59,919 research outputs found
Flexible protein folding by ant colony optimization
Protein structure prediction is one of the most challenging topics in bioinformatics.
As the protein structure is found to be closely related to its functions,
predicting the folding structure of a protein to judge its functions is meaningful to
the humanity. This chapter proposes a flexible ant colony (FAC) algorithm for solving
protein folding problems (PFPs) based on the hydrophobic-polar (HP) square lattice
model. Different from the previous ant algorithms for PFPs, the pheromones in the
proposed algorithm are placed on the arcs connecting adjacent squares in the lattice.
Such pheromone placement model is similar to the one used in the traveling salesmen
problems (TSPs), where pheromones are released on the arcs connecting the cities.
Moreover, the collaboration of effective heuristic and pheromone strategies greatly
enhances the performance of the algorithm so that the algorithm can achieve good
results without local search methods. By testing some benchmark two-dimensional
hydrophobic-polar (2D-HP) protein sequences, the performance shows that the proposed
algorithm is quite competitive compared with some other well-known methods
for solving the same protein folding problems
Singularity formation in three-dimensional vortex sheets
We study singularity formation of three-dimensional (3-D) vortex sheets without surface tension using a new approach. First, we derive a leading order approximation to the boundary integral equation governing the 3-D vortex sheet. This leading order equation captures the most singular contributions of the integral equation. By introducing an appropriate change of variables, we show that the leading order vortex sheet equation degenerates to a two-dimensional vortex sheet equation in the direction of the tangential velocity jump. This change of variables is guided by a careful analysis based on properties of certain singular integral operators, and is crucial in identifying the leading order singular behavior. Our result confirms that the tangential velocity jump is the physical driving force of the vortex sheet singularities. We also show that the singularity type of the three-dimensional problem is similar to that of the two-dimensional problem. Moreover, we introduce a model equation for 3-D vortex sheets. This model equation captures the leading order singularity structure of the full 3-D vortex sheet equation, and it can be computed efficiently using fast Fourier transform. This enables us to perform well-resolved calculations to study the generic type of 3-D vortex sheet singularities. We will provide detailed numerical results to support the analytic prediction, and to reveal the generic form of the vortex sheet singularity
Protein folding in hydrophobic-polar lattice model: a flexible ant colony optimization approach
This paper proposes a flexible ant colony (FAC) algorithm for solving protein folding problems based on the hydrophobic-polar square lattice model. Collaborations of novel pheromone and heuristic strategies in the proposed algorithm make it more effective in predicting structures of proteins compared with other state-of-the-art algorithms
Negative refraction in nonlinear wave systems
People have been familiar with the phenomenon of wave refraction for several
centuries. Recently, a novel type of refraction, i.e., negative refraction,
where both incident and refractory lines locate on the same side of the normal
line, has been predicted and realized in the context of linear optics in the
presence of both right- and left-handed materials. In this work, we reveal, by
theoretical prediction and numerical verification, negative refraction in
nonlinear oscillatory systems. We demonstrate that unlike what happens in
linear optics, negative refraction of nonlinear waves does not depend on the
presence of the special left-handed material, but depends on suitable physical
condition. Namely, this phenomenon can be observed in wide range of oscillatory
media under the Hopf bifurcation condition. The complex Ginzburg-Landau
equation and a chemical reaction-diffusion model are used to demonstrate the
feasibility of this nonlinear negative refraction behavior in practice
Green's function method for single-particle resonant states in relativistic mean field theory
Relativistic mean field theory is formulated with the Green's function method
in coordinate space to investigate the single-particle bound states and
resonant states on the same footing. Taking the density of states for free
particle as a reference, the energies and widths of single-particle resonant
states are extracted from the density of states without any ambiguity. As an
example, the energies and widths for single-neutron resonant states in
Sn are compared with those obtained by the scattering phase-shift
method, the analytic continuation in the coupling constant approach, the real
stabilization method and the complex scaling method. Excellent agreements are
found for the energies and widths of single-neutron resonant states.Comment: 20 pages, 7 figure
SamACO: variable sampling ant colony optimization algorithm for continuous optimization
An ant colony optimization (ACO) algorithm offers
algorithmic techniques for optimization by simulating the foraging behavior of a group of ants to perform incremental solution
constructions and to realize a pheromone laying-and-following
mechanism. Although ACO is first designed for solving discrete
(combinatorial) optimization problems, the ACO procedure is
also applicable to continuous optimization. This paper presents
a new way of extending ACO to solving continuous optimization
problems by focusing on continuous variable sampling as a key
to transforming ACO from discrete optimization to continuous
optimization. The proposed SamACO algorithm consists of three
major steps, i.e., the generation of candidate variable values for
selection, the antsâ solution construction, and the pheromone
update process. The distinct characteristics of SamACO are the
cooperation of a novel sampling method for discretizing the
continuous search space and an efficient incremental solution
construction method based on the sampled values. The performance
of SamACO is tested using continuous numerical functions
with unimodal and multimodal features. Compared with some
state-of-the-art algorithms, including traditional ant-based algorithms
and representative computational intelligence algorithms
for continuous optimization, the performance of SamACO is seen
competitive and promising
A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity
In the first part of this work, we analyzed a Dirichlet boundary control
problem for an elliptic convection diffusion PDE and proposed a new
hybridizable discontinuous Galerkin (HDG) method to approximate the solution.
For the case of a 2D polygonal domain, we also proved an optimal superlinear
convergence rate for the control under certain assumptions on the domain and on
the target state. In this work, we revisit the convergence analysis without
these assumptions; in this case, the solution can have low regularity and we
use a different analysis approach. We again prove an optimal convergence rate
for the control, and present numerical results to illustrate the convergence
theory
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