本文以 B-Spline 的框架研究比較兩種不同的節點估計方法。第一種方法是通過最優化特定 的目標函數並結合相對應的選擇標準選擇出最優化的節點組合。第二種方法則基於幾何控制多 邊形的特性將內部節點的選擇過程與幾何圖形聯繫起來,省去了最優化的過程。另外,本文採 用『節點估計時間』與『誤差平方和』(Mean Squared Error)來評價兩種方法的估計結果。通 過分析各種不同模擬數據下兩種方法的表現情況,本文的主要發現是:第一,無論哪種資料, 第二種方法在計算速度上都是大幅領先第一種方法。第二,在數據資料較小的情況下,第一種 方法中由 Lindstrom 提出的算法並不能很好的配飾模型,最後的估計誤差較大。而在數據資料 較多的情形下,誤差與其他方法較為接近。第三,第一種方法中沒有懲罰項的算法在所有驗證 過的數據中,其表現是所有方法中最穩定且估計誤差最小的。這些發現為如何選擇恰當的節點 估計方法提供了很具價值的參考信息 / This study compares two different methods of knot selection for B-Spline. The first one chooses the best knots through optimizing specific objective functions and corresponding crite- rion. Based on some properties of geometric control polygon, the second one connects the knot selection process with geometric figures, which avoids the tedious optimization. On the other hand, we use the time for estimation and the mean squared error to evaluate the performance of these two methods. There are three main findings of this study. The first finding is that the calculation speed of second method is much higher than that of the first one. Secondly, the algorithm proposed by Lindstrom in the first method is not stable and its estimation error is larger when the sample size is small. On the contrary, the performance of the algorithm proposed by Lindstrom becomes better as the sample size increases. Thirdly, the performance of the algorithm without penalty term in the first method is always better than the second method.

DTN(Delay Tolerant Networks)是一種缺乏網路基礎設備的網路架構，在這類的網路架構下，無線節點之間的通訊連線並非同時存在，而是間歇式建立的。因為節點的移動、或是裝置省電模式運作與環境因素的影響，造成連線可能不定時的失效。有不保證連線特性的網路，在DTN網路中節點間相遇的機會很少，節點間利用 Store-Carry-Forward 的方式傳遞訊息，且有相當長的傳遞延遲(Propagation Delay)。在這樣的網路特性下，傳統的文獻中，都是假設所有節點都會幫忙傳遞。但不幸的，在現實生活中有自私節點(Selfish Nodes)的存在，因自己本身設備資源有限，如電力資源、網路資源...等，節點不願意幫忙傳送訊息，這些自私節點的存在，會對DTN網路架構造成破壞，導致無法傳送訊息到目的地。為了解決自私節點的問題，我們提出了MTBIS(Mobile Trusted Bank of Incentive Strategies)，當發送節點(Source Node)要求傳送訊息時，給予回饋給幫忙轉傳訊息的節點，來鼓勵節點間互相幫忙傳送訊息，我們稱這些回饋為Incentive Credit。而節點也可利用Incentive Credit來要求別的節點幫忙轉傳訊息。另外也加入SI(Social Incentive)機制，與DGT(Dynamic Grudger Threshold) ，吸引自私節點願意幫忙轉傳訊息，改進了 MTBIS 在自私節點環境下的不足， 利用經濟學的角度來解決節點運用Credit的問題，借此提高訊息的傳遞率(Delivery Ratio)。 本篇研究也注重於自私節點的模擬，利用四種不同特性的節點： Sucker(傻瓜)、Cheater (騙子)、Grudger(小氣鬼)、Ecci(投機者)， 這些自私節點會照成DTN在設計上無法使用，甚至降低訊息的傳達率，因此我們模擬了這些自私節點的行為，並且使用我們所提出的獎勵機制，來解決這些自私節點的問題，實驗結果也證明，Grudger可以有效的抑制自私節點對效能大幅降低的問題，與傳統的演算法相較，效能高出34%。 / DTN (Delay Tolerant Networks) is a network structure without need to use any infrastructure. In DTNs, wireless connections between nodes do not always exist, i.e., nodes are connected intermittently. Due to the mobility, power issues, or surrounding environment of nodes, connections between nodes may be disruptive occasionally or randomly. In a DTN, nodes usually transfer the message to the encountering nodes. By this way, the messages are stored, carried, and forwarded to the next nodes, possibly the destination. However, in reality, nodes may not be willing to help each other for the message forwarding. More specifically, there are “Selfish nodes” which refuse to forward messages due to issues such as energy and network bandwidth. Thus it will prevent messages from being forwarded to its destination. In order to solve the problem of message forwarding failure caused by selfish nodes, we proposed an Incentive Strategy called “MTBIS (Mobile Trusted Bank and Incentive Strategies)”. We construct a rewarding scheme called “Incentive Credit” for nodes who forward the messages for the source node. In addition, to increase the intention of the selfish nodes for forwarding messages, we add two more mechanism called SI(Social Incentive) and DGT(Dynamic Grudger Threshold). The DGT uses credits to solve selfish node problems from an economics point of view to enhance MTBIS to work with existence of selfish nodes. In this thesis, we emphasis on the simulation of the behaviors of selfish nodes, using four different types of nodes: the “Sucker”, the “Cheater”, the “Grudger”, and the “Ecci”. These selfish nodes will decrease the success rate of message forwarding, and even make the DTN unusable. We simulated the behaviors of these selfish nodes, using the rewarding scheme we proposed. From the results of our experiment, we see that the Grudger can effectively deal with performance issues caused by selfish nodes, and the system can gain 34% in performance compared to the traditional algorithms.

傘型迴歸函數是類似傘的形狀的迴歸函數，只要符合先上升後下降的趨勢皆為傘型迴歸函數。無母數迴歸函數中最常見的方法之一是樣條(Splines)迴歸函數。樣條為充分平滑分段多項式函數，而節點(knots)為平滑多項式函數連接的地方。在本論文中，將節點以等距離擺放並以AIC(Akaike information criterion)值得到合理的節點數。用三種方法的樣條迴歸函數去估計傘型函數。第一種為RSPL(restrictted spline regression)，也就是有形狀限制時的樣條迴歸函數。第二種是CSPL(concave spline regression)，是參考Meyer寫的樣條迴歸函數，此樣條迴歸函數為凹函數(concave function)。最後一種則稱SPL(spline regression)，為沒有形狀限制也不是凹函數的樣條函數。以IMSE為評估標準，IMSE越小，則代表此方法估計的越好。由模擬結果，在估計先上升後下降的函數時，用RSPL的方法去估計會得到最小的IMSE；而在估計凹函數時，則是CSPL會得到最小的IMSE。利用RSPL和SPL兩個方法估計由中央氣象局蒐集最近13年(1998-2010)的月均溫資料並探討最近幾年的月均溫資料趨勢是否有改變。未來假如需要估計傘型函數時，則可利用本篇所述的方法去估計。 / In this thesis, we consider the problem of estimating a regression function assuming the regression function is unimodal. The proposed method is to model the regression function as linear combination of B-spline basis functions with equally spaced knots, and the number of knots is determined using AIC (Akaike information criterion). Specific constraints are placed on the coefficients of basis functions to ensure that estimated regression function is unimodal. The coefficients are estimated using least square method. The proposed method is refered as RSPL and is compared with two other methods: SPL and CSPL, where SPL is similar to RSPL except that the coefficients of basis functions are estimated without any constraints, and CSPL gives concave regression function estimates. Simulation results show that RSPL outperforms SPL and CSPL when the true regression function is unimodal but not concave, and CSPL outperforms RSPL and SPL when the true regression function is concave. Also, RSPL is applied to temperature data to estimate temperature trend within one year.

在無母數的迴歸當中，因為原始的函數類型未知，所以常用已知特定類型的函數來近似未知的函數，而spline函數也可以用來近似未知的函數，但是要估計spline函數就需要設定節點(knots)，越多的節點越能準確近似原始函數的內容，可是如果節點太多有較多的參數要估計, 就會變得比較不準確，所以選擇適合節點個數就變得很重要。 在本研究中，用交叉驗證的方式來尋找適合的節點個數， 考慮了幾種不同切割資料方式來決定訓練資料和測試資料, 並比較不同切割資料的方式下選擇節點的結果與函數估計的效果。 / In this thesis, I consider the problem of estimating an unknown regression function using spline approximation. Splines are piecewise polynomials jointed at knots. When using splines to approximate unknown functions, it is crucial to determine the number of knots and the knot locations. In this thesis, I determine the knot locations using least squares for given a given number of knots, and use cross-validation to find appropriate number of knots. I consider three methods to split the data into training data and testing data, and compare the estimation results.

行動隨意式網路(MANET)是一種具有高度動態拓撲結構的網路。每一個行動隨意式網路由一組移動節點(Node)組成，彼此之間互相支援轉送封包可以不依靠基地台建構成Intranet。此種網路中，因節點移動之緣故，連線不穩定、頻寬較窄，錯誤率亦較高。傳統的TCP傳輸協定在行動隨意式網路上的效能不免遭受重創。 傳統的TCP在封包遺失時，只能從傳送端進行重傳，而行動隨意式網路傳輸品質極不穩定，常常重送多次才可到達目的地，導致要耗費極長的時間才能將封包送達目的地，然而，在行動隨意式網路中，大量傳輸資料的需求並不大，反而是封包的快速送達更為重要，因此加速封包的送達成為比增大傳送量更為重要的目標。 為了使封包較快送達目的地端，我們提出了Hop-by-Hop TCP的方法，使每個節點使用當地重傳以保證封包成功的傳到下一個節點，遺失的封包不必重新由傳送端重傳，能更快反應封包遺失，並且提昇傳輸可靠度，使封包在高遺失率的情形之下能順利且較為快速的送達目的地端。 我們利用NS-2網路模擬器進行實驗，驗證我們的機制，實驗在不同的拓樸及負載等參數下進行，觀察傳輸成功率及封包傳輸時間，以及公平性。實驗結果指出，本方法在網路環境不穩定時吞吐量能有25.7%以上的提昇，而延遲時間也能有25%的提昇，亦有相當好的公平性。 / A Mobile Ad hoc Network (MANET) MANET is composed of a group of mobile computing devices (nodes) that are equipped with Wireless LAN (WLAN) capability. Nodes can transmit packets to each other to construct Intranet without any base station. In an MANET environment, the communication links are unstable due to various reasons. Error rate is higher and bandwidth is smaller than fixed networks. Running regular TCP protocol on MANET will suffer from serious performance degradation in MANET. To handle packet lost, regular TCP can only retransmit lost packets from the source. However, when error rate is high, several retransmissions may be needed to transmit a packet to its destination successfully. As a result, the effective bandwidth is much lower and the average time to transmit a packet will be much longer. Considering that most applications on MANET prefer shorter transmission time to higher bandwidth, this thesis proposes Hop-by-Hop TCP protocol aiming to accelerate the transmission of packets. Hop-by-Hop TCP makes every intermediate node in the transmission path running a local TCP to guarantee the transmission of each packet on each link. The retransmission of a lost packet is right at the transmitting end of the link where the packet is lost. It doesn't need to retransmit a lost packet from its source node. It takes less time in average to transmit a packet to its destination in a high error rate environment. We evaluate the performance of our approach by simulation using NS-2 simulator. Our experiments show that our proposed protocol outperforms TCP Reno by 25.7% in throughput and 25% reduction in average transmission time. The fairness requirement is also achieved while our proposed protocol coexists with other major TCP variants.

在迴歸分析中，若變數間具有非線性的關係時，B-Spline線性迴歸是以無母數的方式建立模型。B-Spline函數為具有節點(knots)的分段多項式，選取合適節點的位置對B-Spline的估計有重要的影響，在近年來許多的文獻中已提出一些尋找節點位置的估計方法，而本文中我們提出了一種基於Bayesian information criterion(BIC)的節點估計方式。 我們想要深入了解在不同類型的迴歸函數間，各種選取節點方法的配適效果與模擬時間，並且加以比較，在使用B-Spline函數估計時，能夠使用合適的方法尋找節點。 / In regression analysis, when the relation between the response variable and the explanatory variable is nonlinear, one can use nonparametric methods to estimate the regression function. B-Spline regression is one of the popular nonparametric regression methods. B-Splines are piecewise polynomial joint at knots, and the choice of knot locations is crucial. Zhou and Shen (2001) proposed to use spatially adaptive regression splines (SARS), where the knots are estimated using a selection scheme. Dimatteo, Genovese, and Kass (2001) proposed to use Bayesian adaptive regression splines (BARS), where certain priors for knot locations are considered. In this thesis, a knot estimation method based on the Bayesian information criterion (BIC) is proposed, and simulation studies are carried out to compare BARS, SARS and the proposed BIC-based method.

本文是針對Catalan 族中部分成員：「n個運算符號之結合律運算」、「n組正規中括號」、「n個節點之相異二元樹」、「圓上2n個點可畫幾種不相交之弦」，做彼此間對應關係的探討。 藉由操作方法，找出Catalan 族成員彼此間對應關係，再利用對射函數方法證明是對的。在證明Catalan 族中任兩個成員間的對應關係，我們先造一個對應函數，再證明此函數是一對一且映成（onto），即此函數為對射函數，則我們的操作方法是可行的。

大部的類神經網路均為解決特定問題而設計，並非真正去模擬人腦的功能 ，在本論文中介紹一個模擬人類學習方式的類神經網路，稱為推理類神經 網路（The Reasoning Neural Network），其主要兩個組成為強記（ cram -ming）及推理（reasoning）部份，透過彈性的組合這兩個部份可 使類神經網路具有類似人類的學習程序。在本論文中介紹其中一個學習程 序並用四個實驗來評估推理類神經網路的績效，從實結果得知，推理類神 經網路能以合理的隱藏節點數（hidden nodes）達到學習的目標，並建立 一個網路內部表示方式（internal representation），及具有好的推理 能力（g eneralization ability）。 / Most of artification Neural Networks are designed to resolve spe -cific problems, rather than to model the brain. The Reasoning N -eural Network (RNN) that imitates the way of human learning is presented here. Two key components of RNN are the cramming and t -he reasoning. These components coulds be arranged flexibly to a -chieve the human-like learning procedure. One edition of the RNN used in experiments is introduces, and four different proble -ms are used to evaluate the RNN's performance. From simulation results, the RNN accomplishes the goal of learning with a reason -able number of hidden nodes, and evolves a good internal repres -entation and a generalization ability.

在迴歸分析中，若變數間具有非線性 (nonlinear) 的關係時，B-Spline線性迴歸是以無母數的方式建立模型。B-Spline函數為具有節點(knots)的分段多項式，選取合適節點的位置對B-Spline函數的估計有重要的影響，在希望得到B-Spline較好的估計量的同時，我們也想要只用少數的節點就達成想要的成效，於是Huang (2013) 提出了一種選擇節點的方式APLS (Adaptive penalized least squares)，在本文中，我們以此方法進行一些更一般化的設定，並在不同的設定之下，判斷是否有較好的估計效果，且已修正後的方法與基於BIC (Bayesian information criterion)的節點估計方式進行比較，在本文中我們將一般化設定的APLS法稱為GAPLS，並且經由模擬結果我們發現此兩種以B-Spline進行迴歸函數近似的方法其近似效果都很不錯，只是節點的個數略有不同，所以若是對節點選取的個數有嚴格要求要取較少的節點的話，我們建議使用基於BIC的節點估計方式，除此之外GAPLS法也是不錯的選擇。 / In regression analysis, if the relationship between the response variable and the explanatory variables is nonlinear, B-splines can be used to model the nonlinear relationship. Knot selection is crucial in B-spline regression. Huang (2013) propose a method for adaptive estimation, where knots are selected based on penalized least squares. This method is abbreviated as APLS (adaptive penalized least squares) in this thesis. In this thesis, a more general version of APLS is proposed, which is abbreviated as GAPLS (generalized APLS). Simulation studies are carried out to compare the estimation performance between GAPLS and a knot selection method based on BIC (Bayesian information criterion). The simulation results show that both methods perform well and fewer knots are selected using the BIC approach than using GAPLS.

本文研究的主要問題為北大西洋公約組織（North Atlantic Treaty Organization）於後冷戰時期的發展。由於北約組織在冷戰期間的主要功能為防止蘇聯與共產勢力在歐洲地區的擴張，因此於冷戰結束後，許多學者紛紛預測北約組織將會走向衰敗的道路。過去國際關係學界皆以傳統的國際關係理論來檢視北約組織的發展，儘管各家學說皆有其獨到之處，然而仍缺乏較具說服力的定論。而本文採用歷史制度主義(historical institutionalism)中的路徑依賴(path dependence)概念來探討此議題，並將發展的範圍限定於北約組織於後冷戰時期的延續以及轉型這兩個方面。路徑依賴下包含的兩個重要概念：「報酬遞增」 (increasing returns)以及「關鍵節點」 (critical juncture)，則將分別用來解釋北約組織於後冷戰時期的延續與轉型。經過研究後證實，歷史制度主義的路徑依賴概念可以用來解釋北約組織於後冷戰時期的延續與轉型，但此種分析途徑仍需要對組織的發展歷史掌握得更加詳細明確，才得以在論證組織的發展演變時，更具說服力。