Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?

Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the critical finite-size scaling functions has been derived by employing a scaling limit that differs from the traditional finite-size scaling limit. In this paper the analytical predictions are compared with Monte Carlo simulations. We find good agreement between the analytical expression and the simulation results. The agreement is consistent with the possibility that the functional form of the critical finite-size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters, most notably the equation of state exponent.Comment: 11 pages postscript, plus 2 separate postscript figures, all as uuencoded gzipped tar file. To appear in J. Phys. A

Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model

We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$ of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$, versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ``Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ``connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of $\chi^{(3)}$ and $\chi^{(4)}$. We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the $n$-particle contributions $\chi^{(n)}$ and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlev\'e oriented approach.Comment: 21 pages Proceedings of the Counting Complexity conferenc

Anomalous diffusion and the first passage time problem

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H-functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.Comment: 25 pages, 4 figure

The importance of quantitative MÖssbauer spectroscopy of MoFe-protein from Azotobacter vinelandii

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65965/1/j.1432-1033.1985.tb08679.x.pd

An inventory of the Aspergillus niger secretome by combining in silico predictions with shotgun proteomics data

<p>Abstract</p> <p>Background</p> <p>The ecological niche occupied by a fungal species, its pathogenicity and its usefulness as a microbial cell factory to a large degree depends on its secretome. Protein secretion usually requires the presence of a N-terminal signal peptide (SP) and by scanning for this feature using available highly accurate SP-prediction tools, the fraction of potentially secreted proteins can be directly predicted. However, prediction of a SP does not guarantee that the protein is actually secreted and current <it>in silico </it>prediction methods suffer from gene-model errors introduced during genome annotation.</p> <p>Results</p> <p>A majority rule based classifier that also evaluates signal peptide predictions from the best homologs of three neighbouring <it>Aspergillus </it>species was developed to create an improved list of potential signal peptide containing proteins encoded by the <it>Aspergillus niger </it>genome. As a complement to these <it>in silico </it>predictions, the secretome associated with growth and upon carbon source depletion was determined using a shotgun proteomics approach. Overall, some 200 proteins with a predicted signal peptide were identified to be secreted proteins. Concordant changes in the secretome state were observed as a response to changes in growth/culture conditions. Additionally, two proteins secreted via a non-classical route operating in <it>A. niger </it>were identified.</p> <p>Conclusions</p> <p>We were able to improve the <it>in silico </it>inventory of <it>A. niger </it>secretory proteins by combining different gene-model predictions from neighbouring Aspergilli and thereby avoiding prediction conflicts associated with inaccurate gene-models. The expected accuracy of signal peptide prediction for proteins that lack homologous sequences in the proteomes of related species is 85%. An experimental validation of the predicted proteome confirmed <it>in silico </it>predictions.</p

Proteomic Analysis of the Secretory Response of Aspergillus niger to D-Maltose and D-Xylose

Fungi utilize polysaccharide substrates through extracellular digestion catalyzed by secreted enzymes. Thus far, protein secretion by the filamentous fungus Aspergillus niger has mainly been studied at the level of individual proteins and by genome and transcriptome analyses. To extend these studies, a complementary proteomics approach was applied with the aim to investigate the changes in secretome and microsomal protein composition resulting from a shift to a high level secretion condition. During growth of A. niger on d-sorbitol, small amounts of d-maltose or d-xylose were used as inducers of the extracellular amylolytic and xylanolytic enzymes. Upon induction, protein compositions in the extracellular broth as well as in enriched secretory organelle (microsomal) fractions were analyzed using a shotgun proteomics approach. In total 102 secreted proteins and 1,126 microsomal proteins were identified in this study. Induction by d-maltose or d-xylose resulted in the increase in specific extracellular enzymes, such as glucoamylase A on d-maltose and β-xylosidase D on d-xylose, as well as of microsomal proteins. This reflects the differential expression of selected genes coding for dedicated extracellular enzymes. As expected, the addition of extra d-sorbitol had no effect on the expression of carbohydrate-active enzymes, compared to addition of d-xylose or d-maltose. Furthermore, d-maltose induction caused an increase in microsomal proteins related to translation (e.g., Rpl15) and vesicular transport (e.g., the endosomal-cargo receptor Erv14). Millimolar amounts of the inducers d-maltose and d-xylose are sufficient to cause a direct response in specific protein expression levels. Also, after induction by d-maltose or d-xylose, the induced enzymes were found in microsomes and extracellular. In agreement with our previous findings for d-xylose induction, d-maltose induction leads to recruitment of proteins involved in proteasome-mediated degradation

Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator

This is a pre-print. The definitive version: COOMBES, S. and OSBALDESTIN, A.H., 2000. Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator. Physical Review E, 62(3), pp.4057-4066 Part B.The response of an excitable neuron to trains of electrical spikes is relevant to the understanding of the neural code. In this paper we study a neurobiologically motivated relaxation oscillator, with appropriately identified fast and slow coordinates, that admits an explicit mathematical analysis. An application of geometric singular perturbation theory shows the existence of an attracting invariant manifold which is used to construct the Fenichel normal form for the system. This facilitates the calculation of the response of the system to pulsatile stimulation and allows the construction of a so-called extended isochronal map. The isochronal map is shown to have a single discontinuity and be of a type that can admit three types of response: mode-locked, quasi-periodic and chaotic. The bifurcation structure of the system is seen to be extremely rich and supports period-adding bifurcations separated by windows of both chaos and periodicity. A bifurcation analysis of the isochronal map is presented in conjunction with a description of the various routes to chaos in this system