We have investigated several monomial and permutation progenitors, including 2*8 : [8 : 2], 2*18 : [(22 x 3) : (3x2)], 2*16 : [22 : 4], and 2*16 : 24, 5*2 :m [4•22], 5*2 :m [(4x2) :• 2], 103∗2 :m [17 : 2] and 103∗4 :m [17 : 4]. We have discovered original, to the best of our knowledge, symmetric presentations of a number of finite groups, including PSL(2, 7), M12 , A6 : 2, A7 , PSL(2, 25), 25 :• S4, 24 : S3, PSL(2, 271), 12 x PSL(2, 13), and U(3, 7) : 2. We will present our construction of several of these images, including the Mathieu sporadic simple group M12 over the maximal subgroup PSL(2, 11), PSL(2, 17) over D9, PSL(2, 16) : 2 over [24 : 5] and PGL(2, 7) over S3. We will also give our method of finding isomorphism classes of images.

"Uncertainty" is used broadly to refer to things that are unknown or incompletely understood. In operations management, basic sources of uncertainty may include decision uncertainty, model uncertainty, analytical uncertainty, data uncertainty, and so on. Although uncertainty is unavoidable in decision making, different mechanisms can be designed to mitigate the impact of uncertainty. One commonly used strategy is "decision postponement," wherein the decision maker purposefully delays some of the decisions to a time when uncertainty is reduced or resolved. This type of a recourse action provides the decision maker with increased ability to match supply with demand. In this dissertation, we study the value of decision postponement in the context of different settings, including capacity investment, revenue management, and supply chain coordination. These problems share one characteristic in common: decision postponement, and as such, are all modeled as two-stage stochastic programming problems. In the first stage, a set of decisions are made under uncertainty so as to maximize the expected profit or utility. Then in the second stage, all uncertainty is resolved and a deterministic optimization problem is solved to determine the postponed decisions, constrained by the first stage decisions. In capacity investment, we study the capacity, pricing, and production decisions of a monopolist producing substitutable products with flexible or dedicated resources. While the capacity decision needs to be made ex-ante, under demand uncertainty, pricing and production decisions can be postponed until after uncertainty is resolved. We show how key demand parameters (the nature of uncertainty, market size, market risk, and risk attitude) impact the optimal capacity decision under the linear demand function. In particular, we show that if the demand shock is multiplicative, then in terms of the "invest or not" decision, the firm will be immune to forecast errors in parameters of the underlying demand shock distribution. Furthermore, incorrectly modeling the demand shock as additive, when, in fact, it is multiplicative, may lead to overinvestment. On the other hand, while the concept of a growth in market size leads to similar conclusions under both additive and multiplicative demand shocks, how market risk affects the optimal capacity decision depends critically on the form of the demand shock. In addition, the decision-maker's attitude toward risk significantly affects the optimal capacity level, and its impact highly depends on the structure of the resource network. Our analysis provides insights and principles on the optimal capacity investment decision under various settings. In airline revenue management, a well-studied problem is the optimal allocation of seat inventory among different fare-classes, given a capacity for the flight and a demand distribution for each class. In practice, capacity on a flight does not have to be fixed; airlines can exercise some flexibility on the supply side by swapping aircraft of different capacities between flights as partial booking information is gathered. This provides the airline with the capability to more effectively match their supply and demand. In this dissertation, we study the seat inventory control problem considering the aircraft swapping option. Our analytical results demonstrate that booking limits considering the swapping option can be considerably different from those under fixed capacity. We also show that principles on the relationship between the optimal booking limits and demand characteristics (size and risk) developed for the fixed-capacity problem no longer hold when swapping is an option. We develop new principles and insights on how demand characteristics affect the optimal seat allocation under the swapping possibility. We also perform a numerical study, which indicates that the revenue impact of using the "true" optimal booking limits under the swapping possibility can be significant. In supply chain coordination, we consider the influenza vaccine supply chain, which, due to the biological complexity of the production process, has a unique characteristic in that production yield is highly uncertain. Given the market demand and price, a monopolist supplier must decide how much raw material to input into production in the first stage. However, since the yield is unknown and production is costly, it is not necessarily in the supplier's best interest to ensure that all market demand is met. The supplier's input quantity depends on the trade-off between the costs of overproduction and undersupply. This, in fact, is one of the reasons why the influenza vaccine manufacturers in the United States lack motivation to produce sufficient amounts of vaccine to meet all demand [Williams (2005), Chick et al. (2008)]. In operations management, it is a well-known result that decentralized supply chains, where each player is only interested in optimizing her own objective, often lead to poor overall performance for the supply chain. However, a higher efficiency is achievable through contracting on a set of transfer payments [Cachon (2004)]. A "coordinating" contract is referred to as one in which each player's objective is in accordance with the supply chain's objective. Given the fact that influenza vaccine plays an important role in health care industry, it is important to study how different contracts impact the influenza vaccine supply chain, where the uncertainty is on the supply side. We study a game in which the supplier and the retailer are engaged in certain type of contracts that specify how risk is shared between the players. We study both the pre-ordering and the post-ordering settings, which respectively refer to the cases where the retailer orders the vaccine before or after the vaccine production is completed. We show that pre-ordering wholesale price contracts dominate post-ordering wholesale price contracts in terms of the resulting supply chain efficiency, but neither of them are able to fully coordinate the supply chain. We also find that cost-sharing contracts are able to coordinate the supply chain, while payback and advance-ordering wholesale price contracts fail to do so. Finally, we prove that if the unsold vaccine can be salvaged with some positive value, then the supply chain can be easily coordinated with wholesale price contracts. In studying this type of stochastic programming problems, it is not only important to characterize the optimal solution, but also important to gain an understanding of how the optimal solution will be affected by environmental parameters. Since the most inaccurate part in stochastic programming often lies in the parameters of the distribution functions, it is both interesting and meaningful to investigate how the optimal solution varies with the intrinsic nature of the random variables. Consequently, we make use of stochastic order relationships to study the behavior of the optimal solutions when the underlying random variables become either "larger" or "more risky." / Ph. D.

隨著科技的進步以及網際網路的普及，影像資訊的傳遞已經漸漸取代文字的表達，人們對於影像的需求也越來越多元，使得影像處理技術以及影像資訊分析也就越來越重要。然而，影像中其中一項重要的資訊為特徵描述子，強而有力的描述子能使得影像在辨識、分類等應用上有較佳的回饋，描述子的建構方式根據編碼原則分為：基於區域梯度統計、基於點對關係以及基於點群關係。其中，基於點群關係的編碼方式因為點群的選取及排序過程中，可能會產生過多的關係表示方法數，以至於不利於計算，因此過去較少有利用點群關係的編碼方式所建構而成的特徵描述子。 本論文提出描述子建構方式-LIOR，是以點群排序關係為基礎的編碼方式，相較於LIOP方法隨著點群內的點數增加，元素關係數大幅度的成長，造成描述子維度過大，計算時間和空間皆可能需要大量的消耗，而本研究方法足以改善計算維度的問題，重新定義點群關係的排名機制，並以像素值為基準加入權重分配，以區別加權排序之間不同大小差值所造成的影響程度。 實驗結果顯示本研究方法對於不同影像劣化效果的資料集，不僅能提升選取多點為一群的影像比對評估效能，同時也能改善點群內元素關係過多的排名表示法，降低以多點為群集的特徵描述子維度，節省了影像比對的計算時間以及空間，仍可維持整體影像配對之效能。

We define valuations and dominance relations in torsion-free abelian groups and prove that they are essentially the same objects. Next we show that valuations correspond with ltrations of subgroups closed under division by integers. We also prove that every torsion-free abelian valued group can be embedded in the Hahn product of subgroups defined by the respective valuations. / En este trabajo definimos valoraciones y relaciones de dominación en grupos abelianos sin torsión y probamos que estos son esencialmente los mismos objetos. Adicionalmente probamos que las valoraciones también se corresponden con filtraciones de subgrupos cerrados por división por enteros y que todo grupo abeliano valorado y sin torsión puede sumergirse en el producto de Hahn de subgrupos definidos por la valoración.

隨著智慧型手機的普及，在移動裝置上直接處理圖像的需求也大幅增加，故對於影像特徵描述子的要求，除了要表現出區域特徵的穩健性，同時也要維持良好的特徵比對效率與合理的儲存空間。過去所提出的區域影像特徵描述子建構方法之中，LIOP方法具有相當不錯的表現力，但其特徵描述子維度會隨著點群取樣數量的提高而以倍數增加，因此本研究提出Dynamic Local Intensity Order Relations (DLIOR)特徵描述子建構方法，利用LIOR方法探討點群中點與點之間的關係，減緩其維度增長幅度；透過動態設定像素差距門檻值，處理影像間像素差距分佈不均的問題，並使用線性轉換、點對歐幾里德距離等方式，重新定義描述子欄位的權重設定。經過實驗證實，DLIOR方法能夠使用比LIOP方法更少的維度空間，描述更多點群數的特徵資訊，並且具有更高的特徵比對能力。 / With the popularity of smart phones, the amounts of images being captured and processed on mobile devices have grown significantly in recent years. Image feature descriptors, which play crucial roles in recognition tasks, are expected to exhibit robust matching performance while at the same time maintain reasonable storage requirement. Among the local feature descriptors that have been proposed previously, local intensity order patterns (LIOP) demonstrated superior performance in many benchmark studies. As LIOP encodes the ranking relation in a point set (with N elements), however, its feature dimension increases drastically (N!) with the number of the neighboring sampling points around a pixel. To alleviate the dimensionality issue, this thesis presents a local feature descriptor by considering pairwise intensity relation in a pixel group, thereby reducing feature dimension to the order of C^N_2. In the proposed method, the threshold for assigning order relation is set dynamically according to local intensity distribution. Different weighting schemes, including linear transformation and Euclidean distance, have also been investigated to adjust the contribution of each pairing relation. Ultimately, the dynamic local intensity order relations (DLIOR) is devised to effectively encode intensity order relation of each pixel group. Experimental results indicate that DLIOR consumes less storage space than LIOP but achieves better feature matching performance using benchmark dataset.

La zeitgesit contemporaine sur la reconnaissance des visages suggère que le processus de reconnaissance reposerait essentiellement sur le traitement des distances entre les attributs internes du visage. Il est toutefois surprenant de noter que cette hypothèse n’a jamais été évaluée directement dans la littérature. Pour ce faire, 515 photographies de visages ont été annotées afin d’évaluer l’information véhiculée par de telles distances. Les résultats obtenus suggèrent que les études précédentes ayant utilisé des modifications de ces distances ont présenté 4 fois plus d’informations que les distances inter-attributs du monde réel. De plus, il semblerait que les observateurs humains utilisent difficilement les distances inter-attributs issues de visages réels pour reconnaître leurs semblables à plusieurs distances de visionnement (pourcentage correct maximal de 65%). Qui plus est, la performance des observateurs est presque parfaitement restaurée lorsque l’information des distances inter-attributs n’est pas utilisable mais que les observateurs peuvent utiliser les autres sources d’information de visages réels. Nous concluons que des indices faciaux autre que les distances inter-attributs tel que la forme des attributs et les propriétés de la peau véhiculent l’information utilisée par le système visuel pour opérer la reconnaissance des visages. / According to an influential view, based on studies of development and of the face inversion effect, human face recognition relies mainly on the treatment of the distances among internal facial features. However, there is surprisingly little evidence supporting this claim. Here, we first use a sample of 515 face photographs to estimate the face recognition information available in interattribute distances. We demonstrate that previous studies of interattribute distances generated faces that exaggerated 4 times this information compared to real-world faces. When interattribute distances are sampled from a real-world distribution, we show that human observers recognize faces poorly across a broad range of viewing distances (with a maximum accuracy of 65%). In contrast, recognition performance is restored when observers only use facial cues of real-world faces other than interattribute distances. We conclude that facial cues other than interattribute distances such as attribute shapes and skin properties are the dominant information of face recognition mechanisms.

La zeitgesit contemporaine sur la reconnaissance des visages suggère que le processus de reconnaissance reposerait essentiellement sur le traitement des distances entre les attributs internes du visage. Il est toutefois surprenant de noter que cette hypothèse n’a jamais été évaluée directement dans la littérature. Pour ce faire, 515 photographies de visages ont été annotées afin d’évaluer l’information véhiculée par de telles distances. Les résultats obtenus suggèrent que les études précédentes ayant utilisé des modifications de ces distances ont présenté 4 fois plus d’informations que les distances inter-attributs du monde réel. De plus, il semblerait que les observateurs humains utilisent difficilement les distances inter-attributs issues de visages réels pour reconnaître leurs semblables à plusieurs distances de visionnement (pourcentage correct maximal de 65%). Qui plus est, la performance des observateurs est presque parfaitement restaurée lorsque l’information des distances inter-attributs n’est pas utilisable mais que les observateurs peuvent utiliser les autres sources d’information de visages réels. Nous concluons que des indices faciaux autre que les distances inter-attributs tel que la forme des attributs et les propriétés de la peau véhiculent l’information utilisée par le système visuel pour opérer la reconnaissance des visages. / According to an influential view, based on studies of development and of the face inversion effect, human face recognition relies mainly on the treatment of the distances among internal facial features. However, there is surprisingly little evidence supporting this claim. Here, we first use a sample of 515 face photographs to estimate the face recognition information available in interattribute distances. We demonstrate that previous studies of interattribute distances generated faces that exaggerated 4 times this information compared to real-world faces. When interattribute distances are sampled from a real-world distribution, we show that human observers recognize faces poorly across a broad range of viewing distances (with a maximum accuracy of 65%). In contrast, recognition performance is restored when observers only use facial cues of real-world faces other than interattribute distances. We conclude that facial cues other than interattribute distances such as attribute shapes and skin properties are the dominant information of face recognition mechanisms.

Informelle Berichte zeigten größere Amplituden der durch Gesichter ausgelösten N170 Komponente im Ereigniskorrelierten Potenzial (EKP) bei asiatischen als bei kaukasischen Probanden. Als mögliche Ursache vermutete ich unterschiedliche Erfahrungen mit logographischen bzw. alphabetischen Schriftsystemen (Schriftsystem-Hypothese) oder die verstärkte Exposition mit unbekannten Gesichtern während der Immersion in eine neue soziale oder ethnische Umgebung (soziale Immersions-Hypothese). Zur Überprüfung dieser Hypothesen führte ich zwei kulturvergleichende Studien mit Erwachsenen bzw. Kindern durch. In Studie 1 untersuchte ich einheimische Chinesen und nicht-chinesische Auswärtige in Hongkong und deutsche Einheimische und chinesische Auswärtige in Berlin. Die Auswärtigen an beiden Orten zeigten größere N170 Amplituden auf Gesichter als die Einheimischen. Außerdem zeigten Deutsche, die erst kurze Zeit in Berlin lebten ähnliche Amplituden wie langjährige Einheimische. Insgesamt unterstützt Studie 1 die soziale Immersions-Hypothese, dass die Immersion in eine neue ethnische Umgebung zu einer Vergrößerung der N170 führt. Studie 2 untersuchte die Schriftsystem-Hypothese bei chinesischen und deutschen Erstlesern am Ende der ersten oder zu Beginn des zweiten Schuljahres an ihrem jeweiligen Heimatort. Die Ergebnisse unterstützen die Schriftsystem-Hypothese, dass chinesische Kinder eine größere N170 auf Gesichter zeigen als deutsche. Insgesamt konnte die vorliegende Dissertation zwei neue Einfluss-Faktoren auf das Gesichterverarbeitungs-System nachweisen, das erworbene Schriftsystem (logographische versus alphabetisch) und die Erfahrung sozialer Immersion in eine neue ethnische Umgebung. Diese Effekte zu ganz unterschiedlichen Zeitpunkten der Entwicklung (Kindheit vs. junges Erwachsenen-Alter) zeigen, dass das Gesichterverarbeitungs-System über lange Zeit seine Plastizität behält. / Informal reports have shown larger face-elicited N170 component of event-related potential (ERP) in Asians than Caucasians participants. I proposed that different experience with logographic versus alphabetic scripts (script system hypothesis) or by exposure to abundant novel faces during the immersion into a new social and/or ethnic environment (social immersion hypothesis) as a possible cause. To test these hypotheses, I conducted two cross-cultural ERP studies with adults and Children. In Study 1, I examined Chinese locals and non-Chinese foreigners in Hongkong, and German locals and Chinese foreigners in Berlin. It turned out that the foreigners in both locations showed larger N170 amplitudes to faces than the locals. In addition, Germans who had only lived in Berlin for a short time showed similar face N170 amplitudes as long-term Berlin residents. In sum, Study 1 supports the social immersion hypothesis that immersing into a new ethnic environment drives an increase of face N170. Study 2 investigated the scripts system hypothesis in Chinese and German early readers assessed at the end of the first-grade or at the beginning of the second grade in their respective home towns. The findings support the script system hypothesis that Chinese children showed larger face N170 amplitudes than German children. Overall, the present thesis demonstrated two new influencing factors on the face processing system, the acquired script system (logographic vs. alphabetic) and the social immersion experience in a new ethnic environment. More specifically, learning to read a visually complex logographic Chinese script or immersing into an other-ethnic social environment facilitates early perceptual processing of faces. These effects acquired at different stages of development (early childhood versus young adulthood) show that the face processing system retains its plasticity over a long period of time.