這一篇論文裡，我們討論如何計算開放式有限容量等候系統的穩定機率。其中到達時間和服務時間的機率分配都是Coxian分配。我們利用向量表示法（Product-Form Method）求解穩定機率，並建立C_{k}/C_{m}/1/4與C_{k}/C_{m}/1/6的穩定機率之表格。在使用向量表示法的過程中，計算所需的時間與系統容量無關。因此，在我們計算穩定機率的經驗中，當N>100時，我們可以明顯感覺出向量表示法比一般傳統方法有更快的計算速度。 / In this thesis, we study the C_{k}/C_{m}/1/N open queueing system with finite capacity, N. We use the product-form method to solve the steady-state probabilities and give tables of numerical results in examples of C_{k}/C_{m}/1/4 and C_{k}/C_{m}/1/6. The merit of this method is that the computation time is independent of N. In our computational experiments, we have observed that when the capacity size of queueing system, N>100, the computing efficiency of the product-form method is much better than that of a traditional method.

Les neurones sensoriels réagissent à des stimuli externes en émettant des séquences de potentiels d’action (“spikes”). Ces spikes transmettent collectivement de l’information sur le stimulus en formant des motifs spatio-temporels qui constituent le code neural. On observe expérimentalement que ces motifs se produisent de façon irrégulière, mais avec une structure qui peut être mise en évidence par l’utilisation de descriptions probabilistes et de méthodes statistiques. Cependant, la caractérisation statistique des données expérimentales présente plusieurs contraintes majeures: en dehors de celles qui sont inhérentes aux statistiques empiriques comme la taille de l’échantillonnage, ‘le’ modèle statistique sous-jacent est inconnu. Dans cette thèse, nous abordons le problème d’un point de vue complémentaire à l’approche expérimentale. Nous nous intéressons à des modèles neuro-mimétiques permettant d’étudier la statistique collective des potentiels d’action et la façon dont elle dépend de l’architecture et l’histoire du réseau ainsi que du stimulus. Nous considérons tout d’abord un modèle de type Intègre-et-Tire à conductance incluant synapses électriques et chimiques. Nous montrons que la statistique des potentiels d’action est caractérisée par une distribution non stationnaire et de mémoire infinie, compatible avec les probabilités conditionnelles (left interval-specification), qui est non-nulle et continue, donc une distribution de Gibbs. Nous présentons ensuite une méthode qui permet d’unifier les modèles dits d’entropie maximale spatio-temporelle (dont la mesure invariante est une distribution de Gibbs dans le sens de Bowen) et les modèles neuro-mimétiques, en fou / Sensory neurons respond to external stimulus using sequences of action potentials (“spikes”). They convey collectively to the brain information about the stimulus using spatio-temporal patterns of spikes (spike trains), that constitute a “neural code”. Since spikes patterns occur irregularly (yet highly structured) both within and over repeated trials, it is reasonable to characterize them using statistical methods and probabilistic descriptions. However, the statistical characterization of experimental data presents several major constraints: apart from those inherent to empirical statistics like finite size sampling, ‘the’ underlying statistical model is unknown. In this thesis we adopt a complementary approach to experiments. We consider neuromimetic models allowing the study of collective spike trains statistics and how it depends on network architecture and history, as well as on the stimulus. First, we consider a conductance-based Integrate-and-Fire model with chemical and electric synapses. We show that the spike train statistics is characterized by non-stationary, infinite memory, distribution consistent with conditional probabilities (Left interval specifications), which is continuous and non null, thus a Gibbs distribution. Then, we present a novel method that allows us to unify spatio-temporal Maximum Entropy models (whose invariant measure are Gibbs distributions in the Bowen sense) and neuro-mimetic models, providing a solid ground towards biophysical explanation of spatio-temporal correlations observed in experimental data. Finally, using these tools, we discuss the stimulus response of retinal ganglion cells, and the possible generalization of the co

Cette thèse a pour sujet l'étude de la réaction de la Diffusion Compton Profondément Virtuelle (DVCS) sur le proton e + p -> e' + p' + gamma (DVCS). Cette réaction est mesurée en analysant l'expérience e1-dvcs2 qui a eu lieu dans le Hall B du Jefferson Laboratory avec CLAS. La prise de données s'est déroulée du 22 octobre 2008 jusqu'au 23 janvier 2009. Cette analyse a pour but la détermination des sections efficaces non polarisées et les différences de sections efficaces polarisées du DVCS, dans divers bins en xB, Q^2, t et phi. Cette analyse compare les sections efficaces avec plusieurs mesures existantes du DVCS: une analyse parallèle de e1-dvcs2 et une analyse de e1-dvcs1. En factorisant l'élément de matrice qui correspond au DVCS en deux parties, calculables en QCD perturbative et non perturbative, on peut accéder aux Distributions de Partons Généralisées (GPDs) du proton, et ainsi obtenir une vue en 3D des distributions spatiales et en impulsion des quarks et des gluons dans le proton. / This thesis focuses on the Deeply Virtual Compton Scattering (DVCS) reaction e + p -> e' + p' + gamma (DVCS). The reaction is measured using the e1-dvcs2 experiment run at Jefferson Laboratory in Hall B using CLAS. The experiment took place from 22 October, 2008 to 23 January, 2009, and experiment run time of 90 days. This analysis focuses on the determination of the DVCS cross section in bins of xB, Q^2, t and phi, and makes a comparison with already existing and parallel analyses of DVCS. By factorizing the cross section of the reaction into perturbative and non-perturbative parts, we may relate the cross section of this reaction to Generalized Parton Distributions (GPDs) for the proton, and in doing so, provide better insight as to the distributions of quarks and gluons within it, including spacial distribution and contributions of angular momentum.

The consequences of substituting the denominator Q 3(p) - Q 1(p) by Q 2 - Q 1(p) in Groeneveld's class of quantile measures of kurtosis (γ 2(p)) for symmetric distributions, are explored using the symmetric influence function. The relationship between the measure γ 2(p) and the alternative class of kurtosis measures κ2(p) is derived together with the relationship between their influence functions. The Laplace, Logistic, symmetric Two-sided Power, Tukey and Beta distributions are considered in the examples in order to discuss the results obtained pertaining to unimodal, heavy tailed, bounded domain and U-shaped distributions.

The vast majority of severe storm and tornado research is conducted in the natural laboratory of the Great Plains region of the United States. As a result, much of the knowledge and technology applied to storm forecasting is developed in the Great Plains environment. However, it has been shown that there is a maximum of strong and violent tornadoes in the region extending from Arkansas eastward into Alabama. In addition, various researchers have found strong severe storm thermodynamic signatures unique to regions such as the Northeast and Mid-Atlantic. This study has analyzed five decades of tornado data for the state of Mississippi. Thermodynamic results indicate that Mississippi has a tornado environment distinctly different than that of the Great Plains. The spatial distribution of the tornado events also indicates that mesoscale processes between the Earth's surface and the lower troposphere may play a significant role in determining the genesis location of violent tornadoes in the historical Delta region of Mississippi. It is anticipated that an understanding of environments unique to Mississippi tornadoes will lead to better forecasts and more comprehensive storm analysis, which will ultimately save lives and property.

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In this paper we describe a version of transformed density rejection that requires less uniform random numbers. Random variates below the squeeze are generated by inversion. For the expensive part between squeeze and density an algorithm that uses a coverering with triangles is introduced. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The fossil population structure of the gastropod Neptunea angulata from the late Pliocene and Early Pleistocene was investigated in this project in order to contribute to a wider study on the influence of predation on populations and the evolutionary history of organisms. Over time, predator-prey relationships can drive evolution in a way similar to the Red Queen Hypothesis. However, before the effects of predation can be understood one must determine how the population dynamics functioned without the influence of predation. There are a number of problems that arise when determining population dynamics for fossil assemblages. These are usually caused by missing fossil data and the uncertain nature of their absence. Bias is rife within fossils at various stages from post-portem processes to when they are present in museum collections. One way to estimate these biases is to investigate the population structures of the fossils both directly from the fossil record and from museum collections. The variation in oxygen istopes found in N. angulata shells corresponded to yearly cycles which then were counted to determine the age of the specimen at time of death. Measuring the length of the spiral at yearly intervals provided the growth rate for the organism while it was alive. The growth rates were then used to determine the ages of specimens based on their size. The resulting ages were organized into an age distribution graph which was used to determine any museum bias. Bias in the preservation was also investigated by measuring the taphonomic damage of organisms of different size and then determine the distributions of size vs taphonomy. The ages of three specimens were found to differ even though the organisms had similar whorl lengths. As a result the growth equations differed and so different age distributions were calculated from each growth equation. All the age distributions demonstrated that the museum collections did show some bias against the smaller sized and thus younger specimens. There also appeared to be a size bias towards small N. angulata within the fossil record, with the extremely small individuals missing. The majority of the smallest specimens found in the field collections were not actually N. angulata specimens. A major problem with the results was a lack of data and a small sample size and it is highly recommended that an extensive collection and review of material be undertaken to fully determine the population structure present in the fossil assemblages. Other parts of the study, for example, the growth rates also require larger data sets in order for the confidence of the data to be improved. / I detta projekt studerades snäckpopulationer (Neptunea angulata) från Pliocen och Pleistocen för att besvara bredare frågeställningar om predation och dess inflytande på populationer och evolution. Innan man kan fastställa effekten av predation så behöver man förstå hur populationen betedde sig utan predationstryck. Flertalet problem uppstår när man studerar fossila populationer: tillgången på data kan vara begränsad och det kan vara svårt att se vad som saknas och varför. Information från fossil förloras från tiden som organismen dör fram till att de återfinns i museisamlingar. Ett sätt att uppskatta informationsförlusten är att studera fossil såväl i fossilbäddar som i museisamlingar. Genom att använda sig av den observerade cykliska skillnaden i stabila syreisotoper mellan olika tillväxtzoner i skalen av Neptunea angulata var det möjligt att uppskatta åldern på en organism vid en viss längd. Hastigheten med vilken snäckan växte beräknades genom att mäta förändringen i längd mellan olika åldrar. Genom att beräkna hur snabbt en snäcka växte så var det möjligt att använda storleken på fossilerna för att uppskatta dess ålder då den dog. Fossilen organiserades efter ålder för att visa populationsstrukturer. Förluster av fossil efter deposition uppskattades undersöktes genom att bestämma om mindre storleksgrupper var mer skadad än större storleksgrupper . Den varierade tillväxten hos olika snäckor användes för att beräkna dess åldrar. Det upptäcktes att museisamlingar tenderade att inneha större och äldre individer. Det tycktes också finnas färre små fossil av Neptunea angulata inom opartisk samling. Några av de extrement små individerna saknades helt och majoriteten av de minsta fossilen var inte ens Neptunea angulata. Skador på fossilen var större ju mindre individerna var. Mängden data inverkade negativt på denna studie och därför rekommenderas en omfattande genomgång av de tillgängliga samlingarna för att bättre kunna besvara frågor kring denna population i framtiden.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: This thesis explores how human dictated methods of introduction and species-specific traits interact to define spatial patterns in invasive plant populations using Acacia elata as a model species. I initially asked whether the relatively small invasive extent (when compared to congeners introduced for forestry or dune stabilization) of a species used widely for ornamental purposes (A. elata) is due to low rates of reproduction in South Africa. Results indicate that A. elata has similar traits to other invasive Australia Acacia species: annual seed input into the leaf litter was high (up to 5000 seeds m-2); large seedbanks develop (>20 000 seeds m-2) in established stands; seed germinability is very high (>90%); seeds accumulate mostly in the top soil layers but can infiltrate to depths of 40cm; and seed germination appears to be stimulated by fire. I argue that the current limited distribution of invasive A. elata populations is not attributable to species-specific reproductive traits. Following on from this I addressed the relative importance of species traits, the recipient environment, and introduction dynamics using species distribution models and spread models defined using a range of parameters representative of invasive Australian acacia species. Results indicate that in the early stages of simulated invasions, the number of trees introduced was the most important parameter influencing abundance and extent, while the placement of introduction foci in urban areas associated with ornamental introductions limited the extent and abundance of invasive populations. I suggest that conditions relating to human-mediated introduction events initially mask the influence of intrinsic species traits and help to explain the failure and success of species associated with specific human-shaped pathways. Third, I used scale-area curves to determine how these human-dictated introduction conditions influenced the spatial structure of populations. The fractal dimension (Dij) of A. elata populations indicates plot scale (2.5-25m) spread with high densities that are increasing. Artefacts of introduction history were observed at the regional scale (2.5-25km) - populations are contiguous around introduction foci such as towns and roads. Moreover, fragmentation of A. elata populations at local to landscape scales (0.25-2.5km) is due to a combination of the haphazard regional placement and limited secondary dispersal vectors, both of which can be linked to their introduction history. In summary, this study used a combination of field-based data, modelling techniques and broad-scale sampling methods to assess how intrinsic species traits and introduction conditions mediate invasive spread. I conclude that introduction history can have a long-lasting (100+ years) influence on the spatial structure and distribution of invasive plants, which can mask the influence of individual species traits. / AFRIKAANSE OPSOMMING: Alhoewel menigte plant spesies deur mense ingevoer word, word slegs 'n klein hoeveelheid van plante indringers. Die beperkte aantal spesies wat in nuwe habitatte vestig en versprei, kan grotendeels toegeskryf word aan die omgewing en mensgemaakte hindernisse ten opsigte van oorlewing, voortplanting en verspreiding. In hierdie tesis gebruik ek Acacia elata as ʼn model spesie om te ondersoek hoe die invoeringsproses sowel as spesie spesifieke eienskappe die ruimtelike struktuur van indringende populasies bepaal. Aanvanklik was my vraag of die relatiewe klein indringingsarea van ʼn spesie wat ingevoer is vir ornamentele doeleindes (Acacia elata), teenoor die groot indringingsareas van Australiese Acacia-spesies wat ingevoer is vir bosbou of duin stabilisering, die gevolg is van lae voortplantings tempo in Suid-Afrika. Resultate dui daarop dat A. elata soortgelyke eienskappe as ander indringende Australië akasia spesies het: jaarlikse saad produksie is hoog (tot 5000 sade m - 2); groot ontwikkelde saadbanke (> 20 000 sade m - 2); hoë saad ontkieming (> 90 %); saad versamel in die boonste grondlae, alhoewel dit kan infiltreer tot 'n diepte van 40 cm; laastens, ontkieming word deur vuur gestimuleer. Hierdie resultate stel voor dat die huidige beperkte verspreiding van indringende A. elata populasies nie die gevolg is van spesie spesifieke voortplantings eienskappe nie. Gevolglik het ek 11 indringende Australiese akasia-spesies ondersoek om die relatiewe belangrikheid van spesie eienskappe, die area waar hul geplant is, asook invoerings aspekte te ondersoek. Resultate wys dat die aantal bome wat ingevoer is, die belangrikste eienskap was ten opsigte van digtheid en verspreiding van ʼn indringende spesie, terwyl invoering naby fokuspunte in stedelike gebiede weer spesie digtheid en verspreiding beperk. Hierdie resultate toon dat spesies eienskappe aanvanklik nie ʼn groot invloed het op hul sukses nie, maar dat hul sukses eerder afhang van waar hul geplant word. Derdens, gebruik ek skaal - area kurwes om te bepaal hoe die invoering van A. elata die ruimtelike struktuur van populasies beïnvloed het. Die fraktale dimensie (Dij) van A. elata bevolkings dui op verspreiding by die plaaslike vlak (2,5 - 25m), wat voorstel dat verspreiding nie op hierdie skaal beperk is nie. Eienskappe van die rede/metode van invoering was wel waargeneem op die groter skaal (2.5 - 25km) waar populasies digter was naby dorpe en paaie. Die intermediêre skaal (0,25 - 2.5km) dui daarop dat A. elata populasies huidiglik beperk word deur 'n kombinasie van lukrake plasing en beperkte sekondêre verspreiding, albei wat gekoppel kan word aan hul invoer geskiedenis. Hierdie studie maak dus gebruik van 'n kombinasie van veld gebaseerde data, modellerings tegnieke en breë skaal steekproefmetodes om te evalueer hoe algemene spesies eienskappe en invoer toestande verspreiding bepaal. Sodoende verskaf ek ʼn raamwerk om die invloed van invoer toestande op die ruimtelike struktuur en verspreiding van ornamentele plant indringers te verstaan.

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