Dans cette thèse, nous proposons une analyse probabiliste de deux problèmes de biologie moléculaire dans lesquels la stochasticité joue un rôle essentiel : la polymérisation des protéines dans les maladies neurodégénératives ainsi que le raccourcissement des télomères. L’agrégation des protéines en fibrilles amyloïdes est un important phénomène biologique associé à plusieurs maladies humaines telles que les maladies d’Alzheimer, de Huntington ou de Parkinson, ou encore l’amylose ou bien le diabète de type 2. Comme observé au cours des expériences reproduisant les petits volumes des cellules, les courbes d’évolution cinétique de l’agrégation des protéines présentent une phase de croissance exponentielle précédée d’une phase de latence extrêmement fluctuante, liée au temps de nucléation. Après une introduction au problème de polymérisation des protéines dans le chapitre I, nous étudions dans le chapitre II les origines et les propriétés de la variabilité de ladite phase de latence ; pour ce faire, nous proposons un modèle stochastique minimal qui permet de décrire les caractéristiques principales des courbes expérimentales d’agrégation de protéines. On considère alors deux composants chimiques : les monomères et les monomères polymérisés. Au départ, seuls sont présents les monomères ; par suite, ils peuvent polymériser de deux manières différentes : soit deux monomères se rencontrent et for- ment deux monomères polymérisés, soit un monomère se polymérise à la suite d’une collision avec un autre monomère déjà polymérisé. Malgré son efficacité, la simplicité des hypothèses de ce modèle ne lui permet pas de rendre compte de la variabilité observée au cours des expériences. C’est pourquoi dans un second temps, au cours du chapitre III, nous complexifions ce modèle afin de prendre en compte d’autres mécanismes impliqués dans la polymérisation et qui sont susceptibles d’augmenter la variabilité du temps de nucléation. Lors de ces deux chapitres, des résultats asymptotiques incluant diverses échelles de temps sont obtenus pour les processus de Markov correspondants. Une approximation au premier et au second ordre du temps de nucléation sont obtenus à partir de ces théorèmes limites. Ces résultats re- posent sur une renormalisation en temps et en espace du modèle de population, ainsi que sur un principe d’homogénéisation stochastique lié à une version modifiée d’urne d’Ehrenfest. Dans une seconde partie, un modèle stochastique décrivant le raccourcissement des télomères est pro- posé. Les chromosomes des cellules eucaryotes sont raccourcis à chaque mitose à cause des mécanismes de réplication de l’ADN incapables de répliquer les extrémités du chromosome parental. Afin d’éviter une perte de l’information génétique, ces chromosomes possèdent à chaque extrémité des télomères qui n’encodent pas d’information génétique. Au fil des cycles de réplication, ces télomères sont raccourcis jusqu’à rendre la division cellulaire impossible : la cellule entre alors en sénescence réplicative. L’objectif de ce modèle est de remonter aux caractéristiques de la distribution initiale de la taille des télomères à partir de mesures de temps de sénescence. / This PhD dissertation proposes a stochastic analysis of two questions of molecular biology in which randomness is a key feature of the processes involved: protein polymerisation in neurodegenerative diseases on the one hand, and telomere shortening on the other hand. Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as prion diseases, Alzheimer’s, Huntington’s and Parkinson’s disease, amyloidosis and type-2 diabetes. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration, as seen in bulk experiments and experiments that mimic the small volume of the concerned cells. After an introduction to protein polymerisation in chapter I, we investigate in chapter II the origins and the properties of the observed variability in the lag phase of amyloid assembly. This variability is currently not accounted for by deterministic nucleation-dependent mechanisms. In order to tackle this issue, a stochastic minimal model is proposed, simple, but capable of describing the characteristics of amyloid growth curves. Two populations of chemical components are considered in this model: monomers and polymerised monomers. Initially, there are only monomers and from then, two possible ways of polymerising a monomer: either two monomers collide to combine into two polymerised monomers, or a monomer is polymerised by the encounter of an already polymerised monomer. However efficient, this simple model does not fully explain the variability observed in the experiments, and in chapter III, we extend it in order to take into account other relevant mechanisms of the polymerisation process that may have an impact on fluctuations. In both chapters, asymptotic results involving different time scales are obtained for the corresponding Markov processes. First and second order results for the starting instant of nucleation are derived from these limit theorems. These results rely on a scaling analysis of a population model and the proof of a stochastic averaging principle for a model related to an Ehrenfest urn model. In the second part, a stochastic model for telomere shortening is proposed. In eukaryotic cells, chromosomes are shortened with each occurring mitosis, because the DNA polymerases are unable to replicate the chromosome down to the very end. To prevent potentially catastrophic loss of genetic information, these chromosomes are equipped with telomeres at both ends (repeated sequences that contain no genetic information). After many rounds of replication however, the telomeres are progressively nibbled to the point where the cell cannot divide anymore, a blocked state called replicative senescence. The aim of this model is to trace back to the initial distribution of telomeres from measurements of the time of senescence.

This dissertation introduces work on face recognition using a novel technique based on Hidden Markov Models (HMMs). Through the integration of a priori structural knowledge with statistical information, HMMs can be used successfully to encode face features. The results reported are obtained using a database of images of 40 subjects, with 5 training images and 5 test images for each. It is shown how standard one-dimensional HMMs in the shape of top-bottom models can be parameterised, yielding successful recognition rates of up to around 85%. The insights gained from top-bottom models are extended to pseudo two-dimensional HMMs, which offer a better and more flexible model, that describes some of the twodimensional dependencies missed by the standard one-dimensional model. It is shown how pseudo two-dimensional HMMs can be implemented, yielding successful recognition rates of up to around 95%. The performance of the HMMs is compared with the Eigenface approach and various domain and resolution experiments are also carried out. Finally, the performance of the HMM is evaluated in a fully automated system, where database images are cropped automatically.

The Czech Republic's economic performance is measurable by some macroeconomic indicators which have made variable progress in recent years. Based on general economic conditions, economic development has impacted upon economic results of companies. Over time their progress is recorded by economic time series, which describe it. Through the agency of economic time series, economic development and mutual dependences among indicators can be researched. This problem can be solved by applying the methodology which helps describe and quantify relations among quantities. For the purpose of expression of a single time series, stochastic linear modelling is used, and for quantifying the strength of relation among time series, regression analyses and Granger causality testing are used.

Emergency department (ED) overcrowding is a global concern. To help mitigate this issue, this thesis studies impediments to efficient patient flow in the ED caused by suboptimal worker behaviors and patient routing policies. I focus on three issues: (i) admission batching, (ii) hallway placement and (iii) under-triage behavior, and empirically demonstrate their impact on patient flow and quality of care. These studies are summarized as follows. Admissions batching: We study the behavior of admitting patients back-to-back (i.e., batching) by ED physicians. Using data from a large hospital, we show that the probability of batching admissions is increasing in the hour of an ED physician’s shift, and that batched patients experience a longer delay from hospital admission to receiving an inpatient bed. We further show that this effect is partially due to the increase in the coefficient of variation of inpatient bed-requests caused by batching. However, we also find that batching admissions is associated with a higher shift-level productivity. An important implication of our work is that workers may induce delays in downstream stages, caused by practices that increase their productivity. Hallway utilization: A common practice in busy EDs is to admit patients from the waiting area to hallway beds as the regular beds fill up. Using data from a large ED, we first perform a causal analysis to quantify the impact of hallway placement on wait times and quality of care – as defined by disposition time, room-to-departure (R2D) time and likelihood of adverse outcomes. We find that patients admitted to the hallway experience a significantly lower door-to-doctor time at the cost of longer disposition and R2D times. Hallway patients are also substantially more likely to experience an adverse outcome. Next, using a counterfactual analysis we show that a pooling policy, where hallway beds are used only if all regular beds are full, significantly reduces wait times, albeit at the cost of a slightly higher hallway utilization. Also, too little or too much wait tolerance for rooming patients may result in under- or over-utilization of the hallway space, both of which are detrimental to overall ED length of stay (LOS) and wait times. Under-triage behavior: Triaging ED patients upon arrival to the ED and assessing their urgency for treatment is crucial for timely service to all patients. Despite the standard patient classification algorithm by which all nurses are trained, we hypothesize, and show, that the ED’s workload impacts the perceived patient urgency, and subsequently, patient severity scores. We first use a predictive model to predict a patient’s true triage level using information collected at triage and define under-triage, accordingly. We find that under-triage is decreasing up to a certain point of workload but increasing after (U-shape). We also quantify the impact of under-triage on disposition time, room-to-departure time and risk of readmission. Collectively, this thesis demonstrates how patient-flow may be improved without the need to increase explicit physical capacity in the ED (e.g., beds). It offers practical solutions to managers and contributes to the operations management literature.

Depuis une vingtaine d'années, les problématiques de transport public en région parisienne sont devenues une préoccupation majeure. Pour les usagers qui consacrent en moyenne environ deux heures quotidiennement à leurs déplacements domicile-travail, la qualité de l'offre de transport est un enjeu majeur.La société nationale des chemins de fer français qui exploitent la majeure partie du réseau ferré dans cette région joue un rôle central dans l'organisation des transports. Mais à l'opposé des attentes qui pèsent sur ce secteur, le trafic ferroviaire rencontrent un certain nombre de dysfonctionnements. En s'inscrivant dans une démarche globale de remise en question des principes d'exploitation ferroviaire en zone dense, cette thèse apporte un regard nouveau sur l'origine des retards qui affectent les trains.Un modèle simple qui permet d'étudier la congestion du trafic ferroviaire sous l'influence de perturbations aléatoires est proposé. En s'inspirant des outils du trafic routier et tout particulièrement du diagramme fondamental de réseau,on définit pour le ferroviaire, le diagramme fondamental de ligne ferroviaire qui permet de représenter le débit en fonction de la concentration sur une portion de ligne ferroviaire. Cet outil est ensuite utilisé pour comparer les résultats issus de notre modèle à un jeu de données mesuré sur deux lignes de chemin de fer de la région parisienne.Cette comparaison montre que notre modèle permet de reproduire qualitativement les phénomènes de congestion du trafic observés sur les cas réels. / Over the last twenty years, public transport issues in the Paris region have become a major concern. The French national railway company, which operates most of the rail network in this region, plays a central role in the organisation of transport. However, in contrast to expectations in this sector, rail traffic is experiencing a number of malfunctions. As part of an overall approach to questioning the principles of rail operation in dense areas, this thesis provides a new look at the origin of delays affecting trains. Drawing on road traffic tools and in particular the basic network diagram, the basic railway line diagram is defined for railways, which makes it possible to represent the flow as a function of concentration on a portion of a railway line. This tool is then used to compare the results from our model with a set of data measured on two railway lines in the Paris region, which shows that our model can qualitatively reproduce the traffic congestion phenomena observed on real cases.(Translated with www.DeepL.com/Translator)

There has been a growing interest in stochastic modelling and learning with complex data, whose elements are structured and interdependent. One of the most successful methods to model data dependencies is graphical models, which is a combination of graph theory and probability theory. This thesis focuses on a special type of graphical models known as Conditional Random Fields (CRFs) (Lafferty et al., 2001), in which the output state spaces, when conditioned on some observational input data, are represented by undirected graphical models. The contributions of thesis involve both (a) broadening the current applicability of CRFs in the real world and (b) deepening the understanding of theoretical aspects of CRFs. On the application side, we empirically investigate the applications of CRFs in two real world settings. The first application is on a novel domain of Vietnamese accent restoration, in which we need to restore accents of an accent-less Vietnamese sentence. Experiments on half a million sentences of news articles show that the CRF-based approach is highly accurate. In the second application, we develop a new CRF-based movie recommendation system called Preference Network (PN). The PN jointly integrates various sources of domain knowledge into a large and densely connected Markov network. We obtained competitive results against well-established methods in the recommendation field. / On the theory side, the thesis addresses three important theoretical issues of CRFs: feature selection, parameter estimation and modelling recursive sequential data. These issues are all addressed under a general setting of partial supervision in that training labels are not fully available. For feature selection, we introduce a novel learning algorithm called AdaBoost.CRF that incrementally selects features out of a large feature pool as learning proceeds. AdaBoost.CRF is an extension of the standard boosting methodology to structured and partially observed data. We demonstrate that the AdaBoost.CRF is able to eliminate irrelevant features and as a result, returns a very compact feature set without significant loss of accuracy. Parameter estimation of CRFs is generally intractable in arbitrary network structures. This thesis contributes to this area by proposing a learning method called AdaBoost.MRF (which stands for AdaBoosted Markov Random Forests). As learning proceeds AdaBoost.MRF incrementally builds a tree ensemble (a forest) that cover the original network by selecting the best spanning tree at a time. As a result, we can approximately learn many rich classes of CRFs in linear time. The third theoretical work is on modelling recursive, sequential data in that each level of resolution is a Markov sequence, where each state in the sequence is also a Markov sequence at the finer grain. One of the key contributions of this thesis is Hierarchical Conditional Random Fields (HCRF), which is an extension to the currently popular sequential CRF and the recent semi-Markov CRF (Sarawagi and Cohen, 2004). Unlike previous CRF work, the HCRF does not assume any fixed graphical structures. / Rather, it treats structure as an uncertain aspect and it can estimate the structure automatically from the data. The HCRF is motivated by Hierarchical Hidden Markov Model (HHMM) (Fine et al., 1998). Importantly, the thesis shows that the HHMM is a special case of HCRF with slight modification, and the semi-Markov CRF is essentially a flat version of the HCRF. Central to our contribution in HCRF is a polynomial-time algorithm based on the Asymmetric Inside Outside (AIO) family developed in (Bui et al., 2004) for learning and inference. Another important contribution is to extend the AIO family to address learning with missing data and inference under partially observed labels. We also derive methods to deal with practical concerns associated with the AIO family, including numerical overflow and cubic-time complexity. Finally, we demonstrate good performance of HCRF against rivals on two applications: indoor video surveillance and noun-phrase chunking.

<p>Kunskap om grundvattenbildningen är nödvändig för att man ska kunna förutsäga konsekvenserna av grundvattenuttag och underjordsbyggande. Grundvattenbildningen i berggrunden är dock svår att uppskatta. Syftet med avhandlingen var att öka förståelsen av grundvattenbildningen i kristallin berggrund, att undersöka hur grundvattenbildningen ska uppskattas samt att utveckla nya modeller för att beskriva grundvattenbildningen. Studien grundades på tre angreppssätt: grundvattendatering med freoner (CFC), geohydrauliska observationer och matematisk modellering.</p><p>Koncentrationerna av CFC-11 och CFC-113 befanns vara låga i det undersökta berggrundvattnet, vilket i kombination med låga syrgashalter tyder på anaerob nedbrytning. Koncentrationerna av CFC-12 och tritium överensstämde ganska väl, vilket betyder att den skenbara åldern kan vara den sanna åldern. Resultaten tyder på att CFC-datering inte är pålitlig i skogsmiljöer med finkornigt jordtäcke.</p><p>Vid nederbörd observerades ett snabbt gensvar i den hydrauliska potentialen i den studerade bergakviferen, trots det 10 m mäktiga moräntäcket. En avsevärd del av de observerade potentialvariationerna befanns vara belastningseffekter, som inte innebar någon magasinsförändring eller något vattenflöde. Berggrundens belastningseffektivitet uppskattades, ur potentialens svar på lufttrycksförändringar, till 0,95. Ytbelastningen beräknades från mätningar av lufttryck, vatten i jordtäcket och snö. Omkring 20 % av årstidsvariationen hos den hydrauliska potentialen uppskattades bero på enbart belastningsförändringar. En enkel begreppsmässig modell kunde användas för att simulera den observerade hydrauliska potentialen. För att beskriva enskilda grundvattenbildningstillfällen på bästa sätt var det nödvändigt att ta hänsyn till effekten av ytbelastningen.</p><p>Numeriska experiment gjordes med en modell av en jord–bergprofil. När berget modellerades som ett heterogent kontinuum bildades omättade zoner i berget vid stora hydrauliska gradienter. Fenomenet uppträdde i områden där låggenomsläppliga zoner låg uppströms höggenomsläppliga zoner, och ledde till minskad hydraulisk konduktivitet i berget.</p> / <p>Knowledge about the groundwater recharge is essential for the prediction of impacts of groundwater withdrawal and underground construction. Recharge in the bedrock is, however, difficult to estimate. The objectives of this thesis were to increase the understanding of groundwater recharge in crystalline bedrock, to investigate how the recharge could be estimated, and to develop new models to describe the recharge. The study was based on three approaches: groundwater dating using chlorofluorocarbons (CFCs), geohydraulic field measurements, and mathematical modelling.</p><p>Low concentrations of CFC-11 and CFC-113 were found in the bedrock groundwater, which in combination with low dissolved-oxygen levels indicated anaerobe degradation. The CFC-12 and tritium concentrations agreed fairly well, which means that apparent ages could be true ages. The results suggest that CFC dating may not be reliable at forested, humid sites covered by fine-grained soil.</p><p>A quick response in hydraulic head to precipitation was observed in the studied bedrock, despite the 10-m thick till cover. A substantial portion of observed head variations was found to be loading effects, involving no storage changes or water flow. The loading efficiency of the bedrock was estimated, from the air-pressure response, to be 0.95. The surface loading was calculated from measurements of air pressure, water in the soil, and snow. About 20% of the seasonal variation of the hydraulic head was estimated to be related to loading changes only. A simple conceptual model could be used to simulate the observed hydraulic heads. The loading effect had to be included to properly describe individual recharge events.</p><p>Numerical experiments were performed with a soil–bedrock profile. When the rock was modelled as a heterogeneous continuum, unsaturated zones developed at high hydraulic gradients. The phenomenon appeared in areas where low-conductive zones were located upstream of high-conductive zones, decreasing the effective hydraulic conductivity of the material.</p>

<p>The decrease in number and area of managed hay-meadows over the last century, in combination with the reduction of traditional management, threatens the biodiversity connected to these habitats. I experimentally examined how management intensity affected meadow characteristics and long-term population viability of three vascular plant species in wooded hay-meadows on the Swedish island of Gotland in the Baltic Sea. I discovered that intensified management (extra raking and/or extra mowing) reduced the amount of litter and biomass, even in well-managed meadows. </p><p>The effects of intensified management on population growth rate varied among species. Deterministic demographic models revealed that intensified management increased population growth rate in <i>Succisa pratensis</i>. Stochastic modelling confirmed this; all meadows displayed larger projected population sizes 50 years into the future with intensified management. <i>Polygala amarella</i> responded with lower growth rates in raked plots, a consequence of the plant’s morphology, which makes it prone to being pulled out by raking. <i>Hypochoeris maculata</i> had population growth rates close to unity, and showed no response to an increase in management. Examination of the life-history characteristics of <i>Polygala amarella</i> showed that the species’ strategy is aimed at reproduction and fast growth, which is in contrast to the other two species, with their success relying on the survival of older plants. The species-specific responses to management show that several species should be considered when evaluating management practices for conservation of semi-natural grasslands. Furthermore, I suggest that data on stage distributions alone may not be sufficient for identifying threatened populations.</p><p>In a study of artificial dispersal between meadows, I found that establishment was twice as successful for planted plug-plants compared to sown seeds. Both methods may be useful for introducing or augmenting meadow populations, depending on access to seed sources and possibilities to nurse plants.</p><p>An electronic coordinate measurement device for gathering location data to be used in demographic studies was developed. In the field, the device proved to be a simple and reliable method for locating individuals in permanent plots.</p>

Kunskap om grundvattenbildningen är nödvändig för att man ska kunna förutsäga konsekvenserna av grundvattenuttag och underjordsbyggande. Grundvattenbildningen i berggrunden är dock svår att uppskatta. Syftet med avhandlingen var att öka förståelsen av grundvattenbildningen i kristallin berggrund, att undersöka hur grundvattenbildningen ska uppskattas samt att utveckla nya modeller för att beskriva grundvattenbildningen. Studien grundades på tre angreppssätt: grundvattendatering med freoner (CFC), geohydrauliska observationer och matematisk modellering. Koncentrationerna av CFC-11 och CFC-113 befanns vara låga i det undersökta berggrundvattnet, vilket i kombination med låga syrgashalter tyder på anaerob nedbrytning. Koncentrationerna av CFC-12 och tritium överensstämde ganska väl, vilket betyder att den skenbara åldern kan vara den sanna åldern. Resultaten tyder på att CFC-datering inte är pålitlig i skogsmiljöer med finkornigt jordtäcke. Vid nederbörd observerades ett snabbt gensvar i den hydrauliska potentialen i den studerade bergakviferen, trots det 10 m mäktiga moräntäcket. En avsevärd del av de observerade potentialvariationerna befanns vara belastningseffekter, som inte innebar någon magasinsförändring eller något vattenflöde. Berggrundens belastningseffektivitet uppskattades, ur potentialens svar på lufttrycksförändringar, till 0,95. Ytbelastningen beräknades från mätningar av lufttryck, vatten i jordtäcket och snö. Omkring 20 % av årstidsvariationen hos den hydrauliska potentialen uppskattades bero på enbart belastningsförändringar. En enkel begreppsmässig modell kunde användas för att simulera den observerade hydrauliska potentialen. För att beskriva enskilda grundvattenbildningstillfällen på bästa sätt var det nödvändigt att ta hänsyn till effekten av ytbelastningen. Numeriska experiment gjordes med en modell av en jord–bergprofil. När berget modellerades som ett heterogent kontinuum bildades omättade zoner i berget vid stora hydrauliska gradienter. Fenomenet uppträdde i områden där låggenomsläppliga zoner låg uppströms höggenomsläppliga zoner, och ledde till minskad hydraulisk konduktivitet i berget. / Knowledge about the groundwater recharge is essential for the prediction of impacts of groundwater withdrawal and underground construction. Recharge in the bedrock is, however, difficult to estimate. The objectives of this thesis were to increase the understanding of groundwater recharge in crystalline bedrock, to investigate how the recharge could be estimated, and to develop new models to describe the recharge. The study was based on three approaches: groundwater dating using chlorofluorocarbons (CFCs), geohydraulic field measurements, and mathematical modelling. Low concentrations of CFC-11 and CFC-113 were found in the bedrock groundwater, which in combination with low dissolved-oxygen levels indicated anaerobe degradation. The CFC-12 and tritium concentrations agreed fairly well, which means that apparent ages could be true ages. The results suggest that CFC dating may not be reliable at forested, humid sites covered by fine-grained soil. A quick response in hydraulic head to precipitation was observed in the studied bedrock, despite the 10-m thick till cover. A substantial portion of observed head variations was found to be loading effects, involving no storage changes or water flow. The loading efficiency of the bedrock was estimated, from the air-pressure response, to be 0.95. The surface loading was calculated from measurements of air pressure, water in the soil, and snow. About 20% of the seasonal variation of the hydraulic head was estimated to be related to loading changes only. A simple conceptual model could be used to simulate the observed hydraulic heads. The loading effect had to be included to properly describe individual recharge events. Numerical experiments were performed with a soil–bedrock profile. When the rock was modelled as a heterogeneous continuum, unsaturated zones developed at high hydraulic gradients. The phenomenon appeared in areas where low-conductive zones were located upstream of high-conductive zones, decreasing the effective hydraulic conductivity of the material.

The decrease in number and area of managed hay-meadows over the last century, in combination with the reduction of traditional management, threatens the biodiversity connected to these habitats. I experimentally examined how management intensity affected meadow characteristics and long-term population viability of three vascular plant species in wooded hay-meadows on the Swedish island of Gotland in the Baltic Sea. I discovered that intensified management (extra raking and/or extra mowing) reduced the amount of litter and biomass, even in well-managed meadows. The effects of intensified management on population growth rate varied among species. Deterministic demographic models revealed that intensified management increased population growth rate in Succisa pratensis. Stochastic modelling confirmed this; all meadows displayed larger projected population sizes 50 years into the future with intensified management. Polygala amarella responded with lower growth rates in raked plots, a consequence of the plant’s morphology, which makes it prone to being pulled out by raking. Hypochoeris maculata had population growth rates close to unity, and showed no response to an increase in management. Examination of the life-history characteristics of Polygala amarella showed that the species’ strategy is aimed at reproduction and fast growth, which is in contrast to the other two species, with their success relying on the survival of older plants. The species-specific responses to management show that several species should be considered when evaluating management practices for conservation of semi-natural grasslands. Furthermore, I suggest that data on stage distributions alone may not be sufficient for identifying threatened populations. In a study of artificial dispersal between meadows, I found that establishment was twice as successful for planted plug-plants compared to sown seeds. Both methods may be useful for introducing or augmenting meadow populations, depending on access to seed sources and possibilities to nurse plants. An electronic coordinate measurement device for gathering location data to be used in demographic studies was developed. In the field, the device proved to be a simple and reliable method for locating individuals in permanent plots.