On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

MS-based metabolomics facilitates the discovery of in vivo functional small molecules with a diversity of biological contexts

In vivo small molecules as necessary intermediates are involved in numerous critical metabolic pathways and biological processes associated with many essential biological functions and events. There is growing evidence that MS-based metabolomics is emerging as a powerful tool to facilitate the discovery of functional small molecules that can better our understanding of development, infection, nutrition, disease, toxicity, drug therapeutics, gene modifications and host-pathogen interaction from metabolic perspectives. However, further progress must still be made in MS-based metabolomics because of the shortcomings in the current technologies and knowledge. This technique-driven review aims to explore the discovery of in vivo functional small molecules facilitated by MS-based metabolomics and to highlight the analytic capabilities and promising applications of this discovery strategy. Moreover, the biological significance of the discovery of in vivo functional small molecules with different biological contexts is also interrogated at a metabolic perspective.

Functional magnetic resonance brain imaging of executive cognitive performance in young first-episode schizophrenia patients and age-matched long-term cannabis users

Converging evidence from epidemiological, clinical and neuropsychological research suggests a link between cannabis use and increased risk of psychosis. Long-term cannabis use has also been related to deficit-like “negative” symptoms and cognitive impairment that resemble some of the clinical and cognitive features of schizophrenia. The current functional brain imaging study investigated the impact of a history of heavy cannabis use on impaired executive function in first-episode schizophrenia patients. Whilst performing the Tower of London task in a magnetic resonance imaging scanner, event-related blood oxygenation level-dependent (BOLD) brain activation was compared between four age and gender-matched groups: 12 first-episode schizophrenia patients; 17 long-term cannabis users; seven cannabis using first-episode schizophrenia patients; and 17 healthy control subjects. BOLD activation was assessed as a function of increasing task difficulty within and between groups as well as the main effects of cannabis use and the diagnosis of schizophrenia. Cannabis users and non-drug using first-episode schizophrenia patients exhibited equivalently reduced dorsolateral prefrontal activation in response to task difficulty. A trend towards additional prefrontal and left superior parietal cortical activation deficits was observed in cannabis-using first-episode schizophrenia patients while a history of cannabis use accounted for increased activation in the visual cortex. Cannabis users and schizophrenia patients fail to adequately activate the dorsolateral prefrontal cortex, thus pointing to a common working memory impairment which is particularly evident in cannabis-using first-episode schizophrenia patients. A history of heavy cannabis use, on the other hand, accounted for increased primary visual processing, suggesting compensatory imagery processing of the task.

Functional MRI of facial emotion recognition deficits in schizophrenia and their electrophysiological correlates

Empirical evidence suggests impaired facial emotion recognition in schizophrenia. However, the nature of this deficit is the subject of ongoing research. The current study tested the hypothesis that a generalized deficit at an early stage of face-specific processing (i.e. putatively subserved by the fusiform gyrus) accounts for impaired facial emotion recognition in schizophrenia as opposed to the Negative Emotion-specific Deficit Model, which suggests impaired facial information processing at subsequent stages. Event-related potentials (ERPs) were recorded from 11 schizophrenia patients and 15 matched controls while performing a gender discrimination and a facial emotion recognition task. Significant reduction of the face-specific vertex positive potential (VPP) at a peak latency of 165 ms was confirmed in schizophrenia subjects whereas their early visual processing, as indexed by P1, was found to be intact. Attenuated VPP was found to correlate with subsequent P3 amplitude reduction and to predict accuracy when performing a facial emotion discrimination task. A subset of ten schizophrenia patients and ten matched healthy control subjects also performed similar tasks in the magnetic resonance imaging scanner. Patients showed reduced blood oxygenation level-dependent (BOLD) activation in the fusiform, inferior frontal, middle temporal and middle occipital gyrus as well as in the amygdala. Correlation analyses revealed that VPP and the subsequent P3a ERP components predict fusiform gyrus BOLD activation. These results suggest that problems in facial affect recognition in schizophrenia may represent flow-on effects of a generalized deficit in early visual processing.

Functional MRI BOLD response to Tower of London performance of first-episode schizophrenia patients using cortical pattern matching

Due to its three-dimensional folding pattern, the human neocortex; poses a challenge for accurate co-registration of grouped functional; brain imaging data. The present study addressed this problem by; employing three-dimensional continuum-mechanical image-warping; techniques to derive average anatomical representations for coregistration; of functional magnetic resonance brain imaging data; obtained from 10 male first-episode schizophrenia patients and 10 age-matched; male healthy volunteers while they performed a version of the; Tower of London task. This novel technique produced an equivalent; representation of blood oxygenation level dependent (BOLD) response; across hemispheres, cortical regions, and groups, respectively, when; compared to intensity average co-registration, using a deformable; Brodmann area atlas as anatomical reference. Somewhat closer; association of Brodmann area boundaries with primary visual and; auditory areas was evident using the gyral pattern average model.; Statistically-thresholded BOLD cluster data confirmed predominantly; bilateral prefrontal and parietal, right frontal and dorsolateral; prefrontal, and left occipital activation in healthy subjects, while; patients’ hemispheric dominance pattern was diminished or reversed,; particularly decreasing cortical BOLD response with increasing task; difficulty in the right superior temporal gyrus. Reduced regional gray; matter thickness correlated with reduced left-hemispheric prefrontal/; frontal and bilateral parietal BOLD activation in patients. This is the; first study demonstrating that reduction of regional gray matter in; first-episode schizophrenia patients is associated with impaired brain; function when performing the Tower of London task, and supports; previous findings of impaired executive attention and working memory; in schizophrenia.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Density-potential mapping in time-dependent density-functional theory

The key questions of uniqueness and existence in time-dependent density-functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead, however, to nonanalyticities. We reformulate these questions in terms of a nonlinear Schroedinger equation with a potential that depends nonlocally on the wave function.

Letters in cognitive analytic therapy: The patient's experience

Patient perspectives on how therapeutic letters contributed to their experience of cognitive analytic therapy (CAT) were investigated. Eight patients took part in semistructured interviews. A grounded, thematic analysis of their accounts suggested four general processes. First, letters offered a tangible, lasting framework for the assimilation of a new perspective about themselves and their relationships and facilitated coping with a complex range of emotions and risks this awareness required. Second, they demonstrated therapists’ commitment to patients’ growth. Third, they helped to teach participants about the therapy process as an example of an interpersonal exchange. Fourth, they helped participants consider how they wished to share personal information. These data offer a more complex understanding of this standard CAT intervention. Although some findings are consistent with CAT theory, the range of emotional dilemmas associated with letters has not received specific attention. Clinical implications are discussed.

The analytic torsion of a disc

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Researcher allegiance in psychotherapy outcome research: an overview of reviews

Researcher allegiance (RA) is widely discussed as a risk of bias in psychotherapy outcome research. The relevance attached to RA bias is related to meta-analyses demonstrating an association of RA with treatment effects. However, recent meta-analyses have yielded mixed results. To provide more clarity on the magnitude and robustness of the RA-outcome association this article reports on a meta-meta-analysis summarizing all available meta-analytic estimates of the RA-outcome association. Random-effects methods were used. Primary study overlap was controlled. Thirty meta-analyses were included. The mean RA-outcome association was r=.262 (p=.002, I(2)=28.98%), corresponding to a moderate effect size. The RA-outcome association was robust across several moderating variables including characteristics of treatment, population, and the type of RA assessment. Allegiance towards the RA bias hypothesis moderated the RA-outcome association. The findings of this meta-meta-analysis suggest that the RA-outcome association is substantial and robust. Implications for psychotherapy outcome research are discussed.

Crossing borders: Ethnic minorities matter? A meta analytic examionation of the alliance-outcome relationship

Objectives: The purpose of this meta analysis was to examine the moderating impact of substance use disorder as inclusion/exclusion criterion as well as the percentage of racial/ethnic minorities on the strength of the alliance-outcome relationship in psychotherapy. It was hypothesized that the presence of a dsm axis i substance use disorders as a criterion and the presence of racial/ethnic minority as a psychosocial indicator are confounded client factors reducing the relationship between alliance and outcome. Methods: A random effects restricted maximum-likelihood estimator was used for omnibus and moderator models (k = 94). results: the presence of (a) substance use disorder and, (b) racial/ethnic minorities (overall and specific to african americans) partially moderated the alliance-outcome correlation. The percentage of substance use disorders and racial/ethnic minority status was highly correlated. Conclusions: Socio-cultural contextual variables should be considered along with dsm axis i diagnosis of substance use disorders in analyzing and interpreting mechanisms of change.