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Estimation of GARCH Models and Performance Analysis of Volatility Trading System using Support Vector Regression (Support Vector Regression을 이용한 GARCH 모형의 추정과 투자전략의 성과분석)

  • Kim, Sun Woong;Choi, Heung Sik
    • Journal of Intelligence and Information Systems
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    • v.23 no.2
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    • pp.107-122
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    • 2017
  • Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.

A study of the plan dosimetic evaluation on the rectal cancer treatment (직장암 치료 시 치료계획에 따른 선량평가 연구)

  • Jeong, Hyun Hak;An, Beom Seok;Kim, Dae Il;Lee, Yang Hoon;Lee, Je hee
    • The Journal of Korean Society for Radiation Therapy
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    • v.28 no.2
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    • pp.171-178
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    • 2016
  • Purpose : In order to minimize the dose of femoral head as an appropriate treatment plan for rectal cancer radiation therapy, we compare and evaluate the usefulness of 3-field 3D conformal radiation therapy(below 3fCRT), which is a universal treatment method, and 5-field 3D conformal radiation therapy(below 5fCRT), and Volumetric Modulated Arc Therapy (VMAT). Materials and Methods : The 10 cases of rectal cancer that treated with 21EX were enrolled. Those cases were planned by Eclipse(Ver. 10.0.42, Varian, USA), PRO3(Progressive Resolution Optimizer 10.0.28) and AAA(Anisotropic Analytic Algorithm Ver. 10.0.28). 3fCRT and 5fCRT plan has $0^{\circ}$, $270^{\circ}$, $90^{\circ}$ and $0^{\circ}$, $95^{\circ}$, $45^{\circ}$, $315^{\circ}$, $265^{\circ}$ gantry angle, respectively. VMAT plan parameters consisted of 15MV coplanar $360^{\circ}$ 1 arac. Treatment prescription was employed delivering 54Gy to recum in 30 fractions. To minimize the dose difference that shows up randomly on optimizing, VMAT plans were optimized and calculated twice, and normalized to the target V100%=95%. The indexes of evaluation are D of Both femoral head and aceta fossa, total MU, H.I.(Homogeneity index) and C.I.(Conformity index) of the PTV. All VMAT plans were verified by gamma test with portal dosimetry using EPID. Results : D of Rt. femoral head was 53.08 Gy, 50.27 Gy, and 30.92 Gy, respectively, in the order of 3fCRT, 5fCRT, and VMAT treatment plan. Likewise, Lt. Femoral head showed average 53.68 Gy, 51.01 Gy and 29.23 Gy in the same order. D of Rt. aceta fossa was 54.86 Gy, 52.40 Gy, 30.37 Gy, respectively, in the order of 3fCRT, 5fCRT, and VMAT treatment plan. Likewise, Lt. Femoral head showed average 53.68 Gy, 51.01 Gy and 29.23 Gy in the same order. The maximum dose of both femoral head and aceta fossa was higher in the order of 3fCRT, 5fCRT, and VMAT treatment plan. C.I. showed the lowest VMAT treatment plan with an average of 1.64, 1.48, and 0.99 in the order of 3fCRT, 5fCRT, and VMAT treatment plan. There was no significant difference on H.I. of the PTV among three plans. Total MU showed that the VMAT treatment plan used 124.4MU and 299MU more than the 3fCRT and 5fCRT treatment plan, respectively. IMRT verification gamma test results for the VMAT plan passed over 90.0% at 2mm/2%. Conclusion : In rectal cancer treatment, the VMAT plan was shown to be advantageous in most of the evaluation indexes compared to the 3D plan, and the dose of the femoral head was greatly reduced. However, because of practical limitations there may be a case where it is difficult to select a VMAT treatment plan. 5fCRT has the advantage of reducing the dose of the femoral head as compared to the existing 3fCRT, without regard to additional problems. Therefore, not only would it extend survival time but the quality of life in general, if hospitals improved radiation therapy efficiency by selecting the treatment plan in accordance with the hospital's situation.

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Packing effects on the intracavitary radiation Therapy 3-Dimension plan of the uterine cervix cancer (자궁경부암 강내조사 3차원 치료계획 시 Packing의 유용성 분석)

  • Si, Chang-Keun;Jo, Jung-Kun;Lee, Du-Hyun;Kim, Sun-Yeung;Kim, Tae-Yoon
    • The Journal of Korean Society for Radiation Therapy
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    • v.17 no.1
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    • pp.1-8
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    • 2005
  • Purpose : An effect of a packing to uterine treatment of a cervical cancer using a dose-volume histogram for a point dose and a volume dose of the bladder and the rectum was analyzed by establishing a three-dimensional treatment plan using a CT image. Materials and methods : Reference points of the bladder and the rectum were marked, respectively at a treatment plan device (plato brachytherapy V14.2.4) by photographing CT(marconi, USA) when the packing was used and removed under the same condition and a treatment plan was performed to Apoint depending on ICRU38. However, in case of the rectum, a maximum point was looked up and compared with the above point because the point presented from the ICRU is not proper as a representative value of a rectum point dose. Further, the volume dose depending on volume of $50\%,\;80\%,\;and\;100\%$ point doses of the rectum and the bladder was measured. The measured values were used to analyze the effect of the packing through a Wilcoxon Signed Rank Test (a SAS statistical analysis process program). Result : The reference points at the bladder and rectum doses when the packing was removed were $116.94\;35.42\%$ and $117.59\;21.08\%$, respectively. The points when the packing was used were $107.08\;38.12\%$ and $95.19\;21.32\%$, respectively. After the packing was used, the reference points at the bladder and the rectum were decreased by $9.86\%$ and $22.4\%$, respectively. When the packing was removed, the maximum points at the bladder and the rectum were $164.51\;50.89\%,\;128.81\;33.05\%$, respectively. When the packing was used, the maximum points at the bladder and the rectum were $142.31\;44.79,\;110.08\;37.03\%$, respectively. After the packing was used, the maximum points at the bladder and the rectum were decreased by $22.2\%$ and $18.73\%$, respectively. When the packing was removed, the bladder volume at $50\%,\;80\%,\;and\;100\%$ point doses of the rectum and the bladder were $48.62{\pm}18.09\%,\;16.12{\pm}11.15\%,\;and\;7.51{\pm}6.63\%$, respectively and its rectum volume were $23.41{\pm}14.44\%,\;6.27{\pm}4.28\%,\;2.79{\pm}2.27\%$, respectively. When the packing was used, the bladder volume at $50\%,\;80\%,\;and\;100\%$ point doses of the rectum and the bladder were $40.33{\pm}16.72,\;11.63{\pm}8.72,\;and\;4.87{\pm}4.75\%$, respectively and its rectum volume were $18.96{\pm}8.37\%,\;4.75{\pm}2.58\%,\;and\;1.58{\pm}1.06\%$, respectively. After the packing was used, the bladder volume at $50\%,\;80\%,\;and\;100\%$ point doses of the rectum and the bladder were decreased by $8.29\%,\;4.49\%,\;and\;2.64\%$, respectively and its bladder volume were decreased by $4.45\%,\;1.52\%,\;and\;1.21\%$, respectively. Conclusion : Values at Reference point doses of the bladder and the rectum recommended from the ICRU 38 were 0.0781 and 0.0781, respectively and values of their maximum point doses were 0.0156 and 0.0156, respectively, as a result of which an effect of the packing using at the uterine intracavitary treatment of an uterine cervical cancer through the three-dimensional treatment plan used CT were measured. That is, the values at reference point doses and the values at maximum point doses show similar difference. However, P value was 0.15 at over $50\%,\;80\%,\;and\;100\%$ volume doses and the value shows no similar difference. In other words, the effect of the packing looks like having a difference at the point dose, but actually shows no difference at the volume dose. The reason is that the volume of the bladder and the rectum are wide but the volume of the packing is only a portion. Therefore, the effect of decreasing the point dose was not great. Further, the farer the distance is, the more weak the intensity of radiation is because the intensity of radiation is proportional to inverse square of a distance. Therefore, the effort to minimize an obstacle of the bladder and the rectum by using the packing should be made.

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Pre-operative Concurrent Chemoradiotherapy for Stage IlIA (N2) Non-Small Cell Lung Cancer (N2 병기 비소세포 폐암의 수술 전 동시화학방사선요법)

  • Lee, Kyu-Chan;Ahn, Yong-Chan;Park, Keunchil;Kim, Kwhan-Mien;Kim, Jhin-Gook;Shim, Young-Mog;Lim, Do-Hoon;Kim, Moon-Kyung;Shin, Kyung-Hwan;Kim, Dae-Yong;Huh, Seung-Jae;Rhee, Chong-Heon;Lee, Kyung-Soo
    • Radiation Oncology Journal
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    • v.17 no.2
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    • pp.100-107
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    • 1999
  • Purpose: This is to evaluate the acute complication, resection rate, and tumor down-staging after pre-operative concurrent chemoradiotherapy for stage IIIA (N2) non-small cell lung cancer. Materials and Methods Fifteen patients with non-small cell lung cancer were enrolled in this study from May 1997 to June 1998 in Samsung Medical Center. The median age of the patients was 61 (range, 45~67) years and male to female ratio was 12:3. Pathologic types were squamous cell carcinoma (11) and adenocarcinoma (4). Pre-operative clinical tumor stages were cT1 in 2 patients, cT2 in T2, and cT3 in 1 and all were N2. Ten patients were proved to be N2 with mediastinoscopic biopsy and five had clinically evident mediastinal Iymph node metastases on the chest CT scans. Pre-operative radiation therapy field included the primary tumor, the ipsilateral hilum, and the mediastinum. Total radiation dose was 45 Gy over 5 weeks with daily dose of 1.8 Gy. Pre-operative concurrent chemotherapy consisted of two cycles of intravenous cis-Platin (100 mg/m$^{2}$) on day 1 and oral Etoposide (50 mg/m$^{2}$/day) on days 1 through 14 with 4 weeks' interval. Surgery was followed after the pre-operative re-evaluation including chest CT scan in 3 weeks of the completion of the concurrent chemoradiotherapy if there was no evidence of disease progression. Results : Full dose radiation therapy was administered to all the 15 patients. Planned two cycles of chemotherapy was completed in 11 patients and one cycle was given to four. One treatment related death of acute respiratory distress syndrome occurred In 15 days of surgery. Hospital admission was required in three patients including one with radiation pneumonitis and two with neutropenic fever. Hematologic complications and other acute complications including esophagitis were tolerable. Resection rate was 92.3% (12/l3) in 13 patients excluding two patients who refused surgery. Pleural seeding was found in one patient after thoracotomy and tumor resection was not feasible. Post-operative tumor stagings were pT0 in 3 patients, pTl in 6, and pT2 in 3. Lymph node status findings were pN0 in 8 patients, pN1 in 1, and pN2 in 3. Pathologic tumor down-staging was 61.5% (8/13) including complete response in three patients ($23.7%). Tumor stage was unchanged in four patients (30.8%) and progression was in one (7.7%). Conclusions : Pre-operative concurrent chemoradiotherapy for Stage IIIA (N2) non-small cell lung cancer demonstrated satisfactory results with no increased severe acute complications. This treatment shceme deserves more patinet accrual with long-term follow-up.

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Radiation Dose-escalation Trial for Glioblastomas with 3D-conformal Radiotherapy (3차원 입체조형치료에 의한 아교모세포종의 방사선 선량증가 연구)

  • Cho, Jae-Ho;Lee, Chang-Geol;Kim, Kyoung-Ju;Bak, Jin-Ho;Lee, Se-Byeoung;Cho, Sam-Ju;Shim, Su-Jung;Yoon, Dok-Hyun;Chang, Jong-Hee;Kim, Tae-Gon;Kim, Dong-Suk;Suh, Chang-Ok
    • Radiation Oncology Journal
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    • v.22 no.4
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    • pp.237-246
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    • 2004
  • Purpose: To investigate the effects of radiation dose-escalation on the treatment outcome, complications and the other prognostic variables for glioblastoma patients treated with 3D-conformal radiotherapy (3D-CRT). Materials and Methods: Between Jan 1997 and July 2002, a total of 75 patients with histologically proven diagnosis of glioblastoma were analyzed. The patients who had a Karnofsky Performance Score (KPS) of 60 or higher, and received at least 50 Gy of radiation to the tumor bed were eligible. All the patients were divided into two arms; Arm 1, the high-dose group was enrolled prospectively, and Arm 2, the low-dose group served as a retrospective control. Arm 1 patients received $63\~70$ Gy (Median 66 Gy, fraction size $1.8\~2$ Gy) with 3D-conformal radiotherapy, and Arm 2 received 59.4 Gy or less (Median 59.4 Gy, fraction size 1.8 Gy) with 2D-conventional radiotherapy. The Gross Tumor Volume (GTV) was defined by the surgical margin and the residual gross tumor on a contrast enhanced MRI. Surrounding edema was not included in the Clinical Target Volume (CTV) in Arm 1, so as to reduce the risk of late radiation associated complications; whereas as in Arm 2 it was included. The overall survival and progression free survival times were calculated from the date of surgery using the Kaplan-Meier method. The time to progression was measured with serial neurologic examinations and MRI or CT scans after RT completion. Acute and late toxicities were evaluated using the Radiation Therapy Oncology Group neurotoxicity scores. Results: During the relatively short follow up period of 14 months, the median overall survival and progression free survival times were $15{\pm}1.65$ and $11{\pm}0.95$ months, respectively. The was a significantly longer survival time for the Arm 1 patients compared to those in Arm 2 (p=0.028). For Arm 1 patients, the median survival and progression free survival times were $21{\pm}5.03$ and $12{\pm}1.59$ months, respectively, while for Arm 2 patients they were $14{\pm}0.94$ and $10{\pm}1.63$ months, respectively. Especially in terms of the 2-year survival rate, the high-dose group showed a much better survival time than the low-dose group; $44.7\%$ versus $19.2\%$. Upon univariate analyses, age, performance status, location of tumor, extent of surgery, tumor volume and radiation dose group were significant factors for survival. Multivariate analyses confirmed that the impact of radiation dose on survival was independent of age, performance status, extent of surgery and target volume. During the follow-up period, complications related directly with radiation, such as radionecrosis, has not been identified. Conclusion: Using 3D-conformal radiotherapy, which is able to reduce the radiation dose to normal tissues compared to 2D-conventional treatment, up to 70 Gy of radiation could be delivered to the GTV without significant toxicity. As an approach to intensify local treatment, the radiation dose escalation through 3D-CRT can be expected to increase the overall and progression free survival times for patients with glioblastomas.

Effects of the Development of Cracks into Deeper Zone on Productivity and Dryness of the Clayey Paddy Field (점토질 논 토양의 심층화가 토지생산성 및 유면건조에 미치는 영향)

  • 김철기
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.15 no.3
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    • pp.3059-3088
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    • 1973
  • The Object of research was laid on the dry paddy field which had a low level of underground water, rather than on a paddy field with a high level of underground water. In the treatment of the clay paddy field before transplanting we employed 3 kinds of methods; deep plowing, development of cracks by drying the surface of the field under which pipe drain was built. This study was to find which one, among these three methods, is the most effective to let roots extend to deep zone and increase the yield of rice and at the same time, for trafficability of large scale machinery which will be introduced to the harvest, in the light of the earth bearing capacity in relation with underground drainage. In the treatments of plots, 1) the kyong plot was plowed 39 days before transplanting and dried, 2) the kyun plot was plowed again 2days before transplanting after plowing 39 days before transplanting, leveling field surface in the saturation with water and developing the cracks by drying, 3) the kyunam plot was plowed again 2 days before transplanting after setting the drainage pipe and at the same time plowing 39 days before transplanting, leveling field surface in the saturation with water and developing the cracks by drying. Also each plot above had three different levels of soil depth, respectively; that is 15cm, 25cm, 35cm. The kyong plot with 15cm-depth was he control. The results obtained were as follows; 1. The kyunam plot showed a remarkably lager amount of water consumption by better underground drainage than the kyong and the kyun plot, and the kyong plot indicated a greater amount of water consumption than the kyun plot. Therefore the amount of available rainfall was decreased in the order of kyunam>kyong>kyun. The net duty of water decreased in the order of kyunam>kyong>kyun and its showed about 105cm in depth at the kyunam plot, about 70cm in depth at the kyong plot and about 45cm in depth at kyun plot, regardless of soil depth. 2. According to the tendency that the weight of the total root was effected by the maximum depth of the crack, it seemed that the root development was more affected by the depth of the crack than by only the crack itself. The weight of the total roots tended to increase as the depth of the crack got deeper and deeper, and the weight of the total roots was increased in the order of kyun<kyunam<kyong. 3. In the growing of the plant height, the difference did not appear at the beginning of growing(peak period of tillering) of any plot, But for the mid period of growing(ending period of tillering) to the period of young panicle formation, the deeper the depth of plot is, the more the growing goes down. On the contrary at the late period of growing, growth was more vigorous in the plot with deep depth than in the plot with shallow depth. Since the midperiod of growing, in the light of experimental treatment, the kyun plot was not better in growing than the other two plots and no remarkable defference was shown between the kyunam and the kyong plot, but the kyunam plot had the tendency of superiority in growing plant height. 4. As the depth of plot went deeper, the decreasing tendency was shown in the number of tillers through a whole period of growingi. When the above results were observed concering each plot of experimental treatment, the kyun plot was always smaller in the number of tiilers than the kyunam and the kvong plot, and the kyong plot was slightly larger than the kyunam plot in the number of tillers. 5. When each plot of the different experimental treatments was compared with the control plot(15-kyong), yield(weight of grains) was increased by 17% for the 35-kyong plot, by 10% for the 35-kyunam and yields for the other plots were less or nomore than the control plot. On the whole, as the depth of plot went deeper, yields for plots was increased in the order of kyong>kyunam>kyun. 1% of significance between the levels of depths and 5% of significance between the treatments were shown. 6. The depth of consumptive water which was more effective on the weight of grains is that of the last half period. When the depth of consumptive water was increased at the range of less than 2.7cm/day in the 15cm plot, 3.0cm/day in the 25cm plot and 3.3cm/day in the 35cm plot, the weight of grains was increased, and at the same time the weight of grains was increased as the depth of plot went deeper. The deeper plots was of advantage to the productivity at the same depth of consumptive water. 7. The increase in the weight of grains in propertion to the weighte of root showed a tendency to increase depending on the depth of plot at each plot of the same weight of roots. The weight of roots and grains together increasezd in the order of kyun>kyunam>kyong, considering each treatment of experimental plot. The weight of grains was in relation to the minimum water content ratio during the midperiod of surface drainage and the average earth temperature was mainly affected by the minimum water content ratio because it was relatively increased in proportion to the water content ratio(at less than 40%) 8. The weight ratio of straw to grain showed an increasing tendency at the plot of shallow depth and had a relation of an inversely exponental function to the weight of roots. At the same depth of plot except the 15cm plot, the weight ratio of straw to grain was increased in proportion to the depth of consumptive water. The weight of grains was increased as the depth of consumptive water was increased to some extent, but at the same time the weight of ratio of straw to grain was increased. 9. At a certain texture of soils the increase in the amount of the cracks depends on meteorological conditions, especially increase in amounts of pan evaporation. So if it rains during the progressing of field drying the cracks largely decrease. The amount of cracks of clay soil had relation of inversely exponental function to the water content ratio(at more than 25%). The maximum depth of crack kept generally a constant value at less than 30% of water content ratio. 10. The cone index showed the tendency that it was propertional to the amount of cracks within a certain limit but more or less inversely proportional over a certain limit. The water content ratio at the limit may be about 25%. 11. The increase in the cone index with the progressing of time after final surface drainage showed the tendency that it was proportional to the depth of consumptive water at the last half of growing period. Based on the same depth of if the cone index in the kyunam plot was much larger than in the other two plots and that in the kyong plot was much smaller than in the kyun plott, as long as the depth of plot was deeper, especially in the 35-kyong plot. 12. In the light of a situation where water content ratio of soil decreased and the cone index increased after final surface drainage the porogress of the field dryness was much more rapid in the kyunam plot than in the kyong plot and the kyun plot, especially slowest in the kyong plot. In the plot with deeper zone the progress was much slower. The progress requiring the value of the cone index, $2.5kg/cm^2$, that working machinary can move easily on the field changed with the time of final surface drainage and the amount of rainfall, but without nay rain it required, in the kyunam plot, about 44mm in total amount of pan evaporation and more than 50mm in the other two plots. Therefore the drying in the kyunam plot was generally more rapid in the kyunam plot was generally more rapid over 2days than in the kyun plot, and especially may be more rapid over 5days than in the 35-kyong plot.

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