Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

Spectroscopic study and local coordination of polyphosphate colloidal systems

The interaction between metaphosphate chains and the metal ions Ca2+ and Eu3+ has been studied in water by Eu3+ luminescence, infrared absorption, and P-31 NMR spectroscopy. Two main families of sites could be identified for the metal ions in the aqueous polyphosphate colloidal systems: (1) cagelike sites provided by the polyphosphate chain and (2) a family which arises following saturation of cagelike sites. Occupation of this second family leads to supramolecular interactions between polyphosphate chains and the consequent destabilization of the colloidal system. In the polyphosphate-Ca2+ system, this destabilization appears as a coacervation process. Equilibrium existing between colloidal species as a function of the compositions could be reasoned based on the spectroscopic measurements. The determination of coordination numbers and the correlation of the results with the observation of coacervates show that Eu3+ luminescence properties can be used to probe in a unique way the coacervation process.

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

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

The plant energy-dissipating mitochondrial systems: Depicting the genomic structure and the expression profiles of the gene families of uncoupling protein and alternative oxidase in monocots and dicots

The simultaneous existence of alternative oxidases and uncoupling proteins in plants has raised the question as to why plants need two energy-dissipating systems with apparently similar physiological functions. A probably complete plant uncoupling protein gene family is described and the expression profiles of this family compared with the multigene family of alternative oxidases in Arabidopsis thaliana and sugarcane (Saccharum sp.) employed as dicot and monocot models, respectively. In total, six uncoupling protein genes, AtPUMP1-6, were recognized within the Arabidopsis genome and five (SsPUMP1-5) in a sugarcane EST database. The recombinant AtPUMP5 protein displayed similar biochemical properties as AtPUMP1. Sugarcane possessed four Arabidopsis AOx1-type orthologues (SsAOx1a-1d); no sugarcane orthologue corresponding to Arabidopsis AOx2-type genes was identified. Phylogenetic and expression analyses suggested that AtAOx1d does not belong to the AOx1-type family but forms a new (AOx3-type) family. Tissue-enriched expression profiling revealed that uncoupling protein genes were expressed more ubiquitously than the alternative oxidase genes. Distinct expression patterns among gene family members were observed between monocots and dicots and during chilling stress. These findings suggest that the members of each energy-dissipating system are subject to different cell or tissue/organ transcriptional regulation. As a result, plants may respond more flexibly to adverse biotic and abiotic conditions, in which oxidative stress is involved. © The Author [2006]. Published by Oxford University Press [on behalf of the Society for Experimental Biology]. All rights reserved.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

Tjon Lines and Scaling Limit in Four-Body Systems

The fixed-slope correlation between tetramer and trimer binding energies, observed by Tjon in the context of nuclear physics, is mainly a manifestation of the dominance of the two-nucleon force in the nuclear potential, which makes the four-body scale on the order of the three-body one. In a more general four-boson case, the correlation between tetramer and trimer binding energies has a non-fixed slope, which expresses the dependence on the new scale. The associated scaling function generates a family of Tjon lines. This conclusion relies on a recent study with weakly-bound four identical bosons, within a renormalized zero-range Faddeev-Yakubovsky formalism. © 2012 Springer-Verlag.

Exploring the multifactorial nature of autism through computational systems biology: Calcium and the Rho GTPase RAC1 under the spotlight

Autism is a neurodevelopmental disorder characterized by impaired social interaction and communication accompanied with repetitive behavioral patterns and unusual stereotyped interests. Autism is considered a highly heterogeneous disorder with diverse putative causes and associated factors giving rise to variable ranges of symptomatology. Incidence seems to be increasing with time, while the underlying pathophysiological mechanisms remain virtually uncharacterized (or unknown). By systematic review of the literature and a systems biology approach, our aims were to examine the multifactorial nature of autism with its broad range of severity, to ascertain the predominant biological processes, cellular components, and molecular functions integral to the disorder, and finally, to elucidate the most central contributions (genetic and/or environmental) in silico. With this goal, we developed an integrative network model for gene-environment interactions (GENVI model) where calcium (Ca2+) was shown to be its most relevant node. Moreover, considering the present data from our systems biology approach together with the results from the differential gene expression analysis of cerebellar samples from autistic patients, we believe that RAC1, in particular, and the RHO family of GTPases, in general, could play a critical role in the neuropathological events associated with autism. © 2013 Springer Science+Business Media New York.

Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings

We consider a family of two-dimensional nonlinear area-preserving mappings that generalize the Chirikov standard map and model a variety of periodically forced systems. The action variable diffuses in increments whose phase is controlled by a negative power of the action and hence effectively uncorrelated for small actions, leading to a chaotic sea in phase space. For larger values of the action the phase space is mixed and contains a family of elliptic islands centered on periodic orbits and invariant Kolmogorov-Arnold-Moser (KAM) curves. The transport of particles along the phase space is considered by starting an ensemble of particles with a very low action and letting them evolve in the phase until they reach a certain height h. For chaotic orbits below the periodic islands, the survival probability for the particles to reach h is characterized by an exponential function, well modeled by the solution of the diffusion equation. On the other hand, when h reaches the position of periodic islands, the diffusion slows markedly. We show that the diffusion coefficient is scaling invariant with respect to the control parameter of the mapping when h reaches the position of the lowest KAM island. © 2013 American Physical Society.

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Parental Ethnotheories of Child Development: Looking Beyond Independence and Individualism in American Belief Systems

Over the past several decades, the topic of child development in a cultural context has received a great deal of theoretical and empirical investigation. Investigators from the fields of indigenous and cultural psychology have argued that childhood is socially and historically constructed, rather than a universal process with a standard sequence of developmental stages or descriptions. As a result, many psychologists have become doubtful that any stage theory of cognitive or socialemotional development can be found to be valid for all times and places. In placing more theoretical emphasis on contextual processes, they define culture as a complex system of common symbolic action patterns (or scripts) built up through everyday human social interaction by means of which individuals create common meanings and in terms of which they organize experience. Researchers understand culture to be organized and coherent, but not homogenous or static, and realize that the complex dynamic system of culture constantly undergoes transformation as participants (adults and children) negotiate and re-negotiate meanings through social interaction. These negotiations and transactions give rise to unceasing heterogeneity and variability in how different individuals and groups of individuals interpret values and meanings. However, while many psychologists—both inside and outside the fields of indigenous and cultural psychology–are now willing to give up the idea of a universal path of child development and a universal story of parenting, they have not necessarily foreclosed on the possibility of discovering and describing some universal processes that underlie socialization and development-in-context. The roots of such universalities would lie in the biological aspects of child development, in the evolutionary processes of adaptation, and in the unique symbolic and problem-solving capacities of the human organism as a culture-bearing species. For instance, according to functionalist psychological anthropologists, shared (cultural) processes surround the developing child and promote in the long view the survival of families and groups if they are to demonstrate continuity in the face of ecological change and resource competition, (e.g. Edwards & Whiting, 2004; Gallimore, Goldenberg, & Weisner, 1993; LeVine, Dixon, LeVine, Richman, Leiderman, Keefer, & Brazelton, 1994; LeVine, Miller, & West, 1988; Weisner, 1996, 2002; Whiting & Edwards, 1988; Whiting & Whiting, 1980). As LeVine and colleagues (1994) state: A population tends to share an environment, symbol systems for encoding it, and organizations and codes of conduct for adapting to it (emphasis added). It is through the enactment of these population-specific codes of conduct in locally organized practices that human adaptation occurs. Human adaptation, in other words, is largely attributable to the operation of specific social organizations (e.g. families, communities, empires) following culturally prescribed scripts (normative models) in subsistence, reproduction, and other domains [communication and social regulation]. (p. 12) It follows, then, that in seeking to understand child development in a cultural context, psychologists need to support collaborative and interdisciplinary developmental science that crosses international borders. Such research can advance cross-cultural psychology, cultural psychology, and indigenous psychology, understood as three sub-disciplines composed of scientists who frequently communicate and debate with one another and mutually inform one another’s research programs. For example, to turn to parental belief systems, the particular topic of this chapter, it is clear that collaborative international studies are needed to support the goal of crosscultural psychologists for findings that go beyond simply describing cultural differences in parental beliefs. Comparative researchers need to shed light on whether parental beliefs are (or are not) systematically related to differences in child outcomes; and they need meta-analyses and reviews to explore between- and within-culture variations in parental beliefs, with a focus on issues of social change (Saraswathi, 2000). Likewise, collaborative research programs can foster the goals of indigenous psychology and cultural psychology and lay out valid descriptions of individual development in their particular cultural contexts and the processes, principles, and critical concepts needed for defining, analyzing, and predicting outcomes of child development-in-context. The project described in this chapter is based on an approach that integrates elements of comparative methodology to serve the aim of describing particular scenarios of child development in unique contexts. The research team of cultural insiders and outsiders allows for a look at American belief systems based on a dialogue of multiple perspectives.

Optimal Code Set Selection and Security Issues in Spectral Phase-Encoded Time Spreading (SPECTS) OCDMA Systems

In this paper, we perform a thorough analysis of a spectral phase-encoded time spreading optical code division multiple access (SPECTS-OCDMA) system based on Walsh-Hadamard (W-H) codes aiming not only at finding optimal code-set selections but also at assessing its loss of security due to crosstalk. We prove that an inadequate choice of codes can make the crosstalk between active users to become large enough so as to cause the data from the user of interest to be detected by other user. The proposed algorithm for code optimization targets code sets that produce minimum bit error rate (BER) among all codes for a specific number of simultaneous users. This methodology allows us to find optimal code sets for any OCDMA system, regardless the code family used and the number of active users. This procedure is crucial for circumventing the unexpected lack of security due to crosstalk. We also show that a SPECTS-OCDMA system based on W-H 32(64) fundamentally limits the number of simultaneous users to 4(8) with no security violation due to crosstalk. More importantly, we prove that only a small fraction of the available code sets is actually immune to crosstalk with acceptable BER (<10(-9)) i.e., approximately 0.5% for W-H 32 with four simultaneous users, and about 1 x 10(-4)% for W-H 64 with eight simultaneous users.

TYPE-ZERO SADDLE-NODE BIFURCATIONS AND STABILITY REGION ESTIMATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS

A complete characterization of the stability boundary of a class of nonlinear dynamical systems that admit energy functions is developed in this paper. This characterization generalizes the existing results by allowing the type-zero saddle-node nonhyperbolic equilibrium points on the stability boundary. Conceptual algorithms to obtain optimal estimates of the stability region (basin of attraction) in the form of level sets of a given family of energy functions are derived. The behavior of the stability region and the corresponding estimates are investigated for parameter variation in the neighborhood of a type-zero saddle-node bifurcation value.

McMaster Model of Family Functioning: adattamento alla realtà italiana, implicazioni cliniche e di ricerca

Il presente lavoro comincia con una descrizione dettagliata del “McMaster Model of Family Functionig” (MMFF), modello che al suo interno integra una teoria multidimensionale sul funzionamento familiare, diversi strumenti di auto ed etero valutazione e chiare indicazioni terapeutiche racchiuse all’interno della “Problem Centered System Therapy of the Family” (PCSTF). Grazie alla sua completezza il Modello fornisce ai clinici metodi coerenti, pratici ed empiricamente validi per valutare e trattare le famiglie, essi inoltre, sono stati formulati in modo da essere adattabili a differenti setting clinici e di ricerca, applicabili ad un’ampia gamma di problematiche e verificabili empiricamente. Obiettivo finale della presente ricerca è stato quello di porre le basi per l’esportazione del MMFF in Italia e poter quindi procedere alla sua applicazione in ambito clinico. La ricerca è cominciata alla Brown University con la traduzione dall’inglese all’italiano del Family Assessment Device (FAD), uno degli strumenti di autovalutazione compresi nel MMFF, ed è in seguito continuata con la validazione del suddetto strumento in un campione di 317 soggetti appartenenti alla popolazione generale italiana. Il FAD si è dimostrato uno strumento valido ed affidabile, in grado quindi di fornire valutazioni stabili e coerenti anche nella sua versione italiana. Il passo successivo è stato caratterizzato dalla somministrazione di FAD, Symptom Questionnaire (SQ) e delle Psychological Well-Being scales (PWB) a 289 soggetti reclutati nella popolazione generale. In accordo con il modello bipsicosociale che vede l’ambiente familiare come il più immediato gruppo di influenza psicosociale dello stato di benessere o malessere dell’individuo, i nostri dati confermano una stretta relazione tra scarso funzionamento familiare, spesso espresso attraverso difficoltà di comunicazione, di problem solving e scarso coinvolgimento affettivo e distress psicologico esperito con sintomi depressivi, ansiogeni ed ostilità. I nostri dati sottoliano inoltre come un funzionamento familiare positivo sia altamente correlato ad elevati livelli di benessere psicologico. Obiettivo della parte finale del lavoro ed anche il più importante, è stato quello di esplorare l’efficacia della Problem Centered Systems Therapy of the Family nella gestione della perdita di efficacia degli antidepressivi nel trattamento della depressione ricorrente. 20 soggetti con diagnosi di depressione maggiore ricorrente secondo il DSM-IV sono stati randomizzati a due diverse condizioni di trattamento: 1) aumento del dosaggio dell’antidepressivo e clinical management, oppure 2) mantenimento dello stesso dosaggio di antidepressivo e PCSTF. I dati di questo studio mettono in evidenza come, nel breve termine, PCSTF e farmacoterapia sono ugualmente efficaci nel ridurre la sintomatologia depressiva. Diversamente, ad un follow-up di 12 mesi, la PCSTF si è dimostrata altamente superiore all’aumento del farmaco ner prevenire le ricadute. Nel gruppo sottoposto all’aumento del farmaco infatti ben 6 soggetti su 7 ricadono entro l’anno. Nel gruppo assegnato a terapia familiare invece solo 1 soggetto su 7 ricade. Questi risultati sono in linea con i dati della letteratura che sottolineano l’elevata probabilità di una seconda ricaduta dopo l’aumento dell’antidepressivo all’interno di una farmacoterapia di mantenimento e suggeriscono l’efficacia dell’utilizzo di strategie psicoterapiche nella prevenzione della ricaduta in pazienti con depressione ricorrente.

Photo- and redox-active supramolecular systems containing metal complexes

The aim of this Ph.D. project has been the photophysical and photochemical characterization of new photo- and redox-active supramolecular systems. In particular we studied two different classes of compounds: metal complexes and dendrimers. Two different families of bis-cyclometalated neutral Ir(III) complexes are presented and their photophysical properties are discussed. The first family of complexes contains two 2-phenylpyridyl (ppy) or 2-(4,6-difluorophenyl)pyridyl (F2ppy) cyclometalated ligands and an ancillary ligand constituted by a phenol-oxazoline (phox), which can be substituted in the third position with a fluorine group (Fphox). In the second part of this study, we present another family of bis-cyclometalated Ir(III) complexes in which the ancillary ligand could be a chiral or an achiral bis-oxazoline (box). We report on their structural, electrochemical, photophysical, and photochemical properties. Complexes containing phox and Fphox ancillary ligands show blue luminescence with very high quantum yield, while complexes with box ligands do not show particularly interesting photophysical properties. Surprisingly these complexes give an unexpected photoreaction when irradiated with UV light in presence of dioxygen. This photoreaction originates a stable, strong blue emitting and particularly interesting photoproduct. Three successive generations of a family of polyethyleneglycol (PEG)-coated Pd(II) tetrabenzoporphyrin (PdTBP)-based dendritic nanoprobes are presented, and their ability to sensitize singlet oxygen and inflict cellular photodamage are discussed. It was found that the size of the dendrimer has practically no effect on the singlet oxygen sensitization efficiency, that approximate the unity, in spite of the strong attenuation of the triplet quenching rate with an increase in the dendrimer generation. Nevertheless, when compared against a commonly used singlet oxygen sensitizer, as Photofrin, the phosphorescent probes were found to be non-phototoxic. The lack of phototoxicity is presumably due to the inability of PEGylated probes to associate with cell surfaces and/or penetrate cellular membranes. The results suggest that protected phosphorescent probes can be safely used for oxygen measurements in biological systems in vivo. A new family of two photoswitchable (G0(Azo) and G1(Azo)) dendrimers with an azobenzene core, two cyclam units as coordination sites for metal ions, and luminescent naphthalene units at the periphery have been characterized and their coordination abilities have been studied. Because of their proximity, the various functional groups of the dendrimer may interact, so that the properties of the dendrimers are different from those exhibited by the separated functional units. Both the naphthalene fluorescence and the azobenzene photoisomerization can be observed in the dendrimer, but it has been shown that (i) the fluorescent excited state of the naphthalene units is substantially quenched by excimer and exciplex formation and by energy transfer to the azobenzene units, and (ii) in the latter case the fluorescence quenching is accompanied by the photosensitized isomerization of the trans → cis, and, with higher efficiency, the cis → trans reaction. Complexation of these dendrimers, both trans and cis isomers, with Zn(II) ions shows that complexes of 1:1 and 2:1 metal per dendrimer stoichiometry are formed showing different photophysical and photochemical properties compared to the corresponding free ligands. Practically unitary efficiency of the sensitized isomerization of trans → cis and cis → trans reaction is observed, as well as a slight increase in the naphthalene monomer emission. These results are consistent with the coordination of the cyclam amine units with Zn(II), which prevents exciplex formation. No indication of a concomitant coordination of both cyclam to a single metal ion has been obtained both for trans and cis isomer.