High b-value Diffusion-weighted Imaging: A Sensitive Method to Reveal White Matter Changes in Schizophrenia

Background: b-value is the parameter characterizing the intensity of the diffusion weighting during image acquisition. Data acquisition is usually performed with low b value (b~1000 s/mm2). Evidence shows that high b-values (b>2000 s/mm2) are more sensitive to the slow diffusion compartment (SDC) and maybe more sensitive in detecting white matter (WM) anomalies in schizophrenia.Methods: 12 male patients with schizophrenia (mean age 35 +/-3 years) and 16 healthy male controls matched for age were scanned with a low b-value (1000 s/mm2) and a high b-value (4000 s/mm2) protocol. Apparent diffusion coefficient (ADC) is a measure of the average diffusion distance of water molecules per time unit (mm2/s). ADC maps were generated for all individuals. 8 region of interests (frontal and parietal region bilaterally, centrum semi-ovale bilaterally and anterior and posterior corpus callosum) were manually traced blind to diagnosis.Results: ADC measures acquired with high b-value imaging were more sensitive in detecting differences between schizophrenia patients and healthy controls than low b-value imaging with a gain in significance by a factor of 20- 100 times despite the lower image Signal-to-noise ratio (SNR). Increased ADC was identified in patient's WM (p=0.00015) with major contributions from left and right centrum semi-ovale and to a lesser extent right parietal region.Conclusions: Our results may be related to the sensitivity of high b-value imaging to the SDC believed to reflect mainly the intra-axonal and myelin bound water pool. High b-value imaging might be more sensitive and specific to WM anomalies in schizophrenia than low b-value imaging

Casparian strip diffusion barrier in Arabidopsis is made of a lignin polymer without suberin.

Casparian strips are ring-like cell-wall modifications in the root endodermis of vascular plants. Their presence generates a paracellular barrier, analogous to animal tight junctions, that is thought to be crucial for selective nutrient uptake, exclusion of pathogens, and many other processes. Despite their importance, the chemical nature of Casparian strips has remained a matter of debate, confounding further molecular analysis. Suberin, lignin, lignin-like polymers, or both, have been claimed to make up Casparian strips. Here we show that, in Arabidopsis, suberin is produced much too late to take part in Casparian strip formation. In addition, we have generated plants devoid of any detectable suberin, which still establish functional Casparian strips. In contrast, manipulating lignin biosynthesis abrogates Casparian strip formation. Finally, monolignol feeding and lignin-specific chemical analysis indicates the presence of archetypal lignin in Casparian strips. Our findings establish the chemical nature of the primary root-diffusion barrier in Arabidopsis and enable a mechanistic dissection of the formation of Casparian strips, which are an independent way of generating tight junctions in eukaryotes.

Prospective and retrospective motion correction in diffusion magnetic resonance imaging of the human brain.

Diffusion-weighting in magnetic resonance imaging (MRI) increases the sensitivity to molecular Brownian motion, providing insight in the micro-environment of the underlying tissue types and structures. At the same time, the diffusion weighting renders the scans sensitive to other motion, including bulk patient motion. Typically, several image volumes are needed to extract diffusion information, inducing also inter-volume motion susceptibility. Bulk motion is more likely during long acquisitions, as they appear in diffusion tensor, diffusion spectrum and q-ball imaging. Image registration methods are successfully used to correct for bulk motion in other MRI time series, but their performance in diffusion-weighted MRI is limited since diffusion weighting introduces strong signal and contrast changes between serial image volumes. In this work, we combine the capability of free induction decay (FID) navigators, providing information on object motion, with image registration methodology to prospectively--or optionally retrospectively--correct for motion in diffusion imaging of the human brain. Eight healthy subjects were instructed to perform small-scale voluntary head motion during clinical diffusion tensor imaging acquisitions. The implemented motion detection based on FID navigator signals is processed in real-time and provided an excellent detection performance of voluntary motion patterns even at a sub-millimetre scale (sensitivity≥92%, specificity>98%). Motion detection triggered an additional image volume acquisition with b=0 s/mm2 which was subsequently co-registered to a reference volume. In the prospective correction scenario, the calculated motion-parameters were applied to perform a real-time update of the gradient coordinate system to correct for the head movement. Quantitative analysis revealed that the motion correction implementation is capable to correct head motion in diffusion-weighted MRI to a level comparable to scans without voluntary head motion. The results indicate the potential of this method to improve image quality in diffusion-weighted MRI, a concept that can also be applied when highest diffusion weightings are performed.

Effect of drift on segregation in two-component diffusion-limited aggregation

An effect of drift is investigated on the segregation pattern in diffusion-limited aggregation (DLA) with two components (A and B species). The sticking probability PAB (=PBA) between the different species is introduced into the DLA model with drift, where the sticking probability PAA (=PBB) between the same species equals 1. By using computer simulation it is found that the drift has an important effect on not only the morphology but also the segregation pattern. Under the drift and the small sticking probability, a characteristic pattern appears where elongated clusters of A species and of B species are periodically dispersed. The period decreases with increasing drift. The periodic structure of the deposits is characterized by an autocorrelation function. The shape of the cluster consisting of only A species (or B species) shows a vertically elongated filamentlike structure. Each cluster becomes vertically longer with decreasing sticking probability PAB. The segregation pattern is distinctly different from that with no drift and a small sticking probability PAA. The effect of the concentration on the segregation pattern is also shown.

Characterizing the connectome in schizophrenia with diffusion spectrum imaging.

Schizophrenia is a complex psychiatric disorder characterized by disabling symptoms and cognitive deficit. Recent neuroimaging findings suggest that large parts of the brain are affected by the disease, and that the capacity of functional integration between brain areas is decreased. In this study we questioned (i) which brain areas underlie the loss of network integration properties observed in the pathology, (ii) what is the topological role of the affected regions within the overall brain network and how this topological status might be altered in patients, and (iii) how white matter properties of tracts connecting affected regions may be disrupted. We acquired diffusion spectrum imaging (a technique sensitive to fiber crossing and slow diffusion compartment) data from 16 schizophrenia patients and 15 healthy controls, and investigated their weighted brain networks. The global connectivity analysis confirmed that patients present disrupted integration and segregation properties. The nodal analysis allowed identifying a distributed set of brain nodes affected in the pathology, including hubs and peripheral areas. To characterize the topological role of this affected core, we investigated the brain network shortest paths layout, and quantified the network damage after targeted attack toward the affected core. The centrality of the affected core was compromised in patients. Moreover the connectivity strength within the affected core, quantified with generalized fractional anisotropy and apparent diffusion coefficient, was altered in patients. Taken together, these findings suggest that the structural alterations and topological decentralization of the affected core might be major mechanisms underlying the schizophrenia dysconnectivity disorder. Hum Brain Mapp, 36:354-366, 2015. © 2014 Wiley Periodicals, Inc.

Interobserver and intraobserver variability of apparent diffusion coefficient measurements in treated malignant hepatic lesions: measurements in the whole lesion versus in the area with the most restricted diffusion

Purpose: The increase of apparent diffusion coefficient (ADC) in treated hepatic malignancies compared to pre-therapeutic values has been interpreted as treatment success; however, the variability of ADC measurements remains unknown. Furthermore, ADC has been usually measured in the whole lesion, while measurements should be probably centered on the area with the most restricted diffusion (MRDA) as it represents potential tumoral residue. Our objective was to compare the inter/intraobserver variability of ADC measurements in the whole lesion and in MRDA. Material and methods: Forty patients previously treated with chemoembolization or radiofrequency were evaluated (20 on 1.5T and 20 on 3.0T). After consensual agreement on the best ADC image, two readers measured the ADC values using separate regions of interest that included the whole lesion and the whole MRDA without exceeding their borders. The same measurements were repeated two weeks later. Spearman test and the Bland-Altman method were used. Results: Interobserver correlation in ADC measurements in the whole lesion and MRDA was as follows: 0.962 and 0.884. Intraobserver correlation was, respectively, 0.992 and 0.979. Interobserver limits of variability (mm2/sec*10-3) were between -0.25/+0.28 in the whole lesion and between -0.51/+0.46 in MRDA. Intraobserver limits of variability were, respectively: -0.25/+0.24 and -0.43/+0.47. Conclusion: We observed a good inter/intraobserver correlation in ADC measurements. Nevertheless, a limited variability does exist, and it should be considered when interpreting ADC values of hepatic malignancies.

Microstructural evolution of primary crystallization in diffusion-controlled grain growth

A model has been developed for evaluating grain size distributions in primary crystallizations where the grain growth is diffusion controlled. The body of the model is grounded in a recently presented mean-field integration of the nucleation and growth kinetic equations, modified conveniently in order to take into account a radius-dependent growth rate, as occurs in diffusion-controlled growth. The classical diffusion theory is considered, and a modification of this is proposed to take into account interference of the diffusion profiles between neighbor grains. The potentiality of the mean-field model to give detailed information on the grain size distribution and transformed volume fraction for transformations driven by nucleation and either interface- or diffusion-controlled growth processes is demonstrated. The model is evaluated for the primary crystallization of an amorphous alloy, giving an excellent agreement with experimental data. Grain size distributions are computed, and their properties are discussed.

Diffusion of influenza during the winter of 1889-90 in Switzerland

The influenza of the winter of 1889-90 was one of the first epidemics to spread all over the world. At the time, several people hypothesized that the railway was one of the main vectors of diffusion of this influenza. This hypothesis was defended in Switzerland especially by Schmid, Chief of the Swiss Office of Health, who collected an impressive body of material about the spread of the epidemic in that country. These data on influenza combined with data about the structure of the railway are used in this paper in order to test the hypothesis of a mixed diffusion process, first between communes interconnected by the railway, and secondly, between those communes and neighbouring communes. An event history analysis model taking into account diffusion effects is proposed and estimated. Results show that the hypothesis is supported if the railway network in Switzerland is not taken as a whole but if a distinction between railway companies is made.

Long-term monitoring of post-stroke plasticity after transient cerebral ischemia in mice using in vivo and ex vivo diffusion tensor MRI.

WE USED A MURINE MODEL OF TRANSIENT FOCAL CEREBRAL ISCHEMIA TO STUDY: 1) in vivo DTI long-term temporal evolution of the apparent diffusion coefficient (ADC) and diffusion fractional anisotropy (FA) at days 4, 10, 15 and 21 after stroke 2) ex vivo distribution of a plasticity-related protein (GAP-43) and its relationship with the ex vivo DTI characteristics of the striato-thalamic pathway (21 days). All animals recovered motor function. In vivo ADC within the infarct was significantly increased after stroke. In the stroke group, GAP-43 expression and FA values were significantly higher in the ipsilateral (IL) striatum and contralateral (CL) hippocampus compared to the shams. DTI tractography showed fiber trajectories connecting the CL striatum to the stroke region, where increased GAP43 and FA were observed and fiber tracts from the CL striatum terminating in the IL hippocampus.Our data demonstrate that DTI changes parallel histological remodeling and recovery of function.

Mechanisms underlying functional recovery after in vivo focal cerebral ischemia : from preconditioning to diffusion MRI

Version abregée L'ischémie cérébrale est la troisième cause de mort dans les pays développés, et la maladie responsable des plus sérieux handicaps neurologiques. La compréhension des bases moléculaires et anatomiques de la récupération fonctionnelle après l'ischémie cérébrale est donc extrêmement importante et représente un domaine d'intérêt crucial pour la recherche fondamentale et clinique. Durant les deux dernières décennies, les chercheurs ont tenté de combattre les effets nocifs de l'ischémie cérébrale à l'aide de substances exogènes qui, bien que testées avec succès dans le domaine expérimental, ont montré un effet contradictoire dans l'application clinique. Une approche différente mais complémentaire est de stimuler des mécanismes intrinsèques de neuroprotection en utilisant le «modèle de préconditionnement» : une brève insulte protège contre des épisodes d'ischémie plus sévères à travers la stimulation de voies de signalisation endogènes qui augmentent la résistance à l'ischémie. Cette approche peut offrir des éléments importants pour clarifier les mécanismes endogènes de neuroprotection et fournir de nouvelles stratégies pour rendre les neurones et la glie plus résistants à l'attaque ischémique cérébrale. Dans un premier temps, nous avons donc étudié les mécanismes de neuroprotection intrinsèques stimulés par la thrombine, un neuroprotecteur «préconditionnant» dont on a montré, à l'aide de modèles expérimentaux in vitro et in vivo, qu'il réduit la mort neuronale. En appliquant une technique de microchirurgie pour induire une ischémie cérébrale transitoire chez la souris, nous avons montré que la thrombine peut stimuler les voies de signalisation intracellulaire médiées par MAPK et JNK par une approche moléculaire et l'analyse in vivo d'un inhibiteur spécifique de JNK (L JNK) .Nous avons également étudié l'impact de la thrombine sur la récupération fonctionnelle après une attaque et avons pu démontrer que ces mécanismes moléculaires peuvent améliorer la récupération motrice. La deuxième partie de cette étude des mécanismes de récupération après ischémie cérébrale est basée sur l'investigation des bases anatomiques de la plasticité des connections cérébrales, soit dans le modèle animal d'ischémie transitoire, soit chez l'homme. Selon des résultats précédemment publiés par divers groupes ,nous savons que des mécanismes de plasticité aboutissant à des degrés divers de récupération fonctionnelle sont mis enjeu après une lésion ischémique. Le résultat de cette réorganisation est une nouvelle architecture fonctionnelle et structurelle, qui varie individuellement selon l'anatomie de la lésion, l'âge du sujet et la chronicité de la lésion. Le succès de toute intervention thérapeutique dépendra donc de son interaction avec la nouvelle architecture anatomique. Pour cette raison, nous avons appliqué deux techniques de diffusion en résonance magnétique qui permettent de détecter les changements de microstructure cérébrale et de connexions anatomiques suite à une attaque : IRM par tenseur de diffusion (DT-IR1V) et IRM par spectre de diffusion (DSIRM). Grâce à la DT-IRM hautement sophistiquée, nous avons pu effectuer une étude de follow-up à long terme chez des souris ayant subi une ischémie cérébrale transitoire, qui a mis en évidence que les changements microstructurels dans l'infarctus ainsi que la modification des voies anatomiques sont corrélés à la récupération fonctionnelle. De plus, nous avons observé une réorganisation axonale dans des aires où l'on détecte une augmentation d'expression d'une protéine de plasticité exprimée dans le cône de croissance des axones (GAP-43). En appliquant la même technique, nous avons également effectué deux études, rétrospective et prospective, qui ont montré comment des paramètres obtenus avec DT-IRM peuvent monitorer la rapidité de récupération et mettre en évidence un changement structurel dans les voies impliquées dans les manifestations cliniques. Dans la dernière partie de ce travail, nous avons décrit la manière dont la DS-IRM peut être appliquée dans le domaine expérimental et clinique pour étudier la plasticité cérébrale après ischémie. Abstract Ischemic stroke is the third leading cause of death in developed countries and the disease responsible for the most serious long-term neurological disability. Understanding molecular and anatomical basis of stroke recovery is, therefore, extremely important and represents a major field of interest for basic and clinical research. Over the past 2 decades, much attention has focused on counteracting noxious effect of the ischemic insult with exogenous substances (oxygen radical scavengers, AMPA and NMDA receptor antagonists, MMP inhibitors etc) which were successfully tested in the experimental field -but which turned out to have controversial effects in clinical trials. A different but complementary approach to address ischemia pathophysiology and treatment options is to stimulate and investigate intrinsic mechanisms of neuroprotection using the "preconditioning effect": applying a brief insult protects against subsequent prolonged and detrimental ischemic episodes, by up-regulating powerful endogenous pathways that increase resistance to injury. We believe that this approach might offer an important insight into the molecular mechanisms responsible for endogenous neuroprotection. In addition, results from preconditioning model experiment may provide new strategies for making brain cells "naturally" more resistant to ischemic injury and accelerate their rate of functional recovery. In the first part of this work, we investigated down-stream mechanisms of neuroprotection induced by thrombin, a well known neuroprotectant which has been demonstrated to reduce stroke-induced cell death in vitro and in vivo experimental models. Using microsurgery to induce transient brain ischemia in mice, we showed that thrombin can stimulate both MAPK and JNK intracellular pathways through a molecular biology approach and an in vivo analysis of a specific kinase inhibitor (L JNK1). We also studied thrombin's impact on functional recovery demonstrating that these molecular mechanisms could enhance post-stroke motor outcome. The second part of this study is based on investigating the anatomical basis underlying connectivity remodeling, leading to functional improvement after stroke. To do this, we used both a mouse model of experimental ischemia and human subjects with stroke. It is known from previous data published in literature, that the brain adapts to damage in a way that attempts to preserve motor function. The result of this reorganization is a new functional and structural architecture, which will vary from patient to patient depending on the anatomy of the damage, the biological age of the patient and the chronicity of the lesion. The success of any given therapeutic intervention will depend on how well it interacts with this new architecture. For this reason, we applied diffusion magnetic resonance techniques able to detect micro-structural and connectivity changes following an ischemic lesion: diffusion tensor MRI (DT-MRI) and diffusion spectrum MRI (DS-MRI). Using DT-MRI, we performed along-term follow up study of stroke mice which showed how diffusion changes in the stroke region and fiber tract remodeling is correlating with stroke recovery. In addition, axonal reorganization is shown in areas of increased plasticity related protein expression (GAP 43, growth axonal cone related protein). Applying the same technique, we then performed a retrospective and a prospective study in humans demonstrating how specific DTI parameters could help to monitor the speed of recovery and show longitudinal changes in damaged tracts involved in clinical symptoms. Finally, in the last part of this study we showed how DS-MRI could be applied both to experimental and human stroke and which perspectives it can open to further investigate post stroke plasticity.

Simulation of stromatolite growth using diffusion-limited aggregation and a discrete model of biogeochemical exchanges in microbial mat

Resume : Mieux comprendre les stromatolithes et les tapis microbiens est un sujet important en biogéosciences puisque cela aide à l'étude des premières formes de vie sur Terre, a mieux cerner l'écologie des communautés microbiennes et la contribution des microorganismes a la biominéralisation, et même à poser certains fondements dans les recherches en exobiologie. D'autre part, la modélisation est un outil puissant utilisé dans les sciences naturelles pour appréhender différents phénomènes de façon théorique. Les modèles sont généralement construits sur un système d'équations différentielles et les résultats sont obtenus en résolvant ce système. Les logiciels disponibles pour implémenter les modèles incluent les logiciels mathématiques et les logiciels généraux de simulation. L'objectif principal de cette thèse est de développer des modèles et des logiciels pour aider a comprendre, via la simulation, le fonctionnement des stromatolithes et des tapis microbiens. Ces logiciels ont été développés en C++ en ne partant d'aucun pré-requis de façon a privilégier performance et flexibilité maximales. Cette démarche permet de construire des modèles bien plus spécifiques et plus appropriés aux phénomènes a modéliser. Premièrement, nous avons étudié la croissance et la morphologie des stromatolithes. Nous avons construit un modèle tridimensionnel fondé sur l'agrégation par diffusion limitée. Le modèle a été implémenté en deux applications C++: un moteur de simulation capable d'exécuter un batch de simulations et de produire des fichiers de résultats, et un outil de visualisation qui permet d'analyser les résultats en trois dimensions. Après avoir vérifié que ce modèle peut en effet reproduire la croissance et la morphologie de plusieurs types de stromatolithes, nous avons introduit un processus de sédimentation comme facteur externe. Ceci nous a mené a des résultats intéressants, et permis de soutenir l'hypothèse que la morphologie des stromatolithes pourrait être le résultat de facteurs externes autant que de facteurs internes. Ceci est important car la classification des stromatolithes est généralement fondée sur leur morphologie, imposant que la forme d'un stromatolithe est dépendante de facteurs internes uniquement (c'est-à-dire les tapis microbiens). Les résultats avancés dans ce mémoire contredisent donc ces assertions communément admises. Ensuite, nous avons décidé de mener des recherches plus en profondeur sur les aspects fonctionnels des tapis microbiens. Nous avons construit un modèle bidimensionnel de réaction-diffusion fondé sur la simulation discrète. Ce modèle a été implémenté dans une application C++ qui permet de paramétrer et exécuter des simulations. Nous avons ensuite pu comparer les résultats de simulation avec des données du monde réel et vérifier que le modèle peut en effet imiter le comportement de certains tapis microbiens. Ainsi, nous avons pu émettre et vérifier des hypothèses sur le fonctionnement de certains tapis microbiens pour nous aider à mieux en comprendre certains aspects, comme la dynamique des éléments, en particulier le soufre et l'oxygène. En conclusion, ce travail a abouti à l'écriture de logiciels dédiés à la simulation de tapis microbiens d'un point de vue tant morphologique que fonctionnel, suivant deux approches différentes, l'une holistique, l'autre plus analytique. Ces logiciels sont gratuits et diffusés sous licence GPL (General Public License). Abstract : Better understanding of stromatolites and microbial mats is an important topic in biogeosciences as it helps studying the early forms of life on Earth, provides clues re- garding the ecology of microbial ecosystems and their contribution to biomineralization, and gives basis to a new science, exobiology. On the other hand, modelling is a powerful tool used in natural sciences for the theoretical approach of various phenomena. Models are usually built on a system of differential equations and results are obtained by solving that system. Available software to implement models includes mathematical solvers and general simulation software. The main objective of this thesis is to develop models and software able to help to understand the functioning of stromatolites and microbial mats. Software was developed in C++ from scratch for maximum performance and flexibility. This allows to build models much more specific to a phenomenon rather than general software. First, we studied stromatolite growth and morphology. We built a three-dimensional model based on diffusion-limited aggregation. The model was implemented in two C++ applications: a simulator engine, which can run a batch of simulations and produce result files, and a Visualization tool, which allows results to be analysed in three dimensions. After verifying that our model can indeed reproduce the growth and morphology of several types of stromatolites, we introduced a sedimentation process as an external factor. This lead to interesting results, and allowed to emit the hypothesis that stromatolite morphology may be the result of external factors as much as internal factors. This is important as stromatolite classification is usually based on their morphology, imposing that a stromatolite shape is dependant on internal factors only (i.e. the microbial mat). This statement is contradicted by our findings, Second, we decided to investigate deeper the functioning of microbial mats, We built a two-dimensional reaction-diffusion model based on discrete simulation, The model was implemented in a C++ application that allows setting and running simulations. We could then compare simulation results with real world data and verify that our model can indeed mimic the behaviour of some microbial mats. Thus, we have proposed and verified hypotheses regarding microbial mats functioning in order to help to better understand them, e.g. the cycle of some elements such as oxygen or sulfur. ln conclusion, this PhD provides a simulation software, dealing with two different approaches. This software is free and available under a GPL licence.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Mobile Communications within the European Union: The Role of Location in the Evolution and Forecasting of the Diffusion Process

In the European Union, the importance of mobile communications was realized early on. The process of mobile communications becoming ubiquitous has taken time, as the innovation of mobile communications diffused into the society. The aim of this study is to find out how the evolution and spatial patterns of the diffusion of mobile communications within the European Union could be taken into account in forecasting the diffusion process. There is relatively lot of research of innovation diffusion on the individual (micro) andthe country (macro) level, if compared to the territorial level. Territorial orspatial diffusion refers either to the intra-country or inter-country diffusionof an innovation. In both settings, the dif- fusion of a technological innovation has gained scarce attention. This study adds knowledge of the diffusion between countries, focusing especially on the role of location in this process. The main findings of the study are the following: The penetration rates of the European Union member countries have become more even in the period of observation, from the year 1981 to 2000. The common digital GSM system seems to have hastened this process. As to the role of location in the diffusion process, neighboring countries have had similar diffusion processes. They can be grouped into three, the Nordic countries, the central and southern European countries, and the remote southern European countries. The neighborhood effect is also domi- nating in thegravity model which is used for modeling the adoption timing of the countries. The subsequent diffusion within a country, measured by the logistic model in Finland, is af- fected positively by its economic situation, and it seems to level off at some 92 %. Considering the launch of future mobile communications systemsusing a common standard should implicate an equal development between the countries. The launching time should be carefully selected as the diffusion is probably delayed in economic downturns. The location of a country, measured by distance, can be used in forecasting the adoption and diffusion. Fi- nally, the result of penetration rates becoming more even implies that in a relatively homoge- nous set of countries, such as the European Union member countries, the estimated final pene- tration of a single country can be used for approximating the penetration of the others. The estimated eventual penetration of Finland, some 92 %, should thus also be the eventual level for all the European Union countries and for the European Union as a whole.

Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.