Critical Droplets and Phase Transitions in Two Dimensions

In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing a bond probability p_B<1, the corresponding site-bond clusters keep on percolating at T_c and the exponents do not change, until p_B=p_CK=1-exp(-2J/kT): for this special expression of the bond weight the critical percolation exponents switch to the 2D Ising universality class. We show here that the result is valid for a wide class of bidimensional models with a continuous magnetization transition: there is a critical bond probability p_c such that, for any p_B>=p_c, the onset of percolation of the site-bond clusters coincides with the critical point of the thermal transition. The percolation exponents are the same for p_c<p_B<=1 but, for p_B=p_c, they suddenly change to the thermal exponents, so that the corresponding clusters are critical droplets of the phase transition. Our result is based on Monte Carlo simulations of various systems near criticality.Comment: Final version for publication, minor changes, figures adde

Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models

We consider independent edge percolation models on Z, with edge occupation probabilities p_ = p if |x-y| = 1, 1 - exp{- beta / |x-y|^2} otherwise. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in [Commun. Math. Phys. 104, 547 (1986)]. The proof is based on multi-scale analysis.Comment: 19 pages, 2 figures. See also Commentary on J. Stat. Phys. 150, 804-805 (2013), DOI 10.1007/s10955-013-0702-

Novel aminoquinoline-polycyclic hybrid molecules as potential antimalarial agents

Magister Pharmaceuticae - MPharmPlasmodium falciparum malaria continues to be a worldwide health problem, especially in developing countries in Africa and is responsible for over a million fatalities per annum. Chloroquine (CQ) is low-cost, safe and was the mainstay aminoquinoline derived chemotherapeutic agent that has been used for many years against blood-stage malaria. However, today the control of malaria has been complicated by increased resistance of the malaria parasite to existing antimalarial agents such as CQ. The primary cause of resistance is mutation in a putative ATP-powered multidrug efflux pump known as the p-glycoprotein (pGP) pump, and point mutation in P. falciparum CQ resistance transporter (PfCRT) protein. These mutations are responsible for the reduced accumulation of CQ at its primary site of action, the acidic digestive food vacuole of the parasite.To overcome the challenges of CQ resistance in P. falciparum, chemosensitiser offer an attractive approach. Chemosensitisers or reversal agents are structurally diverse molecules that are known to reverse CQ resistance by inhibiting the pGP efflux pump and/or the PfCRT protein associated with CQ export from the digestive vacuole in CQ resistant parasites. Chemosensitisers include the well-studied calcium channel blocker verapamil and antihistaminic agent chlorpheniramine. These drugs have little or no inherent antimalarial activity but have shown to reverse CQ resistance in P. falciparum when co-administered with CQ. Because of the channel blocking abilities of pentacycloundecylamines (PCUs) such as NGP1-01, it is postulated that these agents may act as chemosensitisers and circumvent the resistance of the Plasmodium parasite against CQ. Therefore as a proof of concept we conducted an experiment using CQ co- administered with different concentrations of NGP1-01 to evaluate the ability of NGP1-01 to act as a chemosensitiser.Herein, we report the ability of NGP1-01, the prototype pentacycloundecylamine (PCU), to reverse CQ resistance (> 50 %) and act as a chemosensitiser. NGP1-01 alone exhibited very low intrinsic antimalarial activity against both the resistant and sensitive strain (> 2000 nM), with no toxicity to the parasite detected at 10 µM. A statistically significant (p < 0.05) dose dependent shift was seen in the CQ IC50 values at both 1 µM and 10 µM concentration of co-administeredNGP1-01 against the resistant strain. Based on this finding we set out to synthesise a series of novel agents comprising of a PCU moiety as the reversal agent (RA) conjugated to a CQ-like aminoquinoline (AM) molecule and evaluate the potential of these PCU-AM derivatives as antimalarial- and/or reversed CQ agents. As recently shown by Peyton et al., (2012), the conjugation of a CQ-like molecule with a RA such as the chemosensitiser imipramine and derivatives thereof is a viable strategy to reverse CQ resistance in multidrug-resistant P. falciparum. The novel compounds were obtained by amination and reductive amination reactions. The synthetic procedures involved the conjugation of the Cookson’s diketone with different tethered 4-aminoquinoline moieties to yield the respective carbinolamines and the subsequent imines. This was followed by a transannular cyclisation using sodium cyanoborohydride as reducing agent to yield the desired PCU-AM derivatives. The CQ-like AMderivatives were obtained using a novel microwave (MW) irradiation method. Structure elucidation was done by utilising 1H- and 13C NMR spectroscopy as well as IR absorption spectrophotometry and mass spectrometry. Five PCU-AM reversed CQ derivatives were successfully synthesised and showed significant in vitro antimalarial activity against the CQ sensitive strain (NF54). PCU-AM derivatives 1.1 – 1.4 showed antimalarial IC50 values in the ranges of 3.74 – 17.6 ng/mL and 27.6 – 253.5 ng/mL against the CQ-sensitive (NF54) and CQ-resistant strains (Dd2) of Plasmodium falciparum, respectively. Compound 1.1 presented with the highest antimalarial activity against both strains and was found to be 5 fold more active against the resistant strain than CQ. The reversed CQ approach resulted in improved resistance reversal and a significantly lower concentration PCU was required compared to NGP1-01 and CQ in combination. This may be attributed to the improved ability of compound 1.1 to actively block the pGP pump and/or the increased permeability thereof because of the lipophilic aza-PCU moiety. Compound 1.1 also showed the lowest RMI value confirming that this compound has the best potential to act as a reversed CQ agent in the series. Cytotoxicity IC50 values observed for compounds 1.1 – 1.4 were in the low micromolar concentrations (2.39 – 9.54 µM) indicating selectivity towards P. falciparum (SI = 149 – 2549) and low toxicity compared to the cytotoxic agent emetine (IC50 = 0.061 µM).These results indicate that PCU channel blockers and PCU-AM derived conjugates can be utilised as lead molecules for further optimisation and development to enhance their therapeuticpotential as reversal agents and reversed CQ compounds

Exact sampling from non-attractive distributions using summary states

Propp and Wilson's method of coupling from the past allows one to efficiently generate exact samples from attractive statistical distributions (e.g., the ferromagnetic Ising model). This method may be generalized to non-attractive distributions by the use of summary states, as first described by Huber. Using this method, we present exact samples from a frustrated antiferromagnetic triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss the advantages and limitations of the method of summary states for practical sampling, paying particular attention to the slowing down of the algorithm at low temperature. In particular, we show that such a slowing down can occur in the absence of a physical phase transition.Comment: 5 pages, 6 EPS figures, REVTeX; additional information at http://wol.ra.phy.cam.ac.uk/mackay/exac

A necklace of Wulff shapes

In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density

Rejection-free Geometric Cluster Algorithm for Complex Fluids

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and non-local nature of the algorithm make it particularly suitable for the efficient simulation of complex fluids with components of widely varying size, such as colloidal mixtures. Compared to conventional simulation algorithms, typical efficiency improvements amount to several orders of magnitude

Thermal Operators in Ising Percolation

We discuss a new cluster representation for the internal energy and the specific heat of the d-dimensional Ising model, obtained by studying the percolation mapping of an Ising model with an arbitrary set of antiferromagnetic links. Such a representation relates the thermal operators to the topological properties of the Fortuin-Kasteleyn clusters of Ising percolation and is a powerful tool to get new exact relations on the topological structure of FK clusters of the Ising model defined on an arbitrary graph.Comment: 17 pages, 2 figures. Improved version. Major changes in the text and in the notations. A missing term added in the specific heat representatio

Group testing with Random Pools: Phase Transitions and Optimal Strategy

The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible queries, a problem which has relevant practical applications in different fields including molecular biology and computer science. Here we study GT in the probabilistic setting focusing on the regime of small defective probability and large number of objects, $p \to 0$ and $N \to \infty$. We construct and analyze one-stage algorithms for which we establish the occurrence of a non-detection/detection phase transition resulting in a sharp threshold, $\bar M$, for the number of tests. By optimizing the pool design we construct algorithms whose detection threshold follows the optimal scaling $\bar M\propto Np|\log p|$. Then we consider two-stages algorithms and analyze their performance for different choices of the first stage pools. In particular, via a proper random choice of the pools, we construct algorithms which attain the optimal value (previously determined in Ref. [16]) for the mean number of tests required for complete detection. We finally discuss the optimal pool design in the case of finite $p$

Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts model. We find that the Li-Sokal bound ($\tau_{int,E} \geq const \times C_H$) is almost but not quite sharp. The ratio $\tau_{int,E} / C_H$ seems to diverge either as a small power ($\approx 0.08$) or as a logarithm.Comment: 35 pages including 3 figures. Self-unpacking file containing the LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 Postscript figures. Revised version fixes a normalization error in \xi (with many thanks to Wolfhard Janke for finding the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997