Tube Width Fluctuations in F-Actin Solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.Comment: Final version, 5 pages, 4 figure

Letters to the Editor

Dear Sirs: I have recently received a brochure advertising the so-called Major Authors Edition of your anthology of English literature. The blurb absurdly advertises it as the essential works of the essential authors. More properly, it should be described as Some Major (and Some Minor) Works by Thirty White Male British Authors ..

Co-regulation of two tandem genes by one blue-light element in Neurospora crassa

Many genes of Neurospora crassa are regulated by blue light: al-1 (Schmidhauser et al. 1990 Mol. Cell. Biol. 10:5064-5070), al-2 (Lauter, Schmidhauser, Yanofsky, Russo unpublished), al-3 (Nelson et al. 1989 Mol. Cell. Biol. 9:1271-1276), bli-3, bli-4, bli-7, bli-13 (Sommer et al. 1989 NAR 17:5713-5723). For none of these genes are the blue light cis-regulatory sequences (blue-light elements, BE) known. Here we report the presence of such BE in front of bli-4

Excitations in confined helium

We design models for helium in matrices like aerogel, Vycor or Geltech from a manifestly microscopic point of view. For that purpose, we calculate the dynamic structure function of 4He on Si substrates and between two Si walls as a function of energy, momentum transfer, and the scattering angle. The angle--averaged results are in good agreement with the neutron scattering data; the remaining differences can be attributed to the simplified model used here for the complex pore structure of the materials. A focus of the present work is the detailed identification of coexisting layer modes and bulk--like excitations, and, in the case of thick films, ripplon excitations. Involving essentially two--dimensional motion of atoms, the layer modes are sensitive to the scattering angle.Comment: Phys. Rev. B (2003, in press

Orienteering with One Endomorphism

In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is known that a small endomorphism enables polynomial-time path-finding and endomorphism ring computation (Love-Boneh [36]). An endomorphism gives an explicit orientation of a supersingular elliptic curve. In this paper, we use the volcano structure of the oriented supersingular isogeny graph to take ascending/descending/horizontal steps on the graph and deduce path-finding algorithms to an initial curve. Each altitude of the volcano corresponds to a unique quadratic order, called the primitive order. We introduce a new hard problem of computing the primitive order given an arbitrary endomorphism on the curve, and we also provide a sub-exponential quantum algorithm for solving it. In concurrent work (Wesolowski [54]), it was shown that the endomorphism ring problem in the presence of one endomorphism with known primitive order reduces to a vectorization problem, implying path-finding algorithms. Our path-finding algorithms are more general in the sense that we don't assume the knowledge of the primitive order associated with the endomorphism.Comment: 40 pages, 1 figure; 3rd revision implements small corrections and expositional improvement

Evidence for nonmonotonic magnetic field penetration in a type-I superconductor

Polarized neutron reflectometry (PNR) provides evidence that nonlocal electrodynamics governs the magnetic field penetration in an extreme low-k superconductor. The sample is an indium film with a large elastic mean free path (11 mkm) deposited on a silicon oxide wafer. It is shown that PNR can resolve the difference between the reflected neutron spin asymmetries predicted by the local and nonlocal theories of superconductivity. The experimental data support the nonlocal theory, which predicts a nonmonotonic decay of the magnetic field.Comment: 5 pages, 4 figures, LaTex, corrected typos and figure

Magnetic phases and reorientation transitions in antiferromagnetically coupled multilayers

In antiferromagnetically coupled superlattices grown on (001) faces of cubic substrates, e.g. based on materials combinations as Co/Cu, Fe/Si, Co/Cr, or Fe/Cr, the magnetic states evolve under competing influence of bilinear and biquadratic exchange interactions, surface-enhanced four-fold in-plane anisotropy, and specific finite-size effects. Using phenomenological (micromagnetic) theory, a comprehensive survey of the magnetic states and reorientation transitions has been carried out for multilayer systems with even number of ferromagnetic sub-layers and magnetizations in the plane. In two-layer systems (N=2) the phase diagrams in dependence on components of the applied field in the plane include ``swallow-tail'' type regions of (metastable) multistate co-existence and a number of continuous and discontinuous reorientation transitions induced by radial and transversal components of the applied field. In multilayers (N \ge 4) noncollinear states are spatially inhomogeneous with magnetization varying across the multilayer stack. For weak four-fold anisotropy the magnetic states under influence of an applied field evolve by a complex continuous reorientation into the saturated state. At higher anisotropy they transform into various inhomogeneous and asymmetric structures. The discontinuous transitions between the magnetic states in these two-layers and multilayers are characterized by broad ranges of multi-phase coexistence of the (metastable) states and give rise to specific transitional domain structures.Comment: Manuscript 34 pages, 14 figures; submitted for publicatio

Orientations and cycles in supersingular isogeny graphs

The paper concerns several theoretical aspects of oriented supersingular $\ell$-isogeny volcanoes and their relationship to closed walks in the supersingular $\ell$-isogeny graph. Our main result is a bijection between the rims of the union of all oriented supersingular $\ell$-isogeny volcanoes over $\overline{\mathbb{F}}_p$ (up to conjugation of the orientations), and isogeny cycles (non-backtracking closed walks which are not powers of smaller walks) of the supersingular $\ell$-isogeny graph over $\overline{\mathbb{F}}_p$. The exact proof and statement of this bijection are made more intricate by special behaviours arising from extra automorphisms and the ramification of $p$ in certain quadratic orders. We use the bijection to count isogeny cycles of given length in the supersingular $\ell$-isogeny graph exactly as a sum of class numbers of these orders, and also give an explicit upper bound by estimating the class numbers