Zugl.: Jena, Univ., Diss., 2009

Heidelberg, Univ., Diss., 2003. / Computerdatei im Fernzugriff.

Heidelberg, University, Diss., 2003.

The segmentation problem arises in the elaboration of a radiation therapy plan. After the cancer has been diagnosed and the radiation therapy sessions have been prescribed, the physician has to locate the tumor as well as the organs situated in the radiation field, called the organs at risk. The physician also has to determine the different dosage he wants to deliver in each of them and has to define a lower bound on the dosage for the tumor (which represents the minimum amount of radiation that is needed to have a sufficient control of the tumor) and an upper bound for each organ at risk (which represents the maximum amount of radiation that an organ can receive without damaging). Designing a radiation therapy plan that respects these different bounds of dosage is a complex optimization problem that is usually tackled in three steps. The segmentation problem is one of them. Mathematically, the segmentation problem amounts to decomposing a given nonnegative integer matrix A into a nonnegative integer linear combination of some binary matrices. These matrices have to respect the consecutive ones property. In clinical applications several constraints may arise that reduce the set of binary matrices which respect the consecutive ones property that we can use. We study some of them, as the interleaf distance constraint, the interleaf motion constraint, the tongue-and-groove constraint and the minimum separation constraint. We consider here different versions of the segmentation problem with different objective functions. Hence we deal with the beam-on time problem in order to minimize the total time during which the patient is irradiated. We study this problem under the interleaf distance and the interleaf motion constraints. We consider as well this last problem under the tongue-and-groove constraint in the binary case. We also take into account the cardinality and the lex-min problem. Finally, we present some results for the approximation problem. /Le problème de segmentation intervient lors de l'élaboration d'un plan de radiothérapie. Après que le médecin ait localisé la tumeur ainsi que les organes se situant à proximité de celle-ci, il doit aussi déterminer les différents dosages qui devront être délivrés. Il détermine alors une borne inférieure sur le dosage que doit recevoir la tumeur afin d'en avoir un contrôle satisfaisant, et des bornes supérieures sur les dosages des différents organes situés dans le champ. Afin de respecter au mieux ces bornes, le plan de radiothérapie doit être préparé de manière minutieuse. Nous nous intéressons à l'une des étapes à réaliser lors de la détermination de ce plan: l'étape de segmentation. Mathématiquement, cette étape consiste à décomposer une matrice entière et positive donnée en une combinaison positive entière linéaire de certaines matrices binaires. Ces matrices binaires doivent satisfaire la contrainte des uns consécutifs (cette contrainte impose que les uns de ces matrices soient regroupés en un seul bloc sur chaque ligne). Dans les applications cliniques, certaines contraintes supplémentaires peuvent restreindre l'ensemble des matrices binaires ayant les uns consécutifs (matrices 1C) que l'on peut utiliser. Nous en avons étudié certaines d'entre elles comme celle de la contrainte de chariots, la contrainte d'interdiciton de chevauchements, la contrainte tongue-and-groove et la contrainte de séparation minimum. Le premier problème auquel nous nous intéressons est de trouver une décomposition de la matrice donnée qui minimise la somme des coefficients des matrices binaires. Nous avons développé des algorithmes polynomiaux qui résolvent ce problème sous la contrainte de chariots et/ou la contrainte d'interdiction de chevauchements. De plus, nous avons pu déterminer que, si la matrice donnée est une matrice binaire, on peut trouver en temps polynomial une telle décomposition sous la contrainte tongue-and-groove. Afin de diminuer le temps de la séance de radiothérapie, il peut être désirable de minimiser le nombre de matrices 1C utilisées dans la décomposition (en ayant pris soin de préalablement minimiser la somme des coefficients ou non). Nous faisons une étude de ce problème dans différents cas particuliers (la matrice donnée n'est constituée que d'une colonne, ou d'une ligne, ou la plus grande entrée de celle-ci est bornée par une constante). Nous présentons de nouvelles bornes inférieures sur le nombre de matrices 1C ainsi que de nouvelles heuristiques. Finalement, nous terminons par étudier le cas où l'ensemble des matrices 1C ne nous permet pas de décomposer exactement la matrice donnée. Le but est alors de touver une matrice décomposable qui soit aussi proche que possible de la matrice donnée. Après avoir examiné certains cas polynomiaux nous prouvons que le cas général est difficile à approximer avec une erreur additive de O(mn) où m et n représentent les dimensions de la matrice donnée.

New processes that leads to formation of new carbon-carbon bond (the Michael reaction, the Mannich reaction and alkylation reaction) or carbon-heteroatom bond (á-halogenation, á-hydroxylation and á-amination) on bridged bicyclic ketones such as tropinone and TBON were investigated, utilizing LDA in the deprotonation step. All reactions, in which new carbon-heteroatom bond is formed, were not successful either due to low selectivity and/or yields. In case of new carbon-carbon bond forming processes, careful choice of electrophile (electrophile having the ester group in á-position to leaving group), allows for alkylation of tropinone with moderate yield and good selectivity. Application of new conditions to the aldol reaction of TBON and tropinone (e.g. MgI2 catalyzed aldol reaction), gave new aldol products that were not detected from the lithium enolate chemistry of these ketones. Modification of reaction conditions in case of MgI2 catalyzed aldol reaction provides, in a one pot process, bis-aldol product from TBON in good yield and high selectivity, as a single diastereoisomer. Finally, TBON is used as a suitable scaffold for the synthesis of thiacocaine. The first known synthesis of racemic thiacocaine is presented, via deprotonation of TBON with LDA, as a key step.

Extreme-Mass-Ratio Inspirals (EMRIs) són sistemes binaris que estan compostos per Objectes Estel.lars Compactes (OECs) orbitant al voltant de Forats Negres Massius (FNMs) situats als centres galàctics. Aquests sistemes són una de les fonts pricipals d’Ones Gravitacionals (OGs) per detectors espacials com l’antena espacial LISA (Laser Interferometer Space Antenna). Un EMRI emet senyals molt llargs i complexes dintre del fort camp gravitatori del FNM. Aquests senyals porten codificada l’estructura del FNM. Per aquest motiu, les OGs procedent d’EMRIs són una font valuosa per estudiar els FNMs situats als centres galàctics i la ciencia relacionada amb ells. En aquesta tesi estudiem dos aspectes diferents dels EMRIs: El seu modelatge i l’estimació dels paràmetres del sistema a partir dels seus senyals gravitatoris. La primera part d’aquesta tesi està dedicada al modelatge d’EMRIs, necessari per obtenir les formes d’ona de les OGs que farem servir en la seva detecció. Per aquest motiu, necessitem conèixer com el camp gravitatori del OEC afecta la seva propia trajectoria i el desvia d’un moviment geodèsic. En aquest sentit, degut a la gran diferència entre les masses del sistema, podem considerar l’OEC com a una partícula sense estructura que orbita en una geodèsica del FNM. En aquesta representació, la caiguda en espiral del OSC al voltant del FNM ve descrita per l’acció d’una autoforça local, la qual altera el moviment geodèsic de la partícula. No obstant, la implementació d’aquest mecanisme presenta diverses dificultats, degut principalment a que la descripció de l’OEC com un punt introdueix distribucions del tipus delta de Dirac. Aixó a la pràctica significa que hem de tractar amb escales temporals i espacials molt diferents, les quals estan associades al modelatge del FNM i al modelatge de l’OEC. En aquesta tesi presentem un mètode novel, el qual anomenem l’esquema de la Particle-without-Particle (PwP), que proporciona cálculs molt precisos i eficients de l’autoforça en el domini temporal, el que fa de la nostra tècnica adequada pels càlculs intensius que es requereixen en els escenaris astrofísics relevants. El punt clau del nostre métode és que no resolvem l’OEC. En el seu lloc, evitem incloure la seva presència en el (multi-)domini computacional, sustituint la delta de Dirac per condicions de contorn. Conseqüentment, només hem de proporcionar la resolució numèrica necessaria per descriure el camp aprop l’OSC, però no l’OSC mateix. D’aquesta manera tots el problemes relacionats amb la resolució d’una escala petita desapareixen. El treball desenvolupat en aquesta tesi, pot ser millorat in termes de temps de computació i putser en precisió si explorem diferent tècniques per portar el els contorns exteriors del domini computacional més aprop de la parícula sense degradar la precissió dels valors del camp a prop d’ella. Aixó es podria fer millorant les condicions de contorn exteriors o compactificant el domini físic. Hi han dos possibilitats més que podem explorar per fer els nostres càlculs més rápids, que són: (i) Reduïr el pas temporal de les nostres evolucions numèriques i (ii) paral.lelitzar el nostre codi i fer servir ordinadors amb múltiples cors (encara que aixó no incrementaria el temps de CPU). Degut a que en le cas d’un FNM de tipus Schwarzschild, com el presentat en aquesta tesi, els diferents modes no estan acoplats, en pricipi això no hauria de ser una tasca difícil d’assolir. A més a més, podem fer servir extrapol.lacions Richardson per millorar l’estimació dels valosrs de l’autoforça. Aquestes millores es poden aplicar perfectament dintre del nostre marc computacional i ténen un potencial significatiu per milloar l’eficiència dels nostres càlculs. Finalment, l’objectiu principal de la formulació presentada en aquesta tesi és desenvolupar un mètod acurat i eficient per calcular l’autoforça en situacions d’interés físic. En particular, per sistemes d’interés pel futur observatory espacial LISA. Aixó significa extendre aquestes tècniques pel cas gravitatori i per FNs amb rotació. En aquest sentit, hem de fer menció que encara que transferir les nostres técniques al cas gravitatori és directe, fer el mateix pel cas d’un FN en rotiació requereix noves millores que seran l’objectiu d’investigacions futures. En la segona part de la tesi, investiguem si és o no possible fer servir observacions d’EMRIs per testejar una determinada teoria de la Gravetat, en particular la teoria Dinàmica Chern- Simons de la Gravetat Modificada (DCSGM). La idea és que l’OEC orbita en la part més profunda del potencial gravitatori del FNM, això és els sistemes EMRI emeten OGs desde la regió de camp gravitatori fort del FNM. D’aquesta manera, la forma i el ritme de les OGs emesses pel sistema porten codificades l’estructura de l’espaitemps del FNM i la forma en la que les freqüències característiques del sistema evolucionen. Aquesta informació és la que ens permet realitzar tests de la RG. Amb aquesta finalitat, hem obtingut les forma d’ona emesses per l’OEC en una geometria del FNM que ha sigut modificada amb correccions Chern-Simons (CS). L’estimació dels paràmetres del sistema s’ha dut a terme fent servir anàlisis de Fisher matrix. Hem començat estudiant un sistema típic EMRI en RG i hem trobat que els nostres resultats coincidien amb resultats previs que es troven en la literatura. Seguidament, hem realitzat estudis d’estimacions de paràmetres per determinar l’habilitat de LISA per distingir entre RG i DCSGM, en particular per estimar el paràmetre de CS , el qual diferencia les mètriques de la DCSMG i de la RG. Amb aquesta finalitat, hem realitzat simulacions d’un sistema EMRI que cau en el punt de la banda de LISA amb sensibilitat màxima i que hem fet evolucionar durant els sis mesos abans de la col.lisió de l’OSC amb el FNM. Els nostres reultats indiquen que per determinats sistems EMRI, un detector com LISA podría discriminar entre RG i DCSGM. També hem vist que l’error en estimar disminueix amb la massa del FNM. Per tal de millorar els nostres reusltats, voldriem realitzar un estudi més exhaustiu de l’espai de paràmetres dels EMRIs. En un futur voldriem estudiar tòpics com ara comparar o esimar els errors que poden sorgir fent servir formes d’ones de RG per detectar EMRIs en DCSGM. A tal efecte, hem d’estimar la magnitud de l’error del nostre model. Ens agradaria extrendre l’estudi presentat en aquesta tesis per altres detectors d’OGs com, per exemple, Intermediate-Mass-Ratio Inspirals (IMRIs) en l’Einstein Telescope. / Extreme-Mass-Ratio Inspirals (EMRIs) are binary systems which are made up of a Stellarmass Compact Object (SCO) orbiting around a Massive Black Hole (MBH) located in a galactic centre. These systems are one of the main sources of GWs for space-based detectors like the Laser Interferometer Space Antenna (LISA). EMRIs emit long and complex GWs signals in the strong field regime of the MBHs, which encode the MBH structure. For this reason, EMRI GW signals are a valuable tool to study the MBHs located in the galactic centres and the science related with them. In this thesis, we study two different aspects of EMRIs, namely modelling and the parameter estimation of the system from their gravitational signals. The first part of the thesis is devoted to the modelling of EMRIs, to produce the GW waveforms needed for their detections. To that end, we have to know how the gravitational field of the SCO affects its own trajectory and deviates it from geodesic motion. In this regard, due to the extreme mass-ratio of the system, we can consider the SCO as a structureless particle orbiting in a geodesic of the exact MBH geometry. In this picture, the inspiral of the SCO around the MBH is described through the action of a local self-force, which alters the geodesic motion of the particle. However, the implementation of this mechanism presents several difficulties, mainly due to the point-like description of the SCO, which introduces Dirac delta distributions. This in practice means that one has to deal with very different spatial scales, one associated with the modelling of the SCO and another associated with the MBH. Moreover, the extreme mass ratio of these systems implies that we have to deal with two different time scales in the dynamics of the system, one associated with the orbital evolution of the SCO and another associated with the evolution of its orbit due to GW emission. We present a new method, which we call the Particle-without-Particle (PwP) method, that provides very efficient and accurate computations of the self-force in the time-domain, which makes our technique amenable for the intensive computations required in the astrophysically relevant scenarios. The key point of our scheme is that it does not need to resolve the SCO. Instead, we avoid its presence in the computational (multi-)domain by substituting the Dirac delta distributions by boundary conditions. Consequently, we have just to provide the numerical resolution to describe the field near the SCO, but not the SCO itself. In this way, the equations that we have to solve inside each subdomain are homogeneous wave-type equations for the fields. Consequently, all the problems related with the numerical resolution of a small scale disappear. The work we have presented here can be further improved in terms of computational time, and perhaps in accuracy, by exploring techniques to bring the outer boundaries closer to the particle without degrading the accuracy of the field values near it. This can be done either by improving the outgoing boundary conditions or by compactifying the physical domain. There are two more possibilities for making our computations faster, which are: (i) To reduce the time step of our numerical evolutions and, (ii) to parallelise our numerical code and use computers with many cores (although this does not decrease the CPU time). Since for a Schwarzschild MBH case, like the ones studied in this thesis, the different modes are not coupled, this is in principle a simple task. In addition, we can introduce Richardson extrapolation, to improve the estimations of the values of the self-force. These improvements can be perfectly applied to our framework and have significant potential to improve the efficiency of the computations. Since, the main goal of the formulation presented in this thesis is to develop an accurate and efficient method to compute the self-force in situations of physical interest. In particular, for systems of interest for the future observatory LISA. This means to extend these techniques for the gravitational case and for spinning MBHs. In this sense, we have to mention that while it is straightforward to transfer these techniques discussed here to the gravitational case, to do the same with the case of a spinning black hole may require new technical improvements which we will the subject of future investigations. In the second part of the thesis, we investigate whether we can use EMRI observations to test a particular theory of Gravity, namely Dynamical Chern-Simons Modified Gravity (DCSMG) theory. The idea is that the SCO orbits are deep inside the MBH gravitational potential, that is, EMRI systems emit GWs from the strong field region of the MBH. In this way, the shape and timing of the GWs emitted by the system have encoded the structure of the MBH spacetime and the way in which the characteristic frequencies of the system evolve. This information allows us to perform tests of GR and even of other theories of gravity, in particular, we have focused on the possibility of distinguishing between GR and Dynamical Chern Simons Modified Gravity (DCSMG). To that end, we have computed the waveforms emitted by an SCO orbiting in a MBH geometry which have been modified with CS corrections. The parameter estimation has been performed employing Fisher matrix analysis. First of all, we have studied a typical EMRI system in GR and we have found agreement between our results and previous ones found in the literature. Afterwards, we have performed parameter estimation studies to estimate the ability of LISA to distinguish between GR and DCSMG, in particular by estimating the CS parameter , which differentiates the DCSNG metric from the GR one. To that end, we have performed simulations of an EMRI system which falls in the sweet spot of the LISA sensitivity band and which has been evolved during the last six months before plunge. Our results indicates that for certain EMRI systems a detector like LISA may discriminate between GR and DCSMG. We have also seen that the error in estimating decreases with the MBH mass. In order to improve the present results, we would like to perform a more exhaustive study of the parameter space of EMRIs. In the future, we would like to address topics like to compare or estimate the errors that could arise using GR waveform templates to detect EMRIS in DCSMG. To that end, we should estimate the magnitude of the model errors. We would like to extend the study presented in this thesis to other GW detectors like, for instance, Intermediate-Mass-Ratio Inspirals (IMRIs) in the Einstein Telescope.

New processes that leads to formation of new carbon-carbon bond (the Michael reaction, the Mannich reaction and alkylation reaction) or carbon-heteroatom bond (á-halogenation, á-hydroxylation and á-amination) on bridged bicyclic ketones such as tropinone and TBON were investigated, utilizing LDA in the deprotonation step. All reactions, in which new carbon-heteroatom bond is formed, were not successful either due to low selectivity and/or yields. In case of new carbon-carbon bond forming processes, careful choice of electrophile (electrophile having the ester group in á-position to leaving group), allows for alkylation of tropinone with moderate yield and good selectivity. Application of new conditions to the aldol reaction of TBON and tropinone (e.g. MgI2 catalyzed aldol reaction), gave new aldol products that were not detected from the lithium enolate chemistry of these ketones. Modification of reaction conditions in case of MgI2 catalyzed aldol reaction provides, in a one pot process, bis-aldol product from TBON in good yield and high selectivity, as a single diastereoisomer. Finally, TBON is used as a suitable scaffold for the synthesis of thiacocaine. The first known synthesis of racemic thiacocaine is presented, via deprotonation of TBON with LDA, as a key step.

No description available.

It may sound trivial, but in this episode we’re going to learn to add and subtract…in binary. This will serve as a basis for learning about negative binary representations and the circuitry needed to perform additions in hardware.

<p> Oxetan-2-ones (β-lactones) represent important synthetic targets because they are versatile synthetic intermediates and are present in a wide variety of pharmacologically relevant natural products. Using several reported methods, a homologous series of racemic C4-monosubstituted and trans-1 ,2-disubstituted β-lactones was prepared for investigation as potential inhibitors of yeast 3-hydroxy- 3-methylglutaryl-Coenzyme A (HMG-CoA) synthase. However, no general method were then available for the preparation of the corresponding cis-1 ,2- disubstituted β-lactones. </p> <p> Using the mercury (II) promoted Masamune lactonization of β-hydroxy thiopyridyl ester 3-7, cis-3-methyl-4-decyloxetan-2-one (3-1) was prepared in high yield. The requisite syn thiol ester was prepared starting from undecanal: (1) in one step using a titanium {IV) promoted Mukaiyama aldol condensation with silyl ketene acetal 1-28; and (2) in three steps using a titanium (IV) promoted Evans-type aldol condensation with N-propionyl thiazolidinethione 4-24, followed by conversion of the thiazolidinethione aldol adduct to thiol ester 3-7 through the corresponding free acid. Substituting N-propionyl thiazolidinethione 4-24 for chiral N-acetyl and N-propionyl thiazolidinethiones 4-26 and 5-16, respectively, the Evans-type aldol condensations with undecanal proceeded with excellent diastereoselectivity (> 90 %de); this is necessary for the preparation of optically active cis-1 ,2-disubstituted and C4-monosubstituted β-lactones. </p> <p> A tandem-Evans aldol-lactonization (TEAL) reaction was developed using the lithium enolates of N-acetyl (5-16) and N-propionyl thiazolidinethione 4-24. Thus far, trisubstituted spiro β-lactones 6-17 and 6-19, and C4-disubstituted spiro β-lactone 6-22, have been successfully prepared in one-pot. </p> <p> In addition to using aldol condensations to prepare the carbon skeleton for C4-monosubstituted β-lactones, a Claisen-type condensation on a glycoluril template was attempted; the advantage of this route was the potential use of well developed asymmetric reductions of the product β-keto carboxylic acid derivative to introduce optical activity in an enantioselective preparation of C4- monosubstituted β-lactones. Unfortunately, using glycoluril 7-11, racemic 4- nonyloxetan-2-one (2-7v) was produced in poor yield because of difficulties encountered removing the aldol adduct-like β-hydroxy carboxylic acid derivative from the template. </p> / Thesis / Doctor of Philosophy (PhD)