Biased random satisfiability problems: From easy to hard instances

In this paper we study biased random K-SAT problems in which each logical variable is negated with probability $p$. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K-SAT problems. The exact solution of 1-SAT case is given. The critical point of K-SAT problems and results of replica method are derived in the replica symmetry framework. It is found that in this approximation $\alpha_c \propto p^{-(K-1)}$ for $p\to 0$. Solving numerically the survey propagation equations for K=3 we find that for $p<p^* \sim 0.17$ there is no replica symmetry breaking and still the SAT-UNSAT transition is discontinuous.Comment: 17 pages, 8 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

Evaluation of lysosomal stability and red blood cell membrane fragility in mudskipper (Boleophthalmus dussumieri) as a biomarker of poly aromatic hydrocarbons

This research was carried out to study some physiological responses of mudskipper (i.e., Boleophthalmus dussumieri) as a biomarker Poly Aromatic Hydrocarbons (PAHs). Fish specimens were obtained 5 stations (Arvand, Jafari, Zangi, Samayeli, Bahrakan) along north western coast of the Persian Gulf (Khuzestan Coast). PAHs concentration was measured by HPLC method. Lysosomal membrane change was measured by NRR time method and stability of red blood cell membrane was evaluated by EOF test. Total PAH concentrations in the sediments and the liver tissue ranged between 113.50-3384.34 ng g-1dw, 3.99-46.64ng g-1 dw, respectively. Highest PAHs pollution was found at Jafari while the lowest was detected at Bahrakan, with significant between these 2 stations. Values of mean RT of the dye ranged from 34 (for the blood samples of mudskipper collected from Jafari site) to 78 minutes (for the blood samples of mudskipper collected from Bahrakan). Preliminary results showed a significant difference among stations except between Arvand and Zangi. Osmotic fragility curves indicated that erythrocytes collected from mudskippers at Jafari were the most fragile followed by Zangi> Arvand> Samayeli> and Bahrakan. The results suggest that lysosomal membrane change and red blood cell membrane stability in B. dussumieri could be extended as a biomarker of oil pollution in marine biomonitoring programs

A note on the convergence of the Zakharov-Kuznetsov equation by homotopy analysis method

Abstract. In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homotopy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence of HAM and to find the series solution of this equation via a reliable algorithm