Preconditioning strategies for the numerical solution of convection-diffusion partial differential equations

Il trattamento numerico dell'equazione di convezione-diffusione con le relative condizioni al bordo, comporta la risoluzione di sistemi lineari algebrici di grandi dimensioni in cui la matrice dei coefficienti è non simmetrica. Risolutori iterativi basati sul sottospazio di Krylov sono ampiamente utilizzati per questi sistemi lineari la cui risoluzione risulta particolarmente impegnativa nel caso di convezione dominante. In questa tesi vengono analizzate alcune strategie di precondizionamento, atte ad accelerare la convergenza di questi metodi iterativi. Vengono confrontati sperimentalmente precondizionatori molto noti come ILU e iterazioni di tipo inner-outer flessibile. Nel caso in cui i coefficienti del termine di convezione siano a variabili separabili, proponiamo una nuova strategia di precondizionamento basata sull'approssimazione, mediante equazione matriciale, dell'operatore differenziale di convezione-diffusione. L'azione di questo nuovo precondizionatore sfrutta in modo opportuno recenti risolutori efficienti per equazioni matriciali lineari. Vengono riportati numerosi esperimenti numerici per studiare la dipendenza della performance dei diversi risolutori dalla scelta del termine di convezione, e dai parametri di discretizzazione.

Equazioni stocastiche backward nel mercato delle emissioni

In questa tesi viene esposto il modello EU ETS (European Union Emission Trading Scheme) per la riduzione delle emissoni di gas serra, il quale viene formalizzato matematicamente da un sistema di FBSDE (Forward Backward Stochastic Differential Equation). Da questo sistema si ricava un'equazione differenziale non lineare con condizione al tempo finale non continua che viene studiata attraverso la teoria delle soluzioni viscosità. Inoltre il modello viene implementato numericamente per ottenere alcune simulazioni dei processi coinvolti.

Differential block coding of bilevel images

Abstract- In this correspondence, a simple one-dimensional (1-D) differencing operation is applied to bilevel images prior to block coding to produce a sparse binary image that can be encoded efficiently using any of a number of well-known techniques. The difference image can be encoded more efficiently than the original bilevel image whenever the average run length of black pixels in the original image is greater than two. Compression is achieved because the correlation between adjacent pixels is reduced compared with the original image. The encoding/decoding operations are described and compression performance is presented for a set of standard bilevel images.

Favourable prognostic value of antibodies anti-HSP20 in patients with cystic echinococcosis: a differential immunoproteomic approach

Seeking biomarkers reflecting disease development in cystic echinococcosis (CE), we used a proteomic approach linked to immunological characterisation for the identification of respective antigens. Two-dimensional gel electrophoresis (2-DE) of sheep hydatid fluid, followed by immunoblot analysis (IB) with sera from patients with distinct phases of disease, enabled us to identify by mass spectrometry heat shock protein 20 (HSP20) as a potential marker of active CE. Using IB, antibodies specific to the 34 kDa band of HSP20 were detected in sera from 61/95 (64%) patients with CE, but not in sera from healthy subjects. IB revealed anti-HSP20 antibodies in a higher percentage of sera from patients with active disease than in sera from patients with inactive disease (81 vs. 24%; P = 10(-4)). These primary results were confirmed in a long-term follow-up study after pharmacological and surgical treatment. Herewith anti-HSP20 antibody levels significantly decreased over the course of treatment in sera from patients with cured disease, relative to sera from patients with progressive disease (P = 0.017). Thus, during CE, a comprehensive strategy of proteomic identification combined with immunological validation represents a promising approach for the identification of biomarkers useful for the prognostic assessment of treatment of CE patients.

Differential regulation of metzincins in experimental chronic renal allograft rejection: potential markers and novel therapeutic targets

Chronic renal allograft rejection is characterized by alterations in the extracellular matrix compartment and in the proliferation of various cell types. These features are controlled, in part by the metzincin superfamily of metallo-endopeptidases, including matrix metalloproteinases (MMPs), a disintegrin and metalloproteinase (ADAM) and meprin. Therefore, we investigated the regulation of metzincins in the established Fisher to Lewis rat kidney transplant model. Studies were performed using frozen homogenates and paraffin sections of rat kidneys at day 0 (healthy controls) and during periods of chronic rejection at day +60 and day +100 following transplantation. The messenger RNA (mRNA) expression was examined by Affymetrix Rat Expression Array 230A GeneChip and by real-time Taqman polymerase chain reaction analyses. Protein expression was studied by zymography, Western blot analyses, and immunohistology. mRNA levels of MMPs (MMP-2/-11/-12/-14), of their inhibitors (tissue inhibitors of metalloproteinase (TIMP)-1/-2), ADAM-17 and transforming growth factor (TGF)-beta1 significantly increased during chronic renal allograft rejection. MMP-2 activity and immunohistological staining were augmented accordingly. The most important mRNA elevation was observed in the case of MMP-12. As expected, Western blot analyses also demonstrated increased production of MMP-12, MMP-14, and TIMP-2 (in the latter two cases as individual proteins and as complexes). In contrast, mRNA levels of MMP-9/-24 and meprin alpha/beta had decreased. Accordingly, MMP-9 protein levels and meprin alpha/beta synthesis and activity were downregulated significantly. Members of metzincin families (MMP, ADAM, and meprin) and of TIMPs are differentially regulated in chronic renal allograft rejection. Thus, an altered pattern of metzincins may represent novel diagnostic markers and possibly may provide novel targets for future therapeutic interventions.

Differential distribution of vasa vasorum in different vascular beds in humans

OBJECTIVE: Vasa vasorum (VV) have been implicated to play a role in the pathogenesis of atherosclerosis. This study was designed to describe the distribution of VV density in different vascular beds in humans and to investigate the association between VV density and the known distribution of atherosclerosis in human arteries. METHODS: Forty-two human arteries, harvested at autopsy or after explantation, were analyzed by three-dimensional microscopic-computed tomography (micro-CT). VV density, endothelial-surface-fraction (Sigma VV endothelial-surface-area/vessel-wall-volume) and vascular-area-fraction (Sigma VV area/vessel-wall-area) were calculated for coronary, renal and femoral arteries. Representatively five coronary, renal and femoral arteries were stained for endothelial cells (von Willebrand-Factor), macrophages (CD68), vascular endothelial growth factor (VEGF) and collagen (Sirius Red). RESULTS: Coronary arteries showed a higher VV density compared to renal and femoral arteries (2.12+/-0.26 n/mm(2) versus 0.61+/-0.06 n/mm(2) and 0.66+/-0.11 n/mm(2); P<0.05 for both) as well as a higher endothelial-surface-fraction and vascular-area-fraction. Histology showed a positive correlation between histologically derived VV density and CD68-positive cells/area (r=0.54, P<0.01), VEGF-immunoreactivity/area (r=0.55, P<0.01) and a negative correlation between VV density and collagen I content (r=0.66, P<0.05). CONCLUSION: This micro-CT study highlights a higher VV density in coronary than in peripheral arteries, supporting the relation between VV density and the susceptibility to atherosclerosis in different vascular beds in humans.

STOCHASTIC CHARGE TRANSPORT IN MULTI-ISLAND SINGLE-ELECTRON TUNNELING DEVICES

The physics of the operation of singe-electron tunneling devices (SEDs) and singe-electron tunneling transistors (SETs), especially of those with multiple nanometer-sized islands, has remained poorly understood in spite of some intensive experimental and theoretical research. This computational study examines the current-voltage (IV) characteristics of multi-island single-electron devices using a newly developed multi-island transport simulator (MITS) that is based on semi-classical tunneling theory and kinetic Monte Carlo simulation. The dependence of device characteristics on physical device parameters is explored, and the physical mechanisms that lead to the Coulomb blockade (CB) and Coulomb staircase (CS) characteristics are proposed. Simulations using MITS demonstrate that the overall IV characteristics in a device with a random distribution of islands are a result of a complex interplay among those factors that affect the tunneling rates that are fixed a priori (e.g. island sizes, island separations, temperature, gate bias, etc.), and the evolving charge state of the system, which changes as the source-drain bias (VSD) is changed. With increasing VSD, a multi-island device has to overcome multiple discrete energy barriers (up-steps) before it reaches the threshold voltage (Vth). Beyond Vth, current flow is rate-limited by slow junctions, which leads to the CS structures in the IV characteristic. Each step in the CS is characterized by a unique distribution of island charges with an associated distribution of tunneling probabilities. MITS simulation studies done on one-dimensional (1D) disordered chains show that longer chains are better suited for switching applications as Vth increases with increasing chain length. They are also able to retain CS structures at higher temperatures better than shorter chains. In sufficiently disordered 2D systems, we demonstrate that there may exist a dominant conducting path (DCP) for conduction, which makes the 2D device behave as a quasi-1D device. The existence of a DCP is sensitive to the device structure, but is robust with respect to changes in temperature, gate bias, and VSD. A side gate in 1D and 2D systems can effectively control Vth. We argue that devices with smaller island sizes and narrower junctions may be better suited for practical applications, especially at room temperature.

Differential effects of anti-hypertensive treatment on the retinal microcirculation: an Anglo-Scandinavian Cardiac Outcomes Trial (ASCOT) sub- study

Changes in the retinal microcirculation are associated with hypertension and predict cardiovascular mortality. There are few data describing the impact of antihypertensive therapy on retinal vascular changes. This substudy of the Anglo-Scandinavian Cardiac Outcomes Trial compared the effects of an amlodipine-based regimen (373 patients) with an atenolol-based regimen (347 patients) on retinal microvascular measurements made from fundus photographs. The retinal photographs were taken at a stage in the trial when treatments were stable and blood pressure was well controlled. Amlodipine-based treatment was associated with a smaller arteriolar length:diameter ratio than atenolol-based treatment (13.32 [10.75 to 16.04] versus 14.12 [11.27 to 17.81], median [interquartile range]; P<0.01). The association remained significant after adjustment for age, sex, cholesterol, systolic and diastolic blood pressures, body mass index, smoking, and statin treatment. This effect appeared to be largely attributable to shorter retinal arteriolar segment lengths in the amlodipine-treated group and is best explained by the vasodilator effects of amlodipine causing the visible emergence of branching side vessels. Photographic assessment of the retinal vascular network may be a useful approach to evaluating microvascular structural responses in clinical trials of antihypertensive therapy.

Differential effects of captopril and nitrates on muscle sympathetic nerve activity in volunteers

BACKGROUND The sympathetic nervous system (SNS) is an important regulator of cardiovascular function. Activation of SNS plays an important role in the pathophysiology and the prognosis of cardiovascular diseases such as heart failure, acute coronary syndromes, arrhythmia, and possibly hypertension. Vasodilators such as adenosine and sodium nitroprusside are known to activate SNS via baroreflex mechanisms. Because vasodilators are widely used in the treatment of patients with cardiovascular diseases, the aim of the present study was to assess the influence of clinically used dosages of isosorbide dinitrate and captopril on sympathetic nerve activity at rest and during stimulatory maneuvers. METHODS AND RESULTS Twenty-eight healthy volunteers were included in this double-blind placebo-controlled study, and muscle sympathetic nerve activity (MSA; with microelectrodes in the peroneal nerve), blood pressure, heart rate, and neurohumoral parameters were measured before and 90 minutes after the oral administration of 40 mg isosorbide dinitrate or 6.25 mg captopril. Furthermore, a 3-minute mental stress test and a cold pressor test were performed before and 90 minutes after drug administration. Resting MSA did not change after captopril and decreased compared with placebo (P < .05 versus placebo), whereas isosorbide dinitrate led to a marked increase in MSA (P < .05). Systolic blood pressure was reduced by isosorbide dinitrate (P < .05), whereas captopril decreased diastolic blood pressure (P < .05). The increases in MSA, blood pressure, and heart rate during mental stress were comparable before and after drug administration regardless of the medication. During cold pressor test, MSA and systolic and diastolic blood pressures increased to the same degree independent of treatment, but after isosorbide dinitrate, the increase in MSA seemed to be less pronounced. Heart rate did not change during cold stimulation. Plasma renin activity increased after captopril and isosorbide dinitrate (P < .05), whereas placebo had no effect. Endothelin-1 increased after placebo and isosorbide dinitrate (P < .05) but not after captopril. CONCLUSIONS Thus, captopril suppressed MSA despite lowering of diastolic blood pressure but allowed normal adaptation of the SNS during mental or physical stress. In contrast, the nitrate strongly activated the SNS under baseline conditions. These findings demonstrate that vasodilators differentially interact with the SNS, which could be of importance in therapeutic strategies for the treatment of patients with cardiovascular diseases.

Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma

The in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound states at finite temperature through a Schrödinger equation with an instantaneous potential. Here we review recent progress in devising a comprehensive approach to define such a potential from first principles QCD and extract its, in general complex, values from non-perturbative lattice QCD simulations. Based on the theory of open quantum systems we will show how to interpret the role of the imaginary part in terms of spatial decoherence by introducing the concept of a stochastic potential. Shortcomings as well as possible paths for improvement are discussed.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Cognitive-Behavioural Analysis System of Psychotherapy (CBASP), a drug, or their combination: differential therapeutics for persistent depressive disorder: a study protocol of an individual participant data network meta-analysis.

INTRODUCTION Despite important advances in psychological and pharmacological treatments of persistent depressive disorders in the past decades, their responses remain typically slow and poor, and differential responses among different modalities of treatments or their combinations are not well understood. Cognitive-Behavioural Analysis System of Psychotherapy (CBASP) is the only psychotherapy that has been specifically designed for chronic depression and has been examined in an increasing number of trials against medications, alone or in combination. When several treatment alternatives are available for a certain condition, network meta-analysis (NMA) provides a powerful tool to examine their relative efficacy by combining all direct and indirect comparisons. Individual participant data (IPD) meta-analysis enables exploration of impacts of individual characteristics that lead to a differentiated approach matching treatments to specific subgroups of patients. METHODS AND ANALYSIS We will search for all randomised controlled trials that compared CBASP, pharmacotherapy or their combination, in the treatment of patients with persistent depressive disorder, in Cochrane CENTRAL, PUBMED, SCOPUS and PsycINFO, supplemented by personal contacts. Individual participant data will be sought from the principal investigators of all the identified trials. Our primary outcomes are depression severity as measured on a continuous observer-rated scale for depression, and dropouts for any reason as a proxy measure of overall treatment acceptability. We will conduct a one-step IPD-NMA to compare CBASP, medications and their combinations, and also carry out a meta-regression to identify their prognostic factors and effect moderators. The model will be fitted in OpenBUGS, using vague priors for all location parameters. For the heterogeneity we will use a half-normal prior on the SD. ETHICS AND DISSEMINATION This study requires no ethical approval. We will publish the findings in a peer-reviewed journal. The study results will contribute to more finely differentiated therapeutics for patients suffering from this chronically disabling disorder. TRIAL REGISTRATION NUMBER CRD42016035886.

Desarrollo de un Procedimiento Basado en Algoritmos de Optimización para el Dimensionado de Absorbedores Puntuales Aplicados a la Conversión de Energía Undimotriz

La energía transportada por el oleaje a través de los océanos (energía undimotriz) se enmarca dentro de las denominadas energías oceánicas. Su aprovechamiento para generar energía eléctrica (o ser aprovechada de alguna otra forma) es una idea reflejada ya hace más de dos siglos en una patente (1799). Desde entonces, y con especial intensidad desde los años 70, ha venido despertando el interés de instituciones ligadas al I+D+i y empresas del sector energético y tecnológico, debido principalmente a la magnitud del recurso disponible. Actualmente se puede considerar al sector en un estado precomercial, con un amplio rango de dispositivos y tecnologías en diferente grado de desarrollo en los que ninguno destaca sobre los otros (ni ha demostrado su viabilidad económica), y sin que se aprecie una tendencia a converger un único dispositivo (o un número reducido de ellos). El recurso energético que se está tratando de aprovechar, pese a compartir la característica de no-controlabilidad con otras fuentes de energía renovable como la eólica o la solar, presenta una variabilidad adicional. De esta manera, diferentes localizaciones, pese a poder presentar recursos de contenido energético similar, presentan oleajes de características muy diferentes en términos de alturas y periodos de oleaje, y en la dispersión estadística de estos valores. Esta variabilidad en el oleaje hace que cobre especial relevancia la adecuación de los dispositivos de aprovechamiento de energía undimotriz (WEC: Wave Energy Converter) a su localización, de cara a mejorar su viabilidad económica. Parece razonable suponer que, en un futuro, el proceso de diseño de un parque de generación undimotriz implique un rediseño (en base a una tecnología conocida) para cada proyecto de implantación en una nueva localización. El objetivo de esta tesis es plantear un procedimiento de dimensionado de una tecnología de aprovechamiento de la energía undimotriz concreta: los absorbedores puntuales. Dicha metodología de diseño se plantea como un problema de optimización matemático, el cual se resuelve utilizando un algoritmo de optimización bioinspirado: evolución diferencial. Este planteamiento permite automatizar la fase previa de dimensionado implementando la metodología en un código de programación. El proceso de diseño de un WEC es un problema de ingería complejo, por lo que no considera factible el planteamiento de un diseño completo mediante un único procedimiento de optimización matemático. En vez de eso, se platea el proceso de diseño en diferentes etapas, de manera que la metodología desarrollada en esta tesis se utilice para obtener las dimensiones básicas de una solución de referencia de WEC, la cual será utilizada como punto de partida para continuar con las etapas posteriores del proceso de diseño. La metodología de dimensionado previo presentada en esta tesis parte de unas condiciones de contorno de diseño definidas previamente, tales como: localización, características del sistema de generación de energía eléctrica (PTO: Power Take-Off), estrategia de extracción de energía eléctrica y concepto concreto de WEC). Utilizando un algoritmo de evolución diferencial multi-objetivo se obtiene un conjunto de soluciones factibles (de acuerdo con una ciertas restricciones técnicas y dimensionales) y óptimas (de acuerdo con una serie de funciones objetivo de pseudo-coste y pseudo-beneficio). Dicho conjunto de soluciones o dimensiones de WEC es utilizado como caso de referencia en las posteriores etapas de diseño. En el documento de la tesis se presentan dos versiones de dicha metodología con dos modelos diferentes de evaluación de las soluciones candidatas. Por un lado, se presenta un modelo en el dominio de la frecuencia que presenta importantes simplificaciones en cuanto al tratamiento del recurso del oleaje. Este procedimiento presenta una menor carga computacional pero una mayor incertidumbre en los resultados, la cual puede traducirse en trabajo adicional en las etapas posteriores del proceso de diseño. Sin embargo, el uso de esta metodología resulta conveniente para realizar análisis paramétricos previos de las condiciones de contorno, tales como la localización seleccionada. Por otro lado, la segunda metodología propuesta utiliza modelos en el domino estocástico, lo que aumenta la carga computacional, pero permite obtener resultados con menos incertidumbre e información estadística muy útil para el proceso de diseño. Por este motivo, esta metodología es más adecuada para su uso en un proceso de dimensionado completo de un WEC. La metodología desarrollada durante la tesis ha sido utilizada en un proyecto industrial de evaluación energética preliminar de una planta de energía undimotriz. En dicho proceso de evaluación, el método de dimensionado previo fue utilizado en una primera etapa, de cara a obtener un conjunto de soluciones factibles de acuerdo con una serie de restricciones técnicas básicas. La selección y refinamiento de la geometría de la solución geométrica de WEC propuesta fue realizada a posteriori (por otros participantes del proyecto) utilizando un modelo detallado en el dominio del tiempo y un modelo de evaluación económica del dispositivo. El uso de esta metodología puede ayudar a reducir las iteraciones manuales y a mejorar los resultados obtenidos en estas últimas etapas del proyecto. ABSTRACT The energy transported by ocean waves (wave energy) is framed within the so-called oceanic energies. Its use to generate electric energy (or desalinate ocean water, etc.) is an idea expressed first time in a patent two centuries ago (1799). Ever since, but specially since the 1970’s, this energy has become interesting for R&D institutions and companies related with the technological and energetic sectors mainly because of the magnitude of available energy. Nowadays the development of this technology can be considered to be in a pre-commercial stage, with a wide range of devices and technologies developed to different degrees but with none standing out nor economically viable. Nor do these technologies seem ready to converge to a single device (or a reduce number of devices). The energy resource to be exploited shares its non-controllability with other renewable energy sources such as wind and solar. However, wave energy presents an additional short-term variability due to its oscillatory nature. Thus, different locations may show waves with similar energy content but different characteristics such as wave height or wave period. This variability in ocean waves makes it very important that the devices for harnessing wave energy (WEC: Wave Energy Converter) fit closely to the characteristics of their location in order to improve their economic viability. It seems reasonable to assume that, in the future, the process of designing a wave power plant will involve a re-design (based on a well-known technology) for each implementation project in any new location. The objective of this PhD thesis is to propose a dimensioning method for a specific wave-energy-harnessing technology: point absorbers. This design methodology is presented as a mathematical optimization problem solved by using an optimization bio-inspired algorithm: differential evolution. This approach allows automating the preliminary dimensioning stage by implementing the methodology in programmed code. The design process of a WEC is a complex engineering problem, so the complete design is not feasible using a single mathematical optimization procedure. Instead, the design process is proposed in different stages, so the methodology developed in this thesis is used for the basic dimensions of a reference solution of the WEC, which would be used as a starting point for the later stages of the design process. The preliminary dimensioning methodology presented in this thesis starts from some previously defined boundary conditions such as: location, power take-off (PTO) characteristic, strategy of energy extraction and specific WEC technology. Using a differential multi-objective evolutionary algorithm produces a set of feasible solutions (according to certain technical and dimensional constraints) and optimal solutions (according to a set of pseudo-cost and pseudo-benefit objective functions). This set of solutions or WEC dimensions are used as a reference case in subsequent stages of design. In the document of this thesis, two versions of this methodology with two different models of evaluation of candidate solutions are presented. On the one hand, a model in the frequency domain that has significant simplifications in the treatment of the wave resource is presented. This method implies a lower computational load but increased uncertainty in the results, which may lead to additional work in the later stages of the design process. However, use of this methodology is useful in order to perform previous parametric analysis of boundary conditions such as the selected location. On the other hand, the second method uses stochastic models, increasing the computational load, but providing results with smaller uncertainty and very useful statistical information for the design process. Therefore, this method is more suitable to be used in a detail design process for full dimensioning of the WEC. The methodology developed throughout the thesis has been used in an industrial project for preliminary energetic assessment of a wave energy power plant. In this assessment process, the method of previous dimensioning was used in the first stage, in order to obtain a set of feasible solutions according to a set of basic technical constraints. The geometry of the WEC was refined and selected subsequently (by other project participants) using a detailed model in the time domain and a model of economic evaluation of the device. Using this methodology can help to reduce the number of design iterations and to improve the results obtained in the last stages of the project.

Differential Expression of the S-Adenosyl-l-Methionine Synthase Genes during Pea Development1

Two genes coding for S-adenosyl-l-methionine synthase (SAMS, EC 2.5.1.6) were previously isolated from pea (Pisum sativum) ovaries. Both SAMS genes were highly homologous throughout their coding regions but showed a certain degree of sequence divergence within the 5′ and the 3′ untranslated regions. These regions have been used as gene-specific probes to analyze the differential expression of SAMS1 and SAMS2 genes in pea plants. The ribonuclease protection assay revealed different expression patterns for each individual gene. SAMS1 was strongly expressed in nearly all tissues, especially in roots. SAMS2 expression was weaker, reaching its highest level at the apex. Following pollination, SAMS1 was specifically up-regulated, whereas SAMS2 was expressed constitutively. The up-regulation of SAMS1 during ovary development was also observed in unpollinated ovaries treated with auxins. In unpollinated ovaries an increase in SAMS1 expression was observed as a consequence of ethylene production associated with the emasculation process. In senescing ovaries both SAMS1 and SAMS2 genes showed increased expression. Ethylene treatment of unpollinated ovaries led to an increase in the SAMS1 mRNA level. However, SAMS2 expression remained unchangeable after ethylene treatment, indicating that SAMS2 induction during ovary senescence was not ethylene dependent. SAMS mRNAs were localized by in situ hybridization at the endocarp of developing fruits and in the ovules of senescing ovaries. Our results indicate that the transcriptional regulation of SAMS genes is developmentally controlled in a specific way for each gene.