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 $R$ 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 $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for $d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln t$.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

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

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

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]

Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, can not be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish the relation to the Continuous Time Random Walk theory. We show that the distributed order time fractional diffusion equation describes the sub-diffusion random process which is subordinated to the Wiener process and whose diffusion exponent diminishes in time (retarding sub-diffusion) leading to superslow diffusion, for which the square displacement grows logarithmically in time. We also demonstrate that the distributed order space fractional diffusion equation describes super-diffusion phenomena when the diffusion exponent grows in time (accelerating super-diffusion).Comment: 11 pages, LaTe