Roberta Fabbri

A NONAUTONOMOUS SADDLE-NODE BIFURCATION PATTERN

In this paper we study certain differential equations depending on a small parameter e which exhibit a bifurcation of saddle-node type as e passes through zero. We use a classical averaging technique together with methods and results from the modern theory of nonautonomous differential equations.

Memory retrieval of inhibitory avoidance requires histamine H1 receptor activation in the hippocampus.

Significance Several neurotransmitters contribute to memory formation by modulating selectively acquisition, consolidation, and/or retrieval. Integrity of the brain histamine system is necessary for the consolidation of inhibitory avoidance (IA) memory. Here, we report that cerebral histamine depletion also impairs retrieval of IA in rats and blunts retrieval-induced c-Fos activation and cAMP-responsive element binding protein phosphorylation in the CA1 region of the hippocampus. Histamine infusion into the CA1 restores IA retrieval in histamine-depleted rats by targeting brain histamine H1 receptors. Our study uncovers previously unidentified mechanisms involved in memory retrieval and may offer possible targets for eventual pharmacotherapies to treat dysfunctional aversive memories, including phobias, panic attacks, and posttraumatic stress disorders, as well as improve the efficacy of exposure psychotherapies. Retrieval represents a dynamic process that may require neuromodulatory signaling. Here, we report that the integrity of the brain histaminergic system is necessary for retrieval of inhibitory avoidance (IA) memory, because rats depleted of histamine through lateral ventricle injections of α-fluoromethylhistidine (a-FMHis), a suicide inhibitor of histidine decarboxylase, displayed impaired IA memory when tested 2 d after training. a-FMHis was administered 24 h after training, when IA memory trace was already formed. Infusion of histamine in hippocampal CA1 of brain histamine-depleted rats (hence, amnesic) 10 min before the retention test restored IA memory but was ineffective when given in the basolateral amygdala (BLA) or the ventral medial prefrontal cortex (vmPFC). Intra-CA1 injections of selective H1 and H2 receptor agonists showed that histamine exerted its effect by activating the H1 receptor. Noteworthy, the H1 receptor antagonist pyrilamine disrupted IA memory retrieval in rats, thus strongly supporting an active involvement of endogenous histamine; 90 min after the retention test, c-Fos–positive neurons were significantly fewer in the CA1s of a-FMHis–treated rats that displayed amnesia compared with in the control group. We also found reduced levels of phosphorylated cAMP-responsive element binding protein (pCREB) in the CA1s of a-FMHis–treated animals compared with in controls. Increases in pCREB levels are associated with retrieval of associated memories. Targeting the histaminergic system may modify the retrieval of emotional memory; hence, histaminergic ligands might reduce dysfunctional aversive memories and improve the efficacy of exposure psychotherapies.

Genericity of exponential dichotomy for two-dimensional differential systems

We consider the setD of two-dimensional, quasi-periodic, traceless linear systems with a fixed number k>-2 of frequencies, which exhibit an exponential dichotomy. We show thatD is generic in the C0-topology in the set of all such two-dimensional linear systems.

Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

Nonautonomous linear Hamiltonian systems.- The rotation number and the Lyapunov index for real nonautonomous linear Hamiltonian systems.- The Floquet coeffcient for nonautonomous linear Hamiltonian systems: Atkinson problems.- The Weyl functions.- Weak disconjugacy for linear Hamiltonian systems.- Nonautonomous control theory. Linear regulator problem and the Kalman-Bucy filter.- Nonautonomous control theory. A general version of the Yakubovich Frequency Theorem.- Nonautonomous control theory. Linear-quadratic dissipative control processes.- Index.- References

Chain recurrence, growth rates and ergodic limits

Averages of functionals along trajectories are studied by evaluating the averages along chains. This yields results for the possible limits and, in particular, for ergodic limits. Applications to Lyapunov exponents and to concepts of rotation numbers of linear Hamiltonian flows and of general linear flows are given.

Histaminergic Neurotransmission as a Gateway for the Cognitive Effect of Oleoylethanolamide in Contextual Fear Conditioning.

Abstract Background: The integrity of the brain histaminergic system is necessary for the unfolding of homeostatic and cognitive processes through the recruitment of alternative circuits with distinct temporal patterns. We recently demonstrated that the fat-sensing lipid mediator oleoylethanolamide indirectly activates histaminergic neurons to exerts its hypophagic effects. The present experiments investigated whether histaminergic neurotransmission is necessary also for the modulation of emotional memory induced by oleoylethanolamide in a contextual fear conditioning paradigm. Methods: We examined the acute effect of i.p. administration of oleoylethanolamide immediately posttraining in the contextual fear conditioning test. Retention test was performed 72 hours after training. To test the participation of the brain histaminergic system in the cognitive effect of oleoylethanolamide, we depleted rats of brain histamine with an i.c.v. injection of alpha-fluoromethylhistidine (a suicide inhibitor of histidine decarboxylase) or bilateral intra-amygdala infusions of histamine H1 or H2 receptor antagonists. We also examined the effect of oleoylethanolamide on histamine release in the amygdala using in vivo microdialysis. Results: Posttraining administration of oleoylethanolamide enhanced freezing time at retention. This effect was blocked by both i.c.v. infusions of alpha-fluoromethylhistidine or by intra-amygdala infusions of either pyrilamine or zolantidine (H1 and H2 receptor antagonists, respectively). Microdialysis experiments showed that oleoylethanolamide increased histamine release from the amygdala of freely moving rats. Conclusions: Our results suggest that activation of the histaminergic system in the amygdala has a “permissive” role on the memory-enhancing effects of oleoylethanolamide. Hence, targeting the H1 and H2 receptors may modify the expression of emotional memory and reduce dysfunctional aversive memories as found in phobias and posttraumatic stress disorder.

The hypophagic factor oleoylethanolamide differentially increases c-fos expression in appetite regulating centres in the brain of wild type and histamine deficient mice.

Histaminergic neurons in the hypothalamic tuberomamillary nucleus (TMN) establish connections with virtually all brain areas. Recent evidence suggests that feeding-related motivation is correlated with the activation of a subpopulation of histamine neurons in the ventral TMN that project to hypothalamic and subcortical areas controlling feeding behaviour. Oleoylethanolamide (OEA) is a hypophagic lipid-amide released by the small intestine in response to daily fat intake that indirectly activates hypothalamic oxytocin-neurons in the paraventricular (PVN) and supraoptic (SON) nuclei. We recently showed that OEA requires the integrity of neuronal histamine to fully display its hypophagic effect. Here we aimed to investigate if differences exist in OEA-induced c-Fos expression in several brain regions of fasted, histidine decarboxylase (HDC)-KO mice that do not synthesize histamine, and wild type (WT) littermates. All the brain regions examined receive histaminergic innervation and are involved in different aspects of feeding behaviour. We found that OEA increased c-Fos expression in the SON, arcuate nucleus (ARC) and the amygdala of WT mice, but not HDC-KO mice, whereas neither genotype nor treatment differences were observed in the lateral and dorsomedial hypothalamus. Furthermore, oxytocin-immunostaining was markedly increased in the neurohypophysis of WT and not in HDC-KO mice. Of note, OEA increased c-Fos expression in the nucleus of solitary tract of both genotypes. Our findings suggest that the TMN serves as a relay station to elaborate peripheral signals that control homeostatic and adaptive behavioural responses.

Nonautonomous Linear Hamiltonian Systems

In this chapter, the framework of analysis of the book is described, and the many foundational facts required for this analysis are stated. The first two sections present fundamental notions and properties of topological dynamics and ergodic theory, as well as basic results concerning spaces of matrices, the Grassmannian and Lagrangian manifolds, and matrix-valued functions. In the third section, the different flows induced by a family of linear Hamiltonian systems varying over a compact metric space (which usually arises in a natural way from a nonautonomous system) are described. Special attention is paid to the skew-product flows induced on the Lagrange bundle and on the bundle whose fiber is given by the set of of symmetric matrices. The last section is devoted to a discussion of one of the most fundamental concepts for the forthcoming analysis: that of exponential dichotomy. The dynamical properties implied by its existence are carefully described, some aspects of the Sacker–Sell perturbation theory are explained, and a somewhat nonstandard analysis of the behavior of the Grassmannian flows in the presence of exponential dichotomy is presented.

Nutritional evaluation of geriatric patients with Alzheimer’s disease in Southern Brazil: case-control study

INTRODUCTION elderlys malnutrition is linked, among other factors, to chronic-degenerative diseases, requiring an improvement in the clinical evaluation of nutritional status of this population. Studies have tried to find out new tools to assess aged-people nutritional status. One of most used scales to investigate nutritional status on geriatric patients is the Mini Nutritional Assessment (MNA). OBJECTIVE the present study aims to evaluate nutritional status of Alzheimers disease (AD) patients, by comparison with a control group, via Mini Nutritional Assessment. METHODS a cross-sectional study, which includes 35 alzheimers old-people and 43 control old-people, was performed evaluating nutritional status with MNA. RESULTS total score of MNA in the alzheimer group shows that 71.42% were in malnutrition risk, 14.28% were malnourished and 14.25% presented normal nutritional status. In addition, in the control group 79.06% of patients (n = 34) were classified as having normal nutritional status and 20.93% (n = 9), as being at risk of malnutrition. CONCLUSION results reinforce the purpose that MNA can be used as a proper instrument to evaluate nutritional status in elderly, mainly in AD, because measuring risk and nutritional status of this population is indispensable.

Nonautonomous Control Theory: Linear Regulator Problem and the Kalman–Bucy Filter

Two goals will be achieved in this chapter. The first one concerns the feedback stabilization problem for a nonautonomous linear control system: the stabilizing feedback control is determined by formulating and solving an infinite horizon linear regulator problem. The minimizing pairs for the corresponding functional will be in a one-to-one correspondence with certain solutions of a nonautonomous linear Hamiltonian system constructed from the minimizing problem. Results of the previous chapters concerning the occurrence of exponential dichotomy and the properties of the rotation number will be applied, and only some basic elements of control theory, introduced for the most part in Chap. 3, will be required. The second goal is to give information concerning the Kalman–Bucy filter in a nonautonomous setting. Once more, the concepts of exponential dichotomy and rotation number for linear Hamiltonian systems are used to produce direct proofs of some basic results, including the asymptotic limit and the stability properties of the error covariance matrix, and the Hurwitz property at \(+\infty \) of the error propagation system.