723 research outputs found
On post-Lie algebras, Lie--Butcher series and moving frames
Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on
differential manifolds. They have been studied extensively in recent years,
both from algebraic operadic points of view and through numerous applications
in numerical analysis, control theory, stochastic differential equations and
renormalization. Butcher series are formal power series founded on pre-Lie
algebras, used in numerical analysis to study geometric properties of flows on
euclidean spaces. Motivated by the analysis of flows on manifolds and
homogeneous spaces, we investigate algebras arising from flat connections with
constant torsion, leading to the definition of post-Lie algebras, a
generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately
associated with euclidean geometry, post-Lie algebras occur naturally in the
differential geometry of homogeneous spaces, and are also closely related to
Cartan's method of moving frames. Lie--Butcher series combine Butcher series
with Lie series and are used to analyze flows on manifolds. In this paper we
show that Lie--Butcher series are founded on post-Lie algebras. The functorial
relations between post-Lie algebras and their enveloping algebras, called
D-algebras, are explored. Furthermore, we develop new formulas for computations
in free post-Lie algebras and D-algebras, based on recursions in a magma, and
we show that Lie--Butcher series are related to invariants of curves described
by moving frames.Comment: added discussion of post-Lie algebroid
Backward error analysis and the substitution law for Lie group integrators
Butcher series are combinatorial devices used in the study of numerical
methods for differential equations evolving on vector spaces. More precisely,
they are formal series developments of differential operators indexed over
rooted trees, and can be used to represent a large class of numerical methods.
The theory of backward error analysis for differential equations has a
particularly nice description when applied to methods represented by Butcher
series. For the study of differential equations evolving on more general
manifolds, a generalization of Butcher series has been introduced, called
Lie--Butcher series. This paper presents the theory of backward error analysis
for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio
Cellular Scaling Rules of Insectivore Brains
Insectivores represent extremes in mammalian body size and brain size, retaining various “primitive” morphological characteristics, and some species of Insectivora are thought to share similarities with small-bodied ancestral eutherians. This raises the possibility that insectivore brains differ from other taxa, including rodents and primates, in cellular scaling properties. Here we examine the cellular scaling rules for insectivore brains and demonstrate that insectivore scaling rules overlap somewhat with those for rodents and primates such that the insectivore cortex shares scaling rules with rodents (increasing faster in size than in numbers of neurons), but the insectivore cerebellum shares scaling rules with primates (increasing isometrically). Brain structures pooled as “remaining areas” appear to scale similarly across all three mammalian orders with respect to numbers of neurons, and the numbers of non-neurons appear to scale similarly across all brain structures for all three orders. Therefore, common scaling rules exist, to different extents, between insectivore, rodent, and primate brain regions, and it is hypothesized that insectivores represent the common aspects of each order. The olfactory bulbs of insectivores, however, offer a noteworthy exception in that neuronal density increases linearly with increasing structure mass. This implies that the average neuronal cell size decreases with increasing olfactory bulb mass in order to accommodate greater neuronal density, and represents the first documentation of a brain structure gaining neurons at a greater rate than mass. This might allow insectivore brains to concentrate more neurons within the olfactory bulbs without a prohibitively large and metabolically costly increase in structure mass
Continuous and discrete Clebsch variational principles
The Clebsch method provides a unifying approach for deriving variational
principles for continuous and discrete dynamical systems where elements of a
vector space are used to control dynamics on the cotangent bundle of a Lie
group \emph{via} a velocity map. This paper proves a reduction theorem which
states that the canonical variables on the Lie group can be eliminated, if and
only if the velocity map is a Lie algebra action, thereby producing the
Euler-Poincar\'e (EP) equation for the vector space variables. In this case,
the map from the canonical variables on the Lie group to the vector space is
the standard momentum map defined using the diamond operator. We apply the
Clebsch method in examples of the rotating rigid body and the incompressible
Euler equations. Along the way, we explain how singular solutions of the EP
equation for the diffeomorphism group (EPDiff) arise as momentum maps in the
Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch
variational principle is discretised to produce a variational integrator for
the dynamical system. We obtain a discrete map from which the variables on the
cotangent bundle of a Lie group may be eliminated to produce a discrete EP
equation for elements of the vector space. We give an integrator for the
rotating rigid body as an example. We also briefly discuss how to discretise
infinite-dimensional Clebsch systems, so as to produce conservative numerical
methods for fluid dynamics
A new class of IMP dehydrogenase with a role in self-resistance of mycophenolic acid producing fungi
<p>Abstract</p> <p>Background</p> <p>Many secondary metabolites produced by filamentous fungi have potent biological activities, to which the producer organism must be resistant. An example of pharmaceutical interest is mycophenolic acid (MPA), an immunosuppressant molecule produced by several <it>Penicillium </it>species. The target of MPA is inosine-5'-monophosphate dehydrogenase (IMPDH), which catalyses the rate limiting step in the synthesis of guanine nucleotides. The recent discovery of the MPA biosynthetic gene cluster from <it>Penicillium brevicompactum </it>revealed an extra copy of the IMPDH-encoding gene (<it>mpaF</it>) embedded within the cluster. This finding suggests that the key component of MPA self resistance is likely based on the IMPDH encoded by <it>mpaF</it>.</p> <p>Results</p> <p>In accordance with our hypothesis, heterologous expression of <it>mpaF </it>dramatically increased MPA resistance in a model fungus, <it>Aspergillus nidulans</it>, which does not produce MPA. The growth of an <it>A. nidulans </it>strain expressing <it>mpaF </it>was only marginally affected by MPA at concentrations as high as 200 μg/ml. To further substantiate the role of <it>mpaF </it>in MPA resistance, we searched for <it>mpaF </it>orthologs in six MPA producer/non-producer strains from <it>Penicillium </it>subgenus <it>Penicillium</it>. All six strains were found to hold two copies of IMPDH. A cladistic analysis based on the corresponding cDNA sequences revealed a novel group constituting <it>mpaF </it>homologs. Interestingly, a conserved tyrosine residue in the original class of IMPDHs is replaced by a phenylalanine residue in the new IMPDH class.</p> <p>Conclusions</p> <p>We identified a novel variant of the IMPDH-encoding gene in six different strains from <it>Penicillium </it>subgenus <it>Penicillium</it>. The novel IMPDH variant from MPA producer <it>P. brevicompactum </it>was shown to confer a high degree of MPA resistance when expressed in a non-producer fungus. Our study provides a basis for understanding the molecular mechanism of MPA resistance and has relevance for biotechnological and pharmaceutical applications.</p
Wide field CO J = 3->2 mapping of the Serpens Cloud Core
Context. Outflows provide indirect means to get an insight on diverse star
formation associated phenomena. On scales of individual protostellar cores,
outflows combined with intrinsic core properties can be used to study the mass
accretion/ejection process of heavily embedded protostellar sources. Methods.
An area comprising 460"x230" of the Serpens cloud core has been mapped in 12 CO
J = 3\to 2 with the HARP-B heterodyne array at the James Clerk Maxwell
Telescope; J = 3\to 2 observations are more sensitive tracers of hot outflow
gas than lower J CO transitions; combined with the high sensitivity of the
HARP-B receptors outflows are sharply outlined, enabling their association with
individual protostellar cores. Results. Most of ~20 observed outflows are found
to be associated with known protostellar sources in bipolar or unipolar
configurations. All but two outflow/core pairs in our sample tend to have a
projected orientation spanning roughly NW-SE. The overall momentum driven by
outflows in Serpens lies between 3.2 and 5.1 x 10^(-1) M\odot km s^(-1), the
kinetic energy from 4.3 to 6.7 x 10^(43) erg and momentum flux is between 2.8
and 4.4 x 10^(-4) M\odot km s^(-1) yr^(-1). Bolometric luminosities of
protostellar cores based on Spitzer photometry are found up to an order of
magnitude lower than previous estimations derived with IRAS/ISO data.
Conclusions. We confirm the validity of the existing correlations between the
momentum flux and bolometric luminosity of Class I sources for the homogenous
sample of Serpens, though we suggest that they should be revised by a shift to
lower luminosities. All protostars classified as Class 0 sources stand well
above the known Class I correlations, indicating a decline in momentum flux
between the two classes.Comment: 15 pages, 10 figures, accepted for publication in A&
Evolution of the polarization of the optical afterglow of the gamma-ray burst GRB 030329
We report 31 polarimetric observations of the afterglow of GRB 030329 with
high signal-to-noise and high sampling frequency. We establish the polarization
light curve, detect sustained polarization at the percent level, and find
significant variability of polarization degree and angle. The data imply that
the afterglow magnetic field has small coherence length and is mostly random,
probably generated by turbulence.Comment: Nature 426 (13. Nov. 2003), 2 figure
Hopf algebras in dynamical systems theory
The theory of exact and of approximate solutions for non-autonomous linear
differential equations forms a wide field with strong ties to physics and
applied problems. This paper is meant as a stepping stone for an exploration of
this long-established theme, through the tinted glasses of a (Hopf and
Rota-Baxter) algebraic point of view. By reviewing, reformulating and
strengthening known results, we give evidence for the claim that the use of
Hopf algebra allows for a refined analysis of differential equations. We
revisit the renowned Campbell-Baker-Hausdorff-Dynkin formula by the modern
approach involving Lie idempotents. Approximate solutions to differential
equations involve, on the one hand, series of iterated integrals solving the
corresponding integral equations; on the other hand, exponential solutions.
Equating those solutions yields identities among products of iterated Riemann
integrals. Now, the Riemann integral satisfies the integration-by-parts rule
with the Leibniz rule for derivations as its partner; and skewderivations
generalize derivations. Thus we seek an algebraic theory of integration, with
the Rota-Baxter relation replacing the classical rule. The methods to deal with
noncommutativity are especially highlighted. We find new identities, allowing
for an extensive embedding of Dyson-Chen series of time- or path-ordered
products (of generalized integration operators); of the corresponding Magnus
expansion; and of their relations, into the unified algebraic setting of
Rota-Baxter maps and their inverse skewderivations. This picture clarifies the
approximate solutions to generalized integral equations corresponding to
non-autonomous linear (skew)differential equations.Comment: International Journal of Geometric Methods in Modern Physics, in
pres
Applying GRADE-CERQual to qualitative evidence synthesis findings-paper 7: Understanding the potential impacts of dissemination bias
This is the final version. Available from BMC via the DOI in this record. Additional materials are available on the GRADE-CERQual website (www.cerqual.org).Background: The GRADE-CERQual (Confidence in Evidence from Reviews of Qualitative research) approach has been developed by the GRADE (Grading of Recommendations Assessment, Development and Evaluation) Working Group. The approach has been developed to support the use of findings from qualitative evidence syntheses in decision-making, including guideline development and policy formulation. CERQual includes four components for assessing how much confidence to place in findings from reviews of qualitative research (also referred to as qualitative evidence syntheses): (1) methodological limitations, (2) coherence, (3) adequacy of data and (4) relevance. This paper is part of a series providing guidance on how to apply CERQual and focuses on a probable fifth component, dissemination bias. Given its exploratory nature, we are not yet able to provide guidance on applying this potential component of the CERQual approach. Instead, we focus on how dissemination bias might be conceptualised in the context of qualitative research and the potential impact dissemination bias might have on an overall assessment of confidence in a review finding. We also set out a proposed research agenda in this area. Methods: We developed this paper by gathering feedback from relevant research communities, searching MEDLINE and Web of Science to identify and characterise the existing literature discussing or assessing dissemination bias in qualitative research and its wider implications, developing consensus through project group meetings, and conducting an online survey of the extent, awareness and perceptions of dissemination bias in qualitative research. Results: We have defined dissemination bias in qualitative research as a systematic distortion of the phenomenon of interest due to selective dissemination of studies or individual study findings. Dissemination bias is important for qualitative evidence syntheses as the selective dissemination of qualitative studies and/or study findings may distort our understanding of the phenomena that these syntheses aim to explore and thereby undermine our confidence in these findings. Dissemination bias has been extensively examined in the context of randomised controlled trials and systematic reviews of such studies. The effects of potential dissemination bias are formally considered, as publication bias, within the GRADE approach. However, the issue has received almost no attention in the context of qualitative research. Because of very limited understanding of dissemination bias and its potential impact on review findings in the context of qualitative evidence syntheses, this component is currently not included in the GRADE-CERQual approach. Conclusions: Further research is needed to establish the extent and impacts of dissemination bias in qualitative research and the extent to which dissemination bias needs to be taken into account when we assess how much confidence we have in findings from qualitative evidence syntheses.WHONorad (Norwegian Agency for Development Cooperation)Research Council of NorwayCochrane Methods Innovation FundSouth African Medical Research Counci
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