• Title/Summary/Keyword: selection probability

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A study on the validity of reference points for edentulous patient (무치악 환자를 위한 참고점들의 효용성에 대한 연구)

  • Park, Jeong-Jae;Kim, Myung-Joo
    • The Journal of Korean Academy of Prosthodontics
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    • v.53 no.4
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    • pp.310-317
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    • 2015
  • Purpose: The purpose of this study was to evaluate the validity of reference points for edentulous patient by examining the correlation of teeth and face, and intraoral anatomic landmarks. Materials and methods: We examined a facial outline, length, bizygomatic width, nasion - gnathion length, glabella - nasion distance in 270 men and 280 women satisfied with inclusion criteria from Seoul National School of Dentistry. The shape of maxillary central incisor, mesiodistal crown width and length of maxillary 6 incisors, distance from incisive papilla to labial surface of maxillary central incisor, and perpendicular distance from incisive papilla to intercanine line were measured in the stone model. We analyzed the ratio and relevant relation statistically. Results: The probability on having the same shape of face and the relative same shape maxillary incisor was 55.56% and 46.43% for men and women. The facial length proved to be a more valuable measurement in women in the tooth selection. The ratio of bizygomatic width to mesiodistal width of maxillary central incisor, and the ratio of bizygomatic width to width of maxillary 6 incisors were 16.8 : 1 and 3.0 : 1 and were positively correlated with each other. The distance of the canines from the maxillary incisal papilla was $1.33{\pm}1.28mm$. The distance between the center of the incisal papilla and the labial surface of their maxillary central incisor was $9.23{\pm}1.20mm$. Conclusion: It was showed that anatomical reference points in tooth selection and arrangement for edentulous patient are useful and have validity in our limited study.

Preliminary Inspection Prediction Model to select the on-Site Inspected Foreign Food Facility using Multiple Correspondence Analysis (차원축소를 활용한 해외제조업체 대상 사전점검 예측 모형에 관한 연구)

  • Hae Jin Park;Jae Suk Choi;Sang Goo Cho
    • Journal of Intelligence and Information Systems
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    • v.29 no.1
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    • pp.121-142
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    • 2023
  • As the number and weight of imported food are steadily increasing, safety management of imported food to prevent food safety accidents is becoming more important. The Ministry of Food and Drug Safety conducts on-site inspections of foreign food facilities before customs clearance as well as import inspection at the customs clearance stage. However, a data-based safety management plan for imported food is needed due to time, cost, and limited resources. In this study, we tried to increase the efficiency of the on-site inspection by preparing a machine learning prediction model that pre-selects the companies that are expected to fail before the on-site inspection. Basic information of 303,272 foreign food facilities and processing businesses collected in the Integrated Food Safety Information Network and 1,689 cases of on-site inspection information data collected from 2019 to April 2022 were collected. After preprocessing the data of foreign food facilities, only the data subject to on-site inspection were extracted using the foreign food facility_code. As a result, it consisted of a total of 1,689 data and 103 variables. For 103 variables, variables that were '0' were removed based on the Theil-U index, and after reducing by applying Multiple Correspondence Analysis, 49 characteristic variables were finally derived. We build eight different models and perform hyperparameter tuning through 5-fold cross validation. Then, the performance of the generated models are evaluated. The research purpose of selecting companies subject to on-site inspection is to maximize the recall, which is the probability of judging nonconforming companies as nonconforming. As a result of applying various algorithms of machine learning, the Random Forest model with the highest Recall_macro, AUROC, Average PR, F1-score, and Balanced Accuracy was evaluated as the best model. Finally, we apply Kernal SHAP (SHapley Additive exPlanations) to present the selection reason for nonconforming facilities of individual instances, and discuss applicability to the on-site inspection facility selection system. Based on the results of this study, it is expected that it will contribute to the efficient operation of limited resources such as manpower and budget by establishing an imported food management system through a data-based scientific risk management model.

Relationships on Magnitude and Frequency of Freshwater Discharge and Rainfall in the Altered Yeongsan Estuary (영산강 하구의 방류와 강우의 규모 및 빈도 상관성 분석)

  • Rhew, Ho-Sang;Lee, Guan-Hong
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.16 no.4
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    • pp.223-237
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    • 2011
  • The intermittent freshwater discharge has an critical influence upon the biophysical environments and the ecosystems of the Yeongsan Estuary where the estuary dam altered the continuous mixing of saltwater and freshwater. Though freshwater discharge is controlled by human, the extreme events are mainly driven by the heavy rainfall in the river basin, and provide various impacts, depending on its magnitude and frequency. This research aims to evaluate the magnitude and frequency of extreme freshwater discharges, and to establish the magnitude-frequency relationships between basin-wide rainfall and freshwater inflow. Daily discharge and daily basin-averaged rainfall from Jan 1, 1997 to Aug 31, 2010 were used to determine the relations between discharge and rainfall. Consecutive daily discharges were grouped into independent events using well-defined event-separation algorithm. Partial duration series were extracted to obtain the proper probability distribution function for extreme discharges and corresponding rainfall events. Extreme discharge events over the threshold 133,656,000 $m^3$ count up to 46 for 13.7y years, following the Weibull distribution with k=1.4. The 3-day accumulated rain-falls which occurred one day before peak discharges (1day-before-3day -sum rainfall), are determined as a control variable for discharge, because their magnitude is best correlated with that of the extreme discharge events. The minimum value of the corresponding 1day-before-3day-sum rainfall, 50.98mm is initially set to a threshold for the selection of discharge-inducing rainfall cases. The number of 1day-before-3day-sum rainfall groups after selection, however, exceeds that of the extreme discharge events. The canonical discriminant analysis indicates that water level over target level (-1.35 m EL.) can be useful to divide the 1day-before-3day-sum rainfall groups into discharge-induced and non-discharge ones. It also shows that the newly-set threshold, 104mm, can just separate these two cases without errors. The magnitude-frequency relationships between rainfall and discharge are established with the newly-selected lday-before-3day-sum rainfalls: $D=1.111{\times}10^8+1.677{\times}10^6{\overline{r_{3day}}$, (${\overline{r_{3day}}{\geqq}104$, $R^2=0.459$), $T_d=1.326T^{0.683}_{r3}$, $T_d=0.117{\exp}[0.0155{\overline{r_{3day}}]$, where D is the quantity of discharge, ${\overline{r_{3day}}$ the 1day-before-3day-sum rainfall, $T_{r3}$ and $T_d$, are respectively return periods of 1day-before-3day-sum rainfall and freshwater discharge. These relations provide the framework to evaluate the effect of freshwater discharge on estuarine flow structure, water quality, responses of ecosystems from the perspective of magnitude and frequency.

Assessment Study on Educational Programs for the Gifted Students in Mathematics (영재학급에서의 수학영재프로그램 평가에 관한 연구)

  • Kim, Jung-Hyun;Whang, Woo-Hyung
    • Communications of Mathematical Education
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    • v.24 no.1
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    • pp.235-257
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    • 2010
  • Contemporary belief is that the creative talented can create new knowledge and lead national development, so lots of countries in the world have interest in Gifted Education. As we well know, U.S.A., England, Russia, Germany, Australia, Israel, and Singapore enforce related laws in Gifted Education to offer Gifted Classes, and our government has also created an Improvement Act in January, 2000 and Enforcement Ordinance for Gifted Improvement Act was also announced in April, 2002. Through this initiation Gifted Education can be possible. Enforcement Ordinance was revised in October, 2008. The main purpose of this revision was to expand the opportunity of Gifted Education to students with special education needs. One of these programs is, the opportunity of Gifted Education to be offered to lots of the Gifted by establishing Special Classes at each school. Also, it is important that the quality of Gifted Education should be combined with the expansion of opportunity for the Gifted. Social opinion is that it will be reckless only to expand the opportunity for the Gifted Education, therefore, assessment on the Teaching and Learning Program for the Gifted is indispensible. In this study, 3 middle schools were selected for the Teaching and Learning Programs in mathematics. Each 1st Grade was reviewed and analyzed through comparative tables between Regular and Gifted Education Programs. Also reviewed was the content of what should be taught, and programs were evaluated on assessment standards which were revised and modified from the present teaching and learning programs in mathematics. Below, research issues were set up to assess the formation of content areas and appropriateness for Teaching and Learning Programs for the Gifted in mathematics. A. Is the formation of special class content areas complying with the 7th national curriculum? 1. Which content areas of regular curriculum is applied in this program? 2. Among Enrichment and Selection in Curriculum for the Gifted, which one is applied in this programs? 3. Are the content areas organized and performed properly? B. Are the Programs for the Gifted appropriate? 1. Are the Educational goals of the Programs aligned with that of Gifted Education in mathematics? 2. Does the content of each program reflect characteristics of mathematical Gifted students and express their mathematical talents? 3. Are Teaching and Learning models and methods diverse enough to express their talents? 4. Can the assessment on each program reflect the Learning goals and content, and enhance Gifted students' thinking ability? The conclusions are as follows: First, the best contents to be taught to the mathematical Gifted were found to be the Numeration, Arithmetic, Geometry, Measurement, Probability, Statistics, Letter and Expression. Also, Enrichment area and Selection area within the curriculum for the Gifted were offered in many ways so that their Giftedness could be fully enhanced. Second, the educational goals of Teaching and Learning Programs for the mathematical Gifted students were in accordance with the directions of mathematical education and philosophy. Also, it reflected that their research ability was successful in reaching the educational goals of improving creativity, thinking ability, problem-solving ability, all of which are required in the set curriculum. In order to accomplish the goals, visualization, symbolization, phasing and exploring strategies were used effectively. Many different of lecturing types, cooperative learning, discovery learning were applied to accomplish the Teaching and Learning model goals. For Teaching and Learning activities, various strategies and models were used to express the students' talents. These activities included experiments, exploration, application, estimation, guess, discussion (conjecture and refutation) reconsideration and so on. There were no mention to the students about evaluation and paper exams. While the program activities were being performed, educational goals and assessment methods were reflected, that is, products, performance assessment, and portfolio were mainly used rather than just paper assessment.

Serological Approach for Selection of Bradyrhizobium japonicum Strain with Superior Symbiotic Effectiveness (Bradyrhizobium japonicum의 공생효과(共生效果) 우수균주(優秀菌株) 선발(選拔)을 위한 면역혈청학적(免疫血淸學的) 접근(接近))

  • Kang, Ui-Gum;Ha, Ho-Sung;Park, Kyeong-Bae;Lee, Sang-Kyu;Lim, Dong-Kyu;Yang, Min-Suk
    • Korean Journal of Soil Science and Fertilizer
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    • v.29 no.2
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    • pp.165-172
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    • 1996
  • Symbiotic effectiveness and significance of Bradyrhizobium japonicum strains in five serogroups which were consisted of three corresponding serotype strains, respectively, indigenous to Korean soils were evaluated in terms of utility of strain serogroup for symbiotic improvement on soybean plant. The nodulation by rhizobia of each serogroup on four soybean cultivars(Danweonkong, Kwangkyo, Pangsakong, and Eunhakong) was good in order of USDA 123 > YCK 150 > YCK 117 > YCK 141 > USDA 110 serogroup members. Shoot dry weight of soybean was relatively high with USDA 110 serogroup members as well as with YCK 141 serogroup members, whereas the effectiveness of USDA 123 serogroup members was the lowest among the serogroups examined. In particular, Pangsakong among soybeans inoculated with five-serogroup members was positively outstanding on nodulation and shoot dry weight of the plant. Overall, symbiotic parameters of serogroup members associated with soybean plant such as nodule number, nodule mass, $N_2$ase activity, and shoot dry weight showed significantly different responses at level of 1% probability among both rhizobial serogroups and soybean cultivars, respectively. The rate in symbiotic similarity of the members of each serogroup from F-test ($$P{\leq_-}0.05$$) was 100% for nodule No., 90% for $N_2$ase activity. and 80% for soybean shoot dry weight. Taken together, the results indicated that the serological grouping of B. japonicum could be strongly useful for improving the symbiotic effectiveness hetween soybean and Rhizobium.

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A prognosis discovering lethal-related genes in plants for target identification and inhibitor design (식물 치사관련 유전자를 이용하는 신규 제초제 작용점 탐색 및 조절물질 개발동향)

  • Hwang, I.T.;Lee, D.H.;Choi, J.S.;Kim, T.J.;Kim, B.T.;Park, Y.S.;Cho, K.Y.
    • The Korean Journal of Pesticide Science
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    • v.5 no.3
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    • pp.1-11
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    • 2001
  • New technologies will have a large impact on the discovery of new herbicide site of action. Genomics, combinatorial chemistry, and bioinformatics help take advantage of serendipity through tile sequencing of huge numbers of genes or the synthesis of large numbers of chemical compounds. There are approximately $10^{30}\;to\;10^{50}$ possible molecules in molecular space of which only a fraction have been synthesized. Combining this potential with having access to 50,000 plant genes in the future elevates tile probability of discovering flew herbicidal site of actions. If 0.1, 1.0 or 10% of total genes in a typical plant are valid for herbicide target, a plant with 50,000 genes would provide about 50, 500, and 5,000 targets, respectively. However, only 11 herbicide targets have been identified and commercialized. The successful design of novel herbicides depends on careful consideration of a number of factors including target enzyme selections and validations, inhibitor designs, and the metabolic fates. Biochemical information can be used to identify enzymes which produce lethal phenotypes. The identification of a lethal target site is an important step to this approach. An examination of the characteristics of known targets provides of crucial insight as to the definition of a lethal target. Recently, antisense RNA suppression of an enzyme translation has been used to determine the genes required for toxicity and offers a strategy for identifying lethal target sites. After the identification of a lethal target, detailed knowledge such as the enzyme kinetics and the protein structure may be used to design potent inhibitors. Various types of inhibitors may be designed for a given enzyme. Strategies for the selection of new enzyme targets giving the desired physiological response upon partial inhibition include identification of chemical leads, lethal mutants and the use of antisense technology. Enzyme inhibitors having agrochemical utility can be categorized into six major groups: ground-state analogues, group specific reagents, affinity labels, suicide substrates, reaction intermediate analogues, and extraneous site inhibitors. In this review, examples of each category, and their advantages and disadvantages, will be discussed. The target identification and construction of a potent inhibitor, in itself, may not lead to develop an effective herbicide. The desired in vivo activity, uptake and translocation, and metabolism of the inhibitor should be studied in detail to assess the full potential of the target. Strategies for delivery of the compound to the target enzyme and avoidance of premature detoxification may include a proherbicidal approach, especially when inhibitors are highly charged or when selective detoxification or activation can be exploited. Utilization of differences in detoxification or activation between weeds and crops may lead to enhance selectivity. Without a full appreciation of each of these facets of herbicide design, the chances for success with the target or enzyme-driven approach are reduced.

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A Regression-Model-based Method for Combining Interestingness Measures of Association Rule Mining (연관상품 추천을 위한 회귀분석모형 기반 연관 규칙 척도 결합기법)

  • Lee, Dongwon
    • Journal of Intelligence and Information Systems
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    • v.23 no.1
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    • pp.127-141
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    • 2017
  • Advances in Internet technologies and the proliferation of mobile devices enabled consumers to approach a wide range of goods and services, while causing an adverse effect that they have hard time reaching their congenial items even if they devote much time to searching for them. Accordingly, businesses are using the recommender systems to provide tools for consumers to find the desired items more easily. Association Rule Mining (ARM) technology is advantageous to recommender systems in that ARM provides intuitive form of a rule with interestingness measures (support, confidence, and lift) describing the relationship between items. Given an item, its relevant items can be distinguished with the help of the measures that show the strength of relationship between items. Based on the strength, the most pertinent items can be chosen among other items and exposed to a given item's web page. However, the diversity of the measures may confuse which items are more recommendable. Given two rules, for example, one rule's support and confidence may not be concurrently superior to the other rule's. Such discrepancy of the measures in distinguishing one rule's superiority from other rules may cause difficulty in selecting proper items for recommendation. In addition, in an online environment where a web page or mobile screen can provide a limited number of recommendations that attract consumer interest, the prudent selection of items to be included in the list of recommendations is very important. The exposure of items of little interest may lead consumers to ignore the recommendations. Then, such consumers will possibly not pay attention to other forms of marketing activities. Therefore, the measures should be aligned with the probability of consumer's acceptance of recommendations. For this reason, this study proposes a model-based approach to combine those measures into one unified measure that can consistently determine the ranking of recommended items. A regression model was designed to describe how well the measures (independent variables; i.e., support, confidence, and lift) explain consumer's acceptance of recommendations (dependent variables, hit rate of recommended items). The model is intuitive to understand and easy to use in that the equation consists of the commonly used measures for ARM and can be used in the estimation of hit rates. The experiment using transaction data from one of the Korea's largest online shopping malls was conducted to show that the proposed model can improve the hit rates of recommendations. From the top of the list to 13th place, recommended items in the higher rakings from the proposed model show the higher hit rates than those from the competitive model's. The result shows that the proposed model's performance is superior to the competitive model's in online recommendation environment. In a web page, consumers are provided around ten recommendations with which the proposed model outperforms. Moreover, a mobile device cannot expose many items simultaneously due to its limited screen size. Therefore, the result shows that the newly devised recommendation technique is suitable for the mobile recommender systems. While this study has been conducted to cover the cross-selling in online shopping malls that handle merchandise, the proposed method can be expected to be applied in various situations under which association rules apply. For example, this model can be applied to medical diagnostic systems that predict candidate diseases from a patient's symptoms. To increase the efficiency of the model, additional variables will need to be considered for the elaboration of the model in future studies. For example, price can be a good candidate for an explanatory variable because it has a major impact on consumer purchase decisions. If the prices of recommended items are much higher than the items in which a consumer is interested, the consumer may hesitate to accept the recommendations.

Decision Making on the Non surgical, Surgical Treatment on Chronic Adult Periodontitis (만성 성인성 치주염 치료시 비외과적, 외과적 방법에 대한 의사결정)

  • Song, Si-Eun;Li, Seung-Won;Cho, Kyoo-Sung;Chai, Jung-Kiu;Kim, Chong-Kwan
    • Journal of Periodontal and Implant Science
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    • v.28 no.4
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    • pp.645-660
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    • 1998
  • The purpose of this study was to make and ascertain a decision making process on the base of patient-oriented utilitarianism in the treatment of patients of chronic adult periodontitis. Fifty subjects were chosen in Yonsei Dental hospital and the other fifty were chosen in Severance dental hospital according to the selection criteria. Fifty four patients agreed in this study. NS group(N=32) was treated with scaling and root planing without any surgical intervention, the other S group(N=22) done with flap operation. During the active treatment and healing time, all patients of both groups were educated about the importance of oral hygiene and controlled every visit to the hospital. When periodontal treatment needed according to the diagnostic results, some patients were subjected to professional tooth cleaning and scaling once every 3 months according to an individually designed oral hygienic protocol. Probing depth was recorded on baseline and 18 months after treatments. A questionnaire composed of 6 kinds(hygienic easiness, hypersensitivity, post treatment comfort, complication, functional comfort, compliance) of questions was delivered to each patient to obtain the subjective evaluation regarding the results of therapy. The decision tree for the treatment of adult periodontal disease was made on the result of 2 kinds of periodontal treatment and patient's ubjective evaluation. The optimal path was calculated by using the success rate of the results as the probability and utility according to relative value and the economic value in the insurance system. The success rate to achieve the diagnostic goal of periodontal treatment as the remaining pocket depth less than 3mm and without BOP was $0.83{\pm}0.12$ by non surgical treatment and $0.82{\pm}0.14$ by surgical treatment without any statistically significant difference. The moderate success rate of more than 4mm probing pocket depth were 0.17 together. The utilities of non-surgical treatment results were 100 for a result with less than 3mm probing pocket depth, 80 for the other results with more than 4mm probing pocket depth, 0 for the extraction. Those of surgical treatment results were the same except 75 for the results with more than 4mm. The pooling results of subjective evaluation by using a questionnaire were 60% for satisfaction level and 40% for no satisfaction level in the patient group receiving nonsurgical treatment and 33% and 67% in the other group receiving surgical treatment. The utilities for 4 satisfaction levels were 100, 75, 60, 50 on the base of that the patient would express the satisfaction level with normal distribution. The optimal path of periodontal treatment was rolled back by timing the utility on terminal node and the success rate, the distributed ratio of patient's satisfaction level. Both results of the calculation was non surgical treatment. Therefore, it can be said that non-surgical treatment may be the optimal path for this decision tree of treatment protocol if the goal of the periodontal treatment is to achieve the remaining probing pocket depth of less than 3mm for adult chronic periodontitis and if the utilitarian philosophy to maximise the expected utility for the patients is advocated.

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A Comparative Study of Health Behaviors by Chronic Diseases of the Low-income Middle-aged People in Seoul's Apartment Residents (서울시 임대아파트에 거주하는 일부 저소득 중장년의 만성질병별 건강행태 비교연구)

  • Yang, Junmo;Park, Haemo;Lee, Sundong
    • Journal of Society of Preventive Korean Medicine
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    • v.18 no.2
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    • pp.11-30
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    • 2014
  • Objective : To compare the differences in health behaviors by chronic diseases of middle-aged living in Seoul's low-income housing Method : Of the 1469 residents aged 35 to 60 living in low-income housing in Seoul's District A, 318 were equal probability of selection method selected. t-test, ANOVA, $x^2$, OR(95% CI, P-value) were selected to analyze the data, and the confidence interval was 5%. Results : There were no significant differences in all health behaviors by vascular and metabolic, But there was a statistically significant difference for gastrointestinal diseases caused by sleep hours(p=0.001), liver diseases caused by smoking, drinking and sleep hours(p=0.004, p=0.001, and p=0.033, respectively), musculoskeletal diseases caused by sleep hours and health exam(p=0.0000 and p=0.002, respectively). Also, statistically significant differences were found for tumors caused by sleep hours(p=0.004), depression by the sleep hours and health exam(p=0.001 and p=0.013, respectively), allergies by in sleep hours(p=0.004), thyroid diseases by smoking and health exam(p=0.013 and p=0.007, respectively). After adjusting for the confounding factors for diseases, OR was obtained for each health behavior. There were no statistically significant differences in all health behaviors for vascular, metabolic, and tumors. However, the OR for gastrointestinal diseases 4.10(1.63-10.36, 0.0028) and 2.96(1.05-8.41, 0.0041) at 5-7 and 7-9 sleep hours. The OR for liver diseases was 3.13(1.03-9.48, 0.0437) at 7-9 sleep hours, the OR values for musculoskeletal diseases were 2.91(1.23-6.88, 0.00149), and 4.46(1.68-11.86, 0.0027) at 5-7 and 7-9 sleep hours. OR for depression were 4.82(1.70-13.66, 0.0031) and 4.13(1.19-14.31, 0.0026) at 5-7 and 7-9 sleep hours. OR for allergy were 2.78(1.22-6.32, 0.0015) and 3.93(1.49-10.39, 0.0058) at 5-7 and 7-9 sleep hours. There were statistical significances for liver diseases for 1-2 times of health exam at 0.35(0.14-0.90, 0.00301), for liver diseases for 1-2 times of health exam at 0.35(0.14-0.90, 0.00301), for musculoskeletal diseases for 3-4 times of health exam at 0.26(0.09-0.79, 0.0175), for depression for 3-4 times of health exam at 0.17(0.04-0.66, 0.0106), for allergies for 1-2 times of health exam at 0.30(0.13-0.70, 0.0055), and for thyroid diseases for 1-2 times and annually of health exam at 0.07(0.01-0.60, 0.00154), 0.09(0.01-0.96, 0.0461). We known significant difference the health behaviors by the diseases. especially in sleep hours and health exam times Conclusion : Only sleep hours and health exam caused statistically significant differences in chronic diseases. but the sleep hours was postitively correlated with the risk of disease, while health exam were inversely related.

A Review of the Neurocognitive Mechanisms for Mathematical Thinking Ability (수학적 사고력에 관한 인지신경학적 연구 개관)

  • Kim, Yon Mi
    • Korean Journal of Cognitive Science
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    • v.27 no.2
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    • pp.159-219
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    • 2016
  • Mathematical ability is important for academic achievement and technological renovations in the STEM disciplines. This study concentrated on the relationship between neural basis of mathematical cognition and its mechanisms. These cognitive functions include domain specific abilities such as numerical skills and visuospatial abilities, as well as domain general abilities which include language, long term memory, and working memory capacity. Individuals can perform higher cognitive functions such as abstract thinking and reasoning based on these basic cognitive functions. The next topic covered in this study is about individual differences in mathematical abilities. Neural efficiency theory was incorporated in this study to view mathematical talent. According to the theory, a person with mathematical talent uses his or her brain more efficiently than the effortful endeavour of the average human being. Mathematically gifted students show different brain activities when compared to average students. Interhemispheric and intrahemispheric connectivities are enhanced in those students, particularly in the right brain along fronto-parietal longitudinal fasciculus. The third topic deals with growth and development in mathematical capacity. As individuals mature, practice mathematical skills, and gain knowledge, such changes are reflected in cortical activation, which include changes in the activation level, redistribution, and reorganization in the supporting cortex. Among these, reorganization can be related to neural plasticity. Neural plasticity was observed in professional mathematicians and children with mathematical learning disabilities. Last topic is about mathematical creativity viewed from Neural Darwinism. When the brain is faced with a novel problem, it needs to collect all of the necessary concepts(knowledge) from long term memory, make multitudes of connections, and test which ones have the highest probability in helping solve the unusual problem. Having followed the above brain modifying steps, once the brain finally finds the correct response to the novel problem, the final response comes as a form of inspiration. For a novice, the first step of acquisition of knowledge structure is the most important. However, as expertise increases, the latter two stages of making connections and selection become more important.