Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio

Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

Amplitude of the Electrical Potential Oscillations in the Salt-Water Oscillator

The amplitude of the electrical potential oscillations of the salt water oscillator depends on the character of an electrical double layer formed in the glass capillary or at the interface between the dilute and concentrated salt solutions. When a stationary mercury electrode was used, a new type of periodic behavior, compound oscillation, was observed

Authigenic iron oxide proxies for marine zinc over geological time and implications for eukaryotic metallome evolution

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Geobiology 11 (2013): 295-306, doi:10.1111/gbi.12036.Here we explore enrichments in paleomarine Zn as recorded by authigenic iron oxides including Precambrian iron formations, ironstones and Phanerozoic hydrothermal exhalites. This compilation of new and literature-based iron formation analyses track dissolved Zn abundances and constrain the magnitude of the marine reservoir over geological time. Overall, the iron formation record is characterized by a fairly static range in Zn/Fe ratios throughout the Precambrian, consistent with the shale record (Scott et al., 2013, Nature Geoscience, 6, 125-128). When hypothetical partitioning scenarios are applied to this record, paleomarine Zn concentrations within about an order of magnitude of modern are indicated. We couple this examination with new chemical speciation models used to interpret the iron formation record. We present two scenarios: first, under all but the most sulfidic conditions and with Zn binding organic ligand concentrations similar to modern oceans, the amount of bioavailable Zn remained relatively unchanged through time. Late proliferation of Zn in eukaryotic metallomes has previously been linked to marine Zn biolimitation, but under this scenario, the expansion in eukaryotic Zn metallomes may be better linked to biologically intrinsic evolutionary factors. In this case zinc’s geochemical and biological evolution may be decoupled, and viewed as a function of increasing need for genome regulation and diversification of Zn-binding transcription factors. In the second scenario, we consider Archean organic ligand complexation in such excess that it may render Zn bioavailability low. However, this is dependent on Zn organic ligand complexes not being bioavailable, which remains unclear. In this case, although bioavailability may be low, sphalerite precipitation is prevented, thereby maintaining a constant Zn inventory throughout both ferruginous and euxinic conditions. These results provide new perspectives and constraints 50 on potential couplings between the trajectory of biological and marine geochemical coevolution.This work was supported by a NSERC Discovery Grant to KOK, a NSERC PDF to SVL, a NSERC CGSM to LJR, and an NSF-EAR-PDF to NJP. MAS acknowledges support from the Gordon and Betty Moore Foundation Grant #2724. This work was also supported by grants from the Deutsche Forschungsgemeinschaft (DFG) to A.K. (KA 1736/4-1 and 12-1)

Predicting language learners' grades in the L1, L2, L3 and L4: the effect of some psychological and sociocognitive variables

This study of 89 Flemish high-school students' grades for L1 (Dutch), L2 (French), L3 (English) and L4 (German) investigates the effects of three higher-level personality dimensions (psychoticism, extraversion, neuroticism), one lower-level personality dimension (foreign language anxiety) and sociobiographical variables (gender, social class) on the participants' language grades. Analyses of variance revealed no significant effects of the higher-level personality dimensions on grades. Participants with high levels of foreign language anxiety obtained significantly lower grades in the L2 and L3. Gender and social class had no effect. Strong positive correlations between grades in the different languages could point to an underlying sociocognitive dimension. The implications of these findings are discussed

Regulation of Motor Function and Behavior by Atypical Chemokine Receptor 1

The final publication is available at Springer via http://dx.doi.org/10.1007/s10519-014-9665-7Atypical Chemokine Receptor 1 (ACKR1), previously known as the Duffy Antigen Receptor for Chemokines, stands out among chemokine receptors for its high selective expression on Purkinje cells of the cerebellum, consistent with the ability of ACKR1 ligands to activate Purkinje cells in vitro. Nevertheless, evidence for ACKR1 regulation of brain function in vivo has been lacking. Here we demonstrate that Ackr1−/− mice have markedly impaired balance and ataxia when placed on a rotating rod and increased tremor when injected with harmaline, a drug that induces whole-body tremor by activating Purkinje cells. Ackr1−/− mice also exhibited impaired exploratory behavior, increased anxiety-like behavior and frequent episodes of marked hypoactivity under low-stress conditions. The behavioral phenotype of Ackr1−/− mice was the opposite of the phenotype occurring in mice with cerebellar degeneration and the defects persisted when Ackr1 was deficient only on non-hematopoietic cells. We conclude that normal motor function and behavior depend in part on negative regulation of Purkinje cell activity by Ackr1

The future is now: Model-based clinical trial design for Alzheimer's disease

Failures in trials for Alzheimer's disease (AD) may be attributable to inadequate dosing, population selection, drug inefficacy, or insufficient design optimization. The Coalition Against Major Diseases (CAMD) was formed in 2008 to develop drug development tools (DDT) to expedite drug development for AD and Parkinson's disease.1 CAMD led a process that successfully advanced a clinical trial simulation (CTS) tool for AD through the formal regulatory review process at the US Food and Drug Administration (FDA) and European Medicines Agency (EMA)

Within study comparisons and risk of bias in international development: Systematic review and critical appraisal

Background Many systematic reviews incorporate nonrandomised studies of effects, sometimes called quasi‐experiments or natural experiments. However, the extent to which nonrandomised studies produce unbiased effect estimates is unclear in expectation or in practice. The usual way that systematic reviews quantify bias is through “risk of bias assessment” and indirect comparison of findings across studies using meta‐analysis. A more direct, practical way to quantify the bias in nonrandomised studies is through “internal replication research”, which compares the findings from nonrandomised studies with estimates from a benchmark randomised controlled trial conducted in the same population. Despite the existence of many risks of bias tools, none are conceptualised to assess comprehensively nonrandomised approaches with selection on unobservables, such as regression discontinuity designs (RDDs). The few that are conceptualised with these studies in mind do not draw on the extensive literature on internal replications (within‐study comparisons) of randomised trials. Objectives Our research objectives were as follows: Objective 1: to undertake a systematic review of nonrandomised internal study replications of international development interventions. Objective 2: to develop a risk of bias tool for RDDs, an increasingly common method used in social and economic programme evaluation. Methods We used the following methods to achieve our objectives. Objective 1: we searched systematically for nonrandomised internal study replications of benchmark randomised experiments of social and economic interventions in low‐ and middle‐income countries (L&MICs). We assessed the risk of bias in benchmark randomised experiments and synthesised evidence on the relative bias effect sizes produced by benchmark and nonrandomised comparison arms. Objective 2: We used document review and expert consultation to develop further a risk of bias tool for quasi‐experimental studies of interventions (ROBINS‐I) for RDDs. Results Objective 1: we located 10 nonrandomised internal study replications of randomised trials in L&MICs, six of which are of RDDs and the remaining use a combination of statistical matching and regression techniques. We found that benchmark experiments used in internal replications in international development are in the main well‐conducted but have “some concerns” about threats to validity, usually arising due to the methods of outcomes data collection. Most internal replication studies report on a range of different specifications for both the benchmark estimate and the nonrandomised replication estimate. We extracted and standardised 604 bias coefficient effect sizes from these studies, and present average results narratively. Objective 2: RDDs are characterised by prospective assignment of participants based on a threshold variable. Our review of the literature indicated there are two main types of RDD. The most common type of RDD is designed retrospectively in which the researcher identifies post‐hoc the relationship between outcomes and a threshold variable which determines assignment to intervention at pretest. These designs usually draw on routine data collection such as administrative records or household surveys. The other, less common, type is a prospective design where the researcher is also involved in allocating participants to treatment groups from the outset. We developed a risk of bias tool for RDDs. Conclusions Internal study replications provide the grounds on which bias assessment tools can be evidenced. We conclude that existing risk of bias tools needs to be further developed for use by Campbell collaboration authors, and there is a wide range of risk of bias tools and internal study replications to draw on in better designing these tools. We have suggested the development of a promising approach for RDD. Further work is needed on common methodologies in programme evaluation, for example on statistical matching approaches. We also highlight that broader efforts to identify all existing internal replication studies should consider more specialised systematic search strategies within particular literatures; so as to overcome a lack of systematic indexing of this evidence

Children's Divergent Thinking Improves When They Understand False Beliefs

This research utilized longitudinal and cross sectional methods to investigate the relation between the development of a representational theory of mind and children's growing ability to search their own minds for appropriate problem solutions. In the first experiment 59 pre-school children were given three false-belief tasks and a divergent thinking task. Those children who passed false-belief tasks produced significantly more items, as well as more original items, in response to divergent thinking questions than those children who failed. This significant association persisted even when chronological age, verbal and nonverbal general ability were partialed out. In a second study 20 children who failed the false-belief tasks in the first experiment were re-tested three months later. Again, those who now passed the false-belief tasks were significantly better at the divergent thinking task than those who continued to fail. The associations between measures of divergent thinking and understanding false-beliefs remained significant when controlling for the covariates. Earlier divergent thinking scores did not predict false-belief understanding three months later. Instead, children who passed false-belief tasks on the second measure improved significantly in relation to their own earlier performance and improved significantly more than children who continued to fail. False-belief task performance was significantly correlated to the amount of intra-individual improvement in divergent thinking even when age, verbal and nonverbal skills were partialed out. These findings suggest that developments in common underlying skills are responsible for the improvement in understanding other minds and searching one's own. Changes in representational and executive skills are discussed as potential causes for the improvement

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.