ࡱ;   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry  !"#$%&'()*+,-./012345678:;<=>?@BCE  FMicrosoft Word-Dokument MSWordDocWord.Document.89q [\\Default1$*$3B*OJQJCJmH sH KHPJnH^J aJ_HtHBA@BAbsatz-StandardschriftartJUJ Internet Link B* phmHsH>*nH_HtH22Numbering SymbolsF"FHeading x$OJ QJ CJPJ^J aJ.B". Text body x /!2 List^J @B@Caption xx $CJ6^J aJ]&R&Index $^J &b& Text Body0ar0Table Contents.q. Table HeadingT"&:VtWXYZ[$);>?F.lbt\]^_`abcdefgSNzNNTXXXb$a waS8V$b$YYJbQ#!b$37Jg_0@~"(    NA?C"  NA?C"  NA?C"< C nrKPT&4& 4&{4TTP GTimes New Roman5Symbol3&ArialiLiberation SerifTimes New RomaniLiberation SerifTimes New Roman5Geneva?5Courier New?Angsana New?DejaVu Sans5TahomaS&Liberation SansArial5TahomaBhtu&{}F5 kS tt5 kS tt'0DyK yK 4mailto:supat@supat.eu.orgDyK yK 0mailto:goo555@gmail.comDyK yK 2http://ahatThailand.org/Oh+'0|8 @ L X d p25@@Y%@@|@I,}՜.+,D՜.+,\M 0tCaolan80 qTW\ l4&,Rd@: XC^S  Reverse Threshold Model Theory Supat Faarungsang Department of Animal Science, Kasetsart University, Nakhon Pathom 73140, Thailand;  HYPERLINK "mailto:supat@supat.eu.org"supat@supat.eu.org,  HYPERLINK "mailto:goo555@gmail.com"goo555@gmail.com Abstract A new theory named  Reverse Threshold Model Theory (RTMT) was originated when quantitative genetics models and principles were reversed to eliminate some random errors in the model. Since 1921, a model named  Threshold Model ' was utilized on mice to quantitative estimate genes affecting the number of digits. The idea was extended to cover a wide variety of applications. However, reversion of the model has never been given in any literatures. During an investigation of a difficulty on the internet at Kasetsart University, Thailand, threshold behavior was accidentally discovered. Anylyses by a simple statistical method will lead to a conclusion that is contrary to the natural fact, while simple transformation methods give the correct results. Application to solve problems in education, social sciences, computer sciences, biological sciences, medical sciences, bioinformatics, agricultures, economics, communications, statistics, and so on, will be given. One hundread percent of unwanted random errors may be eliminated from the phenotype to yield natural estimators. Proof of the theory by computer simulation is discussed. Keywords: reverse threshold model, limiting factor, transformation, computer simulation, genetics, phenotype 1 Introduction The study of threshold inheritance using guinea pigs as experiment material was firstly studied by Wright[1]. It was found that normally guinea pigs will have four digits on the front feet and three digits on the hind feet, however, some guinea pigs can have extra digits based on several factors including genetics factors. It was said  It is already clear that this dichotomy cannot correspond to alternative phases of a single factor. It is the result of a physiological threshold in a character affected by many factors. It is therefore reasonable to assume that there is a scale of factor combinations to which each factor makes a fairly constant contribution and that variabilities may be compared on such a scale. It was concluded that  It is assumed that the presence or absence of the little toe depends on whether the combination of factors exceeds or falls below a threshold. On a scale of uniform factor effects, 18 percent of the variance of the Beltsville stock was genetic, due to substrain differences (squared biserial eta .18, also parent-offspring correlation .18). There was no demonstrable genetic variability within substrains. Genetic variability was also negligible in the Chicago stock (parent-offspring correlation .03, after correction for other factors). (Wright[1]). It was also concluded that  A recognition and evaluation of the importance of non-genetic factors in determining the presence or absence of the little toe is a necessary foundation for analysis of the genetic differences between different stocks. (Wright[1]). Probability of animal to fall into several categorical traits were given by Ginula[2]. Parts of complicated derivation using Bayesian statistical approach were shown in Picture 1 and Picture 2. Reverse of Wright[1] and Gianula[2] has never been given. It is the objective of this paper to (1) give basic principles of the Reverse Threshold Model Theory (RTMT), (2) proof of the theory via Monte Carlo simulation, (3) give examples and explainations of RTMT applications in relation to Limiting Factor Theorem (LFT) and Self-Sufficient Economy (SSE) phylosophy principles.   Materials and Methods All earlier models including threshold models for categorical traits will follow below feature: Y = Xb + Za + e {1} While this investigation introduce new algorithm of data transformation method to explain the nature by using below model: P = T + d {2} Where Y is a vector of animal key performance indexes, X is an incident matrix specifically to fixed effects, b is vector of fixed effect parameters, Z is an incident matrix specifically to random effects, e is a vector of effects assumed to be randomly influenced on Y, P is a phenotype of an individual animal, T is transformed threshold affected to animal P with limiting factor theory, and d is disturbance distance deviated by transformation methods and cause error to P but not necessary randomly as earlier methods assumed. From previous experiment, the data was shown in Table 1. Table1. Number of counts (Internet difficulty data). ISP Easy Moderate Difficult KUnet 139 74 5 SSS 50 1 0 It was found that analysis by threshold model on counting number of incidents on categorical trait gave results opposite to normal statistical methods because it violated equal in variabilities among treatments assumption. However, the number of records is limited based on time and budget of the project. So, it cannot prove that the reverse threshold model theory can be applied in general to all events in the world. This study introduce Monte Carlo simulation to: (1) increase the number of records to be unlimitted, (2) varie the variances to be unlimited in values, and (3) varie the ratio of falling in to different categorical cells with difference in probability. Only two hundred and sixty nine records were used in early investigation. While using Monte Carlo simulation, twenty eight thousand nine hundred and twenty records were used. Each record was generated in to two traits, one was named  speed for continuous normal character with variances varies from one hundread units up to ten thousand units, one was named  threshold for discrete character with degenerated in variance but fall in to different categories based on probability assigned from earlier study varies from ratio 1:1 to 50:0 and 50:1. Six method of simulation were made namely sim1, sim2, sim3, sim4, sim5 and sim6. In sim1, totally 5000 records was made in 5 cells of contingency table with equal frequency. In sim2, totally 2555 records was made in 5 cells of contingency table with frequency 1000, 500, 35, 1000 and 20 , respectively. In sim3, totally 1278 records was made in 5 cells of contingency table with frequency 500, 200, 18, 500 and 10 , respectively. In sim4, totally 511 records was made in 5 cells of contingency table with frequency 200, 100, 7, 200 and 4 , respectively. In sim5, totally 269 records was made in 5 cells of contingency table with frequency 139, 74, 5, 50 and 1 , respectively. In sim6, totally 27 records was made in 5 cells of contingency table with frequency 14, 7, 1, 5 and 0 , respectively. Simulation thresholds for Kasetsart University IP were assigned to be at speed of 2000, 500 and 100 Kb/sec, respectively. While simulation thresholds for home IP were assigned to be at speed of 800 and 200 Kb/sec, respectively. Level of judgement to fall in to difficult , intermediate and easy conductions in the program written in Basic was shown in Picture 3 were set to speed 0-127, 128-255 and 255-infinity, respectively. Matvec[6] was used to analyse 36 set of data by a program shown in Picture 2. D = Data(); D.input("f3e","ip$ speed thres"); M = Model(); M.equation("speed = intercept ip"); M.fitdata(D); kp=[0,1,-1]; M.blup(); M.save("math2009f3e.out"); M.estimate(kp) M.contrast(kp); INPUT c$ OPEN c$ FOR READING AS myfile WHILE NOT(ENDFILE(myfile)) DO READLN txt$ FROM myfile IF NOT(ENDFILE(myfile)) THEN m$=MID$(txt$, 8) o$="0" IF (VAL(m$)>127) THEN o$="1" ENDIF IF (VAL(m$)>256) THEN o$="2" ENDIF PRINT txt$," ",o$ ENDIF WEND CLOSE FILE myfile Results Analyses result from 36 experiments were given in Table 1. All analyses certified that conventional methods gave wrong results and contradict to new transformation method. When number of records in experiment is small, say twenty seven, the probability of t-test become small, say 1.xx, and gave nonsignificant estimators. However, it was nonsense to conclude that the effects are not different as it was frequently quoted. Discussions In original papers [1] and [2], it was informed that changing of threshold traits depend on accumulated small effects up to some level. The probability to fall in to different categories were given. However, this study think in reversed order that quantitative phenotypes which are continuous arising from infinite number of effects are influenced from simple model named  RTMT . After transformed quantitative phenotypes in to threshold categorical discreted traits, the random errors will be one hundread percent eradication. New term named  Disturbance Distance Deviation (DDD) is being arisen instead. From this investigation, it was proven that DDD always smaller in value compared to the earlier random errors. Certainly, an earlier result [4] was correctly concluded that internet difficulty was happen in Kasetsart university but was not happen at author's home even if it was contain with much bigger band width. This investigation extended the results to be in general by using Monte Carlo simulation with wide variety of variance and increasing the number of records to an unlimited value. It was assured that new method always leading to the truth by nature while conventional methods can lead to wrong conclusions. Surprisingly, data generated with an intermediate variance become optimum data sets those gave the best estimators shown in Table1. Theoretically, data sets with minimum in variance values should gave the best estimators. This phenomenon happen because the author use different thresholds in simulation and in programming. The values in simulation are 2000, 500, 100, 800 and 200 KB/sec, respectively. While the programming in Basic classified the threshold at speed 0-127, 128-255 and 256 to infinity KB/sec ,respectively. It was used unequal value in simulation of records between the two origins because by nature the performance of two sources of IP were behave with those fashions. The author want data sets that respond to the true mother nature. By the way, further investigation can be made to find out what is really happening. Wright[1] report that not only genetics effects can bring up threshold phenomena but also any fixed and random effects from any sources including unexplained random effects from conventional models. That information support RTMT. In RTMT, it was porposed that threshold can be assigned to any quantitative continuous trait. Threshold can be a single effect of major gene, can be a sum of effects from a group of genes that behave as a marker assisted selection (MAS) and/or can be accumulated random or fixed effects from unknown origins including random errors in conventional model. By this way, totally eradication of errors was possible. However, another error named DDD was arised in replace of conventional random errors. From this study, it was proven by using Monte Carlo simulations that DDD always has smaller effect than random errors. The concept of RTMT get along with the concept of Limitting Factor (LF) presented in [5]. In several cases, the two terms represent the same natural phenomenon. The author proposed that all models and events happen in this world are not complicated as they were originally said. At any moment on specifically incident, the model always compose of a few threshold effects that behave as limiting factors. Of course, it may be contained with infinite factors that can influence on the trait but those factors do not have significant effect to the phenotypes at the current situation. Only after the situation was changed with time, other unnoticeable factors will become the next LF or RTMT. And simple transformation technology used in this study can be again applied to the next simple models to eradicate random errors and give higher efficient estimator. Applications of RTMT can be applied on several fields, for example: Education: In old style grading system, teachers graded students performance on random nonsense effects basis namely: carelessness, memory capability, speed, I.Q., and etc. True good key performance of students never being measured in most students in our world. That is a strong evidence to indicate why the world was won. Applying RTMT to education can make the world to change to be better than it was. Firstly, we have to make problem sets to measure true key performance(KP) without disturbing from those nonsense factors. Secondly, apply the KP in first step to become a threshold or a limiting factor to total score measured in students. Thirdly, build the teaching process in such a way that all students can have equal chance to learn it based on an individual differences in general ability. Of course, retatarded students have to use more time and spend more attempt and effort than to an genious student. The author named this process  Bayesian learning . The author sucessfully applied those 3 steps long time ago and named the problem sets  fine note . After finishing the whole processes , it was founded that half of students in the class got A grade while an another half got A+ grade. No student got F grade in those classes. Social sciences: The first limiting factor of making friend in our society is friendship. After this factor stay in model, the other factors becoming more and more important and friendship can be removed from the model. Infinite number of factors will come in and being removed. But only one at a time, few limitting factors as a threshold will exist in the model in social sciences. Religions: Buddhism normally contain of five rules of living namely: no killing living things, no stealing other person's belonging, no intercoursing to other person's spouse, no lying and no drinking algoholic solution, respectively. However, for an individual, it has only one rule dominated the other rules. In general , the first limitting factor rule is number four (no lying). Lying will lead to violation of all other rules to most persons. Of course, this rule seem to be the smallest in weight but the most difficult to follow. Other of our lord teaching principles are, for example, the moral called  Itthibaht 4 , in this rule, the first limiting factor is  Chanta which means an eager to do good works. The same happen to the teaching named  Mongkol 38 , in the variety of 38 different rules, the first rule which means stay away to connect to bad persons is the first limiting factor for most persons. However, after the first rule being applied, the following rules become more and more significant in values to follow. The same happen to other mother nature models in our world. Computer sciences: The secret of success in this investigation by using several computers donated from several sources are happen because the author knows that the LF and RTMT in computer sciences are namely: Slackware, Matvec, R, SSS/OLPC and etc. It was also found that Self-Sufficient Economy (SSE) phylosophy given by HMJ the King of Thailand is the most important threshold affected to progression of this field. Biological sciences: Most experiments in biological sciences follow the RTMT given in this study. Million of effects were reported in million of articles but it can be proven that at any specific case the model is so simple and RTMT can be applied. By this way, huge reduction of budget in most of experiments can be done after RTMT is spilled over to this field. Medical sciences: Several disease was claimed to be influenced from several factors. For example, cancer can be caused by infinite number of pathogenic agents. Also, cancer can be eradicated by infinite number of unknown factors. But, for a specific case, it can be easily seen that only few pathogenic agents will happen to the patients at specific time. The most importance to cure any disease is to find out what is the LF on that patient. The same applied to other fields. For example, in animal breeding, it was a big waste to argue why dairy husbandry in Thailand was failed. It has several methods to improve it. One method can be applied to one case while one method can be applied globally to animal husbandry. Vermiculture model happen to the author is surely LF that can be applied to dairy cattle husbandry. Because earthworm husbandry in Thailand was introduced from warm climate countries in the same way that dairy cattle was done. So, problem of heat stress follow the same pattern. But vermiculture has a shorter generation and more reproducable with much lower in cost. Also, SSE was easily done, so the author was successed in this husbandry. It was also be proven that random effects cause new greater in size of the worm. At this moment, the author assign new molecular genetics thesis to the students. Bioinformatics: The first limiting factor influencing bioinformatics progress are internet quality and availability of bioinformatics servers. There is only two good encyclopedia of gene and genome servers in the world, one was located in Thailand and one was located in Japan. Again, to dig out what is the first limiting factor is the key stone to success in all tasks and plans. Agricultures: For good and well practice farmers, they can indicate what is the LF and RTMT to improve agricultural products easily. The two group of plants shown in Picture 3 indicated that after the first LF namely water was taken away then the soil preparation will become the second LF affecting growth rate of plants shown in Picture 3. HMJ the King of Thailand propose that SSE applied to agriculture is to reduce the risk of damage from accidentally causes. Mixed farming with several small agricultural units become the first LF in this case. Economics: SSE again directly applied to economics to solve serious world's problem. It was known that monopoly huge capitalism collapse our world economics recently and it is surely LF and RTMT. Communications: Traffic failure in Bangkok arised from bad management in public communication. On some occations the bus to reach Thamasat university will reach the bus stop at 5 minutes interval but for some occations the bus did not come even it was waited there for three hours. This is one of the most important LF that turn most of people who go by bus waste their money to have their own personal car. Similar case happen to Kasetsart microbus service, all microbuses stop 20 minutes at the station and after it was left, it was waiting again for an additional 20 minutes at bus stop in front of the campus. That ridiculous behavor turn most teachers to buy their own car and cause a lot of problem to traffics. Statistics: It was already mention that RTMT can be one hundread percent eradication of random errors and the new error called DDD were proven by this study that has much smaller in effect to the phenotypes and then lead to better estimators. Conclusions Monte Carlo simulation was applied to prior data to prove RTMT presented in [1]. It was found that totally 36 data set got the same result that RTMT is a better method than it were used and gave correct results while conventional method can lead to wrong result in a condition that variance among treatments is not equal as it was generally assumed. Intermediate size of variation is optimum and gave the best estimators from results given in this study. Small data sets are unrecommended for experiments because from this study, it always gave nonsignificant estimators even if it was proven that treatments are huge different. Acknowledgements Internet NX_Server at  HYPERLINK "http://ahatThailand.org/"http://ahatThailand.org/ was donated by Animal Husbandry Association of Thailand (AHAT). Intranet NX_Server at National Swine Research and Training Center was donated by twenty two anonymous poor students. OLPC was donated by an anonymous. Two heads perfect super computer was donated by department of animal science, Kasetsart university. Without those dedication this investigation is impossible. The author is deeply appriciated on their sacrifices.  References [1] S. Wright, Systems of Mating, Genetics, 6(1921), 111-178. [1] S. Wright, An Analysis of Variability in Number of of Digits in an Inbred Strain of Guinea Pigs, Genetics, 19(1933), 506-536. [1] S. Wright, An intensive study of the inheritance of color and of other coat characters in guinea pigs with especial reference to graded variations, Pub. Canegie Instn. Washington, 241 (1916), 59-160. [1] D. Gianola, Sire evaluation for ordered categorical data with a threshold model, Genet. Sel. Evol., 15(1983), 201-224. [1] S. Faarungsang, One Laptop Per Child (OLPC), a self-sufficient and sustainable system, for teaching and learning animal sciences classes, Proceedings of the 4th Agricultural Graduate Conference, Department of Animal Science, Faculty of Agriculture, Chiang Mai University (2006), 90-99. [1] S. Faarungsang and S. Parisuthikul, Statistical analysis using Matvec on co-location NX_servers performance, National Conference on Statistics and Applied Statistics 2009, National Institute of Development and Admistration (2009),485-499. [6] T. 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