Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Weighted Inequalities and Lipschitz Spaces

In this thesis I have characterized the trace measures for particular potential spaces of functions defined on R^n, but "mollified" so that the potentials are de facto defined on the upper half-space of R^n. The potential functions are kind Riesz-Bessel. The characterization of trace measures for these spaces is a test condition on elementary sets of the upper half-space. To prove the test condition as sufficient condition for trace measures, I had give an extension to the case of upper half-space of the Muckenhoupt-Wheeden and Wolff inequalities. Finally I characterized the Carleson-trace measures for Besov spaces of discrete martingales. This is a simplified discrete model for harmonic extensions of Lipschitz-Besov spaces.

Intestinal microbes affect phenotypes and functions of invariant natural killer T cells in mice

Invariant natural killer T (iNKT) cells undergo canonical, Vα14-Jα18 rearrangement of the T-cell receptor (TCR) in mice; this form of the TCR recognizes glycolipids presented by CD1d. iNKT cells mediate many different immune reactions. Their constitutive activated and memory phenotype and rapid initiation of effector functions after stimulation indicate previous antigen-specific stimulation. However, little is known about this process. We investigated whether symbiotic microbes can determine the activated phenotype and function of iNKT cells.

Classification Using Generalized Partial Least Squares

The advances in computational biology have made simultaneous monitoring of thousands of features possible. The high throughput technologies not only bring about a much richer information context in which to study various aspects of gene functions but they also present challenge of analyzing data with large number of covariates and few samples. As an integral part of machine learning, classification of samples into two or more categories is almost always of interest to scientists. In this paper, we address the question of classification in this setting by extending partial least squares (PLS), a popular dimension reduction tool in chemometrics, in the context of generalized linear regression based on a previous approach, Iteratively ReWeighted Partial Least Squares, i.e. IRWPLS (Marx, 1996). We compare our results with two-stage PLS (Nguyen and Rocke, 2002A; Nguyen and Rocke, 2002B) and other classifiers. We show that by phrasing the problem in a generalized linear model setting and by applying bias correction to the likelihood to avoid (quasi)separation, we often get lower classification error rates.

Strengthening of laterality of verbal and visuospatial functions during childhood and adolescence

Cognitive functions in the child's brain develop in the context of complex adaptive processes, determined by genetic and environmental factors. Little is known about the cerebral representation of cognitive functions during development. In particular, knowledge about the development of right hemispheric (RH) functions is scarce. Considering the dynamics of brain development, localization and lateralization of cognitive functions must be expected to change with age. Twenty healthy subjects (8.6-20.5 years) were examined with fMRI and neuropsychological tests. All participants completed two fMRI tasks known to activate left hemispheric (LH) regions (language tasks) and two tasks known to involve predominantly RH areas (visual search tasks). A laterality index (LI) was computed to determine the asymmetry of activation. Group analysis revealed unilateral activation of the LH language circuitry during language tasks while visual search tasks induced a more widespread RH activation pattern in frontal, superior temporal, and occipital areas. Laterality of language increased between the ages of 8-20 in frontal (r = 0.392, P = 0.049) and temporal (r = 0.387, P = 0.051) areas. The asymmetry of visual search functions increased in frontal (r = -0.525, P = 0.009) and parietal (r = -0.439, P = 0.027) regions. A positive correlation was found between Verbal-IQ and the LI during a language task (r = 0.585, P = 0.028), while visuospatial skills correlated with LIs of visual search (r = -0.621, P = 0.018). To summarize, cognitive development is accompanied by changes in the functional representation of neuronal circuitries, with a strengthening of lateralization not only for LH but also for RH functions. Our data show that age and performance, independently, account for the increases of laterality with age.

ON THE DIGITAL-POLITICAL TOPOGRAPHY OF MUSIC

The persuasive power of music is often relegated to the dimension of pathos: that which moves us emotionally. Yet, the music commodity is now situated in and around the liminal spaces of digitality. To think about how music functions, how it argues across media, and how it moves us, we must examine its material and immaterial realities as they present themselves to us and as we so create them. This dissertation rethinks the relationship between rhetoric and music by examining the creation, performance, and distribution of music in its material and immaterial forms to demonstrate its persuasive power. While both Plato and Aristotle understood music as a means to move men toward virtue, Aristotle tells us in his Laws, through the Athenian Stranger, that the very best kinds of music can help guide us to truth. From this starting point, I assess the historical problem of understanding the rhetorical potential of music as merely that which directs or imitates the emotions: that which “Soothes the savage breast,” as William Congreve writes. By furthering work by Vickers and Farnsworth, who suggest that the Baroque fascination with applying rhetorical figures to musical figures is an insufficient framework for assessing the rhetorical potential of music, I demonstrate the gravity of musical persuasion in its political weight, in its violence—the subjective violence of musical torture at Guantanamo and the objective, ideological violence of music—and in what Jacques Attali calls the prophetic nature of music. I argue that music has a significant function, and as a non-discursive form of argumentation, works on us beyond affect. Moreover, with the emergence of digital music distribution and domestic digital recording technologies, the digital music commodity in its material and immaterial forms allows for ruptures in the former methods of musical composition, production, and distribution and in the political potential of music which Jacques Attali describes as being able to foresee new political realities. I thus suggest a new theoretical framework for thinking about rhetoric and music by expanding on Lloyd Bitzer’s rhetorical situation, by offering the idea of “openings” to the existing exigence, audience, and constraints. The prophetic and rhetorical power of music in the aleatoric moment can help provide openings from which new exigencies can be conceived. We must, therefore, reconsider the role of rhetorical-musical composition for the citizen, not merely as a tool for entertainment or emotional persuasion, but as an arena for engaging with the political.

ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

FUNCTIONS OF DEADENYLATION FACTORS IN MRNA DECAY AND MRNA PROCESSING BODY FORMATION

Most newly synthesized messenger RNAs possess a 5’ cap and a 3’ poly(A) tail. The process of poly(A) tail shortening, also termed deadenylation, is important for post-transcriptional gene regulation, because deadenylation not only leads to mRNA translational inhibition but also is the first step of major mRNA degradation. Translationally inhibited mRNAs can be stored and/or degraded in dynamic cytoplasmic foci termed mRNA processing bodies, or P bodies, which are conserved in eukaryotes. To shed new light on the mechanisms of P body formation and P body functions, I focused on the link between deadenylation factors and P bodies. I found that the two major deadenylation complexes, Pan3-Pan2 and Ccr4-Caf1, can both be enriched in P bodies. The deadenylase activity of the Ccr4-Caf1 complex is prerequisite for P body formation. Pan3, but not the deadenylase Pan2, is essential for P body formation. While the C-terminal domain of Pan3 is important for interaction with Pan2, Pan3 N-terminal domain is important for Pan3 to form cytoplasmic foci colocalizing with P bodies and to promote mRNA decay. Interestingly, Pan3 N-terminal domain may be phosphorylated to regulate Pan3 localization and functions. Aside from the functions of the two deadenylation complexes in P bodies, I also studied all reported human P body proteins as a whole using bioinformatics. This effort not only has generated a comprehensive picture of the functions of and interactions among human P body proteins, but also has predicted proteins that may regulate P body formation and/or functions. In summary, my study has established a direct link between mRNA deadenylation and P body formation and has also led to new hypotheses to guide future research on how P body dynamics are controlled.

Generalized resistance resources of informal caregivers: A study of demands for care, competing demands, perception of burden and cognitive stress

This study examines the relationship among psychological resources (generalized resistance resources), care demands (demands for care, competing demands, perception of burden) and cognitive stress in a selected population of primary family caregivers. The study utilizes Antonovsky's Salutogenic Model of Health, specifically the concept of generalized resistance resources (GRRs), to analyze the relative effect of these resources on mediating cognitive stress, controlling for other care demands. The study is based on a sample of 784 eligible caregivers who (1) were relatives, (2) had the main responsibility for care, defined as a primary caregiver, and (3) provided a scaled stress score for the amount of overall care given to the care recipient (family member). The sample was drawn from the 1982 National Long-Term Care Survey (NLTCS) of individuals who assisted a given NLTCS sample person with ADL limitations.^ The study tests the following hypotheses: (a) There will be a negative relationship between generalized resistance resources (GRRs) and cognitive stress controlling for care demands (demands for care, competing demands, and perceptions of burden); (b) of the specific GRRs (material, cognitive, social, cultural-environmental) the social domain will represent the most significant factor predicting a decrease in cognitive stress; and (c) the social domain will be more significant for the female than the male primary family caregiver in decreasing cognitive stress.^ The study found that GRRs had a statistically significant mediating effect on cognitive stress, but the GRRs were a less significant predictor of stress than perception of burden and demands for care. Thus, although the analysis supported the underlying hypothesis, the specific hypothesis regarding GRRs' greater significance in buffering cognitive stress was not supported. Second, the results did not demonstrate the statistical significance or differences among the GRR domains. The hypothesis that the social GRR domain was most significant in mediating stress of family caregivers was not supported. Finally, the results confirmed that there are differences in the importance of social support help in mediating stress based on gender. It was found that gender and social support help were related to cognitive stress and gender had a statistically significant interaction effect with social support help. Implications for clinical practice, public health policy, and research are discussed. ^

Improving executive functions in 5- and 6-year-olds: Evaluation of a small group intervention in prekindergarten and kindergarten children

Research suggests a central role of executive functions for children's cognitive and social development during preschool years, especially in promoting school readiness. Interventions aiming to improve executive functions are therefore being called for. The present study examined the effect of a small group intervention implemented in kindergarten settings focusing on basic components of executive functions, i.e., working memory, interference control and cognitive flexibility. A total of 135 children enrolled in Swiss prekindergarten (5-year-olds) and kindergarten (6-year-olds) were involved. Results revealed that the small group intervention promoted gains in all three included components of executive functions: prekindergarten children substantially improved their working memory and cognitive flexibility processes, whereas significant training effects were found for the kindergarten children in interference control. Implications of these findings for early intervention programs and for tailoring preschool curricula are discussed, particularly with respect to children's school readiness. Copyright © 2011 John Wiley & Sons, Ltd.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

The effects of qualitatively different acute physical activity interventions in real-world settings on executive functions in preadolescent children

There is growing evidence indicating a positive effect of acute physical activity on cognitive performance in children. Most of the evidence originates, however, from studies in highly controlled laboratory settings. The aim of the present study was to investigate whether the same effects can be found in more real-world settings. We examined the effects of qualitatively different acute physical activity interventions on the three core dimensions of executive functions (updating, inhibition, shifting). In an experimental between-subject design, 219 ten to twelve year-olds were assigned to one of four conditions which varied systematically in physical activation and cognitive engagement. Executive functions were measured before and immediately after the intervention. Contrary to the hypothesis, no effects of acute physical activity with and without cognitive engagement were found on executive functions in the overall sample. Only children with higher fitness and/or higher academic achievement benefitted from the interventions in terms of their updating performance. Thus, the results indicate that it may be more difficult to attain positive effects through acute physical activity in real-world settings than in laboratory settings and that physiological and cognitive requirements may have to be adjusted to individual capacity to make an intervention effective.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

Unveiling Protein Functions through the Dynamics of the Interaction Network

Protein interaction networks have become a tool to study biological processes, either for predicting molecular functions or for designing proper new drugs to regulate the main biological interactions. Furthermore, such networks are known to be organized in sub-networks of proteins contributing to the same cellular function. However, the protein function prediction is not accurate and each protein has traditionally been assigned to only one function by the network formalism. By considering the network of the physical interactions between proteins of the yeast together with a manual and single functional classification scheme, we introduce a method able to reveal important information on protein function, at both micro- and macro-scale. In particular, the inspection of the properties of oscillatory dynamics on top of the protein interaction network leads to the identification of misclassification problems in protein function assignments, as well as to unveil correct identification of protein functions. We also demonstrate that our approach can give a network representation of the meta-organization of biological processes by unraveling the interactions between different functional classes