Algorithms2015, 8(4), 895-909; doi:10.3390/a8040895 (registering DOI) - published 9 October 2015 Show/Hide Abstract
Abstract: In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each iteration. The proposed new scheme does not require the evaluation of second or higher order Fréchet derivatives and still reaches fourth order convergence. The multi-step version converges with order 2r+4, where r is a positive integer and r ≥ 1. We have proved that the root α is a point of attraction for a general iterative function, whereas the proposed new schemes also satisfy this result. Numerical experiments including an application to 1-D Bratu problem are given to illustrate the efficiency of the new methods. Also, the new methods are compared with some existing methods.
Algorithms2015, 8(4), 870-894; doi:10.3390/a8040870 (registering DOI) - published 9 October 2015 Show/Hide Abstract
Abstract: Spread Spectrum (SPSP) Communication is the theoretical basis of Direct Sequence Spread Spectrum (DSSS) transceiver technology. Spreading code, modulation, demodulation, carrier synchronization and code synchronization in SPSP communications are the core parts of DSSS transceivers. This paper focuses on the code synchronization problem in SPSP communications. A novel code synchronization algorithm based on segment correlation is proposed. The proposed algorithm can effectively deal with the informational misjudgment caused by the unreasonable data acquisition times. This misjudgment may lead to an inability of DSSS receivers to restore transmitted signals. Simulation results show the feasibility of a DSSS transceiver design based on the proposed code synchronization algorithm. Finally, the communication functions of the DSSS transceiver based on the proposed code synchronization algorithm are implemented on Field Programmable Gate Array (FPGA).
Algorithms2015, 8(4), 850-869; doi:10.3390/a8040850 (registering DOI) - published 9 October 2015 Show/Hide Abstract
Abstract: In this work, we propose a new distance measure for comparing two protein structures based on their contact map representations. We show that our novel measure, which we refer to as the maximum contact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein representations. Having a metric in that space allows one to avoid pairwise comparisons on the entire database and, thus, to significantly accelerate exploring the protein space compared to no-metric spaces. We show on a gold standard superfamily classification benchmark set of 6759 proteins that our exact k-nearest neighbor (k-NN) scheme classifies up to 224 out of 236 queries correctly and on a larger, extended version of the benchmark with 60; 850 additional structures, up to 1361 out of Algorithms 2015, 8 851 1369 queries. Our k-NN classification thus provides a promising approach for the automatic classification of protein structures based on flexible contact map overlap alignments.
Algorithms2015, 8(4), 832-849; doi:10.3390/a8040832 (registering DOI) - published 9 October 2015 Show/Hide Abstract
Abstract: We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and problems from other areas. Moreover, under the same or weaker conditions, we obtain weaker sufficient convergence criteria, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. Special cases are provided where the old convergence criteria cannot apply but the new criteria can apply to locate zeros of operators. Some applications include fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences.
Algorithms2015, 8(4), 810-831; doi:10.3390/a8040810 (registering DOI) - published 9 October 2015 Show/Hide Abstract
Abstract: Subnetwork mining is an essential issue in the analysis of biological, social and communication networks. Recent applications require the simultaneous mining of several networks on the same or a similar vertex set. That is, one searches for subnetworks fulfilling different properties in each input network. We study the case that the input consists of a directed graph D and an undirected graph G on the same vertex set, and the sought pattern is a path P in D whose vertex set induces a connected subgraph of G. In this context, three concrete problems arise, depending on whether the existence of P is questioned or whether the length of P is to be optimized: in that case, one can search for a longest path or (maybe less intuitively) a shortest one. These problems have immediate applications in biological networks and predictable applications in social, information and communication networks. We study the classic and parameterized complexity of the problem, thus identifying polynomial and NP-complete cases, as well as fixed-parameter tractable and W-hard cases. We also propose two enumeration algorithms that we evaluate on synthetic and biological data.
Algorithms2015, 8(4), 799-809; doi:10.3390/a8040799 - published 25 September 2015 Show/Hide Abstract
Abstract: The sign least mean square with reweighted L1-norm constraint (SLMS-RL1) algorithm is an attractive sparse channel estimation method among Gaussian mixture model (GMM) based algorithms for use in impulsive noise environments. The channel sparsity can be exploited by SLMS-RL1 algorithm based on appropriate reweighted factor, which is one of key parameters to adjust the sparse constraint for SLMS-RL1 algorithm. However, to the best of the authors’ knowledge, a reweighted factor selection scheme has not been developed. This paper proposes a Monte-Carlo (MC) based reweighted factor selection method to further strengthen the performance of SLMS-RL1 algorithm. To validate the performance of SLMS-RL1 using the proposed reweighted factor, simulations results are provided to demonstrate that convergence speed can be reduced by increasing the channel sparsity, while the steady-state MSE performance only slightly changes with different GMM impulsive-noise strengths.