The abelianization of the Johnson kernel

We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym H 1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of G. In this setup, we also obtain a precise nilpotence test. © European Mathematical Society 2014.

Hybrid error correction and de novo assembly of single-molecule sequencing reads.

Single-molecule sequencing instruments can generate multikilobase sequences with the potential to greatly improve genome and transcriptome assembly. However, the error rates of single-molecule reads are high, which has limited their use thus far to resequencing bacteria. To address this limitation, we introduce a correction algorithm and assembly strategy that uses short, high-fidelity sequences to correct the error in single-molecule sequences. We demonstrate the utility of this approach on reads generated by a PacBio RS instrument from phage, prokaryotic and eukaryotic whole genomes, including the previously unsequenced genome of the parrot Melopsittacus undulatus, as well as for RNA-Seq reads of the corn (Zea mays) transcriptome. Our long-read correction achieves >99.9% base-call accuracy, leading to substantially better assemblies than current sequencing strategies: in the best example, the median contig size was quintupled relative to high-coverage, second-generation assemblies. Greater gains are predicted if read lengths continue to increase, including the prospect of single-contig bacterial chromosome assembly.

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

The reappearance hypothesis revisited: recurrent involuntary memories after traumatic events and in everyday life.

Recurrent involuntary memories are autobiographical memories that come to mind with no preceding retrieval attempt and that are subjectively experienced as being repetitive. Clinically, they are classified as a symptom of posttraumatic stress disorder. The present work is the first to systematically examine recurrent involuntary memories outside clinical settings. Study 1 examines recurrent involuntary memories among survivors of the tsunami catastrophe in Southeast Asia in 2004. Study 2 examines recurrent involuntary memories in a large general population. Study 3 examines whether the contents of recurrent involuntary memories recorded in a diary study are duplicates of, or differ from, one another. We show that recurrent involuntary memories are not limited to clinical populations or to emotionally negative experiences; that they typically do not come to mind in a fixed and unchangeable form; and that they show the same pattern regarding accessibility as do autobiographical memories in general. We argue that recurrent involuntary memories after traumas and in everyday life can be explained in terms of general and well-established mechanisms of autobiographical memory.

The ocean sampling day consortium.

Ocean Sampling Day was initiated by the EU-funded Micro B3 (Marine Microbial Biodiversity, Bioinformatics, Biotechnology) project to obtain a snapshot of the marine microbial biodiversity and function of the world's oceans. It is a simultaneous global mega-sequencing campaign aiming to generate the largest standardized microbial data set in a single day. This will be achievable only through the coordinated efforts of an Ocean Sampling Day Consortium, supportive partnerships and networks between sites. This commentary outlines the establishment, function and aims of the Consortium and describes our vision for a sustainable study of marine microbial communities and their embedded functional traits.

Polymorphisms at the microRNA binding-site of the stem cell marker gene CD133 modify susceptibility to and survival of gastric cancer.

CD133 is one of the most common stem cell markers, and functional single nucleotide polymorphisms (SNPs) of CD133 may modulate its gene functions and thus cancer risk and patient survival. We hypothesized that potentially functional CD133 SNPs are associated with gastric cancer (GC) risk and survival. To test this hypothesis, we conducted a case-control study of 371 GC patients and 313 cancer-free controls frequency-matched by age, sex, and ethnicity. We genotyped four selected, potentially functional CD133 SNPs (rs2240688A>C, rs7686732C>G, rs10022537T>A, and rs3130C>T) and used logistic regression analysis for associations of these SNPs with GC risk and Cox hazards regression analysis for survival. We found that compared with the miRNA binding site rs2240688 AA genotype, AC + CC genotypes were associated with significantly increased GC risk (adjusted OR = 1.52, 95% CI = 1.09-2.13); for another miRNA binding site rs3130C>T SNP, the TT genotype was associated with significantly reduced GC risk (adjusted OR = 0.68, 95% CI = 0.48-0.97), compared with CC + CT genotypes. In all patients, the risk rs3130 TT variant genotype was significantly associated with overall survival (OS) (adjusted P(trend) = 0.016 and 0.007 under additive and recessive models, respectively). These findings suggest that these two CD133 miRNA binding site variants, rs2240688 and rs3130, may be potential biomarkers for genetic susceptibility to GC and possible predictors for survival in GC patients but require further validation by larger studies.

Explicit DNase sequence bias modeling enables high-resolution transcription factor footprint detection.

DNaseI footprinting is an established assay for identifying transcription factor (TF)-DNA interactions with single base pair resolution. High-throughput DNase-seq assays have recently been used to detect in vivo DNase footprints across the genome. Multiple computational approaches have been developed to identify DNase-seq footprints as predictors of TF binding. However, recent studies have pointed to a substantial cleavage bias of DNase and its negative impact on predictive performance of footprinting. To assess the potential for using DNase-seq to identify individual binding sites, we performed DNase-seq on deproteinized genomic DNA and determined sequence cleavage bias. This allowed us to build bias corrected and TF-specific footprint models. The predictive performance of these models demonstrated that predicted footprints corresponded to high-confidence TF-DNA interactions. DNase-seq footprints were absent under a fraction of ChIP-seq peaks, which we show to be indicative of weaker binding, indirect TF-DNA interactions or possible ChIP artifacts. The modeling approach was also able to detect variation in the consensus motifs that TFs bind to. Finally, cell type specific footprints were detected within DNase hypersensitive sites that are present in multiple cell types, further supporting that footprints can identify changes in TF binding that are not detectable using other strategies.

A population model of folate-mediated one-carbon metabolism.

BACKGROUND: Previous mathematical models for hepatic and tissue one-carbon metabolism have been combined and extended to include a blood plasma compartment. We use this model to study how the concentrations of metabolites that can be measured in the plasma are related to their respective intracellular concentrations. METHODS: The model consists of a set of ordinary differential equations, one for each metabolite in each compartment, and kinetic equations for metabolism and for transport between compartments. The model was validated by comparison to a variety of experimental data such as the methionine load test and variation in folate intake. We further extended this model by introducing random and systematic variation in enzyme activity. OUTCOMES AND CONCLUSIONS: A database of 10,000 virtual individuals was generated, each with a quantitatively different one-carbon metabolism. Our population has distributions of folate and homocysteine in the plasma and tissues that are similar to those found in the NHANES data. The model reproduces many other sets of clinical data. We show that tissue and plasma folate is highly correlated, but liver and plasma folate much less so. Oxidative stress increases the plasma S-adenosylmethionine/S-adenosylhomocysteine (SAM/SAH) ratio. We show that many relationships among variables are nonlinear and in many cases we provide explanations. Sampling of subpopulations produces dramatically different apparent associations among variables. The model can be used to simulate populations with polymorphisms in genes for folate metabolism and variations in dietary input.

Structure of the polyisoprenyl-phosphate glycosyltransferase GtrB and insights into the mechanism of catalysis.

The attachment of a sugar to a hydrophobic polyisoprenyl carrier is the first step for all extracellular glycosylation processes. The enzymes that perform these reactions, polyisoprenyl-glycosyltransferases (PI-GTs) include dolichol phosphate mannose synthase (DPMS), which generates the mannose donor for glycosylation in the endoplasmic reticulum. Here we report the 3.0 Å resolution crystal structure of GtrB, a glucose-specific PI-GT from Synechocystis, showing a tetramer in which each protomer contributes two helices to a membrane-spanning bundle. The active site is 15 Å from the membrane, raising the question of how water-soluble and membrane-embedded substrates are brought into apposition for catalysis. A conserved juxtamembrane domain harbours disease mutations, which compromised activity in GtrB in vitro and in human DPM1 tested in zebrafish. We hypothesize a role of this domain in shielding the polyisoprenyl-phosphate for transport to the active site. Our results reveal the basis of PI-GT function, and provide a potential molecular explanation for DPM1-related disease.

Efficacy of Pharmacokinetics-Directed Busulfan, Cyclophosphamide, and Etoposide Conditioning and Autologous Stem Cell Transplantation for Lymphoma: Comparison of a Multicenter Phase II Study and CIBMTR Outcomes.

Busulfan, cyclophosphamide, and etoposide (BuCyE) is a commonly used conditioning regimen for autologous stem cell transplantation (ASCT). This multicenter, phase II study examined the safety and efficacy of BuCyE with individually adjusted busulfan based on preconditioning pharmacokinetics. The study initially enrolled Hodgkin lymphoma (HL) and non-Hodgkin lymphoma (NHL) patients ages 18 to 80 years but was amended due to high early treatment-related mortality (TRM) in patients > 65 years. BuCyE outcomes were compared with contemporaneous recipients of carmustine, etoposide, cytarabine, and melphalan (BEAM) from the Center for International Blood and Marrow Transplant Research. Two hundred seven subjects with HL (n = 66) or NHL (n = 141) were enrolled from 32 centers in North America, and 203 underwent ASCT. Day 100 TRM for all subjects (n = 203), patients > 65 years (n = 17), and patients ≤ 65 years (n = 186) were 4.5%, 23.5%, and 2.7%, respectively. The estimated rates of 2-year progression-free survival (PFS) were 33% for HL and 58%, 77%, and 43% for diffuse large B cell lymphoma (DLBCL; n = 63), mantle cell lymphoma (MCL; n = 29), and follicular lymphoma (FL; n = 23), respectively. The estimated rates of 2-year overall survival (OS) were 76% for HL and 65%, 89%, and 89% for DLBCL, MCL, and FL, respectively. In the matched analysis rates of 2-year TRM were 3.3% for BuCyE and 3.9% for BEAM, and there were no differences in outcomes for NHL. Patients with HL had lower rates of 2-year PFS with BuCyE, 33% (95% CI, 21% to 46%), than with BEAM, 59% (95% CI, 52% to 66%), with no differences in TRM or OS. BuCyE provided adequate disease control and safety in B cell NHL patients ≤ 65 years but produced worse PFS in HL patients when compared with BEAM.

Patent litigation in Europe

We compare patent litigation cases across four European jurisdictions – Germany, France, the Netherlands, and the UK – covering cases filed during the period 2000-2008. For our analysis, we assemble a new dataset that contains detailed information at the case, litigant, and patent level for patent cases filed at the major courts in the four jurisdictions. We find substantial differences across jurisdictions in terms of case loads. Courts in Germany hear by far the largest number of cases in absolute terms, but also when taking country size into account. We also find important between-country differences in terms of outcomes, the share of cases that is appealed, as well as the characteristics of litigants and litigated patents. A considerable number of patents are litigated in multiple jurisdictions, but the majority of patents are subject to litigation only in one of the four jurisdictions.