An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Ligand-Induced structural changes in TEM‑1 probed by molecular dynamics and relative binding free energy calculations

The TEM family of enzymes has had a crucial impact on the pharmaceutical industry due to their important role in antibiotic resistance. Even with the latest technologies in structural biology and genomics, no 3D structure of a TEM- 1/antibiotic complex is known previous to acylation. Therefore, the comprehension of their capability in acylate antibiotics is based on the protein macromolecular structure uncomplexed. In this work, molecular docking, molecular dynamic simulations, and relative free energy calculations were applied in order to get a comprehensive and thorough analysis of TEM-1/ampicillin and TEM-1/amoxicillin complexes. We described the complexes and analyzed the effect of ligand binding on the overall structure. We clearly demonstrate that the key residues involved in the stability of the ligand (hot-spots) vary with the nature of the ligand. Structural effects such as (i) the distances between interfacial residues (Ser70−Oγ and Lys73−Nζ, Lys73−Nζ and Ser130−Oγ, and Ser70−Oγ−Ser130−Oγ), (ii) side chain rotamer variation (Tyr105 and Glu240), and (iii) the presence of conserved waters can be also influenced by ligand binding. This study supports the hypothesis that TEM-1 suffers structural modifications upon ligand binding.

Big Bang bifurcations and allee effect in Blumberg’s dynamics

This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.

Spatial and temporal evolution of family-farming land use in the Tapajós region of the Brazilian Amazon

Pressures on the Brazilian Amazon forest have been accentuated by agricultural activities practiced by families encouraged to settle in this region in the 1970s by the colonization program of the government. The aims of this study were to analyze the temporal and spatial evolution of land cover and land use (LCLU) in the lower Tapajós region, in the state of Pará. We contrast 11 watersheds that are generally representative of the colonization dynamics in the region. For this purpose, Landsat satellite images from three different years, 1986, 2001, and 2009, were analyzed with Geographic Information Systems. Individual images were subject to an unsupervised classification using the Maximum Likelihood Classification algorithm available on GRASS. The classes retained for the representation of LCLU in this study were: (1) slightly altered old-growth forest, (2) succession forest, (3) crop land and pasture, and (4) bare soil. The analysis and observation of general trends in eleven watersheds shows that LCLU is changing very rapidly. The average deforestation of old-growth forest in all the watersheds was estimated at more than 30% for the period of 1986 to 2009. The local-scale analysis of watersheds reveals the complexity of LCLU, notably in relation to large changes in the temporal and spatial evolution of watersheds. Proximity to the sprawling city of Itaituba is related to the highest rate of deforestation in two watersheds. The opening of roads such as the Transamazonian highway is associated to the second highest rate of deforestation in three watersheds.

Population dynamics of the pea crab Austinixa aidae (Brachyura, Pinnotheridae): a symbiotic of the ghost shrimp Callichirus major (Thalassinidea, Callianassidae) from the southwestern Atlantic

The Pinnotheridae family is one of the most diverse and complex groups of brachyuran crabs, many of them symbionts of a wide variety of invertebrates. The present study describes the population dynamics of the pea crab Austinixa aidae (Righi, 1967), a symbiont associated with the burrows of the ghost shrimp Callichirus major (Say, 1818). Individuals (n = 588) were collected bimonthly from May, 2005 to September, 2006 along a sandy beach in the southwestern Atlantic, state of São Paulo, Brazil. Our data indicated that the population demography of A. aidae was characterized by a bimodal size-frequency distribution (between 2.0 and 4.0 mm and between 8.0 and 9.0 mm CW) that remained similar throughout the study period. Sex ratio does not differ significantly from 1:1 (p > 0.05), which confirms the pattern observed in other symbiontic pinnotherids. Density values (1.72 ± 1.34 ind. • ap.-1) are in agreement with those found for other species of the genus. The mean symbiosis incidence (75.6%) was one of the highest among species of the Pinnotheridae family, but it was the lowest among the three studied species of the genus. Recruitment pattern was annual, beginning in May and peaking in July, in both years, after the peak of ovigerous females in the population (from March to May). Our findings describe ecological and biological aspects of A. aidae similar to those of other species of this genus, even from different geographic localities.

The dynamics of interfaces: Seven authors in search of encounters across levels of description of an event involving a mother, father, and baby

The interfaces between the intrapsychic, interactional, and intergenerational domains are a new frontier. As a pilot, we exposed ourselves to a complex but controllable situation as viewed by people whose main interest is in one of the three interfaces; we also fully integrated the subjects in the team, to learn about their subjective perspectives and to provide them with an enriching experience. We started with a brief "triadification" sequence (i.e., moving from a "two plus one" to a "three together" family organization). Considering this sequence as representing at a micro level many larger family transitions, we proceeded with a microanalytic interview, a psychodynamic investigation, and a family interview. As expected, larger patterns of correspondences are emerging. Central questions under debate are: What are the most appropriate units at each level of description and what are their articulations between these levels? What is the status of "triadification"? Les interfaces entre les domaines intrapsychiques, interactionnels et intergénérationnels représentent une nouvelle frontiére. A titre exploratoire, nous nous sommes exposés à une situation complexe mais contrǒlable ainsi que le voient ceux dont I'intérět principal se porte sur l'une de ces trois interfaces. Nous avons aussi entièrement intégré les sujets dans l'équipe, de facon à comprendre leur perspective subjective et à leur offrir une expérience enrichissante. Nous avons commencé avec une brève séquence de "triadification," c'est-à-dire passer d'une organisation familiale "deux plus un" à Ltne organisation familiale "trois (add sentenc)ensemble." Considérant cette séquence comme representative à un niveau microscopique de transitions familiales bien plus larges, nous avons procedé à l'entretien microanalytique, à une enquěte psychodynamique et à un entretien familial. Comme prévu, de grands patterns de correspondances émergent. Les questions essentielles sur lesquelles portent le débat sont: quelles les unités les plus appropiées à chaque niveau de description et quelles sont les articulations entre ces niveaux? Quel est le statut de la "triadification"?

FABP4 Dynamics in Obesity: Discrepancies in Adipose Tissue and Liver Expression Regarding Circulating Plasma Levels.

BACKGROUND FABP4 is predominantly expressed in adipose tissue, and its circulating levels are linked with obesity and a poor atherogenic profile. OBJECTIVE In patients with a wide BMI range, we analyze FABP4 expression in adipose and hepatic tissues in the settings of obesity and insulin resistance. Associations between FABP4 expression in adipose tissue and the FABP4 plasma level as well as the main adipogenic and lipolytic genes expressed in adipose tissue were also analyzed. METHODS The expression of several lipogenic, lipolytic, PPAR family and FABP family genes was analyzed by real time PCR. FABP4 protein expression in total adipose tissues and its fractions were determined by western blot. RESULTS In obesity FABP4 expression was down-regulated (at both mRNA and protein levels), with its levels mainly predicted by ATGL and inversely by the HOMA-IR index. The BMI appeared as the only determinant of the FABP4 variation in both adipose tissue depots. FABP4 plasma levels showed a significant progressive increase according to BMI but no association was detected between FABP4 circulating levels and SAT or VAT FABP4 gene expression. The gene expression of FABP1, FABP4 and FABP5 in hepatic tissue was significantly higher in tissue from the obese IR patients compared to the non-IR group. CONCLUSION The inverse pattern in FABP4 expression between adipose and hepatic tissue observed in morbid obese patients, regarding the IR context, suggests that both tissues may act in a balanced manner. These differences may help us to understand the discrepancies between circulating plasma levels and adipose tissue expression in obesity.

Integrating receptor interactions and dynamics and Interference with endocrine disruptors in the mechanisms of action of PPAR nuclear receptors

Abstract Peroxisome Proliferator-Activated Receptors (PPARs) form a family of three nuclear receptors regulating important cellular and metabolic functions. PPARs control gene expression by directly binding to target promoters as heterodimers with the Retinoid X Receptor (RXR), and their transcriptional activity is enhanced upon activation by natural or pharmacological ligands. The binding of PPAR/RXR heterodimers on target promoters allows the anchoring of a series of coactivators and corepressors involved in promoter remodeling and the recruitment of the transcription machinery. The transcriptional output finally depends on a complex interplay between (i) the respective expression levels of PPARs, RXRs and of other nuclear receptors competing for DNA binding and RXR recruitment, (ii) the availability and the nature of PPAR and RXR ligands, (iii) the expression levels and the nature of the different coactivators and corepressors and (iv) the sequence and the epigenetic status of the promoter. Understanding how all these factors and signals integrate and fine-tune transcription remains a challenge but is necessary to understand the specificity of the physiological functions regulated by PPARs. The work presented herein focuses on the molecular mechanisms of PPAR action and aims at understanding how the interactions and mobility of the receptor modulate transcription in the physiological context of a living cell: Such observations in vivo rely on the use of engineered fluorescent protein chimeras and require the development and the application of complementary imaging techniques such as Fluorescence Recovery After Photobleaching (FRAP), Fluorescence Resonance Energy Transfer (FRET) and Fluorescence Correlation Spectroscopy (FCS). Using such techniques, PPARs are shown to reside solely in the nucleus where they are constitutively associated with RXR but transcriptional activation by ligand binding -does not promote the formation of sub-nuclear structures as observed with other nuclear receptors. In addition, the engagement of unliganded PPARs in large complexes of cofactors in living cells provides a molecular basis for their ligand-independent activity. Ligand binding reduces receptor diffusion by promoting the recruitment of coactivators which further enlarge the size of PPAR complexes to acquire full transcriptional competence. Using these molecular approaches, we deciphered the molecular mechanisms through which phthalates, a class of pollutants from the plastic industry, interfere with PPARγ signaling. Mono-ethyl-hexyl-phthalate (MEHP) binding induces the recruitment of a specific subset of cofactors and translates into the expression of a specific subset of target genes, the transcriptional output being strongly conditioned by the differentiation status of the cell. This selective PPARγ modulation induces limited adipogenic effects in cellular models while exposure to phthalates in animal models leads to protective effects on glucose tolerance and diet-induced obesity. These results demonstrate that phthalates influence lipid and carbohydrate metabolism through complex mechanisms which most likely involve PPARγ but also probably PPARα and PPARß, Altogether, the molecular and physiological demonstration of the interference of pollutants with PPAR action outlines an important role of chemical exposure in metabolic regulations. Résumé Les PPARs (Peroxisome Proliferator-Activated Receptors) forment une famille de récepteurs nucléaires qui régulent des fonctions cellulaires et métaboliques importantes. Les PPARs contrôlent l'expression des gènes en se liant directement à leurs promoteurs sous forme d'hétérodimères avec les récepteurs RXR (Retinoid X Receptor), et leur activité transcriptionnelle est stimulée par la liaison de ligands naturels ou pharmacologiques. L'association des hétérodimères PPAR/RXR avec les promoteurs des gènes cibles permet le recrutement de coactivateurs et de corépresseurs qui vont permettre le remodelage de la chromatine et le recrutement de la machinerie transcriptionnelle. Les actions transcriptionnelles du récepteur dépendent toutefois d'interactions complexes qui sont régulées par (i) le niveau d'expression des PPARs, des RXRs et d'autres récepteurs nucléaires entrant en compétition pour la liaison à l'ADN et l'association avec RXR, (ii) la disponibilité et la nature de ligands de PPAR et de RXR, (iii) les niveaux d'expression et la nature des différents coactivateurs et corépresseurs et (iv) la séquence et le marquage épigénétique des promoteurs. La compréhension des mécanismes qui permettent d'intégrer ces aspects pour assurer une régulation fine de l'activité transcriptionnelle est un défi qu'il est nécessaire de relever pour comprendre la spécificité des fonctions physiologiques régulées par les PPARs. Ce travail concerne l'étude des mécanismes d'action moléculaire des PPARs et vise à mieux comprendre comment les interactions du récepteur avec d'autres protéines ainsi que la mobilité de ce dernier régulent son activité transcriptionnelle dans le contexte physiologique des cellules vivantes. De telles observations reposent sur l'emploi de protéines fusionnées à des protéines fluorescentes ainsi que sur le développement et l'utilisation de techniques d'imagerie complémentaires telles que le FRAP (Fluorescence Recovery After Photobleaching), le FRET (Fluorescence Resonance Energy Transfer) ou la FCS (Fluorescence Corrélation Spectroscopy). En appliquant ces méthodes, nous avons pu montrer que les PPARs résident toujours dans le noyau où ils sont associés de manière constitutive à RXR, mais que l'ajout de ligand n'induit pas la formation de structures sub-nucléaires comme cela a pu être décrit pour d'autres récepteurs nucléaires. De plus, les PPARs sont engagés dans de larges complexes protéiques de cofacteurs en absence de ligand, ce qui procure une explication moléculaire à leur activité ligand-indépendante. La liaison du ligand réduit la vitesse de diffusion du récepteur en induisant le recrutement de coactivateurs qui augmente encore plus la taille des complexes afin d'acquérir un potentiel d'activation maximal. En utilisant ces approches moléculaires, nous avons pu caractériser les mécanismes permettant aux phtalates, une classe de polluants provenant de l'industrie plastique, d'interférer avec PPARγ. La liaison du mono-ethyl-hexyl-phtalate (NERF) à PPARγ induit un recrutement sélectif de cofacteurs, se traduisant par l'induction spécifique d'un sous-ensemble de gènes qui varie en fonction du niveau de différentiation cellulaire. La modulation sélective de PPARγ par le MEHP provoque une adipogenèse modérée dans des modèles cellulaires alors que l'exposition de modèles animaux aux phtalates induit des effets bénéfiques sur la tolérance au glucose et sur le développement de l'obésité. Toutefois, les phtalates ont une action complexe sur le métabolisme glucido-lipidique en faisant intervenir PPARγ mais aussi probablement PPARα et PPARß. Cette démonstration moléculaire et physiologique de l'interférence des polluants avec les récepteurs nucléaires PPAR souligne un rôle important de l'exposition à de tels composés dans les régulations métaboliques.

Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Study of the SRR1-gene family in Arabidopsis, yeast and mouse cells

Abstract: Light is a very important environmental cue for plants. In addition to the energy for photosynthesis, it also provides information that is essential for many processes including seed germination, seedlings development, neighbours detection or transition from the vegetative to the reproductive state. Plants evolved different photoreceptors, among which the phytochromes (PHY), which are red/far-red photoreceptors. This family is composed of 5 members in Arabidopsis thaliana, among which phyB plays the major role for detection of red light. Phytochromes are also able to reset the phase of the circadian clock, which is composed of a complicated network of genes able to produce rhythms of about 24 hours, even in constant conditions. SRR1 (Sensitivity to Red light Reduced) is a gene that was shown to act in the phyB pathway as well as in the circadian clock. It was proposed to play a role in the maintenance of rhythms of the core oscillator because of the circadian phenotype of the srr1 mutant in constant light and in constant darkness. In the present study, we present data confirming the role of SRR1 in the core oscillator. Moreover, we show that SRR1 levels are not limiting for circadian rhythms nor for light perception. We show that the protein levels, the sub-cellular localisation or the complex in which SRR1 is found are not regulated in a circadian manner. Orthologues of SRR1 exist in numerous eukaryotes, forming a new gene family. None of the members of this family have been described. Here, we present data suggesting that the mouse orthologue of SRR1 may not be required for oscillation of the circadian clock of mouse cells in culture. The yeast gene (called BER1 for Benomyl REsistant) was studied to understand the biochemical function of this gene family. Based on synthetic genetic screens, a role of Ber1 was inferred in microtubules dynamics, N-terminal acetylation of protein and proteasome biogenesis. The effect of Ber1 on microtubules was confirmed by the observation that the ber1Δ mutant is more resistant to microtubule-depolymerising drugs and microscopic examination of microtubules in ber 1 Δ mutants. Complementation assays of ber1 Δ mutants and srrl mutants failed to reveal any obvious functional conservation of the mouse, yeast and Arabidopsis orthologues. In conclusion, the SRR1 family might encode genes that either plays different roles in different organisms, or have similar biochemical function but are involved in diverse pathway. Résumé: La lumière est un des facteurs abiotiques les plus important pour les plantes. En plus de l'énergie fournie pour la photosynthèse, elle fourni également de l'information nécessaire pour différents processus comme la germination, le développement des jeunes plantules, la détection de plantes avoisinantes ou encore la transition entre le développement végétatif et reproductif. Plusieurs types de photorécepteurs sont apparus chez les plantes au cours de l'évolution, notamment les phytochromes (PHI, qui perçoivent la lumière rouge et rouge lointaine. Cette famille est composé de 5 membres chez Arabidopsis thaliana, parmi lesquels phyB est le principal récepteur pour la lumière rouge. Les phytochromes sont aussi utiles pour la synchronisation entre les cycles jour-nuit dus à la rotation de la terre et l'horloge circadienne. Cette dernière est composée d'un réseau compliqué qui permet la production de rythmes capables de perdurer même en conditions constantes. SRRI (Sensitivity to Red light Reduced) est un gène qui agit dans la voie de signalisation de phyB ainsi que dans l'horloge circadienne. Il a été proposé que SRRI joue un rôle dans la maintenance des rythmes de l'oscillateur principal à cause des phénotypes circadiens du mutant srrl observés en lumière et en obscurité continue. Dans ce travail, nous présentons des données confirmant le rôle de SRR1 dans l'oscillateur principal. Nous montrons que les niveaux d'expression de SRRI ne sont pas limitants pour les rythmes circadiens ou la perception de la lumière. Enfin, nous montrons que le niveau d'accumulation de la protéine, sa localisation subcellulaire ou encore la taille du complexe dans lequel SRRl est trouvé ne sont pas régulés de façon circadiennes. Des orthologues de SRRI existent chez de nombreux eucaryotes, formant une nouvelle famille de gènes. Aucun des membres de cette famille n'a été étudié avant ce travail. Nous présentons des données suggérant que l'orthologue de la souris n'est peut-être pas requis pour les oscillations de l'horloge circadienne de cellules de souris en culture. Le gène de la levure (appelé SERI pour Benomyl REsistant) a été étudié afin de mieux comprendre la fonction biochimique de cette famille de gène. Une analyse par crible synthétique léthal a révélé un rôle de Ber1 dans la dynamique des microtubules, l'acétylation des protéines en N-terminal et la biogenèse du protéasome. L'effet de Ber1 sur les microtubules a été confirmé par l'observation du mutant ber1 en présence de drogue capable de dépolymériser les microtubules. Celui-ci est plus résistant à ces drogues que le type sauvage. Des expériences de complémentation n'ont pas montré de conservation de la fonction entre SRRI et ses homologues de souris ou de levure. En conclusion, la famille SRRI code pour des gènes qui pourraient avoir soit des rôles différents selon les organismes, soit la même fonction biochimique mais qui serait utile pour des voies de signalisation différentes.

Big brother is watching you: eavesdropping to resolve family conflicts

Adult animals can eavesdrop on behavioral interactions between potential opponents to assess their competitive ability and motivation to contest resources without interacting directly with them. Surprisingly, eavesdropping is not yet considered as an important factor used to resolve conflicts between family members. In this study, we show that nestling barn owls (Tyto alba) competing for food eavesdrop on nestmates' vocal interactions to assess the dominance status and food needs of opponents. During a first training playback session, we broadcasted to singleton bystander nestlings a simulated vocal interaction between 2 prerecorded individuals, 1 relatively old (i.e., senior) and 1 younger nestling (i.e., junior). One playback individual, the "responder," called systematically just after the "initiator" playback individual, hence displaying a higher hunger level. To test whether nestlings have eavesdropped on this interaction, we broadcasted the same prerecorded individuals separately in a subsequent playback test session. Nestlings vocalized more rapidly after former initiators' than responders' calls and they produced more calls when the broadcasted individual was formerly a junior initiator. They chiefly challenged vocally juniors and initiators against whom the likelihood of winning a vocal contest is higher. Owlets, therefore, identified the age hierarchy between 2 competitors based on their vocalizations. They also memorized the dynamics of competitors' previous vocal interactions, and used this information to optimally adjust signaling level once interacting with only 1 of the competitor. We conclude that siblings eavesdrop on one another to resolve conflicts over parental resources.

Identification of potential small molecule binding pockets on Rho family GTPases

Rho GTPases are conformational switches that control a wide variety of signaling pathways critical for eukaryotic cell development and proliferation. They represent attractive targets for drug design as their aberrant function and deregulated activity is associated with many human diseases including cancer. Extensive high-resolution structures (.100) and recent mutagenesis studies have laid the foundation for the design of new structure-based chemotherapeutic strategies. Although the inhibition of Rho signaling with drug-like compounds is an active area of current research, very little attention has been devoted to directly inhibiting Rho by targeting potential allosteric non-nucleotide binding sites. By avoiding the nucleotide binding site, compounds may minimize the potential for undesirable off-target interactions with other ubiquitous GTP and ATP binding proteins. Here we describe the application of molecular dynamics simulations, principal component analysis, sequence conservation analysis, and ensemble small-molecule fragment mapping to provide an extensive mapping of potential small-molecule binding pockets on Rho family members. Characterized sites include novel pockets in the vicinity of the conformationaly responsive switch regions as well as distal sites that appear to be related to the conformations of the nucleotide binding region. Furthermore the use of accelerated molecular dynamics simulation, an advanced sampling method that extends the accessible time-scale of conventional simulations, is found to enhance the characterization of novel binding sites when conformational changes are important for the protein mechanism.

Understanding triadic and family group interactions during infancy and toddlerhood.

This paper outlines recent conceptual and methodological developments in the assessment of triadic and family group process during infancy and toddlerhood. Foundations of the emerging family group process are identified, and conditions specific to the assessment of the family during the early phases of family formation are summarized. Both microanalytic and global approaches to evaluating mother-father-child interactions are discussed. We highlight both similarities and differences in the strategies and methods employed by several different investigators who have been studying the group dynamics of families with infant and toddler children, and underscore several important family patterns and emerging themes that appear to be cutting across these different methods and measurement strategies. Preliminary evidence for the validity and clinical significance of family-level assessments is summarized, and directions currently being pursued by researchers engaged in studies of the family triad are outlined. We close by identifying several conceptual and clinical issues that remain to be addressed by subsequent work.

Mothers' and fathers' views of the interdependence of their relationships with their infant: a systems perspective on early family relationships.

This study examined the interrelatedness of mother-infant and father-infant relationships as they develop over the first 4 months postpartum as well as the dynamics used by the couple to balance these relationships. First-time mother-father couples (n = 18) were interviewed separately at 1, 6, and 16 weeks postpartum using the Parent-Infant Relationship Interview. The data were analyzed using in-depth qualitative strategies. The parents' core themes of their early family relationships ranged from an undifferentiated unit at 1 week, to being a highly disorganized unit at 6 weeks, to a more integrated unit at 16 weeks. These results suggest that one should be thinking of early family relationships and parenting in terms of "messy processes" out of which new ways of being together are created. This disorganization plays a fundamental role in the establishment of early family relationships and warrants further empirical and clinical attention.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.