Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term

In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation for arbitrary homogeneous kernel. The resulting massdistributions are of Kolmogorov type in the sense that they carry a constant flux of mass from small masses to large. We derive a ``locality criterion'', expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissiblesolution. Whether a given kernel leads to a gelation transition or not can be determined by computing the mass capacity of the Kolmogorov spectrum. As an example, we compute the exact stationary state for the family of kernels,$K_\zeta(m_1,m_2)=(m_1m_2)^{\zeta/2}$ which includes both gelling and non-gelling cases, reproducing the known solution in the case $\zeta=0$. Surprisingly, the Kolmogorov constant is the same for all kernels in this family.Comment: This article is an expanded version of a talk given at IHP workshop "Dynamics, Growth and Singularities of Continuous Media", Paris July 2003. Updated 01/04/04. Revised version with additional discussion, references added, several typographical errors corrected. Revised version accepted for publication by Phys. Rev.

Formation of Supermassive Black Holes

Evidence shows that massive black holes reside in most local galaxies. Studies have also established a number of relations between the MBH mass and properties of the host galaxy such as bulge mass and velocity dispersion. These results suggest that central MBHs, while much less massive than the host (~ 0.1%), are linked to the evolution of galactic structure. In hierarchical cosmologies, a single big galaxy today can be traced back to the stage when it was split up in hundreds of smaller components. Did MBH seeds form with the same efficiency in small proto-galaxies, or did their formation had to await the buildup of substantial galaxies with deeper potential wells? I briefly review here some of the physical processes that are conducive to the evolution of the massive black hole population. I will discuss black hole formation processes for `seed' black holes that are likely to place at early cosmic epochs, and possible observational tests of these scenarios.Comment: To appear in The Astronomy and Astrophysics Review. The final publication is available at http://www.springerlink.co

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

A pragmatic randomised controlled trial of hydrotherapy and land exercises on overall well being and quality of life in rheumatoid arthritis

Background \ud Hydrotherapy is highly valued by people with rheumatoid arthritis yet few studies have compared the benefits of exercises in heated water against exercises on land. In particular, data on quality of life is rarely reported. This is especially important because patients treated with hydrotherapy often report an enhanced sense of well-being. We report a randomised controlled trial in which we compared the effects of hydrotherapy with exercises on land on overall response to treatment, physical function and quality of life in patients with rheumatoid arthritis. \ud \ud Methods \ud One hundred and fifteen patients with RA were randomised to receive a weekly 30-minute session of hydrotherapy or similar exercises on land for 6 weeks. Our primary outcome was a self-rated global impression of change – a measure of treatment effect on a 7-point scale ranging from 1(very much worse) to 7 (very much better) assessed immediately on completion of treatment. Secondary outcomes including EuroQol health related quality of life, EuroQol health status valuation, HAQ, 10 metre walk time and pain scores were collected at baseline, after treatment and 3 months later. Binary outcomes were analysed by Fisher's exact test and continuous variables by Wilcoxon or Mann-Whitney tests. \ud \ud Results \ud Baseline characteristics of the two groups were comparable. Significantly more patients treated with hydrotherapy (40/46, 87%) were much better or very much better than the patients treated with land exercise (19/40, 47.5%), p < 0.001 Fisher's exact test. Eleven patients allocated land exercise failed to complete treatment compared with 4 patients allocated hydrotherapy (p = 0.09). Sensitivity analyses confirmed an advantage for hydrotherapy if we assumed non-completers would all not have responded (response rates 70% versus 38%; p < 0.001) or if we assumed that non-completers would have had the same response as completers (response rates 82% versus 55% p = 0.002). Ten metre walk time improved after treatment in both cases (median pre-treatment time for both groups combined 10.9 seconds, post-treatment 9.1 s, and 3 months later 9.6 s). There was however no difference between treatment groups. Similarly there were no significant differences between groups in terms of changes to HAQ, EQ-5D utility score, EQ VAS and pain VAS. \ud \ud Conclusion \ud Patients with RA treated with hydrotherapy are more likely to report feeling much better or very much better than those treated with land exercises immediately on completion of the treatment programme. This perceived benefit was not reflected by differences between groups in 10-metre walk times, functional scores, quality of life measures and pain scores

Homozygosity for a missense mutation in the 67 kDa isoform of glutamate decarboxylase in a family with autosomal recessive spastic cerebral palsy: parallels with Stiff-Person Syndrome and other movement disorders

Background Cerebral palsy (CP) is an heterogeneous group of neurological disorders of movement and/or posture, with an estimated incidence of 1 in 1000 live births. Non-progressive forms of symmetrical, spastic CP have been identified, which show a Mendelian autosomal recessive pattern of inheritance. We recently described the mapping of a recessive spastic CP locus to a 5 cM chromosomal region located at 2q24-31.1, in rare consanguineous families. Methods Here we present data that refine this locus to a 0.5 cM region, flanked by the microsatellite markers D2S2345 and D2S326. The minimal region contains the candidate gene GAD1, which encodes a glutamate decarboxylase isoform (GAD67), involved in conversion of the amino acid and excitatory neurotransmitter glutamate to the inhibitory neurotransmitter γ-aminobutyric acid (GABA). Results A novel amino acid mis-sense mutation in GAD67 was detected, which segregated with CP in affected individuals. Conclusions This result is interesting because auto-antibodies to GAD67 and the more widely studied GAD65 homologue encoded by the GAD2 gene, are described in patients with Stiff-Person Syndrome (SPS), epilepsy, cerebellar ataxia and Batten disease. Further investigation seems merited of the possibility that variation in the GAD1 sequence, potentially affecting glutamate/GABA ratios, may underlie this form of spastic CP, given the presence of anti-GAD antibodies in SPS and the recognised excitotoxicity of glutamate in various contexts

Interspecies hybridization on DNA resequencing microarrays: efficiency of sequence recovery and accuracy of SNP detection in human, ape, and codfish mitochondrial DNA genomes sequenced on a human-specific MitoChip

Background: Iterative DNA "resequencing" on oligonucleotide microarrays offers a high-throughput method to measure intraspecific biodiversity, one that is especially suited to SNP-dense gene regions such as vertebrate mitochondrial (mtDNA) genomes. However, costs of single-species design and microarray fabrication are prohibitive. A cost-effective, multi-species strategy is to hybridize experimental DNAs from diverse species to a common microarray that is tiled with oligonucleotide sets from multiple, homologous reference genomes. Such a strategy requires that cross-hybridization between the experimental DNAs and reference oligos from the different species not interfere with the accurate recovery of species-specific data. To determine the pattern and limits of such interspecific hybridization, we compared the efficiency of sequence recovery and accuracy of SNP identification by a 15,452-base human-specific microarray challenged with human, chimpanzee, gorilla, and codfish mtDNA genomes. Results: In the human genome, 99.67% of the sequence was recovered with 100.0% accuracy. Accuracy of SNP identification declines log-linearly with sequence divergence from the reference, from 0.067 to 0.247 errors per SNP in the chimpanzee and gorilla genomes, respectively. Efficiency of sequence recovery declines with the increase of the number of interspecific SNPs in the 25b interval tiled by the reference oligonucleotides. In the gorilla genome, which differs from the human reference by 10%, and in which 46% of these 25b regions contain 3 or more SNP differences from the reference, only 88% of the sequence is recoverable. In the codfish genome, which differs from the reference by > 30%, less than 4% of the sequence is recoverable, in short islands ≥ 12b that are conserved between primates and fish. Conclusion: Experimental DNAs bind inefficiently to homologous reference oligonucleotide sets on a resequencing microarray when their sequences differ by more than a few percent. The data suggest that interspecific cross-hybridization will not interfere with the accurate recovery of species-specific data from multispecies microarrays, provided that the species' DNA sequences differ by > 20% (mean of 5b differences per 25b oligo). Recovery of DNA sequence data from multiple, distantly-related species on a single multiplex gene chip should be a practical, highly-parallel method for investigating genomic biodiversity

“I Find It Really Difficult to Control Myself Too”:A Qualitative Study of the Effects on the Family Dynamic When Parent and Child Have ADHD

If having one child with Attention Deficit Hyperactivity Disorder (ADHD) contributes to family stress and dysfunction, then what happens when more than one family member has ADHD? This paper explores this question by drawing on findings from a multi-case study that explored the voices of stakeholders (child and parent/carer) affected by ADHD in Ireland. There were eight case studies (families) included. Each case had one parent/carer with ADHD and a child with ADHD. Eight children (aged 7–17 years; Mean = 12.6; S.D. = 3.4) and ten parents (2 males) participated. Four parentw/carers reported a diagnosis of ADHD themselves (2 females) and 6 mothers participated who had a spouse with ADHD. Triangulation was achieved using multiple interviews (parent/carers and child), a demographic survey, and creative methods with the children to contribute to a highly contextualised understanding of stakeholders’ experiences. Research findings demonstrated that there may be positive and negative consequences when both parent and child have ADHD. On the one hand, it may contribute to greater dysfunction, when parents with ADHD struggle to stick to routines and remain calm and organised. On the other hand, children with ADHD may feel a sense of belonging and less different, parents believe they have greater understanding, and shared interactional preferences may have benefits. Findings will be discussed in terms of their implications for practice with families and future research

The Formation and Evolution of the First Massive Black Holes

The first massive astrophysical black holes likely formed at high redshifts (z>10) at the centers of low mass (~10^6 Msun) dark matter concentrations. These black holes grow by mergers and gas accretion, evolve into the population of bright quasars observed at lower redshifts, and eventually leave the supermassive black hole remnants that are ubiquitous at the centers of galaxies in the nearby universe. The astrophysical processes responsible for the formation of the earliest seed black holes are poorly understood. The purpose of this review is threefold: (1) to describe theoretical expectations for the formation and growth of the earliest black holes within the general paradigm of hierarchical cold dark matter cosmologies, (2) to summarize several relevant recent observations that have implications for the formation of the earliest black holes, and (3) to look into the future and assess the power of forthcoming observations to probe the physics of the first active galactic nuclei.Comment: 39 pages, review for "Supermassive Black Holes in the Distant Universe", Ed. A. J. Barger, Kluwer Academic Publisher

The Formation of the First Massive Black Holes

Supermassive black holes (SMBHs) are common in local galactic nuclei, and SMBHs as massive as several billion solar masses already exist at redshift z=6. These earliest SMBHs may grow by the combination of radiation-pressure-limited accretion and mergers of stellar-mass seed BHs, left behind by the first generation of metal-free stars, or may be formed by more rapid direct collapse of gas in rare special environments where dense gas can accumulate without first fragmenting into stars. This chapter offers a review of these two competing scenarios, as well as some more exotic alternative ideas. It also briefly discusses how the different models may be distinguished in the future by observations with JWST, (e)LISA and other instruments.Comment: 47 pages with 306 references; this review is a chapter in "The First Galaxies - Theoretical Predictions and Observational Clues", Springer Astrophysics and Space Science Library, Eds. T. Wiklind, V. Bromm & B. Mobasher, in pres