284 research outputs found
Symmetry of Magnetically Ordered Quasicrystals
The notion of magnetic symmetry is reexamined in light of the recent
observation of long range magnetic order in icosahedral quasicrystals [Charrier
et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of
a magnetically-ordered (periodic or quasiperiodic) crystal, given in terms of a
``spin space group,'' and its neutron diffraction diagram is established. In
doing so, an outline of a symmetry classification scheme for magnetically
ordered quasiperiodic crystals is provided. Predictions are given for the
expected diffraction patterns of magnetically ordered icosahedral crystals,
provided their symmetry is well described by icosahedral spin space groups.Comment: 5 pages. Accepted for publication in Phys. Rev. Letter
Order statistics of the trapping problem
When a large number N of independent diffusing particles are placed upon a
site of a d-dimensional Euclidean lattice randomly occupied by a concentration
c of traps, what is the m-th moment of the time t_{j,N} elapsed
until the first j are trapped? An exact answer is given in terms of the
probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j
particles is trapped by time t. The Rosenstock approximation is used to
evaluate Phi_M(t), and it is found that for a large range of trap
concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as
x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant
and two corrective terms) is given for for the one-dimensional
lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
Order statistics for d-dimensional diffusion processes
We present results for the ordered sequence of first passage times of arrival
of N random walkers at a boundary in Euclidean spaces of d dimensions
On the joint residence time of N independent two-dimensional Brownian motions
We study the behavior of several joint residence times of N independent
Brownian particles in a disc of radius in two dimensions. We consider: (i)
the time T_N(t) spent by all N particles simultaneously in the disc within the
time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N
particles spend together in the disc within the time interval [0,t]; and (iii)
the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend
together in the disc within the time interval [0,t]. We obtain very simple
exact expressions for the expectations of these three residence times in the
limit t\to\infty.Comment: 8 page
Critical dimensions for random walks on random-walk chains
The probability distribution of random walks on linear structures generated
by random walks in -dimensional space, , is analytically studied
for the case . It is shown to obey the scaling form
, where is
the density of the chain. Expanding in powers of , we find that
there exists an infinite hierarchy of critical dimensions, ,
each one characterized by a logarithmic correction in . Namely, for
, ; for ,
; for , ; for , ; for , , {\it etc.\/} In particular, for
, this implies that the temporal dependence of the probability density of
being close to the origin .Comment: LATeX, 10 pages, no figures submitted for publication in PR
Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies
<p>Abstract</p> <p>Background</p> <p>To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1) experimental measurement of participating molecules, (2) assignment of rate laws to each reaction, and (3) parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem.</p> <p>Results</p> <p>We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in <it>C. glutamicum</it>. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1) coarse-grained comparison of the algorithms on all models and (2) fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis.</p> <p>Conclusion</p> <p>A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics model. A Langevin model is advisable to take stochastic effects into account. To estimate the model parameters, three algorithms are particularly useful: For first attempts the settings-free Tribes algorithm yields valuable results. Particle swarm optimization and differential evolution provide significantly better results with appropriate settings.</p
Tetrakis{2,4-bis[(1-oxo-2-pyridyl)sulfanylmethyl]mesitylene} acetone hemisolvate 11.5-hydrate
In the crystal structure of the title compound, 4C21H22N2O2S2·0.5C3H6O·11.5H2O, there are four crystallographically independent molecules (A, B, C, D) with similar geometries, 11 water molecules and a solvent acetone molecule which is disordered with a water molecule with occupancy factors of 0.5:0.5. The dihedral angles formed by the mesitylene ring with the two pyridyl rings are 82.07 (3) and 78.39 (3)° in molecule A, 86.20 (3) and 82.29 (3)° in molecule B, 81.05 (3) and 76.0 (4)° in molecule C, 86.0 (3) and 80.9 (3)° in moleule D. The two pyridyl rings form dihedral angles of 41.17 (4), 64.01 (3), 81.9 (3) and 82.25 (3)° in molecules A, B, C and D, respectively. The crystal structure is stabilized by intermolecular O—H⋯O hydrogen bonds and possible weak C—H⋯π interactions. Some short intramolecular S⋯O contacts are apparent [2.684 (4)–2.702 (4) Å]
2-(2,3,5,6-Tetramethylbenzylsulfanyl)pyridine N-oxide
In the title compound, C16H19NOS, the durene ring and the oxopyridyl ring form a dihedral angle of 82.26 (7)°. The crystal structure is stabilized by intermolecular C—H⋯O hydrogen bonds, weak C—H⋯π interactions and π–π interactions [centroid–centroid distance of 3.4432 (19) Å], together with intramolecular S⋯O [2.657 (2) Å] short contacts
Assessment of the extent of unpublished studies in prognostic factor research: a systematic review of p53 immunohistochemistry in bladder cancer as an example
Objectives
When study groups fail to publish their results, a subsequent systematic review may come to incorrect conclusions when combining information only from published studies. p53 expression measured by immunohistochemistry is a potential prognostic factor in bladder cancer. Although numerous studies have been conducted, its role is still under debate. The assumption that unpublished studies too harbour evidence on this research topic leads to the question about the attributable effect when adding this information and comparing it with published data. Thus, the aim was to identify published and unpublished studies and to explore their differences potentially affecting the conclusion on its function as a prognostic biomarker.
Design
Systematic review of published and unpublished studies assessing p53 in bladder cancer in Germany between 1993 and 2007.
Results
The systematic search revealed 16 studies of which 11 (69%) have been published and 5 (31%) have not. Key reason for not publishing the results was a loss of interest of the investigators. There were no obviously larger differences between published and unpublished studies. However, a meaningful meta-analysis was not possible mainly due to the poor (ie, incomplete) reporting of study results.
Conclusions
Within this well-defined population of studies, we could provide empirical evidence for the failure of study groups to publish their results that was mainly caused by loss of interest. This fact may be coresponsible for the role of p53 as a prognostic factor still being unclear. We consider p53 and the restriction to studies in Germany as a specific example, but the critical issues are probably similar for other prognostic factors and other countries
Assessment of the extent of unpublished studies in prognostic factor research: a systematic review of p53 immunohistochemistry in bladder cancer as an example
Objectives: When study groups fail to publish their results, a subsequent systematic review may come to incorrect conclusions when combining information only from published studies. p53 expression measured by immunohistochemistry is a potential prognostic factor in bladder cancer. Although numerous studies have been conducted, its role is still under debate. The assumption that unpublished studies too harbour evidence on this research topic leads to the question about the attributable effect when adding this information and comparing it with published data. Thus, the aim was to identify published and unpublished studies and to explore their differences potentially affecting the conclusion on its function as a prognostic biomarker.
Design: Systematic review of published and unpublished studies assessing p53 in bladder cancer in Germany between 1993 and 2007.
Results: The systematic search revealed 16 studies of which 11 (69%) have been published and 5 (31%) have not. Key reason for not publishing the results was a loss of interest of the investigators. There were no obviously larger differences between published and unpublished studies. However, a meaningful meta-analysis was not possible mainly due to the poor (ie, incomplete) reporting of study results.
Conclusions: Within this well-defined population of studies, we could provide empirical evidence for the failure of study groups to publish their results that was mainly caused by loss of interest. This fact may be coresponsible for the role of p53 as a prognostic factor still being unclear. We consider p53 and the restriction to studies in Germany as a specific example, but the critical issues are probably similar for other prognostic factors and other countries
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