This paper presents a two-level protein folding optimization on a three-dimensional AB off-lattice model. The first level is responsible for forming conformations with a good hydrophobic core or a set of compact hydrophobic amino acid positions. These conformations are forwarded to the second level, where an accurate search is performed with the aim of locating conformations with the best energy value. The optimization process switches between these two levels until the stopping condition is satisfied. An auxiliary fitness function was designed for the first level, while the original fitness function is used in the second level. The auxiliary fitness function includes expression about the quality of the hydrophobic core. This expression is crucial for leading the search process to the promising solutions that have a good hydrophobic core and, consequently, improves the efficiency of the whole optimization process. Our differential evolution algorithm was used for demonstrating the efficiency of the two-level optimization. It was analyzed on well-known amino acid sequences that are used frequently in the literature. The obtained experimental results show that the employed two-level optimization improves the efficiency of our algorithm significantly, and that the proposed algorithm is superior to other state-of-the-art algorithms.
An improved stochastic fractal search algorithm was applied to the AB off-lattice model in @cite_17 . In order to avoid the algorithm becoming trapped into the local optimum, L 'e vy flight and internal feedback information are incorporated into the algorithm. The algorithm consists of diffusion and an update process. The L 'e vy flight was used in the diffusion process to generate some new particles around each population particle. In the update process, the best particle generated from the diffusion process is used to generate new particles. To prevent stagnation within a local optimum, the internal feedback information is incorporated into the algorithm. This information is used to trigger the mechanism that generates new particles according to two randomly selected particles from the population.
@cite_17
1562488694 1825700702 1487980058 2154822588
The stochastic block model (SBM) with two communities, or equivalently the planted bisection model, is a popular model of random graph exhibiting a cluster behaviour. In the symmetric case, the graph has two equally sized clusters and vertices connect with probability @math within clusters and @math across clusters. In the past two decades, a large body of literature in statistics and computer science has focused on providing lower-bounds on the scaling of @math to ensure exact recovery. In this paper, we identify a sharp threshold phenomenon for exact recovery: if @math and @math are constant (with @math ), recovering the communities with high probability is possible if @math and impossible if @math . In particular, this improves the existing bounds. This also sets a new line of sight for efficient clustering algorithms. While maximum likelihood (ML) achieves the optimal threshold (by definition), it is in the worst-case NP-hard. This paper proposes an efficient algorithm based on a semidefinite programming relaxation of ML, which is proved to succeed in recovering the communities close to the threshold, while numerical experiments suggest it may achieve the threshold. An efficient algorithm which succeeds all the way down to the threshold is also obtained using a partial recovery algorithm combined with a local improvement procedure. The binary symmetric stochastic block model deals with a random graph of @math vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability @math within clusters and @math across clusters. In the asymptotic regime of @math and @math for fixed @math and @math , we show that the semidefinite programming relaxation of the maximum likelihood estimator achieves the optimal threshold for exactly recovering the partition from the graph with probability tending to one, resolving a conjecture of Abbe14 . Furthermore, we show that the semidefinite programming relaxation also achieves the optimal recovery threshold in the planted dense subgraph model containing a single cluster of size proportional to @math . A new probabilistic background model based on a Hidden Markov Model is presented. The hidden states of the model enable discrimination between foreground, background and shadow. This model functions as a low level process for a car tracker. A particle filter is employed as a stochastic filter for the car tracker. The use of a particle filter allows the incorporation of the information from the low level process via importance sampling. A novel observation density for the particle filter which models the statistical dependence of neighboring pixels based on a Markov random field is presented. The effectiveness of both the low level process and the observation likelihood are demonstrated. This paper presents a method for solving inverse mapping of a continuous function learned by a multilayer feedforward mapping network. The method is based on the iterative update of input vector toward a solution, while escaping from local minima. The input vector update is determined by the pseudo-inverse of the gradient of Lyapunov function, and, should an optimal solution be searched for, the projection of the gradient of a performance index on the null space of the gradient of Lyapunov function. The update rule is allowed to detect an input vector approaching local minima through a phenomenon called "update explosion". At or near local minima, the input vector is guided by an escape trajectory generated based on "global information", where global information is referred to here as predefined or known information on forward mapping; or the input vector is relocated to a new position based on the probability density function (PDF) constructed over the input vector space by Parzen estimate. The constructed PDF reflects the history of local minima detected during the search process, and represents the probability that a particular input vector can lead to a solution based on the update rule. The proposed method has a substantial advantage in computational complexity as well as convergence property over the conventional methods based on Jacobian pseudo-inverse or Jacobian transpose. >