Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

A New Estimate of the Cutoff Value in the Bak-Sneppen Model

We present evidence that the Bak-Sneppen model of evolution on $N$ vertices requires $N^3$ iterates to reach equilibrium. This is substantially more than previous authors suggested (on the order of $N^2$). Based on that estimate, we present a novel algorithm inspired by previous rank-driven analyses of the model allowing for direct simulation of the model with populations of up to $N = 25600$ for $2\cdot N^3$ iterations. These extensive simulations suggest a cutoff value of $x^* = 0.66692 \pm 0.00003$, a value slightly lower than previously estimated yet still distinctly above $2/3$. We also study how the cutoff values $x^*_N$ at finite $N$ approximate the conjectured value $x^*$ at $N=\infty$. Assuming $x^*_N-x^*_\infty \sim N^{-\nu}$, we find that $\nu=0.978\pm 0.025$, which is significantly lower than previous estimates ($\nu\approx 1.4$).Comment: 18 figures, 12 page

Scaffolding School Pupils’ Scientific Argumentation with Evidence-Based Dialogue Maps

This chapter reports pilot work investigating the potential of Evidence-based Dialogue Mapping to scaffold young teenagers’ scientific argumentation. Our research objective is to better understand pupils’ usage of dialogue maps created in Compendium to write scientific ex-planations. The participants were 20 pupils, 12-13 years old, in a summer science course for “gifted and talented” children in the UK. Through qualitative analysis of three case studies, we investigate the value of dialogue mapping as a mediating tool in the scientific reasoning process during a set of learning activities. These activities were published in an online learning envi-ronment to foster collaborative learning. Pupils mapped their discussions in pairs, shared maps via the online forum and in plenary discussions, and wrote essays based on their dialogue maps. This study draws on these multiple data sources: pupils’ maps in Compendium, writings in science and reflective comments about the uses of mapping for writing. Our analysis highlights the diversity of ways, both successful and unsuccessful, in which dialogue mapping was used by these young teenagers

In vitro drug sensitivity of normal peripheral blood lymphocytes and childhood leukaemic cells from bone marrow and peripheral blood.

In vitro drug sensitivity of leukaemic cells might be influenced by the contamination of such a sample with non-malignant cells and the sample source. To study this, sensitivity of normal peripheral blood (PB) lymphocytes to a number of cytostatic drugs was assessed with the MTT assay. We compared this sensitivity with the drug sensitivity of leukaemic cells of 38 children with acute lymphoblastic leukaemia. We also studied a possible differential sensitivity of leukaemic cells from bone marrow (BM) and PB. The following drugs were used: Prednisolone, dexamethasone, 6-mercaptopurine, 6-thioguanine, cytosine arabinoside, vincristine, vindesine, daunorubicin, doxorubicin, mafosfamide (Maf), 4-hydroperoxy-ifosfamide, teniposide, mitoxantrone, L-asparaginase, methotrexate and mustine. Normal PB lymphocytes were significantly more resistant to all drugs tested, except to Maf. Leukaemic BM and PB cells from 38 patients (unpaired samples) showed no significant differences in sensitivity to any of the drugs. Moreover, in 11 of 12 children with acute leukaemia of whom we investigated simultaneously obtained BM and PB (paired samples), their leukaemic BM and PB cells showed comparable drug sensitivity profiles. In one patient the BM cells were more sensitive to most drugs than those from the PB, but the actual differences in sensitivity were small. We conclude that the contamination of a leukaemic sample with normal PB lymphocytes will influence the results of the MTT assay. The source of the leukaemic sample, BM or PB, does not significantly influence the assay results

The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results

The problem of finding the exact energies and configurations for the Frenkel-Kontorova model consisting of particles in one dimension connected to their nearest-neighbors by springs and placed in a periodic potential consisting of segments from parabolas of identical (positive) curvature but arbitrary height and spacing, is reduced to that of minimizing a certain convex function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6 Postscript figures, accepted by Phys. Rev.

MUC5B levels in submandibular gland saliva of patients treated with radiotherapy for head-and-neck cancer: A pilot study

<p>Abstract</p> <p>Background</p> <p>The salivary mucin MUC5B, present in (sero)mucous secretions including submandibular gland (SMG) saliva, plays an important role in the lubrication of the oral mucosa and is thought to be related to the feeling of dry mouth. We investigated if MUC5B levels in SMG saliva could distinguish between the presence or absence of severe dry mouth complaints 12 months after radiotherapy (RT) for head-and-neck cancer (HNC).</p> <p>Findings</p> <p>Twenty-nine HNC patients with a residual stimulated SMG secretion rate of ≥0.2 ml/10 min at 12 months after RT were analyzed. MUC5B (in U; normalized to 1) and total protein levels (mg/ml) were measured in SMG saliva at baseline and 12 months after RT using ELISA and BCA protein assay, respectively. Overall, median MUC5B levels decreased after RT from 0.12 to 0.03 U (<it>p</it> = 0.47). Patients were dichotomized into none/mild xerostomia (n = 12) and severe xerostomia (n = 17) based on a questionnaire completed at 12 months. SMG and whole saliva flow rates decreased after RT but were comparable in both groups. The median MUC5B level was higher in patients with no or mild xerostomia compared to patients with severe xerostomia (0.14 vs 0.01 U, <it>p</it> = 0.22). Half of the patients with severe xerostomia had no detectable MUC5B at 12 months after RT. No differences in total protein levels were observed.</p> <p>Conclusions</p> <p>Qualitative saliva parameters like MUC5B need further investigation in RT-induced xerostomia. This pilot study showed a trend towards lower MUC5B levels in the SMG saliva of patients with severe xerostomia 12 months after RT for HNC.</p

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Polydispersity and ordered phases in solutions of rodlike macromolecules

We apply density functional theory to study the influence of polydispersity on the stability of columnar, smectic and solid ordering in the solutions of rodlike macromolecules. For sufficiently large length polydispersity (standard deviation $\sigma>0.25$) a direct first-order nematic-columnar transition is found, while for smaller $\sigma$ there is a continuous nematic-smectic and first-order smectic-columnar transition. For increasing polydispersity the columnar structure is stabilized with respect to solid perturbations. The length distribution of macromolecules changes neither at the nematic-smectic nor at the nematic-columnar transition, but it does change at the smectic-columnar phase transition. We also study the phase behaviour of binary mixtures, in which the nematic-smectic transition is again found to be continuous. Demixing according to rod length in the smectic phase is always preempted by transitions to solid or columnar ordering.Comment: 13 pages (TeX), 2 Postscript figures uuencode

Computing Chemical Potential using the Phase Space Multi-histogram Method

We present a new simulation method to calculate the free energy and the chemical potential of hard particle systems. The method relies on the introduction of a parameter dependent potential to smoothly transform between the hard particle system and the corresponding ideal gas. We applied the method to study the phase transition behavior of monodispersed infinitely thin square platelets. First, we equilibrated the square platelet system for different reduced pressures with a usual isobaric Monte Carlo (MC) simulation and obtained a reduced pressure-chemical potential plot. Then we introduce the parametrized potential to interpolate the system between the ideal gas and the hard particles. After selecting the potential, we performed isochoric MC runs, ranging from the ideal gas to the hard particle limit. Through an iterative procedure, we compute the free energy and the chemical potential of the square platelet system by evaluating the volume of the phase space attributed to the hard particles, and then we find the coexistence pressure of the system. Our method provides an intuitive approach to investigate the phase transitions of hard particle systems