• Proceedings of the KIEE Conference
• /
• 2005.11b
• /
• pp.230-233
• /
• 2005

This paper proposes power qualify assessment using Markov Chain applied to Ergodic theorem. The Ergodic theorem introduces the state of aperiodic, recurrent, and non-null. The proposed method using Markov Chain presents very well generated harmonic characteristics according to the traction's operation of electric railway system. In case of infinite iteration, the characteristic of Markov Chain that converges on limiting probability Is able to expected harmonic currents posterior transient state. TDD(Total Demand Distortion) is also analyzed in expected current of each harmonic. The TDD for power quality assesment is calculated using Markov Chain theory in the Inceon international airport IAT power system.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.1221-1248
• /
• 2022

In this paper we study the theory of knotoids and braidoids and the theory of pseudo knotoids and pseudo braidoids on the torus T. In particular, we introduce the notion of mixed knotoids in S², that generalizes the notion of mixed links in S³, and we present an isotopy theorem for mixed knotoids. We then generalize the Kauffman bracket polynomial, <; >, for mixed knotoids and we present a state sum formula for <; >. We also introduce the notion of mixed pseudo knotoids, that is, multi-knotoids on two components with some missing crossing information. More precisely, we present an isotopy theorem for mixed pseudo knotoids and we extend the Kauffman bracket polynomial for pseudo mixed knotoids. Finally, we introduce the theories of mixed braidoids and mixed pseudo braidoids as counterpart theories of mixed knotoids and mixed pseudo knotoids, respectively. With the use of the L-moves, that we also introduce here for mixed braidoid equivalence, we formulate and prove the analogue of the Alexander and the Markov theorems for mixed knotoids. We also formulate and prove the analogue of the Alexander theorem for mixed pseudo knotoids.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.983-992
• /
• 1996

Let p(x, dy) be a transition probability function on $(S, \rho)$, where S is a complete separable metric space. Then a Markov process $X_n$ which has p(x, dy) as its transition probability may be generated by random iterations of the form $X_{n+1} = f(X_n, \varepsilon_{n+1})$, where $\varepsilon_n$ is a sequence of independent and identically distributed random variables (See, e.g., Kifer(1986), Bhattacharya and Waymire(1990)).

• Proceedings of the IEEK Conference
• /
• summer
• /
• pp.259-262
• /
• 2004

In most of the character recognition systems, the method of template matching or statistical method using hidden Markov model is used to extract and recognize feature shapes. In this paper, we used modified chain-code which has 8-directions but 4-codes, and made the chain-code of hand-written character, after that, converted it into transition chain-code by applying to HMM(Hidden Markov Model). The transition chain code by HMM is analyzed as signal flow graph by Mason's theory which is generally used to calculate forward gain at automatic control system. If the specific forward gain and feedback gain is properly set, the forward gain of transition chain-code using Mason's theory can be distinguished depending on each object for recognition. This data of the gain is reorganized as tree structure, hence making it possible to distinguish different hand-written characters. With this method, $91\%$ recognition rate was acquired.

• Journal of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.713-725
• /
• 1998

Let X and Y be Ito processes with dX$_{s}$ = $\phi$$_{s}$dB$_{s}$ ＋ $\psi$$_{s}$ds and dY$_{s}$ = (equation omitted)dB$_{s}$ ＋ ξ$_{s}$ds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y$_{0}$│$\leq$│X$_{0}$│,│ζ│$\leq$│$\phi$│, │ξ│$\leq$│$\psi$│ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│$\leq$│$\psi$│ by a more general one │ξ│$\leq$$\alpha$ │$\psi$│ , where a $\geq$ 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a $\geq$ 0, extends the work by Burkholder.der.urkholder.der.

• Genomics & Informatics
• /
• v.10 no.2
• /
• pp.81-87
• /
• 2012

Large-scale copy number variants (CNVs) in the human provide the raw material for delineating population differences, as natural selection may have affected at least some of the CNVs thus far discovered. Although the examination of relatively large numbers of specific ethnic groups has recently started in regard to inter-ethnic group differences in CNVs, identifying and understanding particular instances of natural selection have not been performed. The traditional $F_{ST}$ measure, obtained from differences in allele frequencies between populations, has been used to identify CNVs loci subject to geographically varying selection. Here, we review advances and the application of multinomial-Dirichlet likelihood methods of inference for identifying genome regions that have been subject to natural selection with the $F_{ST}$ estimates. The contents of presentation are not new; however, this review clarifies how the application of the methods to CNV data, which remains largely unexplored, is possible. A hierarchical Bayesian method, which is implemented via Markov Chain Monte Carlo, estimates locus-specific $F_{ST}$ and can identify outlying CNVs loci with large values of FST. By applying this Bayesian method to the publicly available CNV data, we identified the CNV loci that show signals of natural selection, which may elucidate the genetic basis of human disease and diversity.