Tissue specific opsonins for phagocytic cells

Imperial Users onl

Correlation Functions and AdS/LCFT Correspondence

Correlation functions of Logarithmic conformal field theory is investigated using the ADS/CFT correspondence and a novel method based on nilpotent weights and 'super fields'. Adding an specific form of interaction, we introduce a perturbative method to calculate the correlation functions.Comment: 11 pages, 4 figure

Avalanche frontiers in dissipative abelian sandpile model as off-critical SLE(2)

Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with diffusivity parameter $\kappa = 2$. In this paper we consider the dissipative ASM and study the statistics of the avalanche and wave frontiers for various rates of dissipation. We examine the scaling behavior of a number of functions such as the correlation length, the exponent of distribution function of loop lengths and gyration radius defined for waves and avalanches. We find that they do scale with the rate of dissipation. Two significant length scales are observed. For length scales much smaller than the correlation length, these curves show properties close to the critical curves and the corresponding diffusivity parameter is nearly the same as the critical limit. We interpret this as the ultra violet (UV) limit where $\kappa = 2$ corresponding to $c=-2$. For length scales much larger than the correlation length we find that the avalanche frontiers tend to Self-Avoiding Walk, the corresponding driving function is proportional to the Brownian motion with the diffusion parameter $\kappa =8/3$ corresponding to a field theory with $c = 0$. This is the infra red (IR) limit. Correspondingly the central charge decreases from the IR to the UV point.Comment: 11 Pages, 6 Figure

Higher Order and boundary Scaling Fields in the Abelian Sandpile Model

The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing and consider them in the presence of a boundary.Comment: 7 pages, no figure

Spanning Trees in Random Satisfiability Problems

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning trees in the associated factor graph. We introduce a modified survey propagation algorithm which returns null edges of the factor graph and helps us to find satisfiable spanning trees. This allows us to study organization of satisfiable spanning trees in the space spanned by spanning trees.Comment: 12 pages, 5 figures, published versio

Simplifying Random Satisfiability Problem by Removing Frustrating Interactions

How can we remove some interactions in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e. random K-satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will provide directly the solutions of the original problem.Comment: 21 pages, 16 figure