To analyze a communication system without the aid of simulation, the channel noise for the simulation must be assumed to be normal. The assumption is often valid, but the normal distribution may not be able to model the channel noise adequately in some environments. This thesis will explore the generalized exponential distribution for better noise modeling and robustness testing in communication system. When using the generalized exponential distribution for the channel noise, the analysis will become analytically intractable, and simulation becomes mandatory. To generate the noise with the distribution, the rejection method can be used. However, since the distribution can take on different shapes, finding the appropriate Upper Bounding Function (UBF) for the method is very difficult. Thus, two modified versions of the rejection method will be examined. They are the Transformed Density Rejection (TDR) and Ratio-of-Uniform (RoU) method; their quality, efficient, trade-offs, etc will be discussed. Choosing TDR, a simulation of a BPSK communication system will be performed. With the simulation, it can further ascertain that the random variates generated by TDR can be used to model the channel noise and to test the robustness of a communication system. / Master of Science

[EN] Classically, the study of the contact with hyperplanes and hyperspheres has been realized by using the family of height and distance squared functions. On the first part of the thesis, we analyze the Taylor expansion of the exponential map up to order three of a submanifold $M$ immersed in $\r n.$ Our main goal is to show its usefulness for the description of special contacts of the submanifolds with geometrical models. As we analyze the contacts of high order, the complexity of the calculations increases. In this work, through the Taylor expansion of the exponential map, we characterize the geometry of order higher than $3$ in terms of invariants of the immersion, so that the effective computations in specific cases become more affordable. It allows also to get new geometric insights. On the second part of the thesis, we introduce the concept of critical point of a smooth map between submanifolds. If we consider a differentiable $k$-dimensional manifold $M$ immersed in $\r{k+n},$ we know that its focal set can also be interpreted as the image of the critical points of the {\it normal map} $\nu(m,u): NM\to \r{k+n}$ defined by $\nu(m,u)=\pi_N(m,u)+ u,$ for $m\in M$ and $u\in N_mM,$ where $\pi_N:NM\to M$ denotes the normal bundle. In the same way, the parabolic set of a differential submanifold is given through the analysis of the singularities of the height functions over the submanifold. If we consider a differentiable $k$-dimensional manifold $M$ immersed in $\r{k+n},$ we know that its parabolic set can also be interpreted as the image of the critical points of the {\it generalized Gauss map} $\psi(m,u): NM\to \r{k+n}$ defined by $\psi(m,u)= u,$ for $u\in N_mM.$ Finally, we characterize the asymptotic directions as the tangent set of a $k$-dimensional manifold $M$ immersed in $\r{k+n}$ throughout the study of the singularities of the tangent map $\Omega(m,y): TM\to \r{k+n}$ defined by $\Omega(m,y)=\pi(m,y)+y,$ for $y\in T_mM,$ where $\pi:TM\to M$ denotes the tangent bundle. We describe first the focal set and its geometrical relation to the Veronese of curvature for $k$-dimensional immersions in $\r{k+n}.$ Then we define the $r$-critical points of a differential map $f:H \to K$ between two differential manifolds and characterize the $2$ and $3$-critical points of the normal map and generalized Gauss map. The number of these critical points at $m\in M$ may depend on the degeneration of the curvature ellipse and we calculate those numbers in the particular case that $M$ is an immersed surface in $\r{4}$ for the normal map and $\r{5}$ for the generalized Gauss map. / [ES] En general, el estudio del contacto con hiperplanos e hiperesferas se ha llevado a cabo usando la familia de funciones altura y la función distancia al cuadrado. En la primera parte de la tesis analizamos el desarrollo de Taylor de la aplicación exponencial hasta orden 3 de una subvariedad $M$ inmersa en $\r n.$ Nuestro principal objetivo es mostrar su utilidad en el estudio de contactos especiales de subvariedades con modelos geométricos. A medida que analizamos los contactos de orden mayor, la complejidad de las cuentas aumenta. En este trabajo, a través del desarrollo de Taylor de la aplicación exponencial, caracterizamos la geometría de orden mayor que $3$ en términos de invariantes geométricos de la inmersión, por lo que el trabajo con las cuentas en casos especiales se convierte en más manejable. Esto nos permite también obtener nuevos resultados geométricos. En la segunda parte de la tesis se introduce el concepto de punto crítico de una aplicación regular entre subvariedades. Si consideramos una variedad diferenciable $M$ de dimensión $k$ e inmersa en $\r{k+n},$ sabemos que su conjunto focal puede ser interpretado como la imagen de los puntos críticos de la {\it aplicación normal} $\nu(m,u): NM\to \r{k+n}$ definida por $\nu(m,u)=\pi_N(m,u)+ u,$ para $m\in M$ y $u\in N_mM,$ donde $\pi_N:NM\to M$ denota el fibrado normal. De la misma manera, el conjunto parabólico de una subvariedad diferencial viene dado por el análisis de las singularidades de la función altura sobre la subvariedad. Si consideramos una subvariedad $M$ de dimensión $k$ e inmersa en $\r{k+n},$ sabemos que su conjunto parabólico puede ser interpretado como la imagen de los puntos críticos de la {\it aplicación generalizada de Gauss} $\psi(m,u): NM\to \r{k+n}$ definida por $\psi(m,u)= u,$ donde $u\in N_mM.$ Finalmente, caracterizamos las direcciones asintóticas como el conjunto de direcciones del tangente de una subvariedad $M$ de dimensión $k$ e inmersa en $\r{k+n}$ a través del estudio de las singularidades de la aplicación tangente $\Omega(m,y): TM\to \r{k+n}$ definida por $\Omega(m,y)=\pi(m,y)+y,$ para $y\in T_mM,$ donde $\pi:TM\to M$ denota el fibrado tangente. Describimos primero el conjunto focal y su relación geométrica con la Veronese de curvatura para una variedad $k$ dimensional inmersa en $\r{k+n}.$ Entonces, definimos los puntos $r$-críticos de una aplicación $f:H \to K$ entre dos subvariedades y caracterizamos los puntos $2$ y $3$ críticos de la aplicación normal y la aplicación generalizada de Gauss. El número de estos puntos críticos en $m\in M$ depende de la degeneración de la elipse de curvatura y calculamos ese número en el caso particular de una superficie inmersa en $\r{4}$ para la aplicación normal y $\r{5}$ para la aplicación generalizada de Gauss. / [CA] En general, l'estudi del contacte amb hiperplans i hiperesferes s'ha dut a terme utilitzant la família de funcions altura i la funció distància al quadrat. A la primera part de la tesi analitzem el desenvolupament de Taylor de l'aplicació exponencial fins a ordre 3 d'una subvarietat $M$ immersa en $\r n.$ El nostre principal objectiu és mostrar la seua utilitat en l'estudi de contactes especials de subvarietats amb models geomètrics. A mesura que analitzem els contactes d'ordre major, la complexitat dels comptes augmenta. En aquest treball, a través del desenvolupament de Taylor de l'aplicació exponencial, caracteritzem la geometria d'ordre major que $ 3 $ en termes d'invariants geomètrics de la immersió, de manera que el treball amb els comptes en casos especials es converteix en més manejable. Això ens permet també obtenir nous resultats geomètrics. A la segona part de la tesi s'introdueix el concepte de punt crític d'una aplicació regular entre subvarietats. Si considerem una varietat diferenciable $ M $ de dimensió $ k $ i immersa en $ \r {k + n}, $ sabem que el seu conjunt focal pot ser interpretat com la imatge dels punts crítics de la {\it aplicació normal} $ \nu (m, u): NM \to \r {k + n} $ definida per $ \nu (m, u) = \pi_N (m, u) + o, $ per $ m \in M $ i $ u \in N_mM, $ on $ \pi_N: NM \to M $ denota el fibrat normal. De la mateixa manera, el conjunt parabòlic d'una subvarietat diferencial ve donat per l'anàlisi de les singularitats de la funció altura sobre la subvarietat. Si considerem una subvarietat $ M $ de dimensió $ k $ i immersa en $ \r {k + n}, $ sabem que el seu conjunt parabòlic pot ser interpretat com la imatge dels punts crítics de la {\it aplicació generalitzada de Gauss} $ \psi (m, u): NM \to \r{k + n} $ definida per $ \psi (m, u) = u, $ on $ u \in N_mM. $ Finalment, caracteritzem les direccions asimptòtiques com el conjunt de direccions del tangent d'una subvarietat $ M $ de dimensió $ k $ i immersa en $ \r{k + n} $ a través de l'estudi de les singularitats de l'aplicació tangent $ \Omega (m, y): TM \to \r {k + n} $ definida per $ \Omega (m, y) = \pi (m, y) + y, $ per $ y \in T_mM, $ on $ \pi: TM \to M $ denota el fibrat tangent. Descrivim primer el conjunt focal i la seva relació geomètrica amb la Veronese de curvatura per a una varietat $ k $ dimensional immersa en $ \r{k + n}. $ Llavors, definim els punts $ r $-crítics d'una aplicació $ f: H \to K $ entre dues subvarietats i caracteritzem els punts $ 2 $ i $ 3 $ crítics de l'aplicació normal i l'aplicació generalitzada de Gauss. El nombre d'aquests punts crítics en $ m \in M $ depèn de la degeneració de l'el·lipse de curvatura i calculem aquest nombre en el cas particular d'una superfície immersa en $ \r{4} $ per a l'aplicació normal i $ \r{5} $ per a l'aplicació generalitzada de Gauss. / García Monera, M. (2015). r-critical points and Taylor expansion of the exponential map, for smooth immersions in Rk+n [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/50935

[EN] This thesis addresses the treatment of perturbed problems with splitting methods. After motivating these problems in Chapter 1, we give a thorough introduction in Chapter 2, which includes the objectives, several basic techniques and already existing methods. In Chapter 3, we consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative coefficients). We propose to consider a class of methods that allows us to evaluate all time dependent operators at real values of the time, leading to schemes which are stable and simple to implement. If the system can be considered as the perturbation of an exactly solvable problem and the flow of the dominant part is advanced using real coefficients, it is possible to build highly efficient methods for these problems. We show the performance of this class of methods for several numerical examples and present some new improved schemes. In Chapter 4, we propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum A = D+epsilon*B of a sparse and efficiently exponentiable matrix D with sparse exponential exp(D) and a dense matrix epsilon*B which is of small norm in comparison with D. The predominant algorithm is based on scaling the large matrix A by a small number 2^(-s) , which is then exponentiated by efficient Padé or Taylor methods and finally squared in order to obtain an approximation for the full exponential. In this setting, the main portion of the computational cost arises from dense-matrix multiplications and we present a modified squaring which takes advantage of the smallness of the perturbation matrix B in order to reduce the number of squarings necessary. Theoretical results on local error and error propagation for splitting methods are complemented with numerical experiments and show a clear improvement over existing methods when medium precision is sought. In Chapter 5, we consider the numerical integration of the perturbed Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, the Hill's equations originate from a Hamiltonian function and the fundamental matrix solution is a symplectic matrix. This is a very important property to be preserved by the numerical integrators. In this chapter we present new sixth-and eighth-order symplectic exponential integrators that are tailored to the Hill's equation. The methods are based on an efficient symplectic approximation to the exponential of high dimensional coupled autonomous harmonic oscillators and yield accurate results for oscillatory problems at a low computational cost. Several numerical examples illustrate the performance of the new methods. Conclusions and pointers to further research are detailed in Chapter 6. / [ES] Esta tesis aborda el tratamiento de problemas perturbados con métodos de escisión (splitting). Tras motivar el origen de este tipo de problemas en el capítulo 1, introducimos los objetivos, varias técnicas básicas y métodos existentes en capítulo 2. En el capítulo 3 consideramos la integración numérica de ecuaciones no autónomas separables y parabólicas usando métodos de splitting de orden mayor que dos usando coeficientes complejos (métodos con coeficientes reales de orden mayor de dos necesariamente tienen coeficientes negativos). Proponemos una clase de métodos que permite evaluar todos los operadores con dependencia temporal en valores reales del tiempo lo cual genera esquemas estables y fáciles de implementar. Si el sistema se puede considerar como una perturbación de un problema resoluble de forma exacta y si el flujo de la parte dominante se avanza usando coeficientes reales, es posible construir métodos altamente eficientes para este tipo de problemas. Demostramos la eficiencia de estos métodos en varios ejemplos numéricos. En el capítulo 4 proponemos métodos de splitting para el cálculo de la exponencial de matrices perturbadas que se pueden escribir como suma A = D + epsilon*B de una matriz dispersa y eficientemente exponenciable con exponencial dispersa exp(D) y una matriz densa epsilon*B de noma pequeña. El algoritmo predominante se basa en escalar la matriz grande con un número pequeño 2^(-s) para poder exponenciar el resultado con métodos eficientes de Padé o Taylor y finalmente obtener la aproximación a la exponencial elevando al cuadrado repetidamente. En este contexto, el coste computacional proviene de las multiplicaciones de matrices densas y presentamos una cuadratura modificada aprovechando la estructura perturbada para reducir el número de productos. Resultados teóricos sobre errores locales y propagación de error para métodos de splitting son complementados con experimentos numéricos y muestran una clara mejora sobre métodos existentes a precisión media. En el capítulo 5, consideramos la integración numérica de la ecuación de Hill perturbada. Resonancias paramétricas pueden aparecer y esta propiedad es de gran interés en muchas aplicaciones físicas. Habitualmente, las ecuaciones de Hill provienen de una función hamiltoniana y la solución fundamental es una matriz simpléctica, una propiedad muy importante que preservar con los integradores numéricos. Presentamos nuevos integradores simplécticos exponenciales de orden seis y ocho tallados a la ecuación de Hills. Estos métodos se basan en una aproximación simpléctica eficiente a la exponencial de osciladores armónicos acoplados de dimensión alta y dan lugar a resultados precisos para problemas oscilatorios a un coste computacional bajo y varios ejemplos numéricos ilustran su rendimiento. Conclusiones e indicadores para futuros estudios se detallan en el capítulo 6. / [CA] La present tesi està enfocada al tractament de problemes perturbats utilitzant, entre altres, mètodes d'escisió (splitting). Comencem motivant l'oritge d'aquest tipus de problems al capítol 1, i a continuació introduïm el objectius, diferents tècniques bàsiques i alguns mètodes existents al capítol 2. Al capítol 3, consideram la integració numèrica d'equacions no autònomes separables i parabòliques utilitzant mètodes d'splitting d'ordre major que dos utilitzant coeficients complexos (mètodes amb coeficients reials d'ordre major que dos necesariament tenen coeficients negatius). Proposem una clase de mètodes que permeten evaluar tots els operadors amb dependència temporal explícita amb valors reials del temps. Esta forma de procedir genera esquemes estables i fàcils d'implementar. Si el sistema es pot considerar com una perturbació d'un problema exactament resoluble, i la part dominant s'avança utilitzant coeficients reials, es posible construir mètodes altament eficients per aquest tipus de problemes Demostrem la eficiència d'estos mètodes per a diferents exemples numèrics. Al capítol 4, proposem mètodes d'splitting per al càcul de la exponencial de matrius pertorbades que es poden escriure com suma A = D + epsilon*B (una matriu que es pot exponenciar fàcilment i eficientemente, com es el cas d'algunes matrius disperses exp(D), i una matriu densa epsilon*B de norma menuda). L'algorisme predominant es basa en escalar la matriu gran amb un nombre menut 2^(-s) per a poder exponenciar el resultat amb mètodes eficients de Padé o Taylor i finalment obtindre la aproximació a la exponencial elevant al quadrat repetidament. En este context, el cost computacional prové de les multiplicacions de matrius denses i presentem una quadratura modificada aprofitant la estructura de matriu pertorbada per reduir el nombre de productes. Resultats teòrics sobre errors locals i propagació d'error per a mètodes d'splitting son analitzats i corroborats amb experiments numèrics, mostrant una clara millora respecte a mètodes existens quan es busca una precisió moderada. Al capítol 5, considerem la integració numèrica de l'ecuació de Hill pertorbada. En este tipus d'equacions poden apareixer resonàncies paramètriques i esta propietat es de gran interés en moltes aplicacions físiques. Habitualment, les equacions de Hill provenen d'una función hamiltoniana i la solució fonamental es una matriu simplèctica, siguent esta una propietat molt important a preservar pels integradors numèrics. Presentams nous integradors simplèctics exponencials d'orden sis i huit construits especialmente per resoldre l'ecuació de Hill. Estos mètodes es basen en una aproxmiació simplèctica eficient a la exponencial d'osciladors harmònics acoplats de dimensió alta i donen lloc a resultats precisos per a problemas oscilatoris a un cost computacional baix. La eficiencia dels mètodes s'il.lustra en diferents exemples numèrics. Conclusions i indicadors per a futurs estudis es detallen al capítol 6. / Seydaoglu, M. (2016). Splitting methods for autonomous and non-autonomous perturbed equations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/71358

An open queueing network model (QNM) is proposed for wormhole-routed hypercubes with finite buffers and deterministic routing subject to a compound Poisson arrival process (CPP) with geometrically distributed batches or, equivalently, a generalised exponential (GE) interarrival time distribution. The GE/G/1/K queue and appropriate GE-type flow formulae are adopted, as cost-effective building blocks, in a queue-by-queue decomposition of the entire network. Consequently, analytic expressions for the channel holding time, buffering delay, contention blocking and mean message latency are determined. The validity of the analytic approximations is demonstrated against results obtained through simulation experiments. Moreover, it is shown that the wormholerouted hypercubes suffer progressive performance degradation with increasing traffic variability (burstiness).

This research is motivated by identified gaps in contemporary planning practices and production processes within firms. Relying solely on experiential knowledge has proven limiting, necessitating a more systematic approach. Previous instances of data anomalies, particularly ongoing challenges in achieving satisfactory delivery reliability, have underlined the need for deeper insights into underlying patterns. The objectives of this study are: • To identify and analyze specific obstacles and challenges affecting load balance and delivery security in Borl.nge's production system. • To explore various methods or strategies aimed at enhancing the process of generating reliable capacity forecasting methods. Both primary and secondary research methods were employed. Primary methods included interviews and the development of a forecast model, while secondary studies encompassed the latest research in the field. The thesis revealed five primary factors hindering capacity attainment: 1. WIP(work in progress)/ slabs material shortages disrupt production flow and escalate costs due to the need for external sourcing of slabs. 2. Transport issues, including incorrect internal deliveries and the weather conditions, pose challenges. 3. Personnel shortages hinder the efficient utilization of production capacity. 4. Machine breakdowns result in production interruptions, leading to capacity loss and inefficiency. 5. Inventory problems, such as insufficient capacity and poor management, impede smooth production operations. Additionally, the second objective was addressed by implementing exponential smoothing for capacity planning forecasts. By updating forecasts every 13 weeks, this study improves the production forecast.

The development of an economical method for determining accurately group constants of hexagonal and rectangular cells is considered in this dissertation. The mathematical model constructed for this purpose has the capability to characterize the group constants for the entire range of the neutron spectrum. Furthermore, this model is also rigorous enough to predict the group constants with the required accuracy for a specific range of interest in the energy spectrum and for a variety of energy group configurations. The model is implemented separately for the fast and thermal energy regions. These regions are subsequently coupled via the source term. The construction of the model for the fast energy range has been pursued by implementing the transport equation specialized in a two-region cell. The regions are coupled via the escape probability functions. The model for the thermal energy range has been attained by implementing the appropriate Nelkin and Honeck amplitude functions within the kernels of the transport equation. The Nelkin amplitude function is utilized for treating light water moderated systems, and the Honeck amplitude function relates to heavy water moderated systems. The group constants calculated with the economical model have been benchmarked with those computed by the VIM Monte Carlo code. The values obtained for the group constants agree within 1-2% with those computed by VIM for the fast energy region. The agreements for the thermal energy region are within 2-3%. The CPU running time of the implemented model is about 3 1/2 minutes for a four group configuration. On the other hand a typical VIM run comprising 25,000 neutron histories and a four-group structure expends about 30 minuts of CPU time for light water moderated systems. Moreover, similar VIM runs utilizing heavy water as moderator require over one hour of CPU time. Therefore, the implemented model makes utilization of computer resources with a cost advantage of a factor of 10 or better as compared to VIM. This economical benefit of the implemented model enables it to be coupled directly with fuel depletion codes, whereby the group constants and the fuel isotopics are updated at relatively short time intervals. On the other hand, the coupling of VIM with burnup codes would result in prohibitively expensive CPU costs. / Ph. D.

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study. / Mathematical Sciences / M. Sc. (Statistics)

The work done in this thesis is to examine various methods for curve fitting. Linear least squares and non-linear least squares will be described and compared, and the Newton method, Gauss--Newton method and Levenberg--Marquardt method will be applied to example problems. / Syftet med denna uppsats är att beskriva och använda olika metoder för kurvanpassning, det vill säga att passa matematiska funktioner till data. De metoder som undersöks är Newtons metod, Gauss--Newton metoden och Levenberg--Marquardt metoden. Även skillnaden mellan linjär minsta kvadrat anpassning och olinjär minsta kvadrat anpassning. Till sist tillämpas Newton, Gauss Newton och Levenberg--Marquardt metoderna på olika exempel.

Durante o desenvolvimento do sistema nervoso, as oscilações da concentração de cálcio intracelular livre resultam na proliferação celular, migração e diferenciação neuronal. Nesta tese foram investigadas a participação dos receptores ionotrópicos purinérgicos dos tipos P2X2 e P2X4 seletivos ao influxo de cálcio durante a diferenciação neuronal in vitro das células de carcinoma embrionário murino P19. Identificamos o padrão diferencial de expressão de receptores purinérgicos nas células indiferenciadas e neurônios P19. O receptor P2X4 é expresso durante toda a diferenciação neuronal e o receptor P2X2 é detectado na fase tardia da diferenciação em neurônios. Através de ensaios farmacológicos, foi possível identificar a participação dos receptores metabotropicos P2Y e do receptor P2X4 na formação dos corpos embriônicos, na proliferação celular e ou na determinação do fenótipo de progenitor neural. Durante a maturação neuronal os receptores P2X2 e P2Y1 participam da determinação do fenótipo neuronal glutamatérgico NMDA e os receptores P2X2 e P2Y2 no fenótipo neuronal colinérgico. A ausência de inibidores específicos e seletivos aos receptores purinérgicos levou-nos a empregar a técnica SELEX (Systematic Evolution of Ligands by EXponential enrichment) a fim de identificar inibidores seletivos aos receptores P2X2 e P2X4. A técnica envolve a utilização da biblioteca combinatória randômica de RNA 2\'- F pirimidina modificadas resistentes a nucleases. Após 9 ciclos de seleção in vitro de SELEX (ciclo 9-P2X4), as sequências selecionadas mostraram-se seletivas a ligação somente ao receptor P2X4 e não aos receptores P2X2 ou P2X7 através de ensaios de ligação radioligante-receptor. Por patch clamping na configuração whole cell recording identificou-se que além de seletividade ao receptor, que a aplicação do RNA ciclo 9- P2X4 promoveu inibição da corrente ativada pelo ATP somente nos receptores P2X4 e não em P2X2 em celulas 1321N1 astrocitoma transfectadas. A incubação do RNA ciclo 9-P2X4 na concentração de 200 nM com as células no estágio indiferenciado inibiu a formação dos corpos embriônicos. Já utilização de 25 nM, resultou em mudanças morfológicas nas células diferenciadas. Estes dados corroboram com os dados farmacológicos que identificaram a participação do receptor P2X4 na diferenciação precoce. Após 11 ciclos P2X2 de seleção, identificou-se sequências com especificidade de ligação aos receptores P2X2. Aptâmeros, moleculas de RNA com sequência identificada e com alta afinidade ao alvo da seleção, foram isolados de ambas as bibliotecas, ciclo 9 P2X4 e ciclo 11 P2X2. A co-aplicação destes aptâmeros e ATP em ensaios de whole-cell recording resultou na inibição de 30 a 80% da corrente ativada pelo ATP nos receptores P2X2 ou P2X4. Estes testes em células PC12 de rato, que expressa os receptores endógenos, resultou em inibição da corrente ativada pelo ATP de modo semelhante. Além de termos desenvolvido aptâmeros como ferramentas para elucidar as funções dos receptores P2X2 e P2X4 durante o desenvolvimento, diferenciação, em processos fisiológicos e patológicos, estas moléculas resistentes a nucleases são as primeiras identificadas capazes de reconhecer, discernir e inibir dois subtipos de receptores purinérgicos sendo promissores para utilização terapêutica. / During the development of the nervous system, oscillations of intracellular calcium concentrations activate programs of gene expression resulting in proliferation, migration and neuronal differentiation of embryonic cells. In this thesis, the participation of ionotropic P2X2 and P2X4 receptor subtypes, whose receptor channels are highly permeable for calcium influx in the cells, was studied during the process of neuronal differentiation. We have identified differential gene expression of purinergic receptors in undifferentiated and neuronal-differentiated P19 cells. P2X4 receptor expression was present along neuronal differentiation of P19 cells, whereas P2X2 receptor expression was only detected when P19 cells became neurons. Based on purinergic receptor pharmacology we have determined the participation of P2X4 receptors in addition to metabotropic P2Y2 receptors in the formation of embryonic bodies as prerequisites for phenotype determination of P19 neural progenitor cells. Final neuronal maturation of P19 cells in the presence or absence of agonists or antagonists of purinergic receptors implicated the involvement of P2X2, P2Y1, and P2Y2 in the determination of the final neuronal phenotype, such as expression of NMDA-glutamate and cholinergic receptors. In order to further evaluate the functions of these P2X receptors and due to the absence of specific inhibitors for these receptor subtypes, we have used the SELEX technique (Systematic Evolution of Ligands by EXponential enrichment) to select for specific inhibitors for P2X2 and P2X4 receptors. The 2\' -F-pyrimidine modified, nuclease- resistant combinatorial SELEX RNA pool enriched with inhibitors of P2X4 receptors following nine cycles of in vitro selection (cycle 9-P2X4) specifically interacted with P2X4 receptors and not with P2X2 or P2X7 receptors as verified in radioligand-receptor binding studies. Moreover, whole-cell recording measurements using astrocytoma cells expressing recombinant rat P2X2 or P2X4 receptors showed inhibition of P2X4 but not of P2X2 receptors by the selected RNA molecules. RNA molecules selected in vitro in 11 reiterative SELEX cycles using the P2X2 receptor as target specifically bound to membrane extracts containing recombinant P2X2 receptors. From both selected RNA libraries (against P2X4 and P2X2 receptors) aptamers, as RNA molecules with identified sequences and high-affinity binding, were identified by cloning and DNA sequencing. The presence of these aptamers in whole-cell recording experiments resulted in 30-80% inhibition of ATP-induced receptor activity and did not provoke any inhibitory effects on P2X receptors which had not been used as selection target. The activity of the aptamers selected using recombinant receptors as targets in inhibiting wild-type P2X4 or P2X2 receptors was verified in whole-cell recording experiments with PC12 cells which endogenously express both receptor subtypes. In addition of having developed aptamers as tools to elucidate P2X2 and P2X4 receptor functions during neuronal differentiation, these nuclease-resistant aptamers are suitable for in vivo use and may turn into therapeutics in the inhibition of purinergic receptor participation in pathophysiological conditions.

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