Economic modelling of antenatal screening and ultrasound scanning programmes for identification of fetal abnormalities

Objective Within the framework of a health technology assessment and using an economic model, to determine the most clinically and cost effective policy of scanning and screening for fetal abnormalities in early pregnancy. Design A discrete event simulation model of 50,000 singleton pregnancies. Setting Maternity services in Scotland. Population Women during the first 24 weeks of their pregnancy. Methods The mathematical model was populated with data on uptake of screening, prevalence, detection and false positive rates for eight fetal abnormalities and with costs for ultrasound scanning and serum screening. Inclusion of abnormalities was based on the relative prevalence and clinical importance of conditions and the availability of data. Six strategies for the identification of abnormalities prenatally including combinations of first and second trimester ultrasound scanning and first and second trimester screening for chromosomal abnormalities were compared. Main outcome measures The number of abnormalities detected and missed, the number of iatrogenic losses resulting from invasive tests, the total cost of strategies and the cost per abnormality detected were compared between strategies. Results First trimester screening for chromosomal abnormalities costs more than second trimester screening but results in fewer iatrogenic losses. Strategies which include a second trimester ultrasound scan result in more abnormalities being detected and have lower costs per anomaly detected. Conclusions The preferred strategy includes both first and second trimester ultrasound scans and a first trimester screening test for chromosomal abnormalities. It has been recommended that this policy is offered to all women in Scotland.

Improved power-saving medium access protocol for IEEE 802.11e QoS-enabled wireless networks

The performance of a new pointer-based medium-access control protocol that was designed to significantly improve the energy efficiency of user terminals in quality-of-service-enabled wireless local area networks was analysed. The new protocol, pointer-controlled slot allocation and resynchronisation protocol (PCSARe), is based on the hybrid coordination function-controlled channel access mode of the IEEE 802.11e standard. PCSARe reduces energy consumption by removing the need for power-saving stations to remain awake for channel listening. Discrete event network simulations were performed to compare the performance of PCSARe with the non-automatic power save delivery (APSD) and scheduled-APSD power-saving modes of IEEE 802.11e. The simulation results show a demonstrable improvement in energy efficiency without significant reduction in performance when using PCSARe. For a wireless network consisting of an access point and eight stations in power-saving mode, the energy saving was up to 39% when using PCSARe instead of IEEE 802.11e non-APSD. The results also show that PCSARe offers significantly reduced uplink access delay over IEEE 802.11e non-APSD, while modestly improving the uplink throughput. Furthermore, although both had the same energy consumption, PCSARe gave a 25% reduction in downlink access delay compared with IEEE 802.11e S-APSD.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Using vulnerability performance indicators to attain food supply chain robustness

High effectiveness and leanness of modern supply chains (SCs) increase their vulnerability, i.e. susceptibility to disturbances reflected in non-robust SC performances. Both the SC management literature and SC professionals indicate the need for the development of SC vulnerability assessment tools. In this article, a new method for vulnerability assessment, the VULA method, is presented. The VULA method helps to identify how much a company would underperform on a specific Key Performance Indicator in the case of a disturbance, how often this would happen and how long it would last. It ultimately informs the decision about whether process redesign is appropriate and what kind of redesign strategies should be used in order to increase the SC's robustness. The applicability of the VULA method is demonstrated in the context of a meat SC using discrete-event simulation to conduct the performance analysis.

Robust food supply supply chains:An integrated framework for vulnerability assessment and disturbance management

The operation of supply chains (SCs) has for many years been focused on efficiency, leanness and responsiveness. This has resulted in reduced slack in operations, compressed cycle times, increased productivity and minimised inventory levels along the SC. Combined with tight tolerance settings for the realisation of logistics and production processes, this has led to SC performances that are frequently not robust. SCs are becoming increasingly vulnerable to disturbances, which can decrease the competitive power of the entire chain in the market. Moreover, in the case of food SCs non-robust performances may ultimately result in empty shelves in grocery stores and supermarkets.
The overall objective of this research is to contribute to Supply Chain Management (SCM) theory by developing a structured approach to assess SC vulnerability, so that robust performances of food SCs can be assured. We also aim to help companies in the food industry to evaluate their current state of vulnerability, and to improve their performance robustness through a better understanding of vulnerability issues. The following research questions (RQs) stem from these objectives:
RQ1: What are the main research challenges related to (food) SC robustness?
RQ2: What are the main elements that have to be considered in the design of robust SCs and what are the relationships between these elements?
RQ3: What is the relationship between the contextual factors of food SCs and the use of disturbance management principles?
RQ4: How to systematically assess the impact of disturbances in (food) SC processes on the robustness of (food) SC performances?
To answer these RQs we used different methodologies, both qualitative and quantitative. For each question, we conducted a literature survey to identify gaps in existing research and define the state of the art of knowledge on the related topics. For the second and third RQ, we conducted both exploration and testing on selected case studies. Finally, to obtain more detailed answers to the fourth question, we used simulation modelling and scenario analysis for vulnerability assessment.
Main findings are summarised as follows.
Based on an extensive literature review, we answered RQ1. The main research challenges were related to the need to define SC robustness more precisely, to identify and classify disturbances and their causes in the context of the specific characteristics of SCs and to make a systematic overview of (re)design strategies that may improve SC robustness. Also, we found that it is useful to be able to discriminate between varying degrees of SC vulnerability and to find a measure that quantifies the extent to which a company or SC shows robust performances when exposed to disturbances.
To address RQ2, we define SC robustness as the degree to which a SC shows an acceptable performance in (each of) its Key Performance Indicators (KPIs) during and after an unexpected event that caused a disturbance in one or more logistics processes. Based on the SCM literature we identified the main elements needed to achieve robust performances and structured them together to form a conceptual framework for the design of robust SCs. We then explained the logic of the framework and elaborate on each of its main elements: the SC scenario, SC disturbances, SC performance, sources of food SC vulnerability, and redesign principles and strategies.
Based on three case studies, we answered RQ3. Our major findings show that the contextual factors have a consistent relationship to Disturbance Management Principles (DMPs). The product and SC environment characteristics are contextual factors that are hard to change and these characteristics initiate the use of specific DMPs as well as constrain the use of potential response actions. The process and the SC network characteristics are contextual factors that are easier to change, and they are affected by the use of the DMPs. We also found a notable relationship between the type of DMP likely to be used and the particular combination of contextual factors present in the observed SC.
To address RQ4, we presented a new method for vulnerability assessments, the VULA method. The VULA method helps to identify how much a company is underperforming on a specific Key Performance Indicator (KPI) in the case of a disturbance, how often this would happen and how long it would last. It ultimately informs the decision maker about whether process redesign is needed and what kind of redesign strategies should be used in order to increase the SC’s robustness. The VULA method is demonstrated in the context of a meat SC using discrete-event simulation. The case findings show that performance robustness can be assessed for any KPI using the VULA method.
To sum-up the project, all findings were incorporated within an integrated framework for designing robust SCs. The integrated framework consists of the following steps: 1) Description of the SC scenario and identification of its specific contextual factors; 2) Identification of disturbances that may affect KPIs; 3) Definition of the relevant KPIs and identification of the main disturbances through assessment of the SC performance robustness (i.e. application of the VULA method); 4) Identification of the sources of vulnerability that may (strongly) affect the robustness of performances and eventually increase the vulnerability of the SC; 5) Identification of appropriate preventive or disturbance impact reductive redesign strategies; 6) Alteration of SC scenario elements as required by the selected redesign strategies and repeat VULA method for KPIs, as defined in Step 3.
Contributions of this research are listed as follows. First, we have identified emerging research areas - SC robustness, and its counterpart, vulnerability. Second, we have developed a definition of SC robustness, operationalized it, and identified and structured the relevant elements for the design of robust SCs in the form of a research framework. With this research framework, we contribute to a better understanding of the concepts of vulnerability and robustness and related issues in food SCs. Third, we identified the relationship between contextual factors of food SCs and specific DMPs used to maintain robust SC performances: characteristics of the product and the SC environment influence the selection and use of DMPs; processes and SC networks are influenced by DMPs. Fourth, we developed specific metrics for vulnerability assessments, which serve as a basis of a VULA method. The VULA method investigates different measures of the variability of both the duration of impacts from disturbances and the fluctuations in their magnitude.
With this project, we also hope to have delivered practical insights into food SC vulnerability. First, the integrated framework for the design of robust SCs can be used to guide food companies in successful disturbance management. Second, empirical findings from case studies lead to the identification of changeable characteristics of SCs that can serve as a basis for assessing where to focus efforts to manage disturbances. Third, the VULA method can help top management to get more reliable information about the “health” of the company.
The two most important research opportunities are: First, there is a need to extend and validate our findings related to the research framework and contextual factors through further case studies related to other types of (food) products and other types of SCs. Second, there is a need to further develop and test the VULA method, e.g.: to use other indicators and statistical measures for disturbance detection and SC improvement; to define the most appropriate KPI to represent the robustness of a complete SC. We hope this thesis invites other researchers to pick up these challenges and help us further improve the robustness of (food) SCs.

Surveillance for ocular hypertension: An evidence synthesis and economic evaluation

OBJECTIVES: To determine effective and efficient monitoring criteria for ocular hypertension [raised intraocular pressure (IOP)] through (i) identification and validation of glaucoma risk prediction models; and (ii) development of models to determine optimal surveillance pathways.

DESIGN: A discrete event simulation economic modelling evaluation. Data from systematic reviews of risk prediction models and agreement between tonometers, secondary analyses of existing datasets (to validate identified risk models and determine optimal monitoring criteria) and public preferences were used to structure and populate the economic model.

SETTING: Primary and secondary care.

PARTICIPANTS: Adults with ocular hypertension (IOP > 21 mmHg) and the public (surveillance preferences).

INTERVENTIONS: We compared five pathways: two based on National Institute for Health and Clinical Excellence (NICE) guidelines with monitoring interval and treatment depending on initial risk stratification, 'NICE intensive' (4-monthly to annual monitoring) and 'NICE conservative' (6-monthly to biennial monitoring); two pathways, differing in location (hospital and community), with monitoring biennially and treatment initiated for a ≥ 6% 5-year glaucoma risk; and a 'treat all' pathway involving treatment with a prostaglandin analogue if IOP > 21 mmHg and IOP measured annually in the community.

MAIN OUTCOME MEASURES: Glaucoma cases detected; tonometer agreement; public preferences; costs; willingness to pay and quality-adjusted life-years (QALYs).

RESULTS: The best available glaucoma risk prediction model estimated the 5-year risk based on age and ocular predictors (IOP, central corneal thickness, optic nerve damage and index of visual field status). Taking the average of two IOP readings, by tonometry, true change was detected at two years. Sizeable measurement variability was noted between tonometers. There was a general public preference for monitoring; good communication and understanding of the process predicted service value. 'Treat all' was the least costly and 'NICE intensive' the most costly pathway. Biennial monitoring reduced the number of cases of glaucoma conversion compared with a 'treat all' pathway and provided more QALYs, but the incremental cost-effectiveness ratio (ICER) was considerably more than £30,000. The 'NICE intensive' pathway also avoided glaucoma conversion, but NICE-based pathways were either dominated (more costly and less effective) by biennial hospital monitoring or had a ICERs > £30,000. Results were not sensitive to the risk threshold for initiating surveillance but were sensitive to the risk threshold for initiating treatment, NHS costs and treatment adherence.

LIMITATIONS: Optimal monitoring intervals were based on IOP data. There were insufficient data to determine the optimal frequency of measurement of the visual field or optic nerve head for identification of glaucoma. The economic modelling took a 20-year time horizon which may be insufficient to capture long-term benefits. Sensitivity analyses may not fully capture the uncertainty surrounding parameter estimates.

CONCLUSIONS: For confirmed ocular hypertension, findings suggest that there is no clear benefit from intensive monitoring. Consideration of the patient experience is important. A cohort study is recommended to provide data to refine the glaucoma risk prediction model, determine the optimum type and frequency of serial glaucoma tests and estimate costs and patient preferences for monitoring and treatment.

FUNDING: The National Institute for Health Research Health Technology Assessment Programme.

Sequential measurement-based quantum computing with memories

We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the cluster state needed for the computation and its consumption by measurements are carried out simultaneously. As a consequence, effective clusters of one spatial dimension fewer than in the standard approach are sufficient for computation. In particular, universal computation requires only a one-dimensional array of memories. The scheme applies to discrete-variable systems of any dimension as well as to continuous-variable ones, and both are treated equivalently under the light of local complementation of graphs. In this way our formalism introduces a general framework that encompasses and generalizes in a unified manner some previous system-dependent proposals. The procedure is intrinsically well suited for implementations with atom-photon interfaces.

Monitoring ocular hypertension, how much and how often? A cost-effectiveness perspective

OBJECTIVE: To assess the efficiency of alternative monitoring services for people with ocular hypertension (OHT), a glaucoma risk factor.

DESIGN: Discrete event simulation model comparing five alternative care pathways: treatment at OHT diagnosis with minimal monitoring; biennial monitoring (primary and secondary care) with treatment if baseline predicted 5-year glaucoma risk is ≥6%; monitoring and treatment aligned to National Institute for Health and Care Excellence (NICE) glaucoma guidance (conservative and intensive).

SETTING: UK health services perspective.

PARTICIPANTS: Simulated cohort of 10 000 adults with OHT (mean intraocular pressure (IOP) 24.9 mm Hg (SD 2.4).

MAIN OUTCOME MEASURES: Costs, glaucoma detected, quality-adjusted life years (QALYs).

RESULTS: Treating at diagnosis was the least costly and least effective in avoiding glaucoma and progression. Intensive monitoring following NICE guidance was the most costly and effective. However, considering a wider cost-utility perspective, biennial monitoring was less costly and provided more QALYs than NICE pathways, but was unlikely to be cost-effective compared with treating at diagnosis (£86 717 per additional QALY gained). The findings were robust to risk thresholds for initiating monitoring but were sensitive to treatment threshold, National Health Service costs and treatment adherence.

CONCLUSIONS: For confirmed OHT, glaucoma monitoring more frequently than every 2 years is unlikely to be efficient. Primary treatment and minimal monitoring (assessing treatment responsiveness (IOP)) could be considered; however, further data to refine glaucoma risk prediction models and value patient preferences for treatment are needed. Consideration to innovative and affordable service redesign focused on treatment responsiveness rather than more glaucoma testing is recommended.

A dynamic sequential route choice model for micro-simulation

Dans les études sur le transport, les modèles de choix de route décrivent la sélection par un utilisateur d’un chemin, depuis son origine jusqu’à sa destination. Plus précisément, il s’agit de trouver dans un réseau composé d’arcs et de sommets la suite d’arcs reliant deux sommets, suivant des critères donnés. Nous considérons dans le présent travail l’application de la programmation dynamique pour représenter le processus de choix, en considérant le choix d’un chemin comme une séquence de choix d’arcs. De plus, nous mettons en œuvre les techniques d’approximation en programmation dynamique afin de représenter la connaissance imparfaite de l’état réseau, en particulier pour les arcs éloignés du point actuel. Plus précisément, à chaque fois qu’un utilisateur atteint une intersection, il considère l’utilité d’un certain nombre d’arcs futurs, puis une estimation est faite pour le restant du chemin jusqu’à la destination. Le modèle de choix de route est implanté dans le cadre d’un modèle de simulation de trafic par événements discrets. Le modèle ainsi construit est testé sur un modèle de réseau routier réel afin d’étudier sa performance.

Optimisation des horaires des agents et du routage des appels dans les centres d’appels

Nous étudions la gestion de centres d'appels multi-compétences, ayant plusieurs types d'appels et groupes d'agents. Un centre d'appels est un système de files d'attente très complexe, où il faut généralement utiliser un simulateur pour évaluer ses performances. Tout d'abord, nous développons un simulateur de centres d'appels basé sur la simulation d'une chaîne de Markov en temps continu (CMTC), qui est plus rapide que la simulation conventionnelle par événements discrets. À l'aide d'une méthode d'uniformisation de la CMTC, le simulateur simule la chaîne de Markov en temps discret imbriquée de la CMTC. Nous proposons des stratégies pour utiliser efficacement ce simulateur dans l'optimisation de l'affectation des agents. En particulier, nous étudions l'utilisation des variables aléatoires communes. Deuxièmement, nous optimisons les horaires des agents sur plusieurs périodes en proposant un algorithme basé sur des coupes de sous-gradients et la simulation. Ce problème est généralement trop grand pour être optimisé par la programmation en nombres entiers. Alors, nous relaxons l'intégralité des variables et nous proposons des méthodes pour arrondir les solutions. Nous présentons une recherche locale pour améliorer la solution finale. Ensuite, nous étudions l'optimisation du routage des appels aux agents. Nous proposons une nouvelle politique de routage basé sur des poids, les temps d'attente des appels, et les temps d'inoccupation des agents ou le nombre d'agents libres. Nous développons un algorithme génétique modifié pour optimiser les paramètres de routage. Au lieu d'effectuer des mutations ou des croisements, cet algorithme optimise les paramètres des lois de probabilité qui génèrent la population de solutions. Par la suite, nous développons un algorithme d'affectation des agents basé sur l'agrégation, la théorie des files d'attente et la probabilité de délai. Cet algorithme heuristique est rapide, car il n'emploie pas la simulation. La contrainte sur le niveau de service est convertie en une contrainte sur la probabilité de délai. Par après, nous proposons une variante d'un modèle de CMTC basé sur le temps d'attente du client à la tête de la file. Et finalement, nous présentons une extension d'un algorithme de coupe pour l'optimisation stochastique avec recours de l'affectation des agents dans un centre d'appels multi-compétences.

Role of Nuclear Angiotensin-II Receptor Mediated Signalling in Cardiovascular Remodelling

Le remodelage cardiaque est le processus par lequel la structure ou la fonction cardiaque change en réponse à un déséquilibre pathophysiologique tel qu'une maladie cardiaque, un contexte d'arythmie prolongée ou une modification de l'équilibre hormonal. Le système rénine-angiotensine (SRA) est un système hormonal largement étudié et il est impliqué dans de nombreuses activités associées au remodelage cardiovasculaire. L’existence d'un système circulatoire couplé à un système de tissus locaux est une représentation classique, cependant de nouvelles données suggèrent un SRA indépendant et fonctionnellement actif à l'échelle cellulaire. La compréhension de l'activité intracellulaire du SRA pourrait mener à de nouvelles pistes thérapeutiques qui pourraient prévenir un remodelage cardiovasculaire défavorable. L'objectif de cette thèse était d'élucider le rôle du SRA intracellulaire dans les cellules cardiaques. Récemment, les récepteurs couplés aux protéines G (RCPG), les protéines G et leurs effecteurs ont été détectés sur des membranes intracellulaires, y compris sur la membrane nucléaire, et les concepts de RCPG intracellulaires fonctionnels sont en voie d'être acceptés comme une réalité. Nous avons dès lors fait l'hypothèse que la signalisation du SRA délimitant le noyau était impliquée dans le contrôle de l'expression des gènes cardiaques. Nous avons démontré la présence de récepteurs d'angiotensine de type-1 (AT1R) et de type-2 (AT2R) nucléaires dans les cardiomyocytes ventriculaires adultes et dans une fraction nucléaire purifiée de tissu cardiaque. Des quantités d'Ang II ont été détectées dans du lysat de cardiomyocytes et des microinjections d'Ang-II-FITC ont donné lieu à des liaisons préférentielles aux sites nucléaires. L'analyse transcriptionnelle prouve que la synthèse d'ARN de novo dans des noyaux isolés stimulés à l'Ang-II, et l'expression des ARNm de NF-κB étaient beaucoup plus importants lorsque les noyaux étaient exposés à de l'Ang II par rapport aux cardiomyocytes intacts. La stimulation des AT1R nucléaires a engendré une mobilisation de Ca2+ via les récepteurs de l'inositol trisphosphate (IP3R), et le blocage des IP3R a diminué la réponse transcriptionnelle. Les méthodes disponibles actuellement pour l'étude de la signalisation intracrine sont limitées aux méthodes indirectes. L'un des objectifs de cette thèse était de synthétiser et caractériser des analogues d'Ang-II cellule-perméants afin d’étudier spécifiquement dans les cellules intactes l'activité intracellulaire du SRA. Nous avons synthétisé et caractérisé pharmacologiquement des analogues photosensibles Ang-II encapsulée en incorporant un groupement 4,5-diméthoxy-2-nitrobenzyl (DMNB) photoclivable sur les sites actifs identifiés du peptide. Chacun des trois analogues d'Ang II encapsulée synthétisés et purifiés: [Tyr(DMNB)4]Ang-II, Ang-II-ODMNB et [Tyr(DMNB)4]Ang-II-ODMNB a montré une réduction par un facteur deux ou trois de l'affinité de liaison envers AT1R et AT2R dans les dosages par liaison compétitive et une activité réduite dans la contraction de l'aorte thoracique. La photostimulation de [Tyr(DMNB)4]Ang-II dans des cellules HEK a augmenté la phosphorylation d'ERK1/2 (via AT1R) et la production de cGMP (via AT2R) alors que dans les cardiomyocytes isolés elle générait une augmentation de Ca2+ nucléoplasmique et initiait la synthèse d'ARNr 18S et d'ARNm du NF-κB. Les fibroblastes sont les principaux générateurs de remodelage cardiaque structurel, et les fibroblastes auriculaires sont plus réactifs aux stimuli profibrotiques que les fibroblastes ventriculaires. Nous avons émis l'hypothèse que l’Ang-II intracellulaire et l'activation des AT1R et AT2R nucléaires associés contrôlaient les profils d'expression des gènes des fibroblastes via des systèmes de signalisation distincts et de ce fait jouaient un rôle majeur dans le développement de la fibrose cardiaque. Nous avons remarqué que les fibroblastes auriculaires expriment l’AT1R et l’AT2R nucléaire et l'Ang-II au niveau intracellulaire. L’expression d'AT1R nucléaire a été régulés positivement dans les cas d’insuffisance cardiaque (IC), tandis que l'AT2R nucléaire a été glycosylé post-traductionnellement. La machinerie protéique des protéines G, y compris Gαq/11, Gαi/3, et Gβ, a été observée dans des noyaux isolés de fibroblastes. AT1R et AT2R régulent l'initiation de la transcription du fibroblaste via les voies de transduction de signal d'IP3R et du NO. La photostimulation de [Tyr(DMNB)4]Ang-II dans une culture de fibroblastes auriculaire déclenche la libération de Ca2+ nucléoplasmique, la prolifération, et la synthèse et sécrétion de collagène qui ne sont pas inhibées par les bloqueurs d'AT1R et/ou AT2R extracellulaires.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Fractal structures in nonlinear plasma physics

Fractal structures appear in many situations related to the dynamics of conservative as well as dissipative dynamical systems, being a manifestation of chaotic behaviour. In open area-preserving discrete dynamical systems we can find fractal structures in the form of fractal boundaries, associated to escape basins, and even possessing the more general property of Wada. Such systems appear in certain applications in plasma physics, like the magnetic field line behaviour in tokamaks with ergodic limiters. The main purpose of this paper is to show how such fractal structures have observable consequences in terms of the transport properties in the plasma edge of tokamaks, some of which have been experimentally verified. We emphasize the role of the fractal structures in the understanding of mesoscale phenomena in plasmas, such as electromagnetic turbulence.