• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.239-250
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• 2014

Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim$_RH_I^i(M){\leq}k$ for ${\forall}i$ < t, then $$\displaystyle\bigcup_{i=0}^{j}(Ass_RH_I^i(M))_{{\geq}k}=\displaystyle\bigcup_{i=0}^{j}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$$ for ${\forall}j{\leq}t$ and ${\forall}n$ >0. This shows that${\bigcup}_{n>0}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$ is a finite set for ${\forall}i{\leq}t$. Also, we prove that $\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1^{n_1},x_2^{n_2},{\ldots},x_i^{n_i})M)_{{\geq}k}=\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1,x_2,{\ldots},x_i)M)_{{\geq}k}$ if $x_1,x_2,{\ldots},x_r$ is M-sequences in dimension > k and $n_1,n_2,{\ldots},n_r$ are some positive integers. Here, for a subset T of Spec(R), set $T_{{\geq}i}=\{{p{\in}T{\mid}dimR/p{\geq}i}\}$.

• 한국경영정보학회:학술대회논문집
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• 2007.06a
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• pp.608-613
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• 2007

Prediction of corporate bankruptcies has long been an important topic and has been studied extensively in the finance and management literature because it is an essential basis for the risk management of financial institutions. Recently, support vector machines (SVMs) are becoming popular as a tool for bankruptcy prediction because they use a risk function consisting of the empirical error and a regularized term which is derived from the structural risk minimization principle. In addition, they don't require huge training samples and have little possibility of overfitting. However. in order to Use SVM, a user should determine several factors such as the parameters ofa kernel function, appropriate feature subset, and proper instance subset by heuristics, which hinders accurate prediction results when using SVM In this study, we propose a novel hybrid SVM classifier with simultaneous optimization of feature subsets, instance subsets, and kernel parameters. This study introduces genetic algorithms (GAs) to optimize the feature selection, instance selection, and kernel parameters simultaneously. Our study applies the proposed model to the real-world case for bankruptcy prediction. Experimental results show that the prediction accuracy of conventional SVM may be improved significantly by using our model.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.569-572
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• 2002

Terra MODIS is one of the few space-borne sensors currently capable of acquiring radiometric data over the range of view angles. Institute of Industrial Science, University of Tokyo, has been receiving Terra MODIS data at Tokyo since May 2001 and Asian Institute of Technology at Bangkok since May 2001. They can cover whole East Asia and is expected to monitor environmental changes regularly such as deforestation, forest fires, floods and typhoon. Over eight hundred scenes have been archived in the storage system and they occupy 2 TB of disk space so far. In this study, MODIS data processing system on WWW is developed including following functions: spectral subset (250m, 500m, 1000m channels), radiometric correction to radiance, spatial subset of geocoded data as a rectangular area with latitude-longitude grid system in HDF format, generation of a quick look file in JPEG format. Users will be notified just after all the process have finished via e-mail. Using this system enables us to process MODIS data on WWW with a few input parameters and download the processed data by FTP access. An easy to use interface is expected to promote the use of MODIS data. This system is available via the Internet on the following URL from September 1 2002, "http : //webmodis.iis.u-tokyo.ac.jp/".

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1031-1054
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• 2010

Let $\mathbb{Z}^n$ be the Cartesian product of the set of integers $\mathbb{Z}$ and let ($\mathbb{Z}$, T) and ($\mathbb{Z}^n$, $T^n$) be the Khalimsky line topology on $\mathbb{Z}$ and the Khalimsky product topology on $\mathbb{Z}^n$, respectively. Then for a set $X\;{\subset}\;\mathbb{Z}^n$, consider the subspace (X, $T^n_X$) induced from ($\mathbb{Z}^n$, $T^n$). Considering a k-adjacency on (X, $T^n_X$), we call it a (computer topological) space with k-adjacency and use the notation (X, k, $T^n_X$) := $X_{n,k}$. In this paper we introduce the notions of KD-($k_0$, $k_1$)-homotopy equivalence and KD-k-deformation retract and investigate a classification of (computer topological) spaces $X_{n,k}$ in terms of a KD-($k_0$, $k_1$)-homotopy equivalence.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.

• IMMUNE NETWORK
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• v.3 no.2
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• pp.89-95
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• 2003

Background: Unusually high amounts of N region addition and CDR3 length diversity were found in immunoglobulin (Ig) light chain Vk and Jk joins in patients with rheumatoid arthritis (RA). We sought to determine whether this finding is due to excessive activity of the enzyme responsible for N region addition (terminal deoxynucleotidyl transferase [TdT]) in B lineage cells in bone marrow or from positive antigenic selection of B cells with long CDR3 lengths. Methods: We used FACS to isolate $IgM^+/IgD^+$ B cells (predominantly naive) and $IgM^-/IgD^-$ B cells (predominantly class-switched) B cells from peripheral blood of a patient with RA known to have enrichment for long Vk CDR3s and from that of two normal controls. RT-PCR of VkIII transcripts was performed, followed by sequencing of individual cDNA clones. We analyzed the CDR3 lengths and N region additions in 97 clones. Results: There was enrichment for long CDR3 lengths (11 or 12 amino acids) in both $IgM^+/IgD^+$ and $IgM^-/IgD^-$ B cells in RA compared to B cell subsets in the normal controls. The $IgM^+/IgD^+$ B cell subset in RA was markedly enriched for N region addition and was similar to that seen in the $IgM^-/IgD^-$ subset. Conclusion: These data suggest that enrichment for N region addition and long CDR3 lengths in RA may result from unusually high or prolonged activity of TdT in bone marrow.

• Communications of Mathematical Education
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• v.5
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• pp.523-523
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• 1997

Suppose that G is a group of permutations of a set ${\Omega}$. For a finite subset ${\gamma}$of${\Omega}$, the movement of ${\gamma}$ under the action of G is defined as move(${\gamma}$):=$max\limits_{g{\epsilon}G}|{\Gamma}^{g}{\backslash}{\Gamma}|$, and ${\gamma}$ will be said to have restricted movement if move(${\gamma}$)<|${\gamma}$|. Moreover if, for an infinite subset ${\gamma}$of${\Omega}$, the sets|{\Gamma}^{g}{\backslash}{\Gamma}| are finite and bounded as g runs over all elements of G, then we may define move(${\gamma}$)in the same way as for finite subsets. If move(${\gamma}$)${\leq}$m for all ${\gamma}$${\subseteq}$${\Omega}$, then G is said to have bounded movement and the movement of G move(G) is defined as the maximum of move(${\gamma}$) over all subsets ${\gamma}$ of ${\Omega}$. Having bounded movement is a very strong restriction on a group, but it is natural to ask just which permutation groups have bounded movement m. If move(G)=m then clearly we may assume that G has no fixed points is${\Omega}$, and with this assumption it was shown in [4, Theorem 1]that the number t of G=orbits is at most 2m-1, each G-orbit has length at most 3m, and moreover|${\Omega}$|${\leq}$3m+t-1${\leq}$5m-2. Moreover it has recently been shown by P. S. Kim, J. R. Cho and C. E. Praeger in [1] that essentially the only examples with as many as 2m-1 orbits are elementary abelian 2-groups, and by A. Gardiner, A. Mann and C. E. Praeger in [2,3]that essentially the only transitive examples in a set of maximal size, namely 3m, are groups of exponent 3. (The only exceptions to these general statements occur for small values of m and are known explicitly.) Motivated by these results, we would decide what role if any is played by primes other that 2 and 3 for describing the structure of groups of bounded movement.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.583-611
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• 1998

We consider a general class of real-valued Levy processes {X(t), $t\geq0$}, and obtain suitable large deviation results for the empiricals L(t, A) defined by $t^{-1}{\int^t}_01_A$(X(s)ds for t > 0 and a Borel subset A of R. These results are used to obtain the asymptotic behavior of P{Z(t) < a}, where Z(t) = $sup_{u\leqt}\midx(u)\mid$ as $t\longrightarrow\infty$, in terms of the rate function in the large deviation principle. A subclass of these processes is the Feller class: there exist nonrandom functions b(t) and a(t) > 0 such that {(X(t) - b(t))/a(t) : t > 0} is stochastically compact, i.e., each sequence has a weakly convergent subsequence with a nondegenerate limit. The stable processes are in this class, but it is much larger. We consider processes in this class for which b(t) may be taken to be zero. For any t > 0, we consider the renormalized process ${X(u\psi(t))/a(\psi(t)),u\geq0}$, where $\psi$(t) = $t(log log t)^{-1}$, and obtain large deviation probability estimates for $L_{t}(A)$ := $(log log t)^{-1}$${\int_{0}}^{loglogt}1_A$$(X(u\psi(t))/a(\psi(t)))dv$. It turns out that the upper and lower bounds are sharp and depend on the entire compact set of limit laws of {X(t)/a(t)}. The results extend to random walks in the Feller class as well. Earlier results of this nature were obtained by Donsker and Varadhan for symmetric stable processes and by Jain for random walks in the domain of attraction of a stable law.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2003.10a
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• pp.101-106
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• 2003

In this paper, we propose using Hotelling's T2 statistic for the detection of a set of a set of differentially expressed (DE) genes in colorectal cancer based on its gene expression level in tumor tissues compared with those in normal tissues and to evaluate its predictivity which let us rank genes for the development of biomarkers for population screening of colorectal cancer. We compared the prediction rate based on the DE genes selected by Hotelling's T2 statistic and univariate t statistic using various prediction methods, a regulized discrimination analysis and a support vector machine. The result shows that the prediction rate based on T2 is better than that of univatiate t. This implies that it may not be sufficient to look at each gene in a separate universe and that evaluating combinations of genes reveals interesting information that will not be discovered otherwise.

• BMB Reports
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• v.47 no.5
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• pp.241-248
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• 2014

CD1 molecules belong to non-polymorphic MHC class I-like proteins and present lipid antigens to T cells. Five different CD1 genes (CD1a-e) have been identified and classified into two groups. Group 1 include CD1a-c and present pathogenic lipid antigens to ${\alpha}{\beta}$ T cells reminiscence of peptide antigen presentation by MHC-I molecules. CD1d is the only member of Group 2 and presents foreign and self lipid antigens to a specialized subset of ${\alpha}{\beta}$ T cells, NKT cells. NKT cells are involved in diverse immune responses through prompt and massive production of cytokines. CD1d-dependent NKT cells are categorized upon the usage of their T cell receptors. A major subtype of NKT cells (type I) is invariant NKT cells which utilize invariant $V{\alpha}14-J{\alpha}18$ TCR alpha chain in mouse. The remaining NKT cells (type II) utilize diverse TCR alpha chains. Engineered CD1d molecules with modified intracellular trafficking produce either type I or type II NKT cell-defects suggesting the lipid antigens for each subtypes of NKT cells are processed/generated in different intracellular compartments. Since the usage of TCR by a T cell is the result of antigen-driven selection, the intracellular metabolic pathways of lipid antigen are a key in forming the functional NKT cell repertoire.