24 resultados para r-functions


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RESUMO:Os microrganismos reagem à súbita descida de temperatura através de uma resposta adaptativa específica que assegura a sua sobrevivência em condições desfavoráveis. Esta adaptação inclui alterações na composição da membrana, na maquinaria de tradução e transcrição. A resposta ao choque térmico pelo frio induz uma repressão da transcrição. No entanto, a descida de temperatura induz a produção de um grupo de proteínas específicas que ajudam a ajustar/re-ajustar o metabolismo celular às novas condições ambientais. Em E. coli o processo de adaptação demora apenas quatro horas, no qual um grupo de proteínas específicas são induzidas. Depois desde período recomeça lentamente a produção de proteínas.A ribonuclease R, uma das proteínas induzidas durante o choque térmico pelo frio, é uma das principais ribonucleases em E. coli envolvidas na degradação do RNA. É uma exoribonuclease que degrada RNA de cadeia dupla, possui funções importantes na maturação e “turnover” do RNA, libertação de ribossomas e controlo de qualidade de proteínas e RNAs. O nível celular desta enzima aumenta até dez vezes após exposição ao frio e estabiliza em células na fase estacionária. A capacidade de degradar RNA de dupla cadeia é importante a baixas temperaturas quando as estruturas de RNA estão mais estáveis. No entanto, este mecanismo é desconhecido. Embora a resposta específica ao “cold shock” tenha sido descoberta há mais de duas décadas e o número de proteínas envolvidas sugerirem que esta adaptação é rápida e simples, continuamos longe de compreender este processo. No nosso trabalho pretendemos descobrir proteínas que interactuem com a RNase R em condições ambientais diferentes através do método “TAP-tag” e espectrometria de massa. A informação obtida pode ser utilizada para deduzir algumas das novas funções da RNase R durante a adaptação bacteriana ao frio e durante a fase estacionária. Mais importante ainda, RNase R poderá ser recrutada para um complexo de proteínas de elevado peso molecular durante o “cold-shock”.------------ABSTRACT:Microorganisms react to the rapid temperature downshift with a specific adaptative response that ensures their survival in unfavorable conditions. Adaptation includes changes in membrane composition, in translation and transcription machinery. Cold shock response leads to overall repression of translation. However, temperature downshift induces production of a set of specific proteins that help to tune cell metabolism and readjust it to the new environmental conditions. For Escherichia coli the adaptation process takes only about four hours with a relatively small set of specifically induced proteins involved. After this time, protein production resumes, although at a slower rate. One of the cold inducible proteins is RNase R, one of the main E. coli ribonucleases involved in RNA degradation. RNase R is an exoribonuclease that digest double stranded RNA, serves important functions in RNA maturation and turnover, release of stalled ribosomes by trans-translation, and RNA and protein quality control. The level of this enzyme increases about ten-fold after cold induction, and it is also stabilised in cells growing in stationary phase. The RNase R ability to digest structured RNA is important at low temperatures where RNA structures are stabilized but the exact role of this mechanism remains unclear. Although specific bacterial cold shock response was discovered over two decades ago and the number of proteins involved suggests that this adaptation is fast and simple, we are still far from understanding this process. In our work we aimed to discover the proteins interacting with RNase R in different environmental conditions using TAP tag method and mass spectrometry analysis. The information obtained can be used to deduce some of the new functions of RNase R during adaptation of bacteria to cold and in stationary growth phase. Most importantly RNase R can be recruited into a high molecular mass complex of protein in cold shock.

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Stratigraphic Columns (SC) are the most useful and common ways to represent the eld descriptions (e.g., grain size, thickness of rock packages, and fossil and lithological components) of rock sequences and well logs. In these representations the width of SC vary according to the grain size (i.e., the wider the strata, the coarser the rocks (Miall 1990; Tucker 2011)), and the thickness of each layer is represented at the vertical axis of the diagram. Typically these representations are drawn 'manually' using vector graphic editors (e.g., Adobe Illustrator®, CorelDRAW®, Inskape). Nowadays there are various software which automatically plot SCs, but there are not versatile open-source tools and it is very di cult to both store and analyse stratigraphic information. This document presents Stratigraphic Data Analysis in R (SDAR), an analytical package1 designed for both plotting and facilitate the analysis of Stratigraphic Data in R (R Core Team 2014). SDAR, uses simple stratigraphic data and takes advantage of the exible plotting tools available in R to produce detailed SCs. The main bene ts of SDAR are: (i) used to generate accurate and complete SC plot including multiple features (e.g., sedimentary structures, samples, fossil content, color, structural data, contacts between beds), (ii) developed in a free software environment for statistical computing and graphics, (iii) run on a wide variety of platforms (i.e., UNIX, Windows, and MacOS), (iv) both plotting and analysing functions can be executed directly on R's command-line interface (CLI), consequently this feature enables users to integrate SDAR's functions with several others add-on packages available for R from The Comprehensive R Archive Network (CRAN).

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The physiological responses of the clam R. decussatus from the Ria Formosa, southern Portugal, were examined in relation to normoxia, hypoxia (11, 6, 3 and 1.2 kPa) and anoxia; acute elevation of temperature (at 20, 27 and 32 °C), and its effect on the resistance to air exposure (at 20, 28 and 35 °C); current velocity (0.6, 3, 8 17, 24 and 36 cm. s-1) and turbidity (10, 100 and 300 mg. l-1 dry weight of particulate matter), and the efficiency of this species in retaining particles of different size (at 10 and 100 mg. l-1); and to copper contamination considering both short-term acute exposure to high levels (0.1-10 mg Cu. l-1) and chronic environmental levels (0.01 mg Cu. l-1). Clearance rates, respiration rates, absorption efficiency and excretion rates were assessed through the physiological energetics in terms of the energy budget and scope for growth (SFG). Stress independent respiration rates (R) and clearance rates (CR) were observed in relation to hypoxia down to 12 kPa and 6 kPa, respectively. Anoxic rates were 3.6 % of normoxic rates. Scope for growth was greatly reduced under extreme hypoxia (14 % of SFG in normoxia). Respiration rate was temperature independent in the range 20-32 °C but the decline in clearance rate resulted in negative SFG at 32 °C. Gaping during air exposure and the maintenance of faster aerobic metabolism led to 100 % mortality in 20 hours at 35 °C, 4 days at 28 °C and 5 days at 20 °C. Low current velocities (≤ 8 cm. s-1) supported high clearance rates. Shear stresses ≥ 0.9 Pa induced sediment movement and disturbed the feeding processes resulting in decreased clearance rates (at 36 cm. s-1, is 10 % of maximum CR). The observed ability of jetting out depleted water at a different level than the one of the inhalant current results is an important adaptation of clams to the slow currents of sheltered environments. Ingestion at high seston concentrations (> 100 mg. l-1) is controled by reducing the amount filtered, lowering CR (to 30 % of CR at low seston loads) and producing pseudofeces. Observed efficient retention of particles (70-100 %) in the range 3 to 8 μm is beneficial when algal cells are diluted by fine silt particles as it is likely to occur in the clams natural environment. R. decussatus in the short term escaped the exposure to copper by valve closure and therefore acute tests are not applicable to adult clams of this species. At environmental levels chronic exposure to copper did not induce lethal effects during the exposure period (20 days), but scope for growth was reduced to c. 30 %, indicating sustained impairment of physiological functions. The sensitivity of the physiological energetics and the integrated scope for growth measurement in assessing stress effects caused by natural environmental factors was highlighted.

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Pine forests constitute some of the most important renewable resources supplying timber, paper and chemical industries, among other functions. Characterization of the volatiles emitted by different Pinus species has proven to be an important tool to decode the process of host tree selection by herbivore insects, some of which cause serious economic damage to pines. Variations in the relative composition of the bouquet of semiochemicals are responsible for the outcome of different biological processes, such as mate finding, egg-laying site recognition and host selection. The volatiles present in phloem samples of four pine species, P. halepensis, P. sylvestris, P. pinaster and P. pinea, were identified and characterized with the aim of finding possible host-plant attractants for native pests, such as the bark beetle Tomicus piniperda. The volatile compounds emitted by phloem samples of pines were extracted by headspace solid-phase micro extraction, using a 2 cm 50/30 mm divinylbenzene/carboxen/polydimethylsiloxane table flex solid-phase microextraction fiber and its contents analyzed by high-resolution gas chromatography, using flame ionization and a non polar and chiral column phases. The components of the volatile fraction emitted by the phloem samples were identified by mass spectrometry using time-of-flight and quadrupole mass analyzers. The estimated relative composition was used to perform a discriminant analysis among pine species, by means of cluster and principal component analysis. It can be concluded that it is possible to discriminate pine species based on the monoterpenes emissions of phloem samples.

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Ramsey pricing has been proposed in the pharmaceutical industry as a principle to price discriminate among markets while allowing to recover the (fixed) R&D cost. However, such analyses neglect the presence of insurance or the fund raising costs for most of drug reimbursement. By incorporating these new elements, we aim at providing some building blocks towards an economic theory incorporating Ramsey pricing and insurance coverage. We show how coinsurance affects the optimal prices to pay for the R&D investment. We also show that under certain conditions, there is no strategic incentive by governments to set coinsurance rates in order to shift the financial burden of R&D. This will have important implications to the application of Ramsey pricing principles to pharmaceutical products across countries.

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Paper presented at the 9th European Conference on Knowledge Management, Southampton Solent University, Southampton, UK, 4-5 Sep. 2008. URL: http://academic-conferences.org/eckm/eckm2008/eckm08-home.htm

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Cabatuquila conglomerate ferricrete (Malanje Province, located North Central Angola) corresponds to a thick (1O-15m) and hardcornice at the top of "Baixa de Cassanje" escarpment. "Baixa de Cassanje" is a large graben part of South Congo basin. Cabatuquila conglomerate ferricrete seems to correspond to a Plio-Pleistocene morphology which has already disappeared. Laterization dynamics and ferricrete formation processes took place on the Tertiary surface, before being tilted to the Congo Basin. Materials submitted to these processes are mainly alluvial deposits from a pre-Cuanza drainage system. This drainage system flowed to the North before being captured to the Atlantic, as a consequence of the movement which deformed the Tertiary surface during the Pleistocene. The erosion dynamics, which created the Cassanje depression, has occurred after the late Tertiary surface deformation. That dynamics might be related to the Cuango drainage system, which was reorganized after that deformation.

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Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations Research

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Trabalho de Projecto em Ciências da Comunicação, variante Cultura Contemporânea e Novas Tecnologias

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Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

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Dissertation presented to obtain the Ph.D degree in Biology

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RESUMO: Os circuitos fronto-estriatais constituem um sistema em ansa fechada que une diversas regiões do lobo frontal aos gânglios da base, participando, com outras áreas cerebrais, no controlo do movimento, cognição e comportamento. As Distonias Primárias, a Doença de Parkinson e a Hidrocefalia de Pressão Normal, são doenças do movimento caracterizadas por disfunção do circuito fronto-estriatal motor. A conectividade funcional entre as diversas ansas do sistema fronto-estriatal, permite prever que as doenças do movimento possam também acompanhar-se de sintomas da esfera cognitiva e comportamental, cuja avaliação seria importante no manejo diagnóstico e terapêutico dos doentes. Objectivos Os nossos objectivos foram avaliar, por estudos clínicos, a relação entre sintomas motores, cognitivos e comportamentais em três doenças do movimento com fisiopatologias diversas - distonias Primárias, Doença de Parkinson e Hidrocefalia de Pressão Normal - analisando os dados sob a perspectiva teórica fornecida pelo conhecimentos dos vários circuitos frontoestriatais. Os nossos objectivos específicos para cada doença foram: a) Distonias Primárias: avaliação de disfunção executiva em doentes com Distonia Primária e relação com a gravidade dos sintomas motores b) Doença de Parkinson: 1. avaliação breve das funções mentais nas fases iniciais da doença, incluindo análise longitudinal para determinação de factores preditivos para declínio cognitivo; 2. relação entre a função motora e cognitiva e a Perturbação do Comportamento do sono REM, incluindo análise longitudinal; 3.avaliação de sintomas psiquiátricos, de um ponto de vista global e especificamente com incidência sobre as Perturbações do Controlo do Impulso (PCI). c) Hidrocefalia de Pressão Normal: 1. caracterização das alterações da marcha, incluindo comparação com a Doença de Parkinson; 2. caracterização das alterações cognitivas e da relação entre estas e a disfunção da marcha; 3. estudo evolutivo das alterações da marcha e cognitiva em doentes submetido a cirurgia e doentes não submetidos a cirurgia. Métodos: A Distonia Primária, a Doença de Parkinson e a Hidrocefalia de Pressão Normal foram diagnosticadas segundo critérios clínicos validados. Sempre que justificado, foram recrutados grupos de controlo, com indivíduos sem doença, emparelhados para idade, sexo e grau de escolaridade. Os doentes foram avaliados com instrumentos de aplicação clinica directa, incluindo escalas de função motora, testes neuropsicológicos globais e dirigidos às funções executivas e escalas de avaliação psiquiátrica. Testes aplicados nas Distonias Primárias: Unified Dystonia Rating Scale, Wisconsin Card Sorting Test, teste de Stroop, teste de cubos da WAIS, Teste de Retenção Visual de Benton; na Doença de Parkinson: Unified Parkinson's Disease Rating Scale, Frontal Assessment Battery (FAB), Mini-Mental State Examination (MMSE), REM-sleep behaviour disorder Questionnaire; Symptom Chek-list 90-R, Brief Psychiatric Rating Scale, FAS (fluência verbal lexical) Nomeação de Animais (Fluência verbal semântica), prova de repetição de dígitos (WAIS), Rey auditory verbal learning test, teste de Stroop, matrizes progressivas de Raven, Questionnaire for Impulsive-Compulsive Disorders; na HPN: prova cronometrada de marcha,MMSE, prova de memória imediata da WAIS, prova de repetição de dígitos (WAIS), FAB, desenho complexo de Rey, teste de Stroop, cancelamento de letras, teste Grooved Pegboard. Os doentes com HPN foram também submetidos a estudo imagiológico. A avaliação estatística foi adaptada às características de cada um dos estudos.Resultados Distonias Primárias: encontrámos défices de função executiva, envolvendo dificuldade na mudança entre sets cognitivos, bem como correlação significativa entre as pontuações nos testes cronometrados e a gravidade dos sintomas motores. Doença de Parkinson: os doentes com DP obtiveram pontuações significativamente inferiores na FAB e em sub-testes do MMSE (memória e função visuo-espacial). A pontuação no MMSE encontrava-se significativamente correlacionada com itens da função motora não relacionados com o tremor. A disfunção da marcha, a disartria, o fenótipo não tremorígeno, a presença de alucinações e pontuação abaixo do ponto de corte na MMSE, foram factores preditivos de demência na avaliação longitudinal. A rigidez e a disartria foram factores preditivos de declínio nas funções frontais. A disfunção frontal foi factor preditivo de declínio na pontuação do MMSE. Encontrámos uma prevalência elevada de RBD nas fases iniciais da DP, que o estudo longitudinal mostrou ser factor preditivo de declínio motor, nomeadamente por agravamento da bradicinésia. Encontrámos também uma prevalência elevada de sintomas psiquiátricos, nomeadamente psicose, depressão, ansiedade, somatização e sintomas obsessivo-compulsivos. As PCI não se encontravam relacionadas com o fenótipo motor, com as complicações motoras do tratamento dopaminérgico ou com a disfunção cognitiva. HPN: os doentes com HPN e os DP apresentaram um padrão disfunção da marcha semelhante, caraterizado por passos curtos, lentidão e dificuldades de equilíbrio, sendo os sintomas mais graves na HPN. Os doentes de Parkinson com maior duração de doença, maior dose de dopaminérgicos e fenótipo motor acinético-rígido apresentaram um padrão de disfunção da marcha de gravidade semelhante ao encontrado na HPN. As alterações vasculares da substância branca, em particular as encontradas na região frontal, encontravam-se negativamente correlacionadas com a melhoria da marcha após PL. O estudo das funções cognitivas mostrou um padrão de atingimento global, com valores mais baixos na cópia do desenho complexo de Rey. Os resultados nas provas de função cognitiva não se encontravam significativamente correlacionados com os resultados na prova da marcha. A progressão na disfunção da marcha encontrava-se relacionada com o tratamento não cirúrgico, idade superior na primeira avaliação, presença de lesões da substância branca, e presença de factores de risco vascular, ao passo que não foram encontrados factores que predissessem de modo significativo o agravamento da função cognitiva. Conclusões: Os resultados dos diversos estudos, evidenciam a presença de alterações cognitivas e comportamentais nas três doenças de movimento. O padrão destas alterações e o modo como estas se relacionaram com os sintomas motores variou de doença para doença. Nas Distonias primárias, a perseveração cognitiva poderá ser o sintoma correspondente à perseveração motora própria da doença, sugerindo disfunção no circuito dorso-lateral frontoestriatal. A correlação entre a gravidade motora da doença e o resultado nos testes cognitivos cronometrados, poderá ser o efeito da relação entre bradicinésia e bradifrenia. Na Doença de Parkinson, o espectro de alterações é mais acentuado, espelhando a disseminação do processo degenerativo no SNC. Para além dos sintomas de disfunção executiva, sugerindo disfunção das tês ansas não motoras, existem sinais de disfunção cognitiva global, estas com uma influência mais significativa no desenvolvimento da demência. A relação entre os diferentes sintomas motores e cognitivos é também complexa, embora se evidencie uma dissociação significativa entre o tremor, sem relação com os sintomas não motores, e os sintomas motores não tremorígenos, relacionados com o declínio cognitivo. Enquanto que a presença de RBD parece ser um factor preditivo de agravamento motor, os sintomas psiquiátricos, também muito frequentes, apresentam uma relação menos clara com a função motora. Destes, os sintomas obsessivo-compulsivos são aqueles que com mais frequência se atribuem a disfunção do sistema fronto-estriatal, nomeadamente da ansa orbito-frontal. As PCI também não mostraram ter relação com os sintomas motores ou cognitivos. Na HPN, é patente o carácter fronto-estriatal das alterações da marcha, demonstrado tanto na sua caracterização quanto no efeito deletério das lesões vasculares da substância branca do lobo frontal na recuperação da marcha após PL. As alterações cognitivas parecem ter um padrão mais difuso, o que talvez explique a falta de correlação com os sintomas motores - esta dissociação pode ser causada quer por diferença nos mecanismos fisiopatológicos quer por presença de comorbilidades cognitivas. --------- ABSTRACT: Fronto-striatal circuits constitute a closed loop system which connects different parts of the frontal lobes to the basal ganglia. They are engaged in motor, cognitive and behavioural control. Primary Dystonia, Parkinson's Disease and Normal-Pressure Hydrocephalus are movement disorders caused by disturbance of the motor fronto-striatal circuit. The existence of cognitive and behavioural dysfunction in these movement disorders is predictable, given the functional connectivity between the several distinct loops of the circuit. Evaluation of cognitive and behavioural dysfunction in these three disorders is thus both of clinical and theoretical relevance. Objectives Our objectives were to evaluate, by clinical means, the relation between motor, cognitive and behavioural symptoms in three movement disorders with different pathophysiological backgrounds - Primary Dystonia, Parkinson's Disease and Normal-Pressure Hydrocephalus - and to analyse the study results under the theoretical framework formed by present knowledge of the fronto-estriatal system. Specific objectives: a) Primary Dystonia: executive dysfunction assessment and correlation analysis with motor dysfunction severity; b) Parkinson's Disease: 1. brief cognitive assessment in the early stages of disease, including a longitudinal analysis for determination of predictive factors for cognitive decline; 2. to investigate the relation between RBD and cognitive and motor dysfunction, including a longitudinal analysis; 3. psychiatric symptom assessment, with particular incidence on Impulse Control Disorders; c) Normal-Pressure Hydrocephalus: 1. gait dysfunction characterization and comparison with Parkinson's Disease patients; 2. determination of cognitive dysfunction profile and its relation with gait dysfunction; 3. follow-up study of cognitive and motor outcome in patients submitted and not submitted to shunt surgery. Methods: Primary Dystonia, Parkinson's Disease and Normal Pressure Hydrocephalus were diagnosed according to clinically validate criteria. Where warranted, we recruited control groups formed by healthy individuals, matched for age, sex and educational level. Patients were evaluated with instruments of direct clinical application, including motor function scales, neuropsychological tests aimed at global and executive functions and psychiatric rating scales. Tests used in Primary Dystonia: Unified Dystonia Rating Scale, Wisconsin Card Sorting Test, Stroop Test, Cube Assembly test (WAIS), Benton’s Visual Retention Test; in Parkinson's Disease: Unified Parkinson's Disease Rating Scale, Frontal Assessment Battery (FAB) , Mini-mental State Examination (MMSE), REM-sleep behavior disorder Questionnaire, Symptom Check-list 90- R, Brief Psychiatric Rating Scale, FAS (phonetic verbal fluency), semantic verbal fluency test, digit span test (WAIS), auditory verbal learning test,Stroop test, Raven's progressive Matrices, Questionnaire for Impulsive-Compulsive Disorders; in NPH: timed walking test, MMSE, immediate memory task (WAIS), digit span test (WAIS), FAB, Rey’s Complex Figure test, Stroop test, letter cancellation test, Perdue Pegboard test. NPH patients were also subjected to an imaging study. Statistics were adapted to the characteristics of each study.Results: Primary Dystonia: we found set-shifting deficits as well as significant correlation between timed neuropsychological tests and dystonia severity. Parkinson's Disease: PD patients had significantly lower scores on the FAB and on the memory and visuo-spatial tests of the MMSE; MMSE scores were significantly correlated to non-tremor motor scores; gait dysfunction and speech scores, non-tremor motor phenotype, hallucinations and scores bellow cut-off on the MMSE were predictive of dementia at follow-up; speech and rigidity scores were predictive of frontal type decline; frontal dysfunction was predictivy of decline in MMSE scores; RBD bradykinesia worsening; psychiatric symptoms were prevalent, particularly Psychosis, Depression, Anxiety, Somatisation and Obsessive-Compulsive Symptoms; Impulse Control Disorders were unrelated to motor phenotype,motor side effects of dopamine treatment and executive function; NPH: gait dysfunction was worse in NPH when compared to PD patients, although the pattern was similarly characterized by slowness, short steps and disequilibrium; PD patients whose gait disturbance was as severe as that of NPH patients were characterized by longer disease duration, predominance of non-tremor motor scores, more advanced disease stage and higher dopamine dose; frontal white matter lesions correlated negatively with improvement after LP; cognitive function assessment revealed wide spread deficits, with lower results on the drawing of the complex figure of Rey, which were not significantly correlated to gait dysfunction; older age, white matter lesions and the presence of vascular risk factors were predictive factors for motor but not cognitive function worsening. Conclusion: Results from our studies highlight the presence of cognitive and behavioural dysfunction in all three movement disorders. Symptom pattern and the relation with ovement derangement varied according to the disease. In Primary Dystonia, set-shifting difficulties could be the cognitive counterpart of motor perseveration characteristic of this disorder, suggesting dysfunction of the dorso-lateral circuit. The relation between timed tests and dystonia severity could suggest a relation between bradyphrenia and bradykinesia in Primary Dystonia. In Parkinson's Disease patients, the spectrum of non-motor symptoms is wider, probably reflecting the spread of neurodegeneration beyond the fronto-striatal circuits. While frontal type deficits predominate, suggestive of dorso-lateral and orbito-frontal dysfunction, non-frontal deficits were also apparent in the initial stages of disease, and were predictive of dementia at follow-up. The relationship between cognitive and motor symptoms is complex, although the results strongly suggest a dissociation between tremor symptoms, which bore no relation with non-motor symptoms, and non-tremor symptoms,whichwas frequent, and a predictive factor for which were related with cognitive decline. While RBD was found to be a predictive factor for bradykinesia worsening, psychiatric symptoms, which were also frequent, showed no apparent relation with motor dysfunction. Relevant to our theoretical consideration was the high prevalence of OCS, which have been attributed to orbito-frontal dysfunction. As to the particular case of ICD, we found no relation either with motor or cognitive dysfunction. The fronto-striatal nature of gait dysfunction in NPH is suggest by the clinical characterization study and by the effects of frontal white matter lesions on gait recovery after LP, whereas cognitive dysfunction presented a more diffuse pattern, which could explain the lack or relation with gait assessment results and also the different outcome on the longitudinal study - this dissociation could be caused by a real difference in pathophysiological mechanisms or, in alternative, be due to the existence of cognitive comorbidities.

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There is a family of models with Physical, Human capital and R&D for which convergence properties have been discussed (Arnold, 2000a; Gómez, 2005). However, spillovers in R&D have been ignored in this context. We introduce spillovers in this model and derive its steady-state and stability properties. This new feature implies that the model is characterized by a system of four differential equations. A unique Balanced Growth Path along with a two dimensional stable manifold are obtained under simple and reasonable conditions. Transition is oscillatory toward the steady-state for plausible values of parameters.

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Until now, in models of endogenous growth with physical capital, human capital and R&D such as in Arnold [Journal of Macroeconomics 20 (1998)] and followers, steady-state growth is independent of innovation activities. We introduce absorption in human capital accumulation and describe the steady-state and transition of the model. We show that this new feature provides an effect of R&D in growth, consumption and welfare. We compare the quantitative effects of R&D productivity with the quantitative effects of Human Capital productivity in wealth and welfare.