On a Subposet of the Tamari Lattice

We explore some of the properties of a subposet of the Tamari lattice introduced by Pallo, which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page

Tamari Lattices and the symmetric Thompson monoid

We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F+sym. As an application, we show that, for every n, there exists a length l chain in the nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page

Duplications of the critical Rubinstein-Taybi deletion region on chromosome 16p13.3 cause a novel recognisable syndrome

Background The introduction of molecular karyotyping technologies facilitated the identification of specific genetic disorders associated with imbalances of certain genomic regions. A detailed phenotypic delineation of interstitial 16p13.3 duplications is hampered by the scarcity of such patients. Objectives To delineate the phenotypic spectrum associated with interstitial 16p13.3 duplications, and perform a genotype-phenotype analysis. Results The present report describes the genotypic and phenotypic delineation of nine submicroscopic interstitial 16p13.3 duplications. The critically duplicated region encompasses a single gene, CREBBP, which is mutated or deleted in Rubinstein-Taybi syndrome. In 10 out of the 12 hitherto described probands, the duplication arose de novo. Conclusions Interstitial 16p13.3 duplications have a recognizable phenotype, characterized by normal to moderately retarded mental development, normal growth, mild arthrogryposis, frequently small and proximally implanted thumbs and characteristic facial features. Occasionally, developmental defects of the heart, genitalia, palate or the eyes are observed. The frequent de novo occurrence of 16p13.3 duplications demonstrates the reduced reproductive fitness associated with this genotype. Inheritance of the duplication from a clinically normal parent in two cases indicates that the associated phenotype is incompletely penetrant

Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence

We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near-horizon geometry. Moreover, we find that the asymptotic behaviour of the metric perturbations in NHEK-AdS violates the fall-off conditions imposed in the formulation of the Kerr/CFT correspondence (the only exception being the axisymmetric sector of perturbations).Comment: 26 pages. 4 figures. v2: references added. matches published versio

An archival case study : revisiting the life and political economy of Lauchlin Currie

This paper forms part of a wider project to show the significance of archival material on distinguished economists, in this case Lauchlin Currie (1902-93), who studied and taught at Harvard before entering government service at the US Treasury and Federal Reserve Board as the intellectual leader of Roosevelt's New Deal, 1934-39, as FDR's White House economic adviser in peace and war, 1939-45, and as a post-war development economist. It discusses the uses made of the written and oral material available when the author was writing his intellectual biography of Currie (Duke University Press 1990) while Currie was still alive, and the significance of the material that has come to light after Currie's death

The identification of informative genes from multiple datasets with increasing complexity

Background In microarray data analysis, factors such as data quality, biological variation, and the increasingly multi-layered nature of more complex biological systems complicates the modelling of regulatory networks that can represent and capture the interactions among genes. We believe that the use of multiple datasets derived from related biological systems leads to more robust models. Therefore, we developed a novel framework for modelling regulatory networks that involves training and evaluation on independent datasets. Our approach includes the following steps: (1) ordering the datasets based on their level of noise and informativeness; (2) selection of a Bayesian classifier with an appropriate level of complexity by evaluation of predictive performance on independent data sets; (3) comparing the different gene selections and the influence of increasing the model complexity; (4) functional analysis of the informative genes. Results In this paper, we identify the most appropriate model complexity using cross-validation and independent test set validation for predicting gene expression in three published datasets related to myogenesis and muscle differentiation. Furthermore, we demonstrate that models trained on simpler datasets can be used to identify interactions among genes and select the most informative. We also show that these models can explain the myogenesis-related genes (genes of interest) significantly better than others (P < 0.004) since the improvement in their rankings is much more pronounced. Finally, after further evaluating our results on synthetic datasets, we show that our approach outperforms a concordance method by Lai et al. in identifying informative genes from multiple datasets with increasing complexity whilst additionally modelling the interaction between genes. Conclusions We show that Bayesian networks derived from simpler controlled systems have better performance than those trained on datasets from more complex biological systems. Further, we present that highly predictive and consistent genes, from the pool of differentially expressed genes, across independent datasets are more likely to be fundamentally involved in the biological process under study. We conclude that networks trained on simpler controlled systems, such as in vitro experiments, can be used to model and capture interactions among genes in more complex datasets, such as in vivo experiments, where these interactions would otherwise be concealed by a multitude of other ongoing events

Dynamic Perturbations of the T-Cell Receptor Repertoire in Chronic HIV Infection and following Antiretroviral Therapy

HIV infection profoundly affects many parameters of the immune system and ultimately leads to AIDS, yet which factors are most important for determining resistance, pathology, and response to antiretroviral treatment - and how best to monitor them - remain unclear. We develop a quantitative high-throughput sequencing pipeline to characterize the TCR repertoires of HIV-infected individuals before and after antiretroviral therapy, working from small, unfractionated samples of peripheral blood. This reveals the TCR repertoires of HIV(+) individuals to be highly perturbed, with considerably reduced diversity as a small proportion of sequences are highly overrepresented. HIV also causes specific qualitative changes to the repertoire including an altered distribution of V gene usage, depletion of public TCR sequences, and disruption of TCR networks. Short-term antiretroviral therapy has little impact on most of the global damage to repertoire structure, but is accompanied by rapid changes in the abundance of many individual TCR sequences, decreases in abundance of the most common sequences, and decreases in the majority of HIV-associated CDR3 sequences. Thus, high-throughput repertoire sequencing of small blood samples that are easy to take, store, and process can shed light on various aspects of the T-cell immune compartment and stands to offer insights into patient stratification and immune reconstitution

Congenital anterolateral tibial bowing and polydactyly: a case report

Congenital anterolateral bowing of the tibia is a rare deformity that may lead to pseudarthrosis and risk of fracture. This is commonly associated with neurofibromatosis type 1. In this report, we describe a 15-month old male with congenital anterolateral bowing of the right tibia and associated hallux duplication. This is a distinct entity with a generally favourable prognosis that should not be confused with other conditions such as neurofibromatosis type 1. Previously published cases are reviewed

Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds), Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 180--204, http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-