Development of Models for Performance Index (PI) and Score Index(SI) of Individual players based on 5 European Soccer Leagues
Most football managers are not aware of the need for analysis of soccer data, which is one of the dynamic sports. In this study, we developed a statistical model with performance indicators and score indicators of individual soccer player based on various event data including dynamic features such as goal, assist, pass, etc. In this study, the correlation between the dependent variables and the explanatory variables, and each explanatory variable was confirmed through the correlation analysis to solve the problem of multiple communicability from the regression model and to analyze the statistically significant preliminary model. In addition, we analyzed the correlation between individual rating of the players and the data recorded in the soccer games, and found that there has been a problem with the rating of the soccer players evaluated by the reporters and the soccer statistics site. To solve this problem, we developed a model that best fit the performance indicators of individual soccer player using the linear regression model and the beta regression model. The performance index model of the athletes was developed by comparing the R-squared value and the mean absolute percentage error of two models, the linear regression model and the beta regression model, and found out the beta regression model is better model to use. By using the estimated regression coefficients of the regression model we made new PI model. Score Index, which is the attractive point of soccer, was developed by comparing Poisson regression model and negative binomial regression model based on AIC value, and the one using negative binomial regression model was found to be better. Through the model developed by this study, it is possible to collect the event data recorded by individual athletes for each soccer game, and obtain the PI & SI index which are the athlete performance index models. This allows us to evaluate each team's players objectively, analyze the team's deficiencies, and provide tools to find players, who can fill in the missing positions of the teams. This study can also be utilized to grasp the performance of athlete in real time by simulating the resultative model.
Graphene Nanoplatelet-Embedded Acrylic Paint for Low Cost Waterproof Paintable Capacitive Sensors and Free Standing Supercapacitors
Modern capacitive touch input and proximity sensing technologies are rigid and limited to flat substrates making it impossible to apply them onto objects with irregular geometries like textiles or car handles. Furthermore, the high cost restricts the applications to small surfaces and cannot be scaled up to be applied on large surfaces such as walls. Therefore, a paint-on scheme would broaden the applications of capacitive touch input and proximity sensing devices. Paintable capacitive sensors are an emerging technology hindered by the high cost and lackluster properties of conductive paints. Existing conductive paints utilize expensive filler materials such as silver and gold to achieve high conductivity but suffer from low surface area. High surface area is critical for capacitive proximity sensors to detect objects from far distances and for overall sensitivity. Carbonaceous alternatives using micronized graphite exhibit low conductivity, require high loadings and most disintegrate when in contact with water. Multilayer graphene nanoplatelets are investigated for their high conductivity, high surface area, low cost, flexibility and eco friendliness. A waterproof acrylic latex is combined with multilayer graphene and dispersed via bath sonication. The optimal time of sonication and optimal graphene loading is determined through systematic testing. An Arduino Uno is loaded with a CapSense library and the graphene based paint is utilized as the interface to sense both touch and proximity.
費馬多邊形數定理之延伸探討
本研究旨在研究費馬多邊形數定理(任意非負整數必可表成k個k邊形數的和)的一般化情況，也就是說，任意非負整數是否能表成給定的二次多項式數列中所選取的γ項和。以數學模型敘述，就是探討對一個已知的二次多項式an2+bn+c，是否可找到一正整數γ，滿足∀x∈N∪{0},∃α1,α2,…αγ,使得x=∑γi=1(aαi2+bαi+c)。 本作品主要探討若此探究模型存在，那麼數列〈an 〉的一般式an2+bn+c與γ值之間會存在什麼關係，並期望能運用一個簡潔明瞭又一般化的數學式表示。本文亦提供另一個數學模型，探討γ值與某些特殊係數a,b,c之間的關聯性。而本文探尋[a/2]n2+[b/2]n+1,a∈N,b∈Z,a+b≡0(mod 2)(此為本文主要探討的二次式)，求得此二次式所對應之γ值的方法為先令p=[2a/(a+b)]+2，再藉由所建立的模型二，求出[(p-2)/2] n2+[(4-p)/2] n的γ值，接著再用所建立的模型一來求得[a/2]n2+[b/2]n+1的γ值，進而依循此方法最後得出任意形如[a/2]n2+[b/2]n+1的二次式之γ值。
New approach to the synthesis of functionalized fluoroalkenes
Fluorine has a big influence on physical, chemical and biological properties of organic structures. Organofluorine compounds are widely used in modern medical chemistry to develop new drugs. Insertion of fluorine atom into organic molecules can improve their reactivity in biological systems, increase their metabolic stability, lipophilicity and permeability through membranes. As a consequence, in recent years, the percentage of drugs containing one or more fluorine atoms has increased rapidly up to 40%. The fluoroallylic fragment is also able to change properties of bioactive molecules. Its introduction into such structures as inhibitors of histonedeacetylase, inhibitors of matrix metalloproteinase, asparagine, glutamine, etc. increases their biological activity and electronic properties. We propose a new method for the synthesis of functionalized fluoroalkenes, based on the generation of fluoroallyl nucleophiles from silyl- and boronyl-substituted fluorocyclopropanes and their further usage in the allylation of carbonyl compounds or their derivatives. Due to the fact that the cyclopropanation of alkenyl boronates is not possible under conditions of alkaline dehydrohalogenation of dibromofluoromethane, we have developed a new method for the preparation of silyl- and boronyl-substituted cyclopropanes, which consist of carbene cyclopropanation of multiple C=C bonds by sodium dibromofluoroacetate catalyzed by (IPr)AgCl. The new method is effective for the cyclopropanation of not only boronyl- and silyl-substituted olefins, but also for low-reactivity alkenes, such as monoalkyl substituted alkenes, allyl alcohol ethers and α,β-unsaturated carbonyl compounds. The conditions for isomerization of silyl- and boronyl-substituted fluorohalocyclopropanes in the presence of catalytic amounts of copper (I) bromide in acetonitrile was selected. It was shown that the regioselectivity of the process is determined by the thermodynamic control. Thus, the formation of fluorovinylsilanes or fluorovinylboranes in the isomerization of α-silyl- or α-boronyl-gem-bromofluorophenylcyclopropanes and fluoroallylsilanes upon isomerization of β-silyl-gem-bromofluorophenylcyclopropanes was observed. Thus, new types of fluorinated reagents were obtained that are not previously described in the literature (...)
Random number generators and their applications in Computer Science with the Monte Carlo Method
Monte Carlo methods are non-parametric algorithms that use random numbers and theorems of probability theory to approximate values that are not random. The purpose of my research was to approximate the surface of different geographical areas that can be easily approximated to polygons (e.g. lakes, glaciers, deserts) with Monte Carlo simulations starting from either Cartesian coordinates or pictures. Computer science would not exist without math, and this research project showed me the importance of a deep understanding of probability theory in the world of simulations and, more generally, the importance of developing new theorems and algorithms. The results of my research could be developed in different ways: it would be interesting to produce software that allows one to approximate areas from pictures taken from a smartphone; as well, the theorem I found has to be proven, and also Monte Carlo methods as a means of random number generation can always be improved. There are still many possibilities.