Surface topography and mixed-pixel effects on the simulated L-band brightness temperatures.

The impact of topography and mixed pixels on L-band radiometric observations over land needs to be quantified to improve the accuracy of soil moisture retrievals. For this purpose, a series of simulations has been performed with an improved version of the soil moisture and ocean salinity (SMOS) end-to-end performance simulator (SEPS). The brightness temperature generator of SEPS has been modified to include a 100-m-resolution land cover map and a 30-m-resolution digital elevation map of Catalonia (northeast of Spain). This high-resolution generator allows the assessment of the errors in soil moisture retrieval algorithms due to limited spatial resolution and provides a basis for the development of pixel disaggregation techniques. Variation of the local incidence angle, shadowing, and atmospheric effects (up- and downwelling radiation) due to surface topography has been analyzed. Results are compared to brightness temperatures that are computed under the assumption of an ellipsoidal Earth.

Variability of apparently homogeneous soilscapes in São Paulo state, Brazil: I. spatial analysis

The spatial variability of strongly weathered soils under sugarcane and soybean/wheat rotation was quantitatively assessed on 33 fields in two regions in São Paulo State, Brazil: Araras (15 fields with sugarcane) and Assis (11 fields with sugarcane and seven fields with soybean/wheat rotation). Statistical methods used were: nested analysis of variance (for 11 fields), semivariance analysis and analysis of variance within and between fields. Spatial levels from 50 m to several km were analyzed. Results are discussed with reference to a previously published study carried out in the surroundings of Passo Fundo (RS). Similar variability patterns were found for clay content, organic C content and cation exchange capacity. The fields studied are quite homogeneous with respect to these relatively stable soil characteristics. Spatial variability of other characteristics (resin extractable P, pH, base- and Al-saturation and also soil colour), varies with region and, or land use management. Soil management for sugarcane seems to have induced modifications to greater depths than for soybean/wheat rotation. Surface layers of soils under soybean/wheat present relatively little variation, apparently as a result of very intensive soil management. The major part of within-field variation occurs at short distances (< 50 m) in all study areas. Hence, little extra information would be gained by increasing sampling density from, say, 1/km² to 1/50 m². For many purposes, the soils in the study regions can be mapped with the same observation density, but residual variance will not be the same in all areas. Bulk sampling may help to reveal spatial patterns between 50 and 1.000 m.

Spatial analysis of corresponding fingerprint features from match and close non-match populations

The development of statistical models for forensic fingerprint identification purposes has been the subject of increasing research attention in recent years. This can be partly seen as a response to a number of commentators who claim that the scientific basis for fingerprint identification has not been adequately demonstrated. In addition, key forensic identification bodies such as ENFSI [1] and IAI [2] have recently endorsed and acknowledged the potential benefits of using statistical models as an important tool in support of the fingerprint identification process within the ACE-V framework. In this paper, we introduce a new Likelihood Ratio (LR) model based on Support Vector Machines (SVMs) trained with features discovered via morphometric and spatial analyses of corresponding minutiae configurations for both match and close non-match populations often found in AFIS candidate lists. Computed LR values are derived from a probabilistic framework based on SVMs that discover the intrinsic spatial differences of match and close non-match populations. Lastly, experimentation performed on a set of over 120,000 publicly available fingerprint images (mostly sourced from the National Institute of Standards and Technology (NIST) datasets) and a distortion set of approximately 40,000 images, is presented, illustrating that the proposed LR model is reliably guiding towards the right proposition in the identification assessment of match and close non-match populations. Results further indicate that the proposed model is a promising tool for fingerprint practitioners to use for analysing the spatial consistency of corresponding minutiae configurations.

Temporal and spatial origin of Gesneriaceae in the New World inferred from plastid DNA sequences

Gesneriaceae are represented in the New World (NW) by a major clade (c. 1000 species) currently recognized as subfamily Gesnerioideae. Radiation of this group occurred in all biomes of tropical America and was accompanied by extensive phenotypic and ecological diversification. Here we performed phylogenetic analyses using DNA sequences from three plastid loci to reconstruct the evolutionary history of Gesnerioideae and to investigate its relationship with other lineages of Gesneriaceae and Lamiales. Our molecular data confirm the inclusion of the South Pacific Coronanthereae and the Old World (OW) monotypic genus Titanotrichum in Gesnerioideae and the sister-group relationship of this subfamily to the rest of the OW Gesneriaceae. Calceolariaceae and the NW genera Peltanthera and Sanango appeared successively sister to Gesneriaceae, whereas Cubitanthus, which has been previously assigned to Gesneriaceae, is shown to be related to Linderniaceae. Based on molecular dating and biogeographical reconstruction analyses, we suggest that ancestors of Gesneriaceae originated in South America during the Late Cretaceous. Distribution of Gesneriaceae in the Palaeotropics and Australasia was inferred as resulting from two independent long-distance dispersals during the Eocene and Oligocene, respectively. In a short time span starting at 34 Mya, ancestors of Gesnerioideae colonized several Neotropical regions including the tropical Andes, Brazilian Atlantic forest, cerrado, Central America and the West Indies. Subsequent diversification within these areas occurred largely in situ and was particularly extensive in the mountainous systems of the Andes, Central America and the Brazilian Atlantic forest. Only two radiations account for 90% of the diversity of Gesneriaceae in the Brazilian Atlantic forest, whereas half of the species richness in the northern Andes and Central America originated during the last 10 Myr from a single radiation.

Traducción técnica del capítulo III del libro Advanced Data Warehouse design: from conventional to spatial and temporal applications

The proposal to work on this final project came after several discussions held with Dr. Elzbieta Malinowski Gadja, who in 2008 published the book entitled Advanced Data Warehouse Design: From Conventional to Spatial and Temporal Applications (Data-Centric Systems and Applications). The project was carried out under the technical supervision of Dr. Malinowski and the direct beneficiary was the University of Costa Rica (UCR) where Dr. Malinowski is a professor at the Department of Computer Science and Informatics. The purpose of this project was twofold: First, to translate chapter III of said book with the intention of generating educational material for the use of the UCR and, second, to venture in the field of technical translation related to data warehouse. For the first component, the goal was to generate a final product that would eventually serve as an educational tool for the post-graduate courses of the UCR. For the second component, this project allowed me to acquire new skills and put into practice techniques that have helped me not only to perfom better in my current job as an Assistant Translator of the Inter-American BAnk (IDB), but also to use them in similar projects. The process was lenggthy and required torough research and constant communication with the author. The investigation focused on the search of terms and definitions to prepare the glossary, which was the basis to start the translation project. The translation process itself was carried out by phases, so that comments and corrections by the author could be taken into account in subsequent stages. Later, based on the glossary and the translated text, illustrations had been created in the Visio software were translated. In addition to the technical revision by the author, professor Carme Mangiron was in charge of revising the non-technical text. The result was a high-quality document that is currently used as reference and study material by the Department of Computer Science and Informatics of Costa Rica.

Uncertainty Quantification with Support Vector Regression Prediction Models

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. The paper considers a data driven approach in modelling uncertainty in spatial predictions. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic features and describe stochastic variability and non-uniqueness of spatial properties. It is able to capture and preserve key spatial dependencies such as connectivity, which is often difficult to achieve with two-point geostatistical models. Semi-supervised SVR is designed to integrate various kinds of conditioning data and learn dependences from them. A stochastic semi-supervised SVR model is integrated into a Bayesian framework to quantify uncertainty with multiple models fitted to dynamic observations. The developed approach is illustrated with a reservoir case study. The resulting probabilistic production forecasts are described by uncertainty envelopes.

Bayesian image reconstruction with space-variant noise suppression

In this paper we present a Bayesian image reconstruction algorithm with entropy prior (FMAPE) that uses a space-variant hyperparameter. The spatial variation of the hyperparameter allows different degrees of resolution in areas of different statistical characteristics, thus avoiding the large residuals resulting from algorithms that use a constant hyperparameter. In the first implementation of the algorithm, we begin by segmenting a Maximum Likelihood Estimator (MLE) reconstruction. The segmentation method is based on using a wavelet decomposition and a self-organizing neural network. The result is a predetermined number of extended regions plus a small region for each star or bright object. To assign a different value of the hyperparameter to each extended region and star, we use either feasibility tests or cross-validation methods. Once the set of hyperparameters is obtained, we carried out the final Bayesian reconstruction, leading to a reconstruction with decreased bias and excellent visual characteristics. The method has been applied to data from the non-refurbished Hubble Space Telescope. The method can be also applied to ground-based images.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

High specificity of line-immunoassay based algorithms for recent HIV-1 infection independent of viral subtype and stage of disease.

ABSTRACT: BACKGROUND: Serologic testing algorithms for recent HIV seroconversion (STARHS) provide important information for HIV surveillance. We have shown that a patient's antibody reaction in a confirmatory line immunoassay (INNO-LIATM HIV I/II Score, Innogenetics) provides information on the duration of infection. Here, we sought to further investigate the diagnostic specificity of various Inno-Lia algorithms and to identify factors affecting it. METHODS: Plasma samples of 714 selected patients of the Swiss HIV Cohort Study infected for longer than 12 months and representing all viral clades and stages of chronic HIV-1 infection were tested blindly by Inno-Lia and classified as either incident (up to 12 m) or older infection by 24 different algorithms. Of the total, 524 patients received HAART, 308 had HIV-1 RNA below 50 copies/mL, and 620 were infected by a HIV-1 non-B clade. Using logistic regression analysis we evaluated factors that might affect the specificity of these algorithms. RESULTS: HIV-1 RNA <50 copies/mL was associated with significantly lower reactivity to all five HIV-1 antigens of the Inno-Lia and impaired specificity of most algorithms. Among 412 patients either untreated or with HIV-1 RNA ≥50 copies/mL despite HAART, the median specificity of the algorithms was 96.5% (range 92.0-100%). The only factor that significantly promoted false-incident results in this group was age, with false-incident results increasing by a few percent per additional year. HIV-1 clade, HIV-1 RNA, CD4 percentage, sex, disease stage, and testing modalities exhibited no significance. Results were similar among 190 untreated patients. CONCLUSIONS: The specificity of most Inno-Lia algorithms was high and not affected by HIV-1 variability, advanced disease and other factors promoting false-recent results in other STARHS. Specificity should be good in any group of untreated HIV-1 patients.

Accurate memory for object location by individuals with intellectual disability: Absolute spatial tagging instead of configural processing?

Using head-mounted eye tracker material, we assessed spatial recognition abilities (e.g., reaction to object permutation, removal or replacement with a new object) in participants with intellectual disabilities. The "Intellectual Disabilities (ID)" group (n=40) obtained a score totalling a 93.7% success rate, whereas the "Normal Control" group (n=40) scored 55.6% and took longer to fix their attention on the displaced object. The participants with an intellectual disability thus had a more accurate perception of spatial changes than controls. Interestingly, the ID participants were more reactive to object displacement than to removal of the object. In the specific test of novelty detection, however, the scores were similar, the two groups approaching 100% detection. Analysis of the strategies expressed by the ID group revealed that they engaged in more systematic object checking and were more sensitive than the control group to changes in the structure of the environment. Indeed, during the familiarisation phase, the "ID" group explored the collection of objects more slowly, and fixed their gaze for a longer time upon a significantly lower number of fixation points during visual sweeping.

Spatial and temporal variation of natural toxicity in cnidarians, bryozoans and tunicates in Mediterranean caves

The natural toxicity of cnidarians, bryozoans and tunicates in two caves was assessed using the Microtox® technique in spring and autumn. One cave was located in the Cabrera Archipelago (Balearic Islands) and the other in the Medes Islands (Catalan littoral). The organisms analysed were good representatives of the coverage of each Phylum in the communities; however, these Phyla are less abundant than sponges which are the dominant group in these caves. Seventy-one percent of the species of cnidarians and bryozoans analysed were toxic in one of the caves, communities or seasons, which indicates the relevance of bioactive species in these groups. The tunicate Lissoclinum perforatum was the most toxic species. Although all three Phyla had some highly toxic species, a common pattern that related the caves, communities and seasons was not found. Seasonal variation of toxicity in cnidarians and bryozoans was higher in the Cabrera than in the Medes cave. Moreover, variation in toxicity either between communities or between seasons was a common trait for most cnidarians and bryozoans, whereas tunicates remained toxic throughout communities and seasons.

Silver-assisted laser desorption ionization for high spatial resolution imaging mass spectrometry of olefins from thin tissue sections.

Silver has been demonstrated to be a powerful cationization agent in mass spectrometry (MS) for various olefinic species such as cholesterol and fatty acids. This work explores the utility of metallic silver sputtering on tissue sections for high resolution imaging mass spectrometry (IMS) of olefins by laser desorption ionization (LDI). For this purpose, sputtered silver coating thickness was optimized on an assorted selection of mouse and rat tissues including brain, kidney, liver, and testis. For mouse brain tissue section, the thickness was adjusted to 23 ± 2 nm of silver to prevent ion suppression effects associated with a higher cholesterol and lipid content. On all other tissues, a thickness of at 16 ± 2 nm provided the best desorption/ionization efficiency. Characterization of the species by MS/MS showed a wide variety of olefinic compounds allowing the IMS of different lipid classes including cholesterol, arachidonic acid, docosahexaenoic acid, and triacylglyceride 52:3. A range of spatial resolutions for IMS were investigated from 150 μm down to the high resolution cellular range at 5 μm. The applicability of direct on-tissue silver sputtering to LDI-IMS of cholesterol and other olefinic compounds presents a novel approach to improve the amount of information that can be obtained from tissue sections. This IMS strategy is thus of interest for providing new biological insights on the role of cholesterol and other olefins in physiological pathways or disease.

Learning-induced plasticity in auditory spatial representations revealed by electrical neuroimaging.

Auditory spatial representations are likely encoded at a population level within human auditory cortices. We investigated learning-induced plasticity of spatial discrimination in healthy subjects using auditory-evoked potentials (AEPs) and electrical neuroimaging analyses. Stimuli were 100 ms white-noise bursts lateralized with varying interaural time differences. In three experiments, plasticity was induced with 40 min of discrimination training. During training, accuracy significantly improved from near-chance levels to approximately 75%. Before and after training, AEPs were recorded to stimuli presented passively with a more medial sound lateralization outnumbering a more lateral one (7:1). In experiment 1, the same lateralizations were used for training and AEP sessions. Significant AEP modulations to the different lateralizations were evident only after training, indicative of a learning-induced mismatch negativity (MMN). More precisely, this MMN at 195-250 ms after stimulus onset followed from differences in the AEP topography to each stimulus position, indicative of changes in the underlying brain network. In experiment 2, mirror-symmetric locations were used for training and AEP sessions; no training-related AEP modulations or MMN were observed. In experiment 3, the discrimination of trained plus equidistant untrained separations was tested psychophysically before and 0, 6, 24, and 48 h after training. Learning-induced plasticity lasted <6 h, did not generalize to untrained lateralizations, and was not the simple result of strengthening the representation of the trained lateralizations. Thus, learning-induced plasticity of auditory spatial discrimination relies on spatial comparisons, rather than a spatial anchor or a general comparator. Furthermore, cortical auditory representations of space are dynamic and subject to rapid reorganization.

Growth and externalities across economies : an empirical analysis using spatial econometrics

Recent theoretical models of economic growth have emphasised the role of external effects on the accumulation of factors of production. Although most of the literature has considered the externalities across firms within a region, in this paper we go a step further and consider the possibility that these externalities cross the barriers of regional economies. We assess the role of these external effects in explaining growth and economic convergence. We present a simple growth model, which includes externalities across economies, developing a methodology for testing their existence and estimating their strength. In our view, spatial econometrics is naturally suited to an empirical consideration of these externalities. We obtain evidence on the presence of significant externalities both across Spanish and European regions.