330,187 research outputs found
Energy Minimization of Discrete Protein Titration State Models Using Graph Theory
There are several applications in computational biophysics which require the
optimization of discrete interacting states; e.g., amino acid titration states,
ligand oxidation states, or discrete rotamer angles. Such optimization can be
very time-consuming as it scales exponentially in the number of sites to be
optimized. In this paper, we describe a new polynomial-time algorithm for
optimization of discrete states in macromolecular systems. This algorithm was
adapted from image processing and uses techniques from discrete mathematics and
graph theory to restate the optimization problem in terms of "maximum
flow-minimum cut" graph analysis. The interaction energy graph, a graph in
which vertices (amino acids) and edges (interactions) are weighted with their
respective energies, is transformed into a flow network in which the value of
the minimum cut in the network equals the minimum free energy of the protein,
and the cut itself encodes the state that achieves the minimum free energy.
Because of its deterministic nature and polynomial-time performance, this
algorithm has the potential to allow for the ionization state of larger
proteins to be discovered
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 ants’ 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
Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithms
The emergence of Big Data has enabled new research perspectives in the
discrete choice community. While the techniques to estimate Machine Learning
models on a massive amount of data are well established, these have not yet
been fully explored for the estimation of statistical Discrete Choice Models
based on the random utility framework. In this article, we provide new ways of
dealing with large datasets in the context of Discrete Choice Models. We
achieve this by proposing new efficient stochastic optimization algorithms and
extensively testing them alongside existing approaches. We develop these
algorithms based on three main contributions: the use of a stochastic Hessian,
the modification of the batch size, and a change of optimization algorithm
depending on the batch size. A comprehensive experimental comparison of fifteen
optimization algorithms is conducted across ten benchmark Discrete Choice Model
cases. The results indicate that the HAMABS algorithm, a hybrid adaptive batch
size stochastic method, is the best performing algorithm across the
optimization benchmarks. This algorithm speeds up the optimization time by a
factor of 23 on the largest model compared to existing algorithms used in
practice. The integration of the new algorithms in Discrete Choice Models
estimation software will significantly reduce the time required for model
estimation and therefore enable researchers and practitioners to explore new
approaches for the specification of choice models.Comment: 43 page
Solutions to Wiener Filtering and Stationary LQG Problem via H₂ Control Theory - Part II : Discrete - Time System
This paper derives the solutions to the Wiener filtering and stationary LQG problem for a discrete-time system by applying the state-space techniques developed for H₂H∞ optimal controls. As mathematical preliminaries, we collect useful operations for the transfer function matrices. We also provide a new proof for the inner-outer factorization algorithm that appears in the discrete-time H₂ optimization
Applications of ℓ\u3csub\u3e1\u3c/sub\u3e and Mixed H\u3csub\u3e2\u3c/sub\u3e/ℓ\u3csub\u3e1\u3c/sub\u3e Optimization
This thesis explores the use of ℓ1 and mixed H2/ℓ1 optimization methods to design flight control systems. ℓ1 optimization is used to handle tracking issues in the design of digital compensators. Control deflection and rate limitations, overshoot and undershoot limitations and steady-state error requirements are discussed. Model-matching techniques which produce acceptable tracking results with lower order controllers are also examined. New numerical methods for continuous H2/L1 and discrete H2/ℓ1 optimization are presented. These methods are used to design an aircraft controller in continuous and discrete time and the results are compared
Consistent approximations of the zeno behaviour in affine-type switched dynamic systems
This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes
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