Production of trans-Neptunian binaries through chaos-assisted capture

The recent discovery of binary objects in the Kuiper-belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary-object formation model based on the notion of chaos-assisted capture. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity, and orbital element distribu- tions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering in the circular Hill four-body problem and find that the chaos-assisted capture mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also addressed.Comment: submitted to MNRA

Moments of spectral functions: Monte Carlo evaluation and verification

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval $(-\beta \hbar / 2, \beta \hbar/2)$. The algorithmic detail that leads to robust numerical approximations is the fact that the path integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is non-linear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed.Comment: 13 pages, 2 figure

Football (Soccer) as a probable cause of long-term neurological impairment and neurodegeneration: a narrative review of the debate

Football (soccer) is the most widely played sport across the globe. Due to some recent high-profile cases and epidemiological studies suggesting football can lead to neurodegeneration, scientific and public interest has been piqued. This has resulted in research into whether an association between football participation and neurodegeneration or neurological impairment is present. It has been theorised that a combination of repeated sub-concussive and concussive injuries, due to ball-heading and head collisions, may lead to neurodegeneration. However, evidence remains conflicting. Due to the popularity of the sport, and the serious conditions it has been linked to, it is important to determine whether repeated head impacts during football participation can play a causative role in neurodegenerative disease. To answer this question, a review of the current literature was carried out. Epidemiological evidence showed a higher incidence of amyotrophic lateral sclerosis amongst amateur and professional footballers and that footballers in positions that involve less contact and heading, e.g., goalkeepers lead significantly longer lives. Additionally, imaging studies reach a similar conclusion, reporting changes in brain structure, blood flow, and inflammatory markers in footballers when compared to controls. However, studies looking at an association between heading frequency and cognition show a lack of consensus on whether a higher heading exposure results in reduced cognition. Similarly, in neuropathological studies, signs of chronic traumatic encephalopathy (CTE) have been found in some former players, with contrasting studies suggesting low levels of CTE-type pathology are found in the general population, regardless of exposure to head trauma. The majority of studies suggest a link between football and neurodegenerative disease. However, the high prevalence of retrospective cohort and cross-sectional studies, often plagued by recall bias, undermine the conclusions drawn. Therefore, until larger prospective cohort studies are conducted, concrete conclusions cannot be made. However, caution can be exercised to limit head impacts

edgeR: a Bioconductor package for differential expression analysis of digital gene expression data

Summary: It is expected that emerging digital gene expression (DGE) technologies will overtake microarray technologies in the near future for many functional genomics applications. One of the fundamental data analysis tasks, especially for gene expression studies, involves determining whether there is evidence that counts for a transcript or exon are significantly different across experimental conditions. edgeR is a Bioconductor software package for examining differential expression of replicated count data. An overdispersed Poisson model is used to account for both biological and technical variability. Empirical Bayes methods are used to moderate the degree of overdispersion across transcripts, improving the reliability of inference. The methodology can be used even with the most minimal levels of replication, provided at least one phenotype or experimental condition is replicated. The software may have other applications beyond sequencing data, such as proteome peptide count data

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Quality Assessment and Data Analysis for microRNA Expression Arrays

MicroRNAs are small (∼22 nt) RNAs that regulate gene expression and play important roles in both normal and disease physiology. The use of microarrays for global characterization of microRNA expression is becoming increasingly popular and has the potential to be a widely used and valuable research tool. However, microarray profiling of microRNA expression raises a number of data analytic challenges that must be addressed in order to obtain reliable results. We introduce here a universal reference microRNA reagent set as well as a series of nonhuman spiked-in synthetic microRNA controls, and demonstrate their use for quality control and between-array normalization of microRNA expression data. We also introduce diagnostic plots designed to assess and compare various normalization methods. We anticipate that the reagents and analytic approach presented here will be useful for improving the reliability of microRNA microarray experiments

Differential regulation of human bone marrow mesenchymal stromal cell chondrogenesis by hypoxia inducible factor-1α hydroxylase inhibitors

The transcriptional profile induced by hypoxia plays important roles in the chondrogenic differentiation of marrow stromal/stem cells (MSC) and is mediated by the Hypoxia Inducible Factor complex. However, various compounds can also stabilise HIF's oxygen-responsive element, HIF-1α, at normoxia and mimic many hypoxia-induced cellular responses. Such compounds may prove efficacious in cartilage tissue engineering, where microenvironmental cues may mediate functional tissue formation. Here, we investigated three HIF stabilising compounds, which each have distinct mechanisms of action, to understand how they differentially influenced the chondrogenesis of human bone marrow-derived MSC (hBM-MSC) in vitro. hBM-MSCs were chondrogenically-induced in TGF-β3 -containing media in the presence of HIF-stabilising compounds. HIF-1α stabilisation was assessed by HIF-1α immunofluorescence staining, expression of HIF target and articular chondrocyte specific genes by qPCR, and cartilage-like extracellular matrix (ECM) production by immunofluorescence and histochemical staining. We demonstrate that all three compounds induced similar levels of HIF-1α nuclear localisation. However, whilst the 2-oxoglutarate analogue Dimethyloxalylglycine (DMOG) promoted upregulation of a selection of HIF target genes, Desferrioxamine (DFX) and Cobalt Chloride (CoCl2 ), compounds that chelate or compete with Fe2+ , respectively, did not. Moreover, DMOG induced a more chondrogenic transcriptional profile, which was abolished by Acriflavine, an inhibitor of HIF-1α-HIF-β binding, whilst the chondrogenic effects of DFX and CoCl2 were more limited. Together, these data suggest that HIF-1α function during hBM-MSC chondrogenesis may be regulated by mechanisms with a greater dependence on 2-oxoglutarate than Fe2+ availability. These results may have important implications for understanding cartilage disease and developing targeted therapies for cartilage repair. This article is protected by copyright. All rights reserved

SAFEGUI: resampling-based tests of categorical significance in gene expression data made easy

Summary: A large number of websites and applications perform significance testing for gene categories/pathways in microarray data. Many of these packages fail to account for expression correlation between transcripts, with a resultant inflation in Type I error. Array permutation and other resampling-based approaches have been proposed as solutions to this problem. SAFEGUI provides a user-friendly graphical interface for the assessment of categorical significance in microarray studies, while properly accounting for the effects of correlations among genes. SAFEGUI incorporates both permutation and more recently proposed bootstrap algorithms that are demonstrated to be more powerful in detecting differential expression across categories of genes

A Fast Algorithm for Robust Regression with Penalised Trimmed Squares

The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked high leverage outliers in finite samples. An alternative to the LTS estimator, called Penalised Trimmed Squares (PTS) estimator, was introduced by the authors in \cite{ZiouAv:05,ZiAvPi:07} and it appears to be less sensitive to the masking problem. This estimator is defined by a Quadratic Mixed Integer Programming (QMIP) problem, where in the objective function a penalty cost for each observation is included which serves as an upper bound on the residual error for any feasible regression line. Since the PTS does not require presetting the number of outliers to delete from the data set, it has better efficiency with respect to other estimators. However, due to the high computational complexity of the resulting QMIP problem, exact solutions for moderately large regression problems is infeasible. In this paper we further establish the theoretical properties of the PTS estimator, such as high breakdown and efficiency, and propose an approximate algorithm called Fast-PTS to compute the PTS estimator for large data sets efficiently. Extensive computational experiments on sets of benchmark instances with varying degrees of outlier contamination, indicate that the proposed algorithm performs well in identifying groups of high leverage outliers in reasonable computational time.Comment: 27 page

Hypoxia impacts human MSC response to substrate stiffness during chondrogenic differentiation

Tissue engineering strategies often aim to direct tissue formation by mimicking conditions progenitor cells experience within native tissues. For example, to create cartilage in vitro, researchers often aim to replicate the biochemical and mechanical milieu cells experience during cartilage formation in the developing limb bud. This includes stimulating progenitors with TGF-β1/3, culturing under hypoxic conditions, and regulating mechanosensory pathways using biomaterials that control substrate stiffness and/or cell shape. However, as progenitors differentiate down the chondrogenic lineage, the pathways that regulate their responses to mechanotransduction, hypoxia and TGF-β may not act independently, but rather also impact one another, influencing overall cell response. Here, to better understand hypoxia's influence on mechanoregulatory-mediated chondrogenesis, we cultured human marrow stromal/mesenchymal stem cells (hMSC) on soft (0.167 kPa) or stiff (49.6 kPa) polyacrylamide hydrogels in chondrogenic medium containing TGF-β3. We then compared cell morphology, phosphorylated myosin light chain 2 staining, and chondrogenic gene expression under normoxic and hypoxic conditions, in the presence and absence of pharmacological inhibition of cytoskeletal tension. We show that on soft compared to stiff substrates, hypoxia prompts hMSC to adopt more spread morphologies, assemble in compact mesenchymal condensation-like colonies, and upregulate NCAM expression, and that inhibition of cytoskeletal tension negates hypoxia-mediated upregulation of molecular markers of chondrogenesis, including COL2A1 and SOX9. Taken together, our findings support a role for hypoxia in regulating hMSC morphology, cytoskeletal tension and chondrogenesis, and that hypoxia's effects are modulated, at least in part, by mechanosensitive pathways. Our insights into how hypoxia impacts mechanoregulation of chondrogenesis in hMSC may improve strategies to develop tissue engineered cartilage