Bandlimited Lipschitz functions

We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a cancellation condition.

Alteration and Contamination of Archaeological Ceramics: the Perturbation Problem

Alteration and contamination processes modify the chemical composition of ceramic artefacts. This is not restricted solely to the affected elements, but also affects general concentrations. This is due to the compositional nature of chemical data, enclosed by the restriction of unit sum. Since it is impossible to know prior to data treatment whether the original compositions have been changed by such processes, the methodological approach used in provenance studies must be robust enough to handle materials that might have been altered or contaminated. The ability of the logratio transformation proposed by Aitchison to handle compositional data is studied and compared with that of present data treatments. The logaratio transformation appears to offer the most robust approach

Perturbation of EGF-induced MAP kinase activation by TGF-ß1

TGF-ß1 regulates both cellular growth and phenotypic plasticity important for maintaining a growth advantage and increased invasiveness in progressively malignant cells. Recent studies indicate that TGF-ß-1 stimulates the conversion of epitheliod to fibroblastoid phenotype which presumably leads to the inactivation of growth-inhibitory effects by TGF-ß1 (Portella et al. (1998) Cell Growth and Differentiation, 9: 393-404). Therefore, the investigation of TGF-ß1 signaling that leads to altered growth and migration may provide novel targets for the prevention of increased cell growth and invasion. Although much attention has been paid to TGF-ß1 responses in epithelial cells, the above studies suggest that examination of signal transduction pathways in fibroblasts are important as well. Data from our laboratory are consistent with the concept that TGF-ß1 can act as a regulatory switch in density-dependent C3H 10T1/2 fibroblasts capable of either promoting or delaying G1 traverse. The regulation of this switch is proposed to occur prior to pRb phosphorylation, namely prior to activation of cyclin-dependent kinases. The current study is concerned with the evaluation of a key cyclin (cyclin D1) which activates cdk4 and p27KIP1 which in turn inhibit cdk2 in the proliferative responses of epidermal growth factor (EGF) and platelet-derived growth factor (PDGF) and their modulation by TGF-ß1. Although the molecular events that lead to elevation of cyclin D1 are not completely understood, it appears likely that activation of p42/p44MAPK kinases is involved in its transcriptional regulation. TGF-ß1 delayed EGF- or PDGF-induced cyclin D1 expression and blocked the induction of active p42/p44MAPK. The mechanism by which TGF-ß1 induces a block in p42/p44MAPK activation is being examined and the possibility that TGF-ß1 regulates phosphatase activity is being tested.

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

The effect of perturbation warning on attention switching abilities during dual-task performance in young and older adults

This study examined whether providing an auditory warning would facilitate attention switching abilities in older adults during dual-tasking. Fifteen young and 16 older adults performed a tracking task while recovering their balance from a support surface translation. For half of the trials, an auditory warning was presented to inform participants of the upcoming translation. Performance was quantified through electromyographic (EMG) recordings of the lower limb muscles, while the ability to switch attention between tasks was determined by tracking task error. Providing warning of an upcoming loss of balance resulted in both young and older adults increasing their leg EMG activity by 10-165% (p<0.05) in preparation for the upcoming translation. However, no differences in the timing of attention switching were observed with or without the warning (p=0.424). Together, these findings suggest that providing a perturbation warning has minimal benefits in improving attention switching abilities for balance recovery in healthy older adults.

Étude des facteurs de perturbation de chambres d’ionisation sous conditions non standard

Durant la dernière décennie, les développements technologiques en radiothérapie ont transformé considérablement les techniques de traitement. Les nouveaux faisceaux non standard améliorent la conformité de la dose aux volumes cibles, mais également complexifient les procédures dosimétriques. Puisque des études récentes ont démontré l’invalidité de ces protocoles actuels avec les faisceaux non standard, un nouveau protocole applicable à la dosimétrie de référence de ces faisceaux est en préparation par l’IAEA-AAPM. Le but premier de cette étude est de caractériser les facteurs responsables des corrections non unitaires en dosimétrie des faisceaux non standard, et ainsi fournir des solutions conceptuelles afin de minimiser l’ordre de grandeur des corrections proposées dans le nouveau formalisme de l’IAEA-AAPM. Le deuxième but de l’étude est de construire des méthodes servant à estimer les incertitudes d’une manière exacte en dosimétrie non standard, et d’évaluer les niveaux d’incertitudes réalistes pouvant être obtenus dans des situations cliniques. Les résultats de l’étude démontrent que de rapporter la dose au volume sensible de la chambre remplie d’eau réduit la correction d’environ la moitié sous de hauts gradients de dose. Une relation théorique entre le facteur de correction de champs non standard idéaux et le facteur de gradient du champ de référence est obtenue. En dosimétrie par film radiochromique, des niveaux d’incertitude de l’ordre de 0.3% sont obtenus par l’application d’une procédure stricte, ce qui démontre un intérêt potentiel pour les mesures de faisceaux non standard. Les résultats suggèrent également que les incertitudes expérimentales des faisceaux non standard doivent être considérées sérieusement, que ce soit durant les procédures quotidiennes de vérification ou durant les procédures de calibration. De plus, ces incertitudes pourraient être un facteur limitatif dans la nouvelle génération de protocoles.

Contribution du mécanisme d'inhibition présynaptique à l'induction de réactions posturales efficaces suite à une perturbation d'équilibre

Le risque de chute est une problématique bien présente chez les personnes âgées ou ayant une atteinte neurologique et reflète un déficit des mécanismes neuronaux assurant l’équilibre. De précédentes études démontrent que l’intégration des informations sensorielles est essentielle au contrôle de l’équilibre et que l’inhibition présynaptique (IP) serait un mécanisme important dans le contrôle de la transmission sensorielle. Ainsi, le but de cette étude était d’identifier la contribution du mécanisme d’IP à l’induction de réponses posturales efficaces suite à une perturbation d’équilibre. Notre hypothèse est qu’une diminution d’IP contribuerait à l’induction des ces réponses, en augmentant l’influence de la rétroaction sensorielle sur les réseaux de neurones spinaux. Afin de démontrer cette hypothèse, nous avons d’abord évalué l’excitabilité spinale pendant les perturbations vers l’avant ou vers l’arrière, à l’aide du réflexe H. L’excitabilité spinale était modulée selon la direction de la perturbation et cette modulation survenait dès 75 ou 100 ms (p<0.05), soit avant l’induction des réactions posturales. Puis, à l’aide de techniques plus précises de convergence spinale, nous avons démontré que l’IP était diminuée dès 75 et 100 ms dans les deux directions, suggérant que la transmission des informations sensorielles vers la moelle épinière est accrue juste avant le déclenchement de la réponse posturale. Cette étude met en évidence un mécanisme-clé permettant d’augmenter la rétroaction des informations sensorielles nécessaires à l’induction de réponses posturales appropriées. L’évaluation de ce mécanisme pourrait mener à une meilleure identification des individus à risque de chute.

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

Nichtüberlappende Gebietszerlegungsmethoden für lineare und quasilineare (monotone und nichtmonotone) Probleme

In dieser Arbeit werden nichtüberlappende Gebietszerlegungsmethoden einerseits hinsichtlich der zu lösenden Problemklassen verallgemeinert und andererseits in bisher nicht untersuchten Kontexten betrachtet. Dabei stehen funktionalanalytische Untersuchungen zur Wohldefiniertheit, eindeutigen Lösbarkeit und Konvergenz im Vordergrund. Im ersten Teil werden lineare elliptische Dirichlet-Randwertprobleme behandelt, wobei neben Problemen mit dominantem Hauptteil auch solche mit singulärer Störung desselben, wie konvektions- oder reaktionsdominante Probleme zugelassen sind. Der zweite Teil befasst sich mit (gleichmäßig) monotonen koerziven quasilinearen elliptischen Dirichlet-Randwertproblemen. In beiden Fällen wird das Lipschitz-Gebiet in endlich viele Lipschitz-Teilgebiete zerlegt, wobei insbesondere Kreuzungspunkte und Teilgebiete ohne Außenrand zugelassen sind. Anschließend werden Transmissionsprobleme mit frei wählbaren $L^{\infty}$-Parameterfunktionen hergeleitet, wobei die Konormalenableitungen als Funktionale auf geeigneten Funktionenräumen über den Teilrändern ($H_{00}^{1/2}(\Gamma)$) interpretiert werden. Die iterative Lösung dieser Transmissionsprobleme mit einem Ansatz von Deng führt auf eine Substrukturierungsmethode mit Robin-artigen Transmissionsbedingungen, bei der eine Auswertung der Konormalenableitungen aufgrund einer geschickten Aufdatierung der Robin-Daten nicht notwendig ist (insbesondere ist die bekannte Robin-Robin-Methode von Lions als Spezialfall enthalten). Die Konvergenz bezüglich einer partitionierten $H^1$-Norm wird für beide Problemklassen gezeigt. Dabei werden keine über $H^1$ hinausgehende Regularitätsforderungen an die Lösungen gestellt und die Gebiete müssen keine zusätzlichen Glattheitsvoraussetzungen erfüllen. Im letzten Kapitel werden nichtmonotone koerzive quasilineare Probleme untersucht, wobei das Zugrunde liegende Gebiet nur in zwei Lipschitz-Teilgebiete zerlegt sein soll. Das zugehörige nichtlineare Transmissionsproblem wird durch Kirchhoff-Transformation in lineare Teilprobleme mit nichtlinearen Kopplungsbedingungen überführt. Ein optimierungsbasierter Lösungsansatz, welcher einen geeigneten Abstand der rücktransformierten Dirichlet-Daten der linearen Teilprobleme auf den Teilrändern minimiert, führt auf ein optimales Kontrollproblem. Die dabei entstehenden regularisierten freien Minimierungsprobleme werden mit Hilfe eines Gradientenverfahrens unter minimalen Glattheitsforderungen an die Nichtlinearitäten gelöst. Unter zusätzlichen Glattheitsvoraussetzungen an die Nichtlinearitäten und weiteren technischen Voraussetzungen an die Lösung des quasilinearen Ausgangsproblems, kann zudem die quadratische Konvergenz des Newton-Verfahrens gesichert werden.

Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes. Against this background the relevance of perturbations and subcompositions can be clearly seen. Moreover we can identify a number of hypotheses of interest involving the specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules

El mètode APT (Auto Adjusting Perturbation Theory) de diagonalització de matrius

Es presenta un nou algorisme per a la diagonalització de matrius amb diagonal dominant. Es mostra la seva eficàcia en el tractament de matrius no simètriques, amb elements definits sobre el cos complex i, fins i tot, de grans dimensions. Es posa de manifest la senzillesa del mètode així com la facilitat d'implementació en forma de codi de programació. Es comenten els seus avantatges i característiques limitants, així com algunes de les millores que es poden implementar. Finalment, es mostren alguns exemples numèrics