• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.397-404
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• 2005

In this note, we characterize the limiting diffusion of a diploid model by defining the discrete generator for the resealed Markov chain. We conclude that this limiting diffusion model is with uncountable state space and mutation selection and special 'mutation or gene conversion rate'.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.241-246
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• 2013

Choi [1] identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. In this note, we define the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. We show the martingale property on this operator and measure. Also we conclude that the martingale problem for diffusion operator of projection is well-posed.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1043-1048
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• 2011

W. Choi([1]) identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. We denote by F the homozygosity and by S the average selection intensity. In this note, we define the Fleming-Viot process with generator of limiting diffusion and provide exact result for the relations of F and S.

• Korean Journal of Animal Reproduction
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• v.13 no.1
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• pp.49-55
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• 1989

The Results of colchicine and pretreatment time have shown that the cells of Coho Salmon(Oncorhynchus Kisutch) were effectively injected 6 hours prior to the harvest at a final concentration of 10$\mu\textrm{g}$/g body weight. The cell-density from 8,000 cells/㎣ (=8${\times}$106 ml) was found as ideal. The best effect of hypotonic solution in proportion to the cell is 20 : 1 and 50 minutes. The model number of diploid chromosome in this species was 2n=60. The karyotype analysis proved that the diploid complement consisted of 19 pairs of metacentric-, 4 pairs of submetacentric- and 7 paris of acrocentric-chromosomes. The diagrammatic representation proved that the diploid complement consisted of 7 pairs of metacentric-, 2 pairs of submetacentric- and 1 pair of acrocentric-chromosomes.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.29-36
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• 2014

The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. and showed the martingale property on this operator and measure. Let $P_{\rho}$ be the unique solution of the martingale problem for $\mathcal{L}_0$ starting at ${\rho}$ and ${\pi}_1,{\pi}_2,{\cdots},{\pi}_n$ the projection of $E^n$ on $x_1,x_2,{\cdots},x_n$. In this note we define $$dQ_{\rho}=S_tdP_{\rho}$$ and show that $Q_{\rho}$ solves the martingale problem for $\mathcal{L}_{\pi}$ starting at ${\rho}$.

• Plant Biotechnology Reports
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• v.5 no.3
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• pp.265-271
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• 2011

The cultivated potato as well as its tuber-bearing relatives are considered model plants for cell and tissue culture, and therefore for exploiting the genetic variation induced by in vitro culture. The association between molecular stability and tissue culture in different genetic backgrounds and ploidy levels has already been explored. However, it still remains to be ascertained whether somaclonal variation differs between callus-derived chromosome-doubled and undoubled regenerants. Our research aimed at investigating, through amplified fragment length polymorphism (AFLP) markers, the genetic changes in marker-banding patterns of diploid and tetraploid regenerants obtained from one clone each of Solanum bulbocastanum Dunal and S. cardiophyllum Lindl (both 2n = 2x = 24) and tetraploids from cultivated S. tuberosum L. (2n = 4x = 48). Pairwise comparisons between the banding patterns of regenerants and parents allowed detecting considerable changes associated to in vitro culture both at diploid and tetraploid level. The percentages of polymorphic bands between diploid and tetraploid regenerants were, respectively, 57 and 69% in S. bulbocastanum and 58 and 63% in S. cardiophyllum. On average, the frequencies of lost parental fragments in regenerants were significantly higher than novel bands both in S. bulbocastanum (48 vs. 22%) and S. tuberosum (36 vs. 18%) regenerants. By contrast, in S. cardiophyllum, a similar incidence of the two events was detected (32 vs. 29%). Our results revealed that structural changes after tissue culture process strongly affected the genome of the species studied, but diploid and tetraploids regenerated plants responded equally.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.67-72
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• 2022

For a locus with two alleles (I^A and I^B), the frequencies of the alleles are represented by $$p=f(I^A)={\frac{2N_{AA}+N_{AB}}{2N},\;q=f(I^B)={\frac{2N_{BB}+N_{AB}}{2N}$$ where N_AA, N_AB and N_BB are the numbers of I^AI^A, I^AI^B and I^BI^B respectively and N is the total number of populations. The frequencies of the genotypes expected are calculated by using p², 2pq and q². Choi showed the method of whether some genotypes is in these probabalities. Also he calculate the probability generating function for offspring number of genotype under a diploid model( [1]). In this paper, let x(t, p) be the probability that I^A become fixed in the population by time t-th generation, given that its initial frequency at time t = 0 is p. We find adapted equations for x using the mean change of frequence of alleles and fitness of genotype. Also we apply this adapted equations to several diploid model and it also will apply to actual examples.

• Korean Journal of Microbiology
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• v.52 no.4
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• pp.406-414
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• 2016

Among 6 leu codons, CUG is the most frequently used codon in E. coli. It is recognized by leu-tRNA(CAG) encoded by four genes scattered on two chromosomal loci (leuT and leuPQV ). In the process of constructing a strain with no functional leu-tRNA (CAG) gene on chromosome, we made two mutant strains separately, one on leuPQV locus (${\Delta}leuPQV$), and the other on leuT locus [$leuT^*$(GAG)], where the anticodon of leuT was changed from CAG to GAG, thereby altering its recognition codon from CUG to CUC. We attempted to combine these two mutations by transduction using $leuT^*$(GAG) strain as a donor and ${\Delta}leuPQV$ strain as a recipient. Large and small colonies appeared from this transduction. From PCR and DNA sequencing, large colony was confirmed to be the reciprocal recombinant as expected, but the small colonies contained both mutant $leuT^*$(GAG) and wild type leuT (CAG) genes in the cell. This heterozygous diploid strain did not show any unusual morphology under microscopic observation, but, interestingly, it showed a linear growth curve in rich medium with much slower growth rate than wild type cell. It always formed homogenous small colonies in the selection medium, but, when there was no selection, it readily segregated into $leuT^*$(GAG) and leuT (CAG). From these observations, we suggested that the strain with both $leuT^*$(GAG) and leuT (CAG) genes was not a partial diploid (merodiploid), but a full diploid cell having two different chromosomes. We proposed a model explaining how such a heterozygous diploid cell was formed and how and why its growth showed a linear growth curve.

• Korean Journal of Environmental Biology
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• v.26 no.1
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• pp.1-7
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• 2008

A mathematical model for the synergistic interaction of physical and chemical environmental agents was suggested for quantitative prediction of irreversibly damaged cells after combined exposures. The model took into account the synergistic interaction of agents and was based on the supposition that additional effective damages responsible for the synergy are irreversible and originated from an interaction of ineffective sublesions. The experimental results regarding the irreversible component of radiation damage of diploid yeast cells simultaneous exposed to heat with ionizing radiation ($^{60}Co$) or UV light (254 nm) are presented. It was shown that the cell ability of the liquid holding recovery decreased with an increase in the temperature, at which the exposure was occurred. A good correspondence between experimental results and model prediction was demonstrated. The importance of the results obtained for the interpretation of the mechanism of synergistic interaction of various environmental factors is discussed.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.75-80
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• 2021

For a locus with two alleles (IA and IB), the frequencies of the alleles are represented by $$p=f(I^A)={\frac{2N_{AA}+N_{AB}}{2N} },\;q=f(I^B)={\frac{2N_{BB}+N_{AB}}{2N}}$$ where NAA, NAB and NBB are the numbers of IA IA, IA IB and IB IB respectively and N is the total number of populations. The frequencies of the genotypes expected are calculated by using p2, 2pq and q2. So in this paper, we consider the method of whether some genotypes is in Hardy-Weinburg equilibrium. Also we calculate the probability generating function for the offspring number of genotype produced by a mating of the ith male and jth female under a diploid model of N population with N1 males and N2 females. Finally, we have conditional joint probability generating function of genotype frequencies.