We compare dynamic mean-field and dynamic cavity methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and we compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks, the dynamic cavity method generally predicts magnetizations of individual spins better than both first-order ("naive") and second-order ("TAP") dynamic mean-field theory.
Network structures are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. For TAP approximation, we use two methods to reconstruct the network: a) iteration method; b) casting the inference formula to a set of cubic equations and solving it directly. We investigate inference of the asymmetric Sherrington-Kirkpatrick (S-K) model using asynchronous update. The solutions of the sets cubic equation depend of temperature T in the S-K model, and a critical temperature Tc is found around 2.1. For T < Tc, the solutions of the cubic equation sets are composed of 1 real root and two conjugate complex roots while for T > Tc there are three real roots. The iteration method is convergent only if the cubic equations have three real solutions. The two methods give same results when the iteration method is convergent. Compared to nMF, TAP is somewhat better at low temperatures, but approaches the same performance as temperature increase. Both methods behave better for longer data length, but for improvement arises, TAP is well pronounced.
We study stationary states in a diluted asymmetric (kinetic) Ising model. We apply the recently introduced dynamic cavity method to compute magnetizations of these stationary states. Depending on the update rule, different versions of the dynamic cavity method apply. We here study synchronous updates and random sequential updates, and compare local properties computed by the dynamic cavity method to numerical simulations. Using both types of updates, the dynamic cavity method is highly accurate at high enough temperatures. At low enough temperatures, for sequential updates the dynamic cavity method tends to a fixed point, but which does not agree with numerical simulations, while for parallel updates, the dynamic cavity method may display oscillatory behavior. When it converges and is accurate, the dynamic cavity method offers a huge speed-up compared to Monte Carlo, particularly for large systems.
We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The algorithm allows to analyze large graphs and may find applications in fields such as computational biology. As a proof of concept we use our algorithm to align the similarity graphs of two interacting protein families involved in bacterial signal transduction, and to predict actually interacting protein partners between these families.
The amount of suspicious binary executables submitted to Anti-Virus (AV) companies are in the order of tens of thousands per day. Current hash-based signature methods are easy to deceive and are inefficient for identifying known malware that have undergone minor changes. Examining malware executables using their call graphs view is a suitable approach for overcoming the weaknesses of hash-based signatures. Unfortunately, many operations on graphs are of high computational complexity. One of these is the Graph Edit Distance (GED) between pairs of graphs, which seems a natural choice for static comparison of malware. We demonstrate how Simulated Annealing can be used to approximate the graph edit distance of call graphs, while outperforming previous approaches both in execution time and solution quality. Additionally, we experiment with opcode mnemonic vectors to reduce the problem size and examine how Simulated Annealing is affected.
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