Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions

We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.

Genetic differentiation for size at first reproduction through male versus female functions in the widespread Mediterranean tree Pinus pinaster.

BACKGROUND AND AIMS: The study of local adaptation in plant reproductive traits has received substantial attention in short-lived species, but studies conducted on forest trees are scarce. This lack of research on long-lived species represents an important gap in our knowledge, because inferences about selection on the reproduction and life history of short-lived species cannot necessarily be extrapolated to trees. This study considers whether the size for first reproduction is locally adapted across a broad geographical range of the Mediterranean conifer species Pinus pinaster. In particular, the study investigates whether this monoecious species varies genetically among populations in terms of whether individuals start to reproduce through their male function, their female function or both sexual functions simultaneously. Whether differences among populations could be attributed to local adaptation across a climatic gradient is then considered. METHODS: Male and female reproduction and growth were measured during early stages of sexual maturity of a P. pinaster common garden comprising 23 populations sampled across the species range. Generalized linear mixed models were used to assess genetic variability of early reproductive life-history traits. Environmental correlations with reproductive life-history traits were tested after controlling for neutral genetic structure provided by 12 nuclear simple sequence repeat markers. KEY RESULTS: Trees tended to reproduce first through their male function, at a size (height) that varied little among source populations. The transition to female reproduction was slower, showed higher levels of variability and was negatively correlated with vegetative growth traits. Several female reproductive traits were correlated with a gradient of growth conditions, even after accounting for neutral genetic structure, with populations from more unfavourable sites tending to commence female reproduction at a lower individual size. CONCLUSIONS: The study represents the first report of genetic variability among populations for differences in the threshold size for first reproduction between male and female sexual functions in a tree species. The relatively uniform size at which individuals begin reproducing through their male function probably represents the fact that pollen dispersal is also relatively invariant among sites. However, the genetic variability in the timing of female reproduction probably reflects environment-dependent costs of cone production. The results also suggest that early sex allocation in this species might evolve under constraints that do not apply to other conifers.

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Equivalence of many-photon Green's functions in the Duffin-Kemmer-Petiau and Klein-Gordon-Fock statistical quantum field theories

Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Greens functions in the Duffin-Kennner-Petiau and Klein-Gordon-Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

We defined generalized Heaviside functions for a variable x in R-n, and for variables (x, t) in R-n x R-m. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

Winter sea surface temperature reconstruction from planktic foraminiferal transfer functions in the northeastern Arabian Sea over the last two millennia

The Indian monsoon system is an important climate feature of the northern Indian Ocean. Small variations of the wind and precipitation patterns have fundamental influence on the societal, agricultural, and economic development of India and its neighboring countries. To understand current trends, sensitivity to forcing, or natural variation, records beyond the instrumental period are needed. However, high-resolution archives of past winter monsoon variability are scarce. One potential archive of such records are marine sediments deposited on the continental slope in the NE Arabian Sea, an area where present-day conditions are dominated by the winter monsoon. In this region, winter monsoon conditions lead to distinctive changes in surface water properties, affecting marine plankton communities that are deposited in the sediment. Using planktic foraminifera as a sensitive and well-preserved plankton group, we first characterize the response of their species distribution on environmental gradients from a dataset of surface sediment samples in the tropical and sub-tropical Indian Ocean. Transfer functions for quantitative paleoenvironmental reconstructions were applied to a decadal-scale record of assemblage counts from the Pakistan Margin spanning the last 2000?years. The reconstructed temperature record reveals an intensification of winter monsoon intensity near the year 100 CE. Prior to this transition, winter temperatures were >1.5°C warmer than today. Conditions similar to the present seem to have established after 450 CE, interrupted by a singular event near 950 CE with warmer temperatures and accordingly weak winter monsoon. Frequency analysis revealed significant 75-, 40-, and 37-year cycles, which are known from decadal- to centennial-scale resolution records of Indian summer monsoon variability and interpreted as solar irradiance forcing. Our first independent record of Indian winter monsoon activity confirms that winter and summer monsoons were modulated on the same frequency bands and thus indicates that both monsoon systems are likely controlled by the same driving force.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Visual functions in the healthy and schizophrenic brain : from stimulus control to illusory perceptions using electrical neuroimaging

ABSTRACT (FRENCH)Ce travail de thèse basé sur le système visuel chez les sujets sains et chez les patients schizophrènes, s'articule autour de trois articles scientifiques publiés ou en cours de publication. Ces articles traitent des sujets suivants : le premier article présente une nouvelle méthode de traitement des composantes physiques des stimuli (luminance et fréquence spatiale). Le second article montre, à l'aide d'analyses de données EEG, un déficit de la voie magnocellulaire dans le traitement visuel des illusions chez les patients schizophrènes. Ceci est démontré par l'absence de modulation de la composante PI chez les patients schizophrènes contrairement aux sujets sains. Cette absence est induite par des stimuli de type illusion Kanizsa de différentes excentricités. Finalement, le troisième article, également à l'aide de méthodes de neuroimagerie électrique (EEG), montre que le traitement des contours illusoires se trouve dans le complexe latéro-occipital (LOC), à l'aide d'illusion « misaligned gratings ». De plus il révèle que les activités démontrées précédemment dans les aires visuelles primaires sont dues à des inférences « top- down ».Afin de permettre la compréhension de ces trois articles, l'introduction de ce manuscrit présente les concepts essentiels. De plus des méthodes d'analyses de temps-fréquence sont présentées. L'introduction est divisée en quatre parties : la première présente le système visuel depuis les cellules retino-corticales aux deux voix du traitement de l'information en passant par les régions composant le système visuel. La deuxième partie présente la schizophrénie par son diagnostic, ces déficits de bas niveau de traitement des stimuli visuel et ces déficits cognitifs. La troisième partie présente le traitement des contours illusoires et les trois modèles utilisés dans le dernier article. Finalement, les méthodes de traitement des données EEG seront explicitées, y compris les méthodes de temps-fréquences.Les résultats des trois articles sont présentés dans le chapitre éponyme (du même nom). De plus ce chapitre comprendra les résultats obtenus à l'aide des méthodes de temps-fréquenceFinalement, la discussion sera orientée selon trois axes : les méthodes de temps-fréquence ainsi qu'une proposition de traitement de ces données par une méthode statistique indépendante de la référence. La discussion du premier article en montrera la qualité du traitement de ces stimuli. La discussion des deux articles neurophysiologiques, proposera de nouvelles d'expériences afin d'affiner les résultats actuels sur les déficits des schizophrènes. Ceci pourrait permettre d'établir un marqueur biologique fiable de la schizophrénie.ABSTRACT (ENGLISH)This thesis focuses on the visual system in healthy subjects and schizophrenic patients. To address this research, advanced methods of analysis of electroencephalographic (EEG) data were used and developed. This manuscript is comprised of three scientific articles. The first article showed a novel method to control the physical features of visual stimuli (luminance and spatial frequencies). The second article showed, using electrical neuroimaging of EEG, a deficit in spatial processing associated with the dorsal pathway in chronic schizophrenic patients. This deficit was elicited by an absent modulation of the PI component in terms of response strength and topography as well as source estimations. This deficit was orthogonal to the preserved ability to process Kanizsa-type illusory contours. Finally, the third article resolved ongoing debates concerning the neural mechanism mediating illusory contour sensitivity by using electrical neuroimaging to show that the first differentiation of illusory contour presence vs. absence is localized within the lateral occipital complex. This effect was subsequent to modulations due to the orientation of misaligned grating stimuli. Collectively, these results support a model where effects in V1/V2 are mediated by "top-down" modulation from the LOC.To understand these three articles, the Introduction of this thesis presents the major concepts used in these articles. Additionally, a section is devoted to time-frequency analysis methods not presented in the articles themselves. The introduction is divided in four parts. The first part presents three aspects of the visual system: cellular, regional, and its functional interactions. The second part presents an overview of schizophrenia and its sensoiy-cognitive deficits. The third part presents an overview of illusory contour processing and the three models examined in the third article. Finally, advanced analysis methods for EEG are presented, including time- frequency methodology.The Introduction is followed by a synopsis of the main results in the articles as well as those obtained from the time-frequency analyses.Finally, the Discussion chapter is divided along three axes. The first axis discusses the time frequency analysis and proposes a novel statistical approach that is independent of the reference. The second axis contextualizes the first article and discusses the quality of the stimulus control and direction for further improvements. Finally, both neurophysiologic articles are contextualized by proposing future experiments and hypotheses that may serve to improve our understanding of schizophrenia on the one hand and visual functions more generally.

Genome-wide transposon insertion scanning of environmental survival functions in the polycyclic aromatic hydrocarbon degrading bacterium Sphingomonas wittichii RW1.

Sphingomonas wittichii RW1 is a dibenzofuran and dibenzodioxin-degrading bacterium with potentially interesting properties for bioaugmentation of contaminated sites. In order to understand the capacity of the microorganism to survive in the environment we used a genome-wide transposon scanning approach. RW1 transposon libraries were generated with around 22 000 independent insertions. Libraries were grown for an average of 50 generations (five successive passages in batch liquid medium) with salicylate as sole carbon and energy source in presence or absence of salt stress at -1.5 MPa. Alternatively, libraries were grown in sand with salicylate, at 50% water holding capacity, for 4 and 10 days (equivalent to 7 generations). Library DNA was recovered from the different growth conditions and scanned by ultrahigh throughput sequencing for the positions and numbers of inserted transposed kanamycin resistance gene. No transposon reads were recovered in 579 genes (10% of all annotated genes in the RW1 genome) in any of the libraries, suggesting those to be essential for survival under the used conditions. Libraries recovered from sand differed strongly from those incubated in liquid batch medium. In particular, important functions for survival of cells in sand at the short term concerned nutrient scavenging, energy metabolism and motility. In contrast to this, fatty acid metabolism and oxidative stress response were essential for longer term survival of cells in sand. Comparison to transcriptome data suggested important functions in sand for flagellar movement, pili synthesis, trehalose and polysaccharide synthesis and putative cell surface antigen proteins. Interestingly, a variety of genes were also identified, interruption of which cause significant increase in fitness during growth on salicylate. One of these was an Lrp family transcription regulator and mutants in this gene covered more than 90% of the total library after 50 generations of growth on salicylate. Our results demonstrate the power of genome-wide transposon scanning approaches for analysis of complex traits.

Combined transcriptomic and proteomic studies reveal non-canonical signaling functions in the jasmonate pathway

Abstract Lipid derived signals mediate many stress and defense responses in multicellular eukaryotes. Among these are the jasmonates, potently active signaling compounds in plants. Jasmonic acid (JA) and 12-oxo-phytodienoic acid (OPDA) are the two best known members of the large jasmonate family. This thesis further investigates their roles as signals using genomic and proteomic approaches. The study is based on a simple genetic model involving two key genes. The first is ALLENE OXIDE SYNTHASE (AOS), encoding the most important enzyme in generating jasmonates. The second is CORONATINE INSENSITIVE 1 (COI1), a gene involved in all currently documented canonical signaling responses. We asked the simple question: do null mutations in AOS and COI1 have analogous effects on the transcriptome ? We found that they do not. If most COI1-dependent genes were also AOS-dependent, the expression of a zinc-finger protein was AOS-dependent but was unaffected by the coi1-1 mutation. We thus supposed that a jasmonate member, most probably OPDA, can alter gene expression partially independently of COI1. Conversely, the expression of at least three genes, one of these is a protein kinase, was shown to be COI1-dependent but did not require a functional AOS protein. We conclude that a non-jasmonate signal might alter gene expression through COIL Proteomic comparison of coi1-1 and aos plants confirmed these observations and highlighted probable protein degradation processes controlled by jasmonates and COI1 in the wounded leaf. This thesis revealed new functions for COI1 and for AOS-generated oxylipins in the jasmonate signaling pathway. Résumé Les signaux dérivés d'acides gras sont des médiateurs de réponses aux stress et de la défense des eucaryotes multicellulaires. Parmi eux, les jasmonates sont de puissants composés de sig¬nalisation chez les plantes. L'acide jasmonique (JA) et l'acide 12-oxo-phytodienoïc (OPDA) sont les deux membres les mieux caractérisés de la grande famille des jasmonates. Cette thèse étudie plus profondément leurs rôles de signalisation en utilisant des approches génomique et protéomique. Cette étude est basée sur un modèle génétique simple n'impliquant que deux gènes. Le premier est PALLENE OXYDE SYNTHASE (AOS) qui encode l'enzyme la plus importante pour la fabrication des jasmonates. Le deuxième est CORONATINE INSENSITIVE 1 (COI1) qui est impliqué dans la totalité des réponses aux jasmonates connues à ce jour. Nous avons posé la question suivante : est-ce que les mutations nulles dans les gènes AOS et COI1 ont des effets analogues sur le transcriptome ? Nous avons trouvé que ce n'était pas le cas. Si la majorité des gènes dépendants de COI1 sont également dépendants d'AOS, l'expression d'un gène codant pour une protéine formée de doigts de zinc n'est pas affectée par la mutation de COI1 tout en étant dépendante d'AOS. Nous avons donc supposé qu'un membre de la famille des jasmonates, probablement OPDA, pouvait modifier l'expression de certains gènes indépendamment de COI1. Inversement, nous avons montré que, tout en étant dépendante de COI1, l'expression d'au moins trois gènes, dont un codant pour une protéine kinase, n'était pas affectée par l'absence d'une protéine AOS fonctionnelle. Nous en avons conclu qu'un signal autre qu'un jasmonate devait modifier l'expression de certains gènes à travers COI1. La comparaison par protéomique de plantes aos et coi1-1 a confirmé ces observations et a mis en évidence un probable processus de dégradation de protéines contrôlé par les jasmonates et COU_ Cette thèse a mis en avant de nouvelles fonctions pour COI1 et pour des oxylipines générées par AOS dans le cadre de la signalisation par les jasmonates.

The role of executive functions in the control of aggressive behavior

An extensive literature suggests a link between executive functions and aggressive behavior in humans, pointing mostly to an inverse relationship, i.e., increased tendencies toward aggression in individuals scoring low on executive function tests. This literature is limited, though, in terms of the groups studied and the measures of executive functions. In this paper, we present data from two studies addressing these issues. In a first behavioral study, we asked whether high trait aggressiveness is related to reduced executive functions. A sample of over 600 students performed in an extensive behavioral test battery including paradigms addressing executive functions such as the Eriksen Flanker task, Stroop task, n-back task, and Tower of London (TOL). High trait aggressive participants were found to have a significantly reduced latency score in the TOL, indicating more impulsive behavior compared to low trait aggressive participants. No other differences were detected. In an EEG-study, we assessed neural and behavioral correlates of error monitoring and response inhibition in participants who were characterized based on their laboratory-induced aggressive behavior in a competitive reaction time task. Participants who retaliated more in the aggression paradigm and had reduced frontal activity when being provoked did not, however, show any reduction in behavioral or neural correlates of executive control compared to the less aggressive participants. Our results question a strong relationship between aggression and executive functions at least for healthy, high-functioning people.

Training executive functions in the laboratory and in real life : cognitive consequences of computer-based exercises and bilingualism

The question of the trainability of executive functions and the impact of such training on related cognitive skills has stirred considerable research interest. Despite a number of studies investigating this, the question has not yet been solved. The general aim of this thesis was to investigate two very different types of training of executive functions: laboratory-based computerized training (Studies I-III) and realworld training through bilingualism (Studies IV-V). Bilingualism as a kind of training of executive functions is based on the idea that managing two languages requires executive resources, and previous studies have suggested a bilingual advantage in executive functions. Three executive functions were studied in the present thesis: updating of working memory (WM) contents, inhibition of irrelevant information, and shifting between tasks and mental sets. Studies I-III investigated the effects of computer-based training of WM updating (Study I), inhibition (Study II), and set shifting (Study III) in healthy young adults. All studies showed increased performance on the trained task. More importantly, improvement on an untrained task tapping the trained executive function (near transfer) was seen in Study I and II. None of the three studies showed improvement on untrained tasks tapping some other cognitive function (far transfer) as a result of training. Study I also used PET to investigate the effects of WM updating training on a neurotransmitter closely linked to WM, namely dopamine. The PET results revealed increased striatal dopamine release during WM updating performance as a result of training. Study IV investigated the ability to inhibit task-irrelevant stimuli in bilinguals and monolinguals by using a dichotic listening task. The results showed that the bilinguals exceeded the monolinguals in inhibiting task-irrelevant information. Study V introduced a new, complementary research approach to study the bilingual executive advantage and its underlying mechanisms. To circumvent the methodological problems related to natural groups design, this approach focuses only on bilinguals and examines whether individual differences in bilingual behavior correlate with executive task performances. Using measures that tap the three above-entioned executive functions, the results suggested that more frequent language switching was associated with better set shifting skills, and earlier acquisition of the second language was related to better inhibition skills. In conclusion, the present behavioral results showed that computer-based training of executive functions can improve performance on the trained task and on closely related tasks, but does not yield a more general improvement of cognitive skills. Moreover, the functional neuroimaging results reveal that WM training modulates striatal dopaminergic function, speaking for training-induced neural plasticity in this important neurotransmitter system. With regard to bilingualism, the results provide further support to the idea that bilingualism can enhance executive functions. In addition, the new complementary research approach proposed here provides some clues as to which aspects of everyday bilingual behavior may be related to the advantage in executive functions in bilingual individuals.

Nature of the state economic expanded functions in the Brazilian economy*

ABSTRACT The paper discusses the dynamics of capital accumulation in Latin America economies. The hypothesis is that in these economies the role of the State is comparatively broader than in the economies of the centers of the capitalism by structural reasons. The argument is mainly based on Marx and Kalecki, besides historical elements of Latin America economies, particularly the Brazilian economy. Then the paper explores the dynamics consequences of this nature at the national levels, concluding that this condition gives a higher degree of instability.