• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.287-301
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• 2024

From the mathematical and statistical point of view, a segment of a DNA strand can be viewed as a sequence of four-state (A, C, G, T) trials. Herein, we consider the distributions of runs and patterns related to the run lengths of multi-state sequences, especially for four states (A, B, C, D). Let X₁, X₂, . . . be a sequence of four state independent and identically distributed trials taking values in the set 𝒢 = {A, B, C, D}. In this study, we obtain exact formulas for the probability distribution function for the discrete distribution of runs of B's of order k. We obtain longest run statistics, shortest run statistics, and determine the distributions of waiting times and run lengths.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.35-58
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• 2004

For fixed positive integers and $\textit{k}\;(n\;{\geq}\;{\textit{k}}\;+\;2)$, the exact probability distributions of non-overlapping and overlapping patterns of two failures separated by (i) exactly $textsc{k}$ successes, (ii) at least $\textit{k}$ successes and (iii) at most $\textit{k}$ successes have been obtained for Bernoulli independent and Markov dependent trials by using combinatorial technique. The waiting time distributions for the first occurrence and the $r^{th}$ (r > 1) occurrence of the patterns have also been obtained.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.5
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• pp.412-421
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• 2013

Motion picture industry is one of the most representative fields in the cultural industry and has experienced constant growth both worldwide and within domestic markets. However, little research has been undertaken for diffusion patterns of motion pictures, whereas various issues such as demand forecasting and success factor analysis have been widely explored. To analyze diffusion patterns, we adopted extended Bass model to reflect the potential demand of movies. Four clusters of selected movies were derived by k-means clustering method with criteria of opening strength and profitability and then compared by their diffusion patterns. Results indicated that movies with high profitability and medium opening strength are most significantly influenced by word of mouth effect, while low profitability movies display nearly monotonic decreasing diffusion patterns with noticeable initial adoption rates and relatively early peak points in their runs.

• KIPS Transactions on Software and Data Engineering
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• v.2 no.2
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• pp.119-122
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• 2013

Repetitive strings such as periods have been studied vigorously in so diverse fields as data compression, computer-assisted music analysis, bioinformatics, and etc. In bioinformatics, periods are highly related to repetitive patterns in DNA sequences so called tandem repeats. In some cases, quite similar but not the same patterns are repeated and thus we need approximate string matching algorithms to study tandem repeats in DNA sequences. In this paper, we propose a new definition of approximate periods of strings based on distance sum. Given two strings $p({\mid}p{\mid}=m)$ and $x({\mid}x{\mid}=n)$, we propose an algorithm that computes the minimum approximate period distance based on distance sum. Our algorithm runs in $O(mn^2)$ time for the weighted edit distance, and runs in O(mn) time for the edit distance, and runs in O(n) time for the Hamming distance.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.709-723
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• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• Animal Bioscience
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• v.37 no.8
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• pp.1355-1366
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• 2024

Objective: The analysis of runs of homozygosity (ROH) has been applied to assess the level of inbreeding and identify selection signatures in various livestock species. The objectives of this study were to characterize the ROH pattern, estimate the rate of inbreeding, and identify signatures of selection in the red-brown Korean native chickens. Methods: The Illumina 60K single nucleotide polymorphism chip data of 651 chickens was used in the analysis. Runs of homozygosity were analysed using the PLINK v1.9 software. Inbreeding coefficients were estimated using the GCTA software and their correlations were examined. Genomic regions with high levels of ROH were explored to identify selection signatures. Results: A total of 32,176 ROH segments were detected in this study. The majority of the ROH segments were shorter than 4 Mb. The average ROH inbreeding coefficients (F_ROH) varied with the length of ROH segments. The means of inbreeding coefficients calculated from different methods were also variable. The correlations between different inbreeding coefficients were positive and highly variable (r = 0.18-1). Five ROH islands harbouring important quantitative trait loci were identified. Conclusion: This study assessed the level of inbreeding and patterns of homozygosity in Red-brown native Korean chickens. The results of this study suggest that the level of recent inbreeding is low which indicates substantial progress in the conservation of red-brown Korean native chickens. Additionally, Candidate genomic regions associated with important production traits were detected in homozygous regions.

• Journal of Ecology and Environment
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• v.40 no.2
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• pp.107-119
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• 2016

Background: Previous studies on the biological integrity on habitat and landuse patterns demonstrated ecological stream health in the view of regional or macrohabitat scale, thus ignored the mesoscale habitat patterns of pool, riffle, and runs in the stream health analysis. The objective of this study was to analyze influences on the mesohabitat structures of pool, riffle, and run reaches on the fish guilds and biological integrity in Geum-River Watershed. Results: The mesohabitat structures of pool, riffle, and run reaches influenced the ecological stream health along with some close relations on the fish trophic and tolerance guilds. The mesoscale components altered chemical water quality such as nutrients (TN, TP) and BOD and these, then, determined the primary productions, based on the sestonic chlorophyll-a. The riffle-reach had good chemical conditions, but the pool-reach had nutrient enrichments. The riffle-reach had a predominance of insectivores, while the pool-reach has a predominance of omnivores. Also, the riffle-reach had high proportions of sensitive fish and insectivore fish, and the pool-reach had high proportions of tolerant species in the community composition. The intermediate fish species in tolerance and omnivorous fish species in the food linkage dominated the community in the watershed, and the sensitive and insectivorous fishes decreased rapidly with a degradation of the water quality. All the habitat patterns were largely determined by the land-use patterns in the watershed. Conclusions: Trophic guilds and tolerance guilds of fish were determined by land-use pattern and these determined the stream health, based on the Index of Biological Integrity. This study remarks the necessity to include additional variables to consider information provided by mesohabitats and land-use distributions within the selected stream stretch. Overall, our data suggest that land-use pattern and mesohabitat distribution are important factors to be considered for the trophic and tolerance fish compositions and chemical gradients as well as ecological stream health in the watershed.

• Proceedings of the Korea Society for Simulation Conference
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• 1994.10a
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• pp.32-32
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• 1994

In this example, a message passing based multicomputer system with general interdonnedtion network is considered. After multicomputer systems are developed with morm-hole routing network, topologies of interconecting network are not major considertion for process management and resource sharing. Tehre is an independeent operating system kernel oneach node. It communicates with other kernels using message passingmechanism. Based on this architecture, the problem is how mech does performance degradation will occur in the case of processor sharing on multicomputer systems. Processor sharing between application programs is veryimprotant decision on system performance. In almost cases, application programs running on massively parallel computer systems are not so much user-interactive. Thus, the main performance index is system throughput. Each application program has various communication patterns. and the sharing of processors causes serious performance degradation in hte worst case such that one processor is shared by two processes and another processes are waiting the messages from those processes. As a result, considering this problem is improtant since it gives the reason whether the system allows processor sharingor not. Input data has many parameters in this simulation . It contains the number of threads per task , communication patterns between threads, data generation and also defects in random inupt data. Many parallel aplication programs has its specific communication patterns, and there are computation and communication phases. Therefore, this phase informatin cannot be obtained random input data. If we get trace data from some real applications. we can simulate the problem more realistic . On the other hand, simualtion results will be waseteful unless sufficient trace data with varisous communication patterns is gathered. In this project , random input data are used for simulation . Only controllable data are the number of threads of each task and mapping strategy. First, each task runs independently. After that , each task shres one and more processors with other tasks. As more processors are shared , there will be performance degradation . Form this degradation rate , we can know the overhead of processor sharing . Process scheduling policy can affects the results of simulation . For process scheduling, priority queue and FIFO queue are implemented to support round-robin scheduling and priority scheduling.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.6
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• pp.1439-1450
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• 1995

Bellows is a familiar component in piping systems as it provides a relatively simple means of absorbing thermal expansion and providing system flexibility. In routine piping flexibility analysis by finite element methods, bellows is usually considered to be straight pipe runs modified by an appropriate flexibility factor; maximum stresses are evaluated using a corresponding stress concentration factor. The aim of this study is to develop a bellows finite element, which similarly includes more complex shell type deformation patterns. This element also does not require flexibility or stress factors, but evaluates more detailed deformation and stress patterns. The proposed bellows element is a 3-D, 2-noded line element, with three degrees of freedom per node and no bending. It is formulated by including additional 'internal' degrees of freedom to account for the deformation of the bellows corrugation; specifically a quarter toroidal section of the bellows, loaded by axial force, is considered and the shell type deformation of this is include by way of an approximating trigonometric series. The stiffness of each half bellows section may be found by minimising the potential energy of the section for a chosen deformation shape function. An experiment on the flexibility is performed to verify the reliability for bellows finite element.

• Journal of the Institute of Convergence Signal Processing
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• v.16 no.1
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• pp.9-14
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• 2015

Outlier detection and removal is a crucial step needed for various image processing applications such as image registration. Random Sample Consensus (RANSAC) is known to be the best algorithm so far for the outlier detection and removal. However RANSAC requires a cosiderable computation time. To drastically reduce the computation time while preserving the comparable quality, a outlier detection and removal method based on modified K-means is proposed. The original K-means was conducted first for matching point pairs and then cluster merging and member exclusion step are performed in the modification step. We applied the methods to various images with highly repetitive patterns under several geometric distortions and obtained successful results. We compared the proposed method with RANSAC and showed that the proposed method runs 3~10 times faster than RANSAC.