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The paper examines the impact of fees on the return of a fund investment using different simulation and fee structure models. The results show that fees have a significant expected impact, particularly for well-performing funds. Two simulation models were used, the Geometric Brownian Motion (GBM) model and Merton Jump Diffusion (MJD) model. Two fee structures were also analysed for each simulation, a High-water mark fee structure and a Hurdle fee structure. Comparing the GBM and MJD models, the two tend to generate very similar fee statistics even though the MJD model's day-to-day returns fit better with empirical data. When comparing the HWM and Hurdle fee models, larger differences are observed. While overall average fee statistics are similar, the performance fee statistics are significantly higher in the Hurdle fee structure for assets achieving higher returns, e.g. at least an 8% annual return. However, the HWM fee structure tends to generate higher performance fees for assets with low returns. Regression models are also developed for each combination of the simulation model and fee structure. The regression models reflect the above conclusions and can for investors serve as simple key indicators to estimate expected fund fee payments. The GBM regression results are likely more useful than the MJD regression results, as the parameters of the former are easier to calculate based on historical return data. / Uppsatsen undersöker effekten av avgifter på avkastningen av en fondinvestering med hjälp av olika simuleringar och avgiftsmodeller. Resultaten visar att avgifter förväntas ha en betydande påverkan, särskilt för fonder som genererar hög avkastning. Två simuleringar användes, Geometric Brownian Motion (GBM) och Merton Jump Diffusion (MJD). Två avgiftsstrukturer analyserades också för varje simulering, en High-water mark avgiftsstruktur och en Hurdle avgiftsstruktur. Jämförelse mellan GBM och MJD-modellerna visar att de två tenderar att generera mycket liknande avgiftsstatistik trots att MJD-modellens dagliga avkastning passar bättre med empiriska data. Vid jämförelse av HWM- och Hurdle avgiftsmodellerna observeras större skillnader. Medan den övergripande genomsnittliga avgiftsstatistiken är liknande för avgiftsmodellerna, är resultatbaserade avgifterna betydligt högre i Hurdle avgiftsstrukturen för tillgångar som uppnår högre avkastning, t.ex. minst 8% årlig avkastning. Däremot tenderar HWM-avgiftsstrukturen att generera högre resultatbaserade avgifter för tillgångar med låg avkastning. Regressionsmodeller utvecklades också för varje kombination av simulering och avgiftsstruktur. Regressionmodellerna återspeglar ovanstående slutsatser och kan för investerare fungera som enkla nyckeltal för att uppskatta förväntad kostnad av fondavgifter. GBM-regressionsresultaten är sannolikt mer användbara än MJD-regressionsresultaten, eftersom parametrarna för den förra är lättare att beräkna baserat på historisk avkastningsdata.

The study of neural and behavioural mechanisms of perceptual decision making is often done by experimental tasks involving the categorization of sensory stimuli. Among the key perceptual tasks that decision neuroscience researchers use are motion discrimination paradigms that include tracking and specifying the net direction of a single dot or a group of moving dots. These motion discrimination paradigms, such as the random-dot motion task, allow the measurement of the participant's perceptual decision making abilities in multiple task difficulty levels by varying the amount of noise in the sensory stimuli. Computational models of perceptual decision making, such as the drift-diffusion model, are widely used to analyze the behavioural measurements from these motion discrimination experiments. However, the standard drift-diffusion model can only analyze the average measures like reaction times or the proportion of correct decisions to explain the behavioural data. In the past decade, an emerging computational modeling approach was introduced to analyze the choice behaviour based on precise noise patterns in the sensory stimuli. These computational models that use spatiotemporal stimulus details have shown promise in the single-trial analysis of motion discrimination behaviour. In this thesis, I further develop the advanced computational models of perceptual decision making that use spatiotemporal dynamics of motion stimuli to provide detailed explanations of perceptual choice behaviour. First, I demonstrate the usefulness of equipping an extended Bayesian Model, equivalent to the extended drift-diffusion model, with trial-wise stimulus information leading to a significantly better explanation of behavioural data from a single-dot tracking experiment. Second, I show that the extended drift-diffusion model constrained by spatiotemporal stimulus details can explain the consistent biased choice behaviour in response to stochastic motion stimuli. Based on this model-based analysis, I provide evidence that the source of the observed biased choice behaviour is the presence of subtle motion information in the sensory stimuli. These results further emphasize the effectiveness of using spatiotemporal details of stochastic stimuli in detailed model-based analyses of the experimental data and provide computational interpretations of the data related to underlying mechanisms of perceptual decision making.

網際網路是繼電子計算機發明後，帶給人類最大衝擊的一項革命，它突破了地理的籓籬，資訊的流動可以在極短暫的時間內跨越國界，這是其他媒體所望塵莫及的。而這種傳播特性最為人所詬病的問題之一，就是網路謠言的充斥。透過E-mail、BBS、NEWS、WWW等各種不同的管道散播出來的謠言，不僅可能造成個人的名譽受損、企業的形象破壞，許多的犯罪手法也因而產生。就企業主而言，網路謠言的殺傷力莫過於對公司形象與品牌聲譽的損害，而如何防範與澄清消息的正確性，已成為企業公關與危機管理的重要一環。 本研究則分析現有的謠言與消息來源理論，探討謠言的結構、傳播過程以及其社會心理成因等，並比較電腦中介傳播 (CMC) 與一般謠言口耳相傳 (FtF) 之下的謠言特性，以及探討傳統大眾媒體與網路媒介傳播謠言效果之差異，歸納出影響謠言傳播的可能因素包括謠言的可相信度、渾沌不安、訊息特性、涉入度、網路訊息惰性、人口統計變數與網路使用行為等。利用這些可能的變數，本研究設計兩組實驗來衡量謠言散播與闢謠效果，實驗一利用可相信度與渾沌不安兩個變數操弄謠言，並以小樣本的散播實驗來衡量謠言操弄的結果，探討謠言散播模式與影響變數，並以計數器追溯謠言散播的情形，來了解謠言散播的真實面貌；實驗二則以類似的實驗方法，選擇一則已發生的網路謠言案例來研究謠言散佈模型，並以發送闢謠信件的方式來探討其謠言防治效果。 實驗一在經網路謠言散播實驗之後，發現操弄變數的差異並不顯著，故實驗一改採Regression檢定，最後發現可相信度、訊息特性與渾沌不安是影響謠言散播的主要因素，網路訊息惰性則對謠言散播有間接影響效果，而可相信度有部分的中介效果；在電子郵件闢謠實驗方面，實驗二發現可相信度與網路訊息惰性對訊息的散播有顯著影響效果，而可相信度有部分的中介效果。由此可知，兩個實驗的散佈模式並不相同，其原因有可能是因為涉入度的差異。另外，兩個實驗皆發現經由電子郵件散播的訊息符合創新採用理論，其中實驗一的謠言與實驗二的闢謠訊息為Rogers所說的不完全散佈模式，而實驗二的謠言則為所謂的「S」形創新散佈曲線。 此外，本研究利用謠言的追蹤計數，得到了散播曲線與訊息散播方程式，並估計而求出了謠言的散播速度。由追溯的結果得知，網路謠言傳播的速度十分快速，尤其實驗二的謠言在第2.2日時就達擴散曲線的反曲點，一星期內散佈的人數高達原來樣本數的兩倍；相反的，不被眾人散播的謠言可以在短短幾天之內就趨於平息。而本研究也對網路訊息的「散播者」與「非散播者」作出比較，發現散播者的散佈可能性、對謠言的相信度、渾沌不安等都比非散播者高，但網路訊息惰性則較低。在粗淺的瞭解這群可能的網路「意見領袖」之後，企業界可以專注於這群人作有效的闢謠公關活動，讓網路謠言的管理更有效率。 最後，本研究彙整謠言的應對策略，並對企業因應謠言的危機管理的模式，提出許多的方案與建議，讓企業界在面對網路謠言時，能有參考的依循，並將損害減至最低。 / Not only has the internet increased the efficiency of communication, it has also brought out severe crises in the real world. Messages can be circulated all over the world in just seconds. As a result, geographical barriers have been virtually broken down. However, while rumors and hoaxes can easily be distributed through e-mail, BBS, news group, and so on, such false information may cause severe damage to individuals and corporations concerned, even trigger criminal offenses. How to prevent potential damage of commercial reputations which may cause by internet rumors and clarify the existing grapevines is one of the most important issues each corporation needs to address in the present information society. This thesis is inclined to find out the differences between Computer Mediated Communication (CMC) and Face-to-Face (FtF) Communication in terms of the variables which affect the diffusion of rumors, i.e. Credibility, Anxie-uncertainty, Message Property, Involvement, Internet Inertia, demographical variables, and personal internet behavior. Two experiments are designed in this research. Exp.1 operates Credibility versus Anxie-uncertainty into four rumors and illustrates the correlation between Diffusion Possibility and each of the aforesaid independent variables which can facilitate establishing the diffusion model for Internet Rumors accordingly. Exp.2 is an empirical study based on the diffusion model built up in Exp.1. A pre-selected existing rumor is used as the research sample. It remodels the rumor diffusion and measures the clarification effect through e-mail as well. Moreover, both experiments use Site Meter to trace the mechanism of rumor diffusion. Numbers of the rumor being viewed and its responses and clarifications can be easily counted. According to experiments, Credibility and Anxie-uncertainty are originally well operated in pretests. However, the manipulated variables are not fully distinguished in Exp.1. Hence, Regression is employed to test the hypotheses and as a result, Credibility, Anxie-uncertainty, and Message Property are the key variables that directly influence rumor diffusion in Exp.1 while Internet Inertia has indirect effect on the outspread of a rumor. In Exp.2, both Credibility and Internet Inertia play important roles in the diffusion behavior while Credibility acts as a partial mediating variable in this case. Additionally, this research also shows the possibility and degree that Involvement might be the factor which causes discrepancy between these 2 models. However, it needs to be confirmed by further research. Moreover, both models fit the Distribution Theory of Innovations developed by Rogers. Rumors in Exp.1 and clarify message in Exp.2 are both Unsuccessful Diffusion while rumor in Exp. 2 belongs to S-shaped Normal Diffusion. Incidentally, diffusion curves and the function of rumor diffusion are obtained to work out through simulation equations and so are the diffusion rates, which surprised us for their rapid distribution. The inverse point was reached in the 2.2 days after the rumor message was distributed in Exp.2, and almost two folds of the original group numbers were reached in just one week. On the other hand, rumors which were not circulated would be quelled in few days. Comparisons between the Distributor and the Non-distributor in the Internet society are also made in this study in facilitating the management of corporate grapevines. The Distributor believes rumors and are more aggressive in rumor distribution and shows higher Anxie-uncertainty, while their Internet Inertia are lower than Non-distributor. Knowing more about the so-called Internet “Opinion Leader” helps corporations focus on crisis management by initiating effective public activities not only because they are cores of grapevines but are also easier to approach than others. Finally, various corporate strategies of confining rumors are developed in the thesis. Suggestions and alternatives are provided in conclusion. Corporate administrators can therefore take them for reference when dealing with rumor-caused crises.

Die Forschung an der Hefe Saccharomyces cerevisiae – auch als Bäckerhefe bekannt – hat sich für die biologische Grundlagenforschung als unentbehrlich erwiesen und führte zu wichtigen Erkenntnissen in der Erforschung von Krankheiten wie Krebs. Am Beispiel der Paarung von Hefezellen werden in dieser Arbeit wesentliche Aspekte der eukaryotischen Zellbiologie untersucht. In der Haplophase des Lebenszyklus der Hefe, treten haploide Zellen als Paarungstyp MATa oder MATα auf. Diese Paarungstypen kommunizieren über Pheromone, die in ein extrazelluläres Medium abgesondert werden und von Zelloberflächenrezeptoren des komplementären Paarungstyps erkannt werden. Hefezellen wachsen in die Richtung eines möglichen Paarungspartners, da sie sich nicht aktiv bewegen können. Die Auswertung von empirischen Daten aus der Fluoreszenzmikroskopie und Rasterkraftmikroskopie (AFM) mit mathematischen Modellen ermöglichte die Rekonstruktion wesentlicher Prozesse der Hefepaarung: (i) Interzelluläre Kommunikation über die Sezernierung und Rezeption von Pheromonen, (ii) Aufbau der Zellpolarität als Reaktion auf die Pheromonantwort, (iii) Induktion und Mechanik der Zellformänderung. Folgende Modelle wurden dazu entwickelt: (i) Die interzelluläre Kommunikation wurde unter Verwendung von zellulären Automaten mit Hilfe von Reaktions-Diffusions (RD) Gleichungen modelliert. Das Modell zeigte, dass die gegenseitige Stimulierung und erhöhte Pheromonabsonderung zu einer verbesserten Abstimmung in der Paarung in der Zellpopulation führt. (ii) Ein Turing- und ein Phasenseparations- Mechanismus wurden als Modelle zum Aufbau der Zellpolarität verwendet. Volumen-Oberflächen gekoppelte RD Gleichungen wurden analytisch und numerisch mit der Finite-Elemente-Methode (FEM) untersucht. (iii) Die Zellwandveränderung wurde mit klassischer Kontinuumsmechanik und der FEM Methode modelliert. Dies ermöglichte eine Beschreibung der reversiblen elastischen und der irreversiblen plastischen Verformungen der Zellwand. / Research on the yeast Saccharomyces cerevisiae – also known as baker’s yeast – has been essential not only for fostering basic biological knowledge but even more so for contributing towards understanding diseases such as cancer. In this thesis, general biological phenomena occurring in eukaryotic cells are investigated, exemplified by the mating process of yeast. In the haploid phase of their life cycle, yeast cells occur as mating type MATa or MATα, both of which communicate via pheromones that are secreted in an extracellular medium and can be sensed by cell-surface receptors of the complementary mating type. In order to mate, yeast cells grow towards a potential mating partner, since they are not able to actively move. Mathematical models on the basis of fluorescence and atomic force microscopy (AFM) data were developed. The key aspects of the yeast mating process that I examined were (i) intercellular communication of cells via pheromones, (ii) the initial symmetry break and implementation of cell polarity, and (iii) subsequent morphogenetic changes. The methods used and findings were as follows: (i) Pheromone secretion and sensing motifs were modelled using cellular automata models based on reaction-diffusion (RD) equations. My models show that mutual stimulation and increased pheromone secretion between cells improves mating efficiency in cell populations. (ii) To explain yeast mating decisions, two possible model types for cell polarity were tested: a Turing-type and a phase-separation mechanism. Bulk-surface RD equations were investigated analytically and numerically using the finite element method (FEM). Typical cell shapes were reconstructed in 2D and 3D. (iii) The cell wall was modelled using classical continuum mechanics that allows for reversible elastic and irreversible plastic cell wall deformation. Mathematical modelling demonstrated that all three processes investigated are precisely orchestrated and interlocked during yeast mating.

保險業及再保險業以往對於巨災危險的風險管理方式大部份都佼給全世界的再保險承保能量去承擔。然而從1995年開始，美國芝加哥交易所(CBOT)與產物損失部門(PCS)共同推出巨災保險選擇權，提供保險人以及再保險人利用國際金融市場移轉核保業務上所承擔之巨災危險的管道。此種業務上的巨災危險提供保險業處理巨災損失的新管道，例如產險業因為天然災害或是人為疏失所導致的鉅額核保損失以及壽險業的團體保險和健康保險的鉅額損失。巨災保險選擇權是一種新的衍生性金融商品，其交易標的物是專門針對保險業所承保的業務（尤其是巨災），因此如果運用得當，除了能有效的分散核保風險之外，更可以避免傳統的再保險契約所衍生的問題。 本研究在第一章首先說明台灣地區是地震、颱風以及水患等天然災害頗為集中的地區，因為傳統再保險的分散風險方式有其成本較高以及資訊不對稱的問題，所以保業以及再保險業應該考慮其他類型的危險管理策略。第二章以巨災保險選擇權評價的相關基礎理論為主要的架構，並且探討美國PCS所開發的巨災保險選擇權，並說明如何利用此種金融工具移轉保險與再保險人因地理上的核保因素所產生的風險。 第三章以及第四章討論模擬方法與分析模擬所得的結果，我們並利用情境分析的方式，探討在單位時間內，平均跳躍次數對於每一個模型中假設，交易標的物為損失指數時的影響，以及依此損失指數所得對於巨災保險選擇權價格之變化幅度。第五章則是歸納本研究所得的結果並且提出後續研究的建議。 / The insurance and reinsurance industries traditionally transfer their insurance risk of catastrophe disasters through the international reinsurance market. Since the capacity of the international reinsurance market is not always available to cover the entire risks. In 1995, CBOT (Chicago Board of Trade) and PCS (Property Claims Service) have begun trading the PCS catastrophe options Through the catastrophe options, the insures and reinsures could hedging their operating risks in the international financial market. These risks consist of large amount of underwriting losses from the natural disasters, personal default in property insurance, inflation of claims amount and the large claims in group insurance and health insurance. The loss ratios of the insured business are trading through the catastrophe options. Hedging the operating risks of the insures and reinsures in the financial market could effectively reduce the costs and avoid the complexity from the reinsurance contracts. In this study, we have reviewed the development of the catastrophe option. Asian style call options are illustrated to monitor the process of option pricing. The trading loss ratios are modeled through lognormal distribution based on the claim experience collected from 1970-1996. The methodology of pricing the modified options based on pure jump model proposed by Cox, et al (1976) and the jump diffusion model proposed by Merton (1976) are discussed. Computer simulations and scenario analysis are performed to investigate the pricing of Asian style catastrophe option under various proposed models. Sensitivity analysis is also completed at various parameters in the jump process. Finally, comments on future works and the limitation of the proposed risk-transfer mechanism using catastrophe options are discussed.

Le travail présenté dans ce mémoire avait pour objectif d'étudier le processus de la pénétration d'eau dans les composites en carbone/époxyde dans un premier temps, et dans un deuxième temps, d'étudier l'effet de la prise en eau par ces matériaux sur les performances mécaniques des composites et leur joints collés. L'intégration de ces phénomènes physiques dans la modélisation numérique est d'une grande importance dans la prédiction de la durabilité d'une structure en composite subissant un vieillissement hygrothermique. Par conséquent, ce travail consiste non seulement en des observations expérimentales, mais aussi en des simulations numériques. Des corrélations entre les résultats obtenus permettent d'une part de mieux comprendre ce qui se passe dans un système composite avec l'assemblage collé soumis à des charges mécaniques, de l'initiation d'endommagement jusqu'à la rupture finale ; d'autre part, de valider un modèle numérique robuste dans le but de la conception et de l'optimisation. Les originalités de ce travail se situent à différents niveaux en proposant : 1. un nouveau modèle de diffusion à deux-phases permettant de mieux décrire l'effet de l'épaisseur des stratifiés sur la pénétration de l'eau; 2. un nouveau modèle RPM " Residual Property Model " afin de prévoir la dégradation des propriétés mécaniques due à la prise en eau ; 3. une nouvelle loi de traction-séparation linéaire-exponentiel pour décrire la courbe-R observée dans les essais DCB en mode I pur sur les composites stratifiés afin de les intégrer plus facilement dans les modèles numériques

This thesis consists of a summary and five papers, dealing with financial applications of optimal stopping, optimal control and volatility. In Paper I, we present a method to recover a time-independent piecewise constant volatility from a finite set of perpetual American put option prices. In Paper II, we study the optimal liquidation problem under the assumption that the asset price follows a geometric Brownian motion with unknown drift, which takes one of two given values. The optimal strategy is to liquidate the first time the asset price falls below a monotonically increasing, continuous time-dependent boundary. In Paper III, we investigate the optimal liquidation problem under the assumption that the asset price follows a jump-diffusion with unknown intensity, which takes one of two given values. The best liquidation strategy is to sell the asset the first time the jump process falls below or goes above a monotone time-dependent boundary. Paper IV treats the optimal dividend problem in a model allowing for positive jumps of the underlying firm value. The optimal dividend strategy is of barrier type, i.e. to pay out all surplus above a certain level as dividends, and then pay nothing as long as the firm value is below this level. Finally, in Paper V it is shown that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process.

經由愈來愈多的實證研究發現，的確在利率的變動過程中，除了包含連續性行為，即遵循”擴散”模式(diffusion process)，亦包含了不連續性行為，也就是有著跳躍(jump)的情形發生。因此顯示出假設利率隨機過程僅為連續性的擴散模型已是不足夠的，跳躍-擴散模型(Jump-diffusion model)顯然會比純粹擴散模型有著更好的解釋能力。而市場模型(LIBOR market model)的提出，則說明了遠期LIBOR利率模型較能描述市場實際的利率型態，並且可方便使用市場資訊，進行模型參數校準。 所以本研究旨在以LIBOR market model 加上跳躍過程，即遠期LIBOR利率的跳躍-擴散模型，分別針對歐洲美元期貨與利率結構型債券中的滾雪球式累息債券建立評價方法。由於所選用動態模型的複雜度，使得封閉解的求出不易，因此在文中，最後是採用蒙地卡羅模擬法，求兩商品的數值解。在後續研究上，本文還挑出了幾個最直接影響商品價值的因素，如殖利率、波動度、跳躍幅度等，進行各種情境下商品價值的敏感度分析，以提供投資人與發行商在考量風險因子所在時的一個參考。

L'objectif de ce travail porte sur la généralisation de la modélisation de la gravure du silicium dans les plasmas de fluor ou de chlore à celle de la gravure des éléments de la colonne IV et des composés III-V de structure cristalline de type diamant ou zinc-blende dans les plasmas d'halogènes, i.e. fluor, chlore, brome et iode. Dans ce contexte, les effets stériques et de diffusion en volume et/ou en surface en constituent les problématiques principales. Cette généralisation s'appuie sur le modèle de gravure de Petit et Pelletier qui, par rapport aux modèles antérieurs, prend en compte un certain nombre d'hypothèses distinctes ou additionnelles telles que les interactions répulsives entre adatomes d'halogènes proches voisins, les mécanismes de Langmuir-Hinshelwood pour la formation des produits de réaction, la nature mono-couche ou multi-couches de l'adsorption, et la diffusion des adatomes en surface. Les effets stériques relatifs à la diffusion des atomes d'halogènes à travers les surfaces (100) des structures cristallines des éléments de la colonne IV et des composés III-V définissent une première loi de similitude entre la maille du réseau cristallin et le rayon ionique de Shannon des atomes d'halogènes concernant leurs conditions de diffusion en volume. Cette loi se traduit par un diagramme prévisionnel, commun aux éléments de la colonne IV et aux composés III-V, délimitant les systèmes de gravure de types mono-couche et multi-couches. Les effets stériques relatifs aux mécanismes réactionnels de gravure sur les surfaces (100) aboutissent à des secondes lois de similitude entre la maille du réseau et le rayon covalent des adatomes d'halogènes caractérisant la nature de la gravure : gravure isotrope, gravure anisotrope, ou absence de gravure. Ces lois de similitude, distinctes pour les éléments de la colonne IV et les composés III-V (stœchiométrie différente des produits de réaction), se traduisent par deux diagrammes prévisionnels délimitant les différents domaines de gravure. Les diagrammes prévisionnels pour les éléments de la colonne IV ont pu être validés, d'une part, à partir des résultats expérimentaux antérieurs, et, d'autre part, en l'absence de données, à partir d'études expérimentales complémentaires : gravure de Si et Ge en plasma de brome et d'iode, gravure de Sn en plasma d'iode. / The objective of this work is the generalization of the modeling of the etching of silicon in fluorine or chlorine plasmas to that of the etching of the elements in column IV and of III-V compounds with diamond-like or zinc-blend crystal structure in halogen plasmas (i.e. fluorine, chlorine, bromine and iodine). In this context, steric effects and volume and/or surface diffusion are the main issues. This generalization is based on the etching model of Petit and Pelletier which, compared to previous models, takes into account a number of separate or additional assumptions such as the repulsive interactions between halogen adatoms in nearest neighbor positions, the Langmuir-Hinshelwood mechanisms for the formation of reaction products, the mono-layer or multi-layer nature of the adsorption, and the diffusion of adatoms on the surface. Steric effects related to the diffusion of halogens through the (100) surfaces of the crystal structures of the elements of column IV and III-V compounds define a first law of similarity between the crystal lattice and the Shannon ionic radius of the halogen atoms concerning their bulk diffusion conditions. This law results in a forecast diagram, common to column IV elements and III-V compounds, delimiting the mono-layer or multi-layer type of the etching systems. Steric effects related to the reaction mechanisms of etching on (100) surfaces lead to the second laws of similarity between the crystal lattice and the covalent radius of halogen adatoms characterizing the etching behavior: isotropic etching, anisotropic etching or no etching. These laws of similarity, distinct between the elements of the column IV and III-V compounds (different stoichiometry of the reaction products), result in two forecast diagrams delimiting the distinct etching domains. Forecast diagrams for column IV elements have been validated, first, from previous experimental results, and, secondly, in the absence of data, from additional experimental studies: etching of Si and Ge in bromine and iodine plasmas, and etching of Sn in iodine plasmas.