Mean Area of Self-Avoiding Loops

The mean area of two-dimensional unpressurised vesicles, or self-avoiding loops of fixed length $N$, behaves for large $N$ as $A_0 N^{3/2}$, while their mean square radius of gyration behaves as $R^2_0 N^{3/2}$. The amplitude ratio $A_0/R_0^2$ is computed exactly and found to equal $4\pi/5$. The physics of the pressurised case, both in the inflated and collapsed phases, may be usefully related to that of a complex O(n) field theory coupled to a U(1) gauge field, in the limit $n \to 0$.Comment: 12 pages, plain TeX, (one TeX macro omission corrected

Families of Vicious Walkers

We consider a generalisation of the vicious walker problem in which N random walkers in R^d are grouped into p families. Using field-theoretic renormalisation group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t. For d>2, this is constant, but for d<2 it decays as a power t^(-alpha), which we compute to O(epsilon^2) in an expansion in epsilon=2-d. The second order term depends on the ratios of the diffusivities of the different families. In two dimensions, we find a logarithmic decay (ln t)^(-alpha'), and compute alpha' exactly.Comment: 20 pages, 5 figures. v.2: minor additions and correction

Random walks on combs

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.Comment: 42 pages, 4 figure

Quantum and classical localisation, the spin quantum Hall effect and generalisations

We consider network models for localisation problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet superconductors which have a Bogoliubov - de Gennes Hamiltonian that is invariant under spin rotations but not under time-reversal. Our models include but also generalise the one studied previously in the context of the spin quantum Hall effect. For these systems we express the disorder-averaged conductance and density of states in terms of sums over certain classical random walks, which are self-avoiding and have attractive interactions. A transition between localised and extended phases of the quantum system maps in this way to a similar transition for the classical walks. In the case of the spin quantum Hall effect, the classical walks are the hulls of percolation clusters, and our approach provides an alternative derivation of a mapping first established by Gruzberg, Read and Ludwig, Phys. Rev. Lett. 82, 4254 (1999).Comment: 11 pages, 5 figure

Evidence that cyclic AMP phosphodiesterase inhibitors suppress interleukin-2 release from murine splenocytes by interacting with a ‘low-affinity' phosphodiesterase 4 conformer

1. We have investigated the suppressive effects of rolipram, RP 73401 (piclamilast) and other structurally diverse inhibitors of cyclic AMP-specific phosphodiesterase 4 (PDE4) on interleukin (IL)-2 generation from Balb/c mouse splenocytes exposed to the superantigen, Staphylococcocal enterotoxin-A (Staph. A). The purpose was to determine whether their potencies are more closely correlated with inhibition of PDE4 from CTLL cells, against which rolipram displays weak potency (low-affinity PDE4), or displacement of [(3)H]-(±)-rolipram from its high-affinity binding site (HARBS) in mouse brain cytosol. 2. RP 73401 (IC(50) 0.46±0.07 nM, n=4) was a very potent inhibitor of Staph. A-induced IL-2 release from Balb/c mouse splenocytes, being >1100 fold more potent than (±)-rolipram (IC(50) 540±67 nM, n=3). 3. A close correlation (r=0.95) was observed between suppression of IL-2 release by PDE inhibitors and inhibition of PDE4. In contrast, little correlation (r=0.39) was observed between suppression of IL-2 release and their affinities for the high-affinity rolipram binding site (HARBS). 4. RP 73401 only inhibited partially (30–40%) Staph. A-induced incorporation of [(3)H]-thymidine into splenocyte DNA. The PDE3 inhibitor, siguazodan (10 μM), had little or no effect on IL-2 release or DNA synthesis. This concentration of siguazodan did not enhance the inhibitory action of RP 73401 on IL-2 release but potentiated its effect on DNA synthesis, increasing potency and efficacy. 5. Staph. A-induced DNA synthesis was only partially inhibited by anti-IL-2 neutralizing antibody, whereas dexamethazone (100 nM) and cyclosporine A (100 nM) completely blocked the response. 6. RP 73401 (IC(50) 6.3±1.9 nM, n=4) was 140 fold more potent than rolipram (IC(50) 900±300 nM, n=3) in inhibiting Staph. A-induced [(3)H]-thymidine incorporation into splenocyte DNA. 7. The results implicate a low-affinity form of PDE4 in the suppression of Staph. A-induced IL-2 release from murine splenocytes by PDE inhibitors. The data also indicate that mitogenic factors other than IL-2, whose elaboration or responses to which are regulated by PDE3 as well as PDE4, contribute to the superantigen-induced DNA synthesis