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哈尔滨工程大学:《数学建模》MCM写作模版_表

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表的格式:表头在上注:红字标记代表可通用的句子 在表前对表的来源和数据进行说明 B1 In Table 1, we summarize the minimum number of escorts needed to reach each service 表的解释部分 For each airport, the difference between the good and Adequate service levels roughly a factor of two, with slightly increasing returns to scale, with larger scales the staff are spread more uniformly, so it is less likely that a job will crop up with nobody close enough to take it Table 1 Numbers of escorts needed to achieve service levels Airport Traffic Passengers served Number of escorts Adequate Service Good Service light 4 10 Logan light 155 15 Hare ligh 275 27 heavy 550 例2 表的解释部分 (前面的说出数据的来源,然后筛选出比较代表性的数据进行说明) We determined absolute and relative crit ical ity values for each country for which all the data used in computing parameters was available (108 countries). We then used relative criticality in selecting our most critical countries, by continent. Had we used absolute criticality it would have given precedence to large nations, despite relatively mild HIv/aidS situations Table 2: Most Critical Countries by Continent Country Continent Criticality(relative) Botswana Africa 4.097469 Thailand Asia 0.283505 Ukraine 0.135426 Bahamas North America 0.614664 Guyana South america 04312 例3 The table below is the generated irrigation schedule for the repositioning of the sprinklers given 12-hour work day for a rancher. Each pipe is set in place for 5 hours

表的格式:表头在上 注:红字标记代表可通用的句子 1、 在表前对表的来源和数据进行说明 例1 In Table 1, we summarize the minimum number of escorts needed to reach each service level 表的解释部分 For each airport, the difference between the Good and Adequate service levels is roughly a factor of two, with slightly increasing returns to scale; with larger scales, the staff are spread more uniformly, so it is less likely that a job will crop up with nobody close enough to take it. 例 2 表的解释部分 (前面的说出数据的来源,然后筛选出比较代表性的数据进行说明)。 We determined absolute and relative criticality values for each country for which all the data used in computing parameters was available (108 countries). We then used relative criticality in selecting our most critical countries, by continent. Had we used absolute criticality it would have given precedence to large nations, despite relatively mild HIV/AIDS situations. 例3 The table below is the generated irrigation schedule for the repositioning of the sprinklers, given 12-hour work day for a rancher. Each pipe is set in place for 5 hours

Day Time Sprinkler position(x position, y position) in meters from the lower left corner of the field ay 1 1pm 23.75, 23.75(move the sprinkler and pip Day 1 6pm Turn off sprinkler to avoid over irrigation Day2|8am46.75,23 Day2|1pm6g.5,2375 Day 2 6pm I Turn off sprinkler to avoid over irrigation. Day3|1pm32.75,6.25 Day 3 6pm Turn off sprinkler to avoid over irrigation Day4sam55.5,6.25 Day 4 6pm Turn off sprinkler to avoid over irrigation 例4 And some data processing we can get the relevant statistical data information of patient and donor characteristics for the simulation Table 5: Age distrbutions for new patients used in the simulations Deceased Donor Percent Living Donor Percent All Donor Types Percent Pediatric 17.629 18.02% 48 0.06% 17.677 9939 Adult 80,139 8192% 80.049 9991% 160,188 90.02% Unknown 0.05% 24 0.03% 0.04% AllAges 97,820 80.121 177.941 例 The graft survival rates show in the following UNOS data for kidney transplants in the U.s(based on optn data as of 2006) Table 12: Kidney Graft Survival Rates Time after donation From deceased donors From living donors One year 8840% Three years 77.50% 87.60% Five vears 65.50% 2、在表后对表的内容进行说明 例1 Table 9: Comparison of Linear Fit Parameters for our Models Model Intercept Basic Car Tracking.699 1.738 0.997 macrosc 1.598 1.215 0.998 Cellular Automata 0.228 0.998 Table 9 shows linear fit parameters for all three models note that all three models are well described by a linear equation. 例2

例4 And some data processing we can get the relevant statistical data information of patient and donor characteristics for the simulation. 例5 The graft survival rates show in the following UNOS data for kidney transplants in the U.S (based on OPTN data as of 2006): 2、在表后对表的内容进行说明 例 1 Table 9 shows linear fit parameters for all three models. Note that all three models are well described by a linear equation. 例2

yN·W(B,L)+Bg Using the cellular automata model, we compute waiting time as a function of both the number of lanes and the number of tollbooths. For a fixed L, we compare all values of Ctotal and choose the lowest one The results of this method are presented in table6 例3 Analyzing the organ transplant policies in other countries There is a figure of Legislation, practice and donor rates in several countries, e. g. Spain, US France, Germany, UK and so on.BJ Table 4: Legislation, practice and donor rates C Legislati Donors(pmp) Actual practice Spain Informed consent Presumed consent Presumed consent and family informed 244 Austria Presumed consent Presumed consent US Informed consent with Informed consent with 22.1 According to the above data, we can see that many of the European countries have the high rates of the donor, particularly in Spain. This phenomenon shows that the organ transplant is also hot in Europe. Although the relevant policies and statutes in these countries are less comprehensive than that in U. S, there still a lot what U.S could learn from. Here, we mainly analyze the organ transplant policies in Spain, U. K and Korea this three countries %o Region 53.43 73.43 83.22 93.50 103.19 13321 163.38 14703 22317 27366 28379 29371 able 1: Population Fraction in each Legislative District The population contained in each region is summarized in table I.(在表后对数 据的内容进行总结) 例4 Table 6: Optimization for Cellular Automata Model Highway Lanes Typical da Rush Hour 23+5678

Using the cellular automata model, we compute waiting time as a function of both the number of lanes and the number of tollbooths. For a fixed L, we compare all values of Ctotal and choose the lowest one. The results of this method are presented in Table6. 例3 According to the above data, we can see that many of the European countries have the high rates of the donor, particularly in Spain. This phenomenon shows that the organ transplant is also hot in Europe. Although the relevant policies and statutes in these countries are less comprehensive than that in U.S, there still a lot what U.S could learn from. Here, we mainly analyze the organ transplant policies in Spain, U.K and Korea this three countries. ……The population contained in each region is summarized in table 1.(在表后对数 据的内容进行总结) 例4

图表的解释部分 As indicated in Table 6, there is fairly good agreement between the recommended number of booths for a typical day and for peak hours. However, we note that the optimal booth number for a typical day never exceeds that for rush hour. Rush hour seems to require slightly more booths than a ty pical day in order for the plaza to operate most efficiently Each value in Table 6 is representative of approximately 20 trials. Through these trials, we noted a remarkable stability in our model. Despite the stochastic nature of our algorithm, each number of lanes was almost always optimized to the same number of tollbooths. There were a handful of exceptions; they occurred exclusively for small numbers of highway lanes(<3 lanes). Integer values are presented in Table 6 only because fractional tollbooths have no physical meanin 3、表前表后有引入引出,且中间对两表之间进行比较 例 表的解释部分 We can obtain the data which is involved with the status of the American Organ Transplant from the data banks. We have collected the demand of the various organs in United States to date, the annual donors, transplants and the demand (here taking the kidney for example, by years 1995-2006) Table 1. The demand of the vanous organs in united states to date Based on oPTN dataAll Heart Kidney Liver P Kidney/ Heart Lung Intestin as of February 2, 2007 Organs Lung 9454569983169891,7452,3892.8582,860135239 Percent 174021%17969%61.846%2527%3.023%3.025%0.143%0253% From the above tablel, we can see that the kidney accounts for 73% in the total of the organ transplants. It accounts for a very large proportion as a most important organ which can be transplanted. Therefore, we only need to discuss the status of the kidney transplant here being able to achieve the analysis and research on the organ transplant Table 2: The annual donors, transplants and the demand of the kidney DonoR Transplant aiting list Year Deceased LivingAIl onor Deceased Living Al List Donors Donors Types onors I Donors Iypes Addit removals 199550043.392s3937,694|3.3871.09117.27028067 19965.0363.678s7147,7303661398177352887346608 19975.0833.9390167,7743.9271,70118.43730.27248.7o9 5.394.4219.7608.032441912.45119.49732.46051.9 864.72410106.044.71712.76o21.8e856857.526 2005.4895.49310.928.1245.48813.61222.37338.17960.552 20015,5286,03811,5668,2306.03514,26522,51739.29361,810 0025.6386.2101,8788.596.21014.7723.61141.81165.452 200315.7536.47312.268.6676.47015.13724.69442.686667 20046.3256.64712.9729,3576.64716.00427.29045.61572.905 2006.7006.7013.2709.9136.56816.48129.16650.1479.280 20066.6095,91312.5229.8075,91415.72129.824 o Datel9r.820so,121|7,9a152,678ao.o77|232,755239,79342,26462,057

图表的解释部分 As indicated in Table 6, there is fairly good agreement between the recommended number of booths for a typical day and for peak hours. However, we note that the optimal booth number for a typical day never exceeds that for rush hour. Rush hour seems to require slightly more booths than a typical day in order for the plaza to operate most efficiently. Each value in Table 6 is representative of approximately 20 trials. Through these trials, we noted a remarkable stability in our model. Despite the stochastic nature of our algorithm, each number of lanes was almost always optimized to the same number of tollbooths. There were a handful of exceptions; they occurred exclusively for small numbers of highway lanes (< 3 lanes). Integer values are presented in Table 6 only because fractional tollbooths have no physical meaning. 3、表前表后有引入引出 ,且中间对两表之间进行比较 例1 表的解释部分 We can obtain the data which is involved with the status of the American Organ Transplant from the data banks. We have collected the demand of the various organs in United States to date, the annual donors,transplants and the demand (Here taking the kidney for example, by years 1995-2006) From the above table1, we can see that the kidney accounts for 73% in the total of the organ transplants. It accounts for a very large proportion as a most important organ which can be transplanted. Therefore, we only need to discuss the status of the kidney transplant here, being able to achieve the analysis and research on the organ transplant

According to the above data, we can get the figures as follow 例 So after many times simulation under the cond itions d iscussed above, we obtain tatistic results as follow Table 3: The result of the monte Carlo simulation Not Divide Donor Transplant Matching rate 17232 51.71% 13112 739025282 4607 5148% 17542 average775226369 5172 Divide Transplant Matching rate 6917 55.02% 894931156 表的解释部分 By analyzing the above result, we can find: When there are more donors(more resources), the number of transplant will increase obviously, and the matching rate changes only a little; When the network is divided into 1l regions(small networks), the costs of the transport and preservation of the organ will be reduced greatly 例3 Table 7: The R-C preference simulation result (The first simulation Mechanism Total-Trans%oOwn-Donor- Trans% Trade% Waitlist-Up-g graded risk hla- ange3964 1.93 Paired/ direct 59.12 39.64 1948 1.93 TTCC 84.75 15.72 (n=400, Low quality exchange or waiting list=30%) Table 8: The R-C preference simulation result (The second simulation Total-Trans%JOwn-Donor-Trans%Trade% 38.15 38.15 193 3.03 Paired/direct 58.34 38.15 193 TTCC 82.27 1481 17.7 0.91 2.03 n=200, Low quality exchange or waiting list=30%) Table 7 reports the general patient statistics under each regime in the columns. The first column in these tables reports the total live donor transplants as percentage of the population size, which is the sum of next two columns, transplants from own compatible donor and transplants from trades. The forth column is the percentage of patients upgraded to the top of the waitlist as heads of w-chains. The fifth and sixth columns report the quality of matches in the live donor transplants the risk of graft failure relative to the risk under no-exchange mechanism with population size n=400 is reported in the fifth column and the number of hla mismatches for an average transplant is reported in the sixth column. In the table 8, we change the n into 200 表与表之间的比较

According to the above data, we can get the figures as follow: 例2 So after many times simulation under the conditions discussed above, we obtain statistic results as follow: 表的解释部分 By analyzing the above result, we can find: When there are more donors (more resources), the number of transplant will increase obviously, and the matching rate changes only a little; When the network is divided into 11 regions (small networks), the costs of the transport and preservation of the organ will be reduced greatly. 例3 Table 7 reports the general patient statistics under each regime in the columns. The first column in these tables reports the total live donor transplants as percentage of the population size, which is the sum of next two columns, transplants from own compatible donor and transplants from trades. The forth column is the percentage of patients upgraded to the top of the waitlist as heads of w-chains. The fifth and sixth columns report the quality of matches in the live donor transplants: the risk of graft failure relative to the risk under no-exchange mechanism with population size n=400 is reported in the fifth column and the number of HLA mismatches for an average transplant is reported in the sixth column. In the table 8, we change the n into 200. 表与表之间的比较

By comparison, we can found that the matching proportion become little and the matching quality will get worse as the total number of the patients decrease. The result is consistent with the reality. The 30% probability of the waiting list or low quality exchange is an adjustable parameter 例4 Table 3: Optimized Number of Booths for L Lanes Lanes Booths 457802362 表与表的比较 Also, we wish to explore the situation in which there is one lane per booth Table 4: Waiting Times for L Lanes with L Booths Lanes Booths Av Wait Average Wait 2* Max 28.2400 37.6928 96.1541 2 31.6109 43.2415 103.7251 28.7137 40.8372 0.8517 1024173 294785 44.3510 103.0286 28.2863 43.0457 986186 29.7364 45.700 103.0432 43.9531 962895 1.1367 例 The parameters we choose to modify are p (probability of advancement), 'delay'(number of time steps required to serve a vehicle in a tollbooth), and q( the probability that a flagged vehicle opts to attempt a turn). The results of this analysis are presented in Table 7. Since we have used six lanes as our standard test case. we continue with this choice here Table 7: Sensitivity Analysis for Cellular Automata Model (L=6) Delay Optimal# booths 095 095 44444 0000 100 10 095 As indicated in Table 7, our cellular automata model is relatively insensitive to both p and q Changes of+ 11%and+5.2% in p and g, respectively, had no effect on the optimal number

By comparison, we can found that the matching proportion become little and the matching quality will get worse as the total number of the patients decrease. The result is consistent with the reality. The 30% probability of the waiting list or low quality exchange is an adjustable parameter. 例4 表与表的比较 Also, we wish to explore the situation in which there is one lane per booth: 例5 The parameters we choose to modify are p (probability of advancement), ‘delay’(number of time steps required to serve a vehicle in a tollbooth), and q (the probability that a flagged vehicle opts to attempt a turn). The results of this analysis are presented in Table 7. Since we have used six lanes as our standard test case, we continue with this choice here. As indicated in Table 7, our cellular automata model is relatively insensitive to both p and q. Changes of ± 11% and ± 5.2% in p and q, respectively, had no effect on the optimal number

of tollbooths for a six lane highway. On the other hand, increasing the delay time by 25% shifted the optimal number of booths from 10 to 11(10%) Decreasing the delay by 25%had no effect on the solution. Perhaps additional work could lead to an elucidation of the relation between delay and optimal booth number that could help stabilize the cellular automata nodel

of tollbooths for a six lane highway. On the other hand, increasing the delay time by 25% shifted the optimal number of booths from 10 to 11 (10%). Decreasing the delay by 25% had no effect on the solution. Perhaps additional work could lead to an elucidation of the relation between delay and optimal booth number that could help stabilize the cellular automata model

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