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

Viewpoint: Estimating the causal effects of policies and programs

Estimation, inference and interpretation of the causal effects of programs and policies have all advanced dramatically over the past 25 years. We highlight three particularly important intellectual trends: an improved appreciation of the substantive importance of heterogeneous responses and of their methodological implications, a stronger focus on internal validity brought about by the “credibility revolution,” and the scientific value that follows from grounding estimation and interpretation in economic theory. We discuss a menu of commonly employed partial equilibrium approaches to the identification of causal effects, emphasizing that the researcher’s central intellectual contribution always consists of making an explicit case for a specific causal interpretation given the relevant economic theory, the data, the institutional context and the economic question of interest. We also touch on the importance of general equilibrium effects and full cost–benefit analyses.RésuméPoint de vue: Sur l’estimation des effets causatifs des politiques et programmes. Dans le monde de l’estimation, l’inférence et l’interprétation des effets causatifs des programmes et des politiques, il y a eu des progrès dramatiques au cours des derniers 25 ans. Les auteurs soulignent trois tendances intellectuelles particulièrement importantes : une appréciation améliorée de l’importance substantielle des réponses hétérogènes et de leur importance méthodologique, une focalisation plus robuste sur la validité interne engendrée par la « révolution de la crédibilité », et la valeur scientifique qui découle d’un ancrage de l’estimation et de l’interprétation dans la théorie économique. On discute un éventail d’approches d’équilibre partiel à l’identification des effets causatifs, mettant au premier plan que la contribution intellectuelle centrale du chercheur consiste à bâtir un argumentaire explicite pour une interprétation causale spécifique compte tenu de la théorie économique pertinente, des données, du contexte institutionnel, et de la question économique d’intérêt. On mentionne aussi l’importance des effets d’équilibre général et des analyses de tous les coûts et avantages.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134884/1/caje12217.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134884/2/caje12217_am.pd

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

Birational cobordism invariance of uniruled symplectic manifolds

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and blow-down. This theorem follows from a general Relative/Absolute correspondence for a symplectic manifold together with a symplectic submanifold. A direct consequence is that symplectic uniruledness is a symplectic birational invariant. Here we use Guillemin and Sternberg's notion of cobordism as the symplectic analogue of the birational equivalence.Comment: To appear in Invent. Mat

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.

Identity-by-descent filtering of exome sequence data for disease–gene identification in autosomal recessive disorders

Motivation: Next-generation sequencing and exome-capture technologies are currently revolutionizing the way geneticists screen for disease-causing mutations in rare Mendelian disorders. However, the identification of causal mutations is challenging due to the sheer number of variants that are identified in individual exomes. Although databases such as dbSNP or HapMap can be used to reduce the plethora of candidate genes by filtering out common variants, the remaining set of genes still remains on the order of dozens

Lithium chloride therapy fails to improve motor function in a transgenic mouse model of Machado-Joseph disease

The accumulation of misfolded proteins in neurons, leading to the formation of cytoplasmic and nuclear aggregates, is a common theme in age-related neurodegenerative diseases, possibly due to disturbances of the proteostasis and insufficient activity of cellular protein clearance pathways. Lithium is a well-known autophagy inducer that exerts neuroprotective effects in different conditions and has been proposed as a promising therapeutic agent for several neurodegenerative diseases. We tested the efficacy of chronic lithium 10.4 mg/kg) treatment in a transgenic mouse model of Machado-Joseph disease, an inherited neurodegenerative disease, caused by an expansion of a polyglutamine tract within the protein ataxin-3. A battery of behavioral tests was used to assess disease progression. In spite of activating autophagy, as suggested by the increased levels of Beclin-1, Atg7, and LC3II, and a reduction in the p62 protein levels, lithium administration showed no overall beneficial effects in this model concerning motor performance, showing a positive impact only in the reduction of tremors at 24 weeks of age. Our results do not support lithiumchronic treatment as a promising strategy for the treatment of Machado-Joseph disease (MJD).FCT -Fundação para a Ciência e a Tecnologia(SFRH/BD/51059/2010

Exon-Specific QTLs Skew the Inferred Distribution of Expression QTLs Detected Using Gene Expression Array Data

Mapping of expression quantitative trait loci (eQTLs) is an important technique for studying how genetic variation affects gene regulation in natural populations. In a previous study using Illumina expression data from human lymphoblastoid cell lines, we reported that cis-eQTLs are especially enriched around transcription start sites (TSSs) and immediately upstream of transcription end sites (TESs). In this paper, we revisit the distribution of eQTLs using additional data from Affymetrix exon arrays and from RNA sequencing. We confirm that most eQTLs lie close to the target genes; that transcribed regions are generally enriched for eQTLs; that eQTLs are more abundant in exons than introns; and that the peak density of eQTLs occurs at the TSS. However, we find that the intriguing TES peak is greatly reduced or absent in the Affymetrix and RNA-seq data. Instead our data suggest that the TES peak observed in the Illumina data is mainly due to exon-specific QTLs that affect 3′ untranslated regions, where most of the Illumina probes are positioned. Nonetheless, we do observe an overall enrichment of eQTLs in exons versus introns in all three data sets, consistent with an important role for exonic sequences in gene regulation