Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?

We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both, the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao

Developmental course of psychopathology in youths with and without intellectual disabilities

Background: We aimed to describe similarities and differences in the developmental course of psychopathology between children with and without intellectual disabilities (ID). Method: Multilevel growth curve analysis was used to analyse the developmental course of psychopathology, using the Child Behavior Checklist (CBCL), in two longitudinal multiple-birth-cohort samples of 6- to 18-year-old children with ID (N=978) and without ID (N=2,047) using three repeated measurements across a 6-year period. Results: Children with ID showed a higher level of problem behaviours across all ages compared to children without ID. A significant difference between the samples in the developmental courses was found for Aggressive Behaviour and Attention Problems, where children with ID showed a significantly larger decrease. Gender differences in the development of psychopathology were similar in both samples, except for Social Problems where males with ID showed a larger decrease in problem behaviour across time than females with ID and males and females without ID. Conclusion: Results indicate that children with ID continue to show a greater risk for psychopathology compared to typically developing children, although this higher risk is less pronounced at age 18 than it is at age 6 for Aggressive Behaviour. Contrary to our expectations, the developmental course of psychopathology in children with ID was quite similar from age 6 to 18 compared to children without ID. The normative developmental trajectories of psychopathology in children with ID, presented here, can serve as a yardstick against which development of childhood psychopathology can be detected as deviant. © 2007 The Authors Journal compilation © 2007 Association for Child and Adolescent Mental Health

Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy

Time-resolved measurement techniques are opening a window on nonequilibrium quantum phenomena that is radically different from the traditional picture in the frequency domain. The simulation and interpretation of nonequilibrium dynamics is a conspicuous challenge for theory. This paper presents a novel approach to quantum many-body dynamics that is based on a Hamiltonian formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations of motion for reduced density matrices. These equations have an underlying symplectic structure, and we write them in the form of the classical Hamilton equations for canonically conjugate variables. Applying canonical perturbation theory or the Krylov-Bogoliubov averaging method to the resulting equations yields a systematic approximation scheme. The possibility of using memory-dependent functional approximations to close the Hamilton equations at a particular level of the hierarchy is discussed. The geometric structure of the equations gives rise to reduced geometric phases that are observable even for noncyclic evolutions of the many-body state. The formalism is applied to a finite Hubbard chain which undergoes a quench in on-site interaction energy U. Canonical perturbation theory, carried out to second order, fully captures the nontrivial real-time dynamics of the model, including resonance phenomena and the coupling of fast and slow variables.Comment: 17 pages, revise

Fetching marked items from an unsorted database in NMR ensemble computing

Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.Comment: 4 pages and 1 figur

Evolutionary game theory in growing populations

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperationComment: 4 pages, 2 figures and 2 pages supplementary informatio

Developmental trajectories of externalizing behaviors in childhood and adolescence [IF: 3.3]

This article describes the average and group-based developmental trajectories of aggression, opposition, property violations, and status violations using parent reports of externalizing behaviors on a longitudinal multiple birth cohort study of 2,076 children aged 4 to 18 years. Trajectories were estimated from multilevel growth curve analyses and semiparametric mixture models. Overall, males showed higher levels of externalizing behavior than did females. Aggression, opposition, and property violations decreased on average, whereas status violations increased over time. Group-based trajectories followed the shape of the average curves at different levels and were similar for males and females. The trajectories found in this study provide a basis against which deviations from the expected developmental course can be identified and classified as deviant or nondeviant

Negotiating daughterhood and strangerhood: retrospective accounts of serial migration

Most considerations of daughtering and mothering take for granted that the subjectivities of mothers and daughters are negotiated in contexts of physical proximity throughout daughters’ childhoods. Yet many mothers and daughters spend periods separated from each other, sometimes across national borders. Globally, an increasing number of children experience life in transnational families. This paper examines the retrospective narratives of four women who were serial migrants as children (whose parents migrated before they did) . It focuses on their accounts of the reunion with their mothers and how these fit with the ways in which they construct their mother-daughter relationships. We take a psychosocial approach by using a psychoanalytically-informed reading of these narratives to acknowledge the complexities of the attachments produced in the context of migration and to attend to the multi-layered psychodynamics of the resulting relationships. The paper argues that serial migration positioned many of the daughters in a conflictual emotional landscape from which they had to negotiate ‘strangerhood’ in the context of sadness at leaving people to whom they were attached in order to join their mothers (or parents). As a result, many were resistant to being positioned as daughters, doing daughtering and being mothered in their new homes

Forward-in-Time, Spatially Explicit Modeling Software to Simulate Genetic Lineages Under Selection

SELECTOR is a software package for studying the evolution of multiallelic genes under balancing or positive selection while simulating complex evolutionary scenarios that integrate demographic growth and migration in a spatially explicit population framework. Parameters can be varied both in space and time to account for geographical, environmental, and cultural heterogeneity. SELECTOR can be used within an approximate Bayesian computation estimation framework. We first describe the principles of SELECTOR and validate the algorithms by comparing its outputs for simple models with theoretical expectations. Then, we show how it can be used to investigate genetic differentiation of loci under balancing selection in interconnected demes with spatially heterogeneous gene flow. We identify situations in which balancing selection reduces genetic differentiation between population groups compared with neutrality and explain conflicting outcomes observed for human leukocyte antigen loci. These results and three previously published applications demonstrate that SELECTOR is efficient and robust for building insight into human settlement history and evolution

Psychometric properties of the revised Developmental Behaviour Checklist scales in Dutch children with intellectual disability

The present study assessed the reliability and validity of the revised scales of the Developmental Behaviour Checklist (DBC) in a Dutch sample of children with intellectual disability (ID). The psychometric properties of the parent and teacher versions of the DBC were assessed in various subsamples derived from a sample of 1057 Dutch children (age range = 6-18 years) with ID or borderline intellectual functioning. Good test-retest reliability was shown both for the parent and teacher versions. Moderate inter-parent agreement and high one-year stability was found for the scale scores. Construct validity was satisfactory, although limited by high informant variance. The DBC scales showed good criterion-related validity, as indicated by significant mean differences between referred and non-referred children, and between children with and without a corresponding DSM-IV diagnosis. The reliability and validity of the revised DBC scales are satisfactory, and the checklist is recommended for clinical and research purposes

Fluctuations and correlations in an individual-based model of biological coevolution

We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in previous investigations. The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically. Several specific cases are studied by Monte Carlo simulations, and there is excellent agreement between the data and the theoretical predictions.Comment: 25 pages, 2 figure