• Title/Summary/Keyword: Gompertz 모델

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Development of Shelf-life Prediction Model of Tofu Using Mathematical Quantitative Assessment Model (수학적 정량평가 모델을 이용한 두부의 유통기한 예측 모델의 개발)

  • Shin Il-Shik
    • Food Industry And Nutrition
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    • v.10 no.1
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    • pp.11-16
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    • 2005
  • 식물성 단백질의 주요 공급원이며 우리나라 전통식품 중의 하나인 두부의 유통기한을 정량적으로 예측할 수 있는 수학적 모델을 개발하고자 온도와 초기균수에 따른 두부 부패세균의 성장 실험 결과를 데이터베이스화하여 이를 바탕으로 균의 성장을 정량적으로 평가할 수 있는 수학적 모델을 개발하였다. 근의 증식 지표인 최대증식속도상수(k), 유도기(LT), 세대시간(GT)은 온도에 지배적인 영향을 받았으며, 초기균수에 따른 유의 적 인 차이 는 없었다(p<0.05). 최대증식속도상수와 온도 및 초기균수의 상관관계를 나타내는 수학적 정량평가모델인 square root model을 이 용하여 두부 부패 세균의 성장을 정량적으로 예측할 수 있는 모델$({\surd}{\kappa}=0.016861(T+6.87095))$을 개발하였으며 실험치와 예측치의 상관계수는0.969이었다. 이 예측 정량평가모델로부터 예측한 최대증식속도상수와 두부의 관능적 부패시 점을 반영 한 Gompertz 변형 모델을 이용하여 두부의 유통기한을 예측할 수 있는 모델$(Spoilage-critrion(hr)=\frac{2{\times}Ln2+Ln[(Nmax/No)-1])}{k}$을 개발하였다

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Prediction of Seedling Emergence and Early Growth of Monochoria vaginalis and Scirpus juncoides under Elevated Temperature (상승된 온도 조건에서 물달개비(Monochoria vaginalis)와 올챙이고랭이(Scirpus juncoides)의 출아 및 초기생장 예측)

  • Park, Min-Won;Kim, Jin-Won;Lim, Soo-Hyun;Lee, In-Yong;Kim, Do-Soon
    • Korean Journal of Weed Science
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    • v.30 no.2
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    • pp.103-110
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    • 2010
  • This experiment was conducted to investigate seedling emergence and early growth of Monochoria vaginalis and Scirpus juncoides in the controlled-environment chamber maintained at different temperatures. Non-linear regression analyses of observed data against effective accumulated temperature (EAT) with the Gompertz and logistic models showed that the Gompertz and logistic models worked well in describing seedling emergence and early growth of both weed species, respectively, regardless of temperature. EATs required for 50% of the maximum seedling emergence and the maximum leaf number of M. vaginalis were estimated to be 69.3 and $131^{\circ}C$, respectively, while those of S. juncoides were 94.8 and $137^{\circ}C$, respectively. Models developed in this study thus were used to predict seedling emergence and early growth under elevated temperature condition. If rotary tillage with water is made on 27 May under $+3^{\circ}C$ elevated temperature condition, dates for 50% of the maximum seedling emergence and 4 leaf stage were predicted to be 1 June and 15 June for M. vaginalis and 3 June and 14 June for S. juncoides, respectively. As compared with current temperature, these dates are 1-2 days earlier for the seedling emergence and 3 days earlier for the early growth, suggesting that earlier application of herbicides is required for effective control of M. vaginalis and S. juncoides under elevated temperature condition in the future.

Development of Predictive Growth Model of Vibrio parahaemolyticus Using Mathematical Quantitative Model (수학적 정량평가모델을 이용한 Vibrio parahaemolyticus의 성장 예측모델의 개발)

  • Moon, Sung-Yang;Chang, Tae-Eun;Woo, Gun-Jo;Shin, Il-Shik
    • Korean Journal of Food Science and Technology
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    • v.36 no.2
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    • pp.349-354
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    • 2004
  • Predictive growth model of Vibrio parahaemolyticus in modified surimi-based imitation crab broth was investigated. Growth curves of V. parahaemolyticus were obtained by measuring cell concentration in culture broth under different conditions ($Initial\;cell\;level,\;1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}\;colony\;forming\;unit\;(CFU)/mL$; temperature, 15, 25 37, and $40^{\circ}C$; pH 6, 7, and 8) and applying them to Gompertz model. Microbial growth indicators, maximum specific growth rate (k), lag time (LT), and generation time (GT), were calculated from Gompertz model. Maximum specific growth rate (k) of V. parahaemolyticus increased with increasing temperature, reaching maximum rate at $37^{\circ}C$. LT and GT were also the shortest at $37^{\circ}C$. pH and initial cell number did not influence k, LT, and GT values significantly (p>0.05). Polynomial model, $k=a{\cdot}\exp(-0.5{\cdot}((T-T_{max}/b)^{2}+((pH-pH_{max)/c^{2}))$, and square root model, ${\sqrt{k}\;0.06(T-9.55)[1-\exp(0.07(T-49.98))]$, were developed to express combination effects of temperature and pH under each initial cell number using Gauss-Newton Algorism of Sigma plot 7.0 (SPSS Inc.). Relative coefficients between experimental k and k Predicted by polynomial model were 0.966, 0.979, and 0.965, respectively, at initial cell numbers of $1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}CFU/mL$, while that between experimental k and k Predicted by square root model was 0.977. Results revealed growth of V. parahaemolyticus was mainly affected by temperature, and square root model showing effect of temperature was more credible than polynomial model for prediction of V. parahaemolyticus growth.

Statistical Evaluation of Sigmoidal and First-Order Kinetic Equations for Simulating Methane Production from Solid Wastes (폐기물로부터 메탄발생량 예측을 위한 Sigmoidal 식과 1차 반응식의 통계학적 평가)

  • Lee, Nam-Hoon;Park, Jin-Kyu;Jeong, Sae-Rom;Kang, Jeong-Hee;Kim, Kyung
    • Journal of the Korea Organic Resources Recycling Association
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    • v.21 no.2
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    • pp.88-96
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    • 2013
  • The objective of this research was to evaluate the suitability of sigmoidal and firstorder kinetic equations for simulating the methane production from solid wastes. The sigmoidal kinetic equations used were modified Gompertz and Logistic equations. Statistical criteria used to evaluate equation performance were analysis of goodness-of-fit (Residual sum of squares, Root mean squared error and Akaike's Information Criterion). Akaike's Information Criterion (AIC) was employed to compare goodness-of-fit of equations with same and different numbers of parameters. RSS and RMSE were decreased for first-order kinetic equation with lag-phase time, compared to the first-order kinetic equation without lag-phase time. However, first-order kinetic equations had relatively higher AIC than the sigmoidal kinetic equations. It seemed that the sigmoidal kinetic equations had better goodness-of-fit than the first-order kinetic equations in order to simulate the methane production.

Prediction of Seedling Emergence and Early Growth of Eleocharis kuroguwai Ohwi under Evaluated Temperature (상승된 온도 조건에서 올방개(Eleocharis kuroguwai)의 출아 및 초기생장 예측)

  • Kim, Jin-Won;Moon, Byeong-Chul;Lim, Soo-Hyun;Chung, Ji-Hoon;Kim, Do-Soon
    • Korean Journal of Weed Science
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    • v.30 no.2
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    • pp.94-102
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    • 2010
  • Field and pot experiments were conducted to investigate seedling emergence and early growth of Eleocharis kuroguwai panted on different dates. Non-linear regression analyses of observed data against effective accumulated temperature (EAT) with the Gompertz model showed that the Gompertz model works well in describing seedling emergence and early growth of E. kuroguwai regardless of planting date and soil burial depth. EATs required for 50% of the maximum seedling emergence of E. kuroguwai planted at 1, 3 and 5 cm soil burial depth in the pot experiment were estimated to be 54.5, 84.0 and $118.0^{\circ}C$, respectively, and $56.7^{\circ}C$ when planted at 1 cm in the field experiment. EATs required for 50% of the maximum leaf number of E. kuroguwai planted at 1, 3 and 5 cm soil burial depth in the pot experiment were estimated to be 213.3, 249.0 and $291.6^{\circ}C$, respectively, and $239.5^{\circ}C$ when planted at 1 cm in the field experiment. Therefore, models developed in this study thus predicted that if rotary tillage with water is made on 27 May under $+2^{\circ}C$ elevated temperature condition, dates for 50% of the maximum seedling emergence, 5 leaf stage and 5 cm plant height of E. kuroguwai buried at 3 cm soil depth were predicted to be 2 June, 10 June and 12 June. These dates are 1 day earlier for the seedling emergence and 3 days earlier for the early growth as compared with current temperature condition, suggesting that earlier application of herbicides is required for effective control of E. kuroguwai.

Predicting and Extending the Shelf Life of Red Cabbage Sprouts (적양배추싹의 Shelf Life 예측 및 Aqueous ClO2, Fumaric Acid, UV-C 병합처리)

  • Chun, Ho Hyun;Park, Seung Jong;Jung, Seung Hun;Song, Kyung Bin
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.42 no.9
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    • pp.1518-1523
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    • 2013
  • To estimate the shelf life of red cabbage sprouts (stored at 4 and $10^{\circ}C$), the numbers of total aerobic bacteria were determined during storage. Parameters for the Gompertz model were determined and the shelf life was predicted using a modified Gompertz equation. The estimated shelf lives of red cabbage sprouts packed with polyolefin film and polyamide/polyamide/polyethylene (PA/PA/PE) film at $4^{\circ}C$ were 49.4 and 52.3 h, respectively, whereas those of red cabbage sprouts packed with polyolefin film and PA/PA/PE film at $10^{\circ}C$ were 19.7 and 22.6, respectively. The shelf life prediction equation was appropriate, based on the statistical analysis of the accuracy factor, bias factor, and mean square error. On the other hand, for red cabbage sprouts treated with aqueous $ClO_2$/fumaric acid and UV-C then packed with polyolefin film or PA/PA/PE film, the shelf life was predicted to be longer than 168 h. These results suggest that the combined treatment of aqueous $ClO_2$/fumaric acid and UV-C can be useful for improving microbial safety and extending the shelf life of red cabbage sprouts during storage.

Comparison of Regression Models for Estimating Ventilation Rate of Mechanically Ventilated Swine Farm (강제환기식 돈사의 환기량 추정을 위한 회귀모델의 비교)

  • Jo, Gwanggon;Ha, Taehwan;Yoon, Sanghoo;Jang, Yuna;Jung, Minwoong
    • Journal of The Korean Society of Agricultural Engineers
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    • v.62 no.1
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    • pp.61-70
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    • 2020
  • To estimate the ventilation volume of mechanically ventilated swine farms, various regression models were applied, and errors were compared to select the regression model that can best simulate actual data. Linear regression, linear spline, polynomial regression (degrees 2 and 3), logistic curve, generalized additive model (GAM), and gompertz curve were compared. Overfitting models were excluded even when the error rate was small. The evaluation criteria were root mean square error (RMSE) and mean absolute percentage error (MAPE). The evaluation results indicated that degree 3 exhibited the lowest error rate; however, an overestimation contradiction was observed in a certain section. The logistic curve was the most stable and superior to all the models. In the estimation of ventilation volume by all of the models, the estimated ventilation volume of the logistic curve was the smallest except for the model with a large error rate and the overestimated model.

Characteristics for Co-digestion of Food Waste and Night Soil using BMP Test (BMP실험을 이용한 음식물폐기물 및 분뇨의 병합소화 특성)

  • Cho, Jinkyu;Kim, Hyungjin;Oh, Daemin
    • Journal of the Korean GEO-environmental Society
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    • v.15 no.9
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    • pp.13-18
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    • 2014
  • BMP test was carried out to evaluate the characteristics for co-digestion of night soil and food waste. 6 types of sludge were tested in 30 days which were raw, excess, digested, night soil/septic tank (1:1), food waste (food : dilution water = 1:1), and mixed sludge. Bio gas was produced actively after 2 days, and continued in 2 weeks. Gas generation amount was decreased rapidly after considerable space of time. Especially maximum productivity of gas was shown in 7~8 days. The ultimate methane yields of raw, excess, digested, night soil/septic tank, food waste, and mixed sludge were 64.63, 67.49, 66.45, 72.44, 107.85, and 46.71 mL $CH_4/g$ VS respectively from Modified Gompertz model. The lag growth phase time and maximum specific methane production rate of mixed sludge were 1.88 day and 80.4 mL/day respectively. The methane potential of mixed sludge was higher than individual sludge. So high methane potential was expected by controlling mixing ratio of food waste. Besides stable operation of digestion tank and the solution of oligotrophic problem were possible.

Germination and Seedling Emergence of Ammannia coccinea as Influenced by Environmental Factors

  • Shen, Xiangri;Pyon, Jong-Yeong;Kim, Do-Soon
    • Korean Journal of Weed Science
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    • v.30 no.2
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    • pp.84-93
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    • 2010
  • Petri dish and pot experiments were conducted to investigate germination and seedling emergence of Ammannia coccinea as influenced by environmental factors. The best germination of A. coccinea was obtained at $35/30^{\circ}C$ of temperature and 0 bar of osmotic potential, while no germination at temperatures of ${\leq}$ $15^{\circ}C$ and ${\geq}$ $40^{\circ}C$, osmotic potentials of ${\leq}$ -2.0 bar, or dark condition. The best seedling emergence was observed at $35/30^{\circ}C$, at which the first emergence of A. coccinea was observed at 7 days after sowing (DAS) with its maximum emergence reached at 10 DAS. No seedling emergence was observed at $15/10^{\circ}C$ with significant reduction at $40/35^{\circ}C$. Seedling emergence decreased with increasing soil depth, resulting in no seedling emergence at ${\geq}$ 3 cm. The Gompertz model well described the cumulative germination and seedling emergence of A. coccinea with time. Germination influenced by osmotic potential and seedling emergence influenced by soil burial depth were well described by the logistic model. Overall results indicate that A. coccinea is photoblastic and requires temperatures greater than $15^{\circ}C$, osmotic potential greater than -2.0 bar, and soil burial depth shallower than 3 cm for its germination and seedling emergence, which were faster than M. vaginalis but slower than E. crus-galli.

Predictive Modeling for the Growth of Salmonella Enterica Serovar Typhimurium on Lettuce Washed with Combined Chlorine and Ultrasound During Storage

  • Park, Shin Young;Zhang, Cheng Yi;Ha, Sang-Do
    • Journal of Food Hygiene and Safety
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    • v.34 no.4
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    • pp.374-379
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    • 2019
  • This study developed predictive growth models of Salmonella enterica Serovar Typhimurium on lettuce washed with chlorine (100~300 ppm) and ultrasound (US, 37 kHz, 380 W) treatment and stored at different temperatures ($10{\sim}25^{\circ}C$) using a polynomial equation. The primary model of specific growth rate (SGR) and lag time (LT) showed a good fit ($R^2{\geq}0.92$) with a Gompertz equation. A secondary model was obtained using a quadratic polynomial equation. The appropriateness of the secondary SGR and LT model was verified by coefficient of determination ($R^2=0.98{\sim}0.99$ for internal validation, 0.97~0.98 for external validation), mean square error (MSE=-0.0071~0.0057 for internal validation, -0.0118~0.0176 for external validation), bias factor ($B_f=0.9918{\sim}1.0066$ for internal validation, 0.9865~1.0205 for external validation), and accuracy factor ($A_f=0.9935{\sim}1.0082$ for internal validation, 0.9799~1.0137 for external validation). The newly developed models for S. Typhimurium could be incorporated into a tertiary modeling program to predict the growth of S. Typhimurium as a function of combined chlorine and US during the storage. These new models may also be useful to predict potential S. Typhimurium growth on lettuce, which is important for food safety purposes during the overall supply chain of lettuce from farm to table. Finally, the models may offer reliable and useful information of growth kinetics for the quantification microbial risk assessment of S. Typhimurium on washed lettuce.