the probability for incomplete data including missing values in training data. In the previous method using this data conversion, incomplete data was processed by allocating missing values with an equal probability that missing variables can have. This method applied to many problems and obtained good results, but it was pointed out that there is a loss of information in that all information remaining in the missing variable is ignored and a new value is assigned. On the other hand, in the new proposed method, only complete information not including missing values is input into the well-known classification algorithm (C4.5), and the decision tree is constructed during learning. Then, the probability of the missing value is obtained from this decision tree and assigned as an estimated value of the missing variable. That is, some lost information is recovered using a lot of information that has not been lost from incomplete learning data.

Probabilistic Broadcasting Based on Selfishness and Additional Coverage in MANETs

  • Kim, Jae-Soo;Kim, Jeong-Hong
    • Journal of information and communication convergence engineering
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    • v.10 no.4
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    • pp.329-336
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    • 2012
  • For designing broadcast protocols in mobile ad hoc networks (MANETs), one of the important goals is to reduce the rebroadcast packets redundancy while reaching all the nodes in network. In this paper, we propose a probabilistic broadcasting mechanism based on selfishness and additional coverage in MANETs. Our approach dynamically adjusts the rebroadcast probability according to the extra covered area and number of neighbor nodes. By these two factors, mobile hosts can be classified into three groups: normal, low selfishness, and high selfishness groups. The nodes in the normal group forward packets for other nodes with high probability, whereas the nodes in the low selfishness group rebroadcast packets with low probability and the nodes in the high selfishness group do not rebroadcast packets. We compared our approach with simple flooding and the fixed probabilistic approach. The simulation results show that the proposed schemes can significantly reduce the number of retransmissions by up to 40% compared simple flooding and fixed probabilistic scheme without significant reduction in the network reachability and end-to-end packet delay.

Proportional Backoff Scheme for Data Services in TDMA-based Wireless Networks

  • Lim, In-Taek
    • Journal of information and communication convergence engineering
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    • v.8 no.6
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    • pp.660-664
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    • 2010
  • This paper proposes a backoff control scheme for guaranteeing fair packet transmissions in TDMA wireless networks. In order to maximize the system performance, the number of packets transmitted in a frame should be kept at a proper level. In the proposed scheme, the base station calculates the packet transmission probability according to the offered loads and then broadcasts to all the mobile stations. Mobile stations attempt to transmit a packet with the received probability. Simulation results show that the proposed scheme can offer better system throughput and delay performance than the conventional one regardless of the offered loads.

Approximated Outage Probability for ADF Relay Systems with Burst MPSK and MQAM Symbol Transmission

  • Ko, Kyunbyoung;Lim, Sungmook
    • International Journal of Contents
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    • v.11 no.1
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    • pp.7-14
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    • 2015
  • In this paper, we derive the outage probability for M-ary phase shifting keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) burst transmission (BT) of adaptive decode-and-forward (ADF) cooperative relay systems over quasi-static Rayleigh fading channels. Within a burst, there are pilot symbols and data symbols. Pilot symbols are used for channel estimation schemes and each relay node's transmission mode selection schemes. At first, we focus on ADF relay systems in which the probability density function (PDF) is derived on the basis of error events at relay nodes corresponding to channel estimation errors. Next, the average outage probability is derived as an approximate expression for an arbitrary link signal-to-noise ratio (SNR) for different modulation orders. Its accuracy is demonstrated by comparison with simulation results. Further, it is confirmed that BT-ADF relay systems with pilot symbol based channel estimation schemes enables to select correctly decoded relay nodes without additional signaling between relay nodes and the destination node, and it is verified that the ideal performance is achieved with small SNR loss.

Optimum Conditions of Adaptive Equalizers Based on Zero-Error Probability (영확률에 기반한 적응 이퀄라이져의 최적조건)

  • Kim, Namyong;Lee, Gyoo-Yeong
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.40 no.10
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    • pp.1865-1870
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    • 2015
  • In signal processing, the zero-error probability (ZEP) criterion and related algorithm (MZEP) outperforms MSE-based algorithms and yields superior and stable convergence in impulsive noise environment. In this paper, the analysis of the relationship with MSE criterion proves that ZEP criterion has equivalent optimum solution of MSE criterion. Also this work reveals that the magnitude controlled input of MZEP algorithm plays the role in keeping the optimum solution undisturbed from impulsive noise.

THE WEAK LAW OF LARGE NUMBERS FOR RANDOMLY WEIGHTED PARTIAL SUMS

  • Kim, Tae-Sung;Choi, Kyu-Hyuck;Lee, Il-Hyun
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.273-285
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    • 1999
  • In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.

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A Methodology to Evaluate Industry Convergence Using the Patent Information : Technology Relationship analysis (특허정보를 활용한 산업융합성 평가 방법론 : 기술연관분석)

  • Kim, Jeeeun;Lee, Sungjoo
    • Journal of Korean Institute of Industrial Engineers
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    • v.39 no.3
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    • pp.212-221
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    • 2013
  • As the convergence among technologies is reorganizing industry sectors, it is quite important to evaluate the probability of technological convergence, and to analyze how the technologies in a certain industry sector affect the same or other industry sectors. As a result, the large number of studies have been focused on the industry convergence. However, most of them have dealt mainly with case studies or strategy and policies and few efforts have been made to study it using quantitative data. The investigation of industry convergence using quantitative data will help understand the characteristics of industry and forecast the future of the industry from an objective point of view. Therefore, this research proposes a methodology to evaluate the possibilities of industry convergence using patent data. In particular, we emphasize the possibilities of technology convergence and suggest a technology relationship matrix to evaluate the technology convergence, as an antecedent of industry convergence. The feasibility and utility of the suggested methodology was verified with a case study on the convergence of IT and BT. The research results are expected to provide a useful guideline for developing a measure of convergence.