Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

A fast dual algorithm for kernel logistic regression

This paper gives a new iterative algorithm for kernel logistic regression. It is based on the solution of a dual problem using ideas similar to those of the Sequential Minimal Optimization algorithm for Support Vector Machines. Asymptotic convergence of the algorithm is proved. Computational experiments show that the algorithm is robust and fast. The algorithmic ideas can also be used to give a fast dual algorithm for solving the optimization problem arising in the inner loop of Gaussian Process classifiers.

RACK: RApid Clustering using K-means algorithm

The k-means algorithm is an extremely popular technique for clustering data. One of the major limitations of the k-means is that the time to cluster a given dataset D is linear in the number of clusters, k. In this paper, we employ height balanced trees to address this issue. Specifically, we make two major contributions, (a) we propose an algorithm, RACK (acronym for RApid Clustering using k-means), which takes time favorably comparable with the fastest known existing techniques, and (b) we prove an expected bound on the quality of clustering achieved using RACK. Our experimental results on large datasets strongly suggest that RACK is competitive with the k-means algorithm in terms of quality of clustering, while taking significantly less time.

A real coded genetic algorithm for data partitioning and scheduling in networks with arbitrary processor release time

The problem of scheduling divisible loads in distributed computing systems, in presence of processor release time is considered. The objective is to find the optimal sequence of load distribution and the optimal load fractions assigned to each processor in the system such that the processing time of the entire processing load is a minimum. This is a difficult combinatorial optimization problem and hence genetic algorithms approach is presented for its solution.

Delay optimal control algorithm for a multiaccess fading channel with peak power constraint

We consider an optimal power and rate scheduling problem for a multiaccess fading wireless channel with the objective of minimising a weighted sum of mean packet transmission delay subject to a peak power constraint. The base station acts as a controller which, depending upon the buffer lengths and the channel state of each user, allocates transmission rate and power to individual users. We assume perfect channel state information at the transmitter and the receiver. We also assume a Markov model for the fading and packet arrival processes. The policy obtained represents a form of Indexability.

Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems. (C) 2004 Elsevier Ltd. All rights reserved.

A Geometric Algorithm for Learning Oblique Decision Trees

In this paper we present a novel algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess goodness of hyperplanes at each node. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy, based on some recent variants of SVM, to assess the hyperplanes in such a way that the geometric structure in the data is taken into account. We show through empirical studies that our method is effective.

A fast time-domain algorithm for the assessment of tissue blood flow in laser-Doppler flowmetry

In this study, we derive a fast, novel time-domain algorithm to compute the nth-order moment of the power spectral density of the photoelectric current as measured in laser-Doppler flowmetry (LDF). It is well established that in the LDF literature these moments are closely related to fundamental physiological parameters, i.e. concentration of moving erythrocytes and blood flow. In particular, we take advantage of the link between moments in the Fourier domain and fractional derivatives in the temporal domain. Using Parseval's theorem, we establish an exact analytical equivalence between the time-domain expression and the conventional frequency-domain counterpart. Moreover, we demonstrate the appropriateness of estimating the zeroth-, first- and second-order moments using Monte Carlo simulations. Finally, we briefly discuss the feasibility of implementing the proposed algorithm in hardware.

A fast algorithm for macromolecular packing calculation

An algorithm to improve the computation time of packing calculations for macromolecules is presented. This is achieved by reducing the three-dimensional search to a small set of two-dimensional searches.

An approximate algorithm for the minimal vertex nested polygon problem

Given two simple polygons, the Minimal Vertex Nested Polygon Problem is one of finding a polygon nested between the given polygons having the minimum number of vertices. In this paper, we suggest efficient approximate algorithms for interesting special cases of the above using the shortest-path finding graph algorithms.

A reinforcement learning based algorithm for finite horizon Markov decision processes

We develop a simulation based algorithm for finite horizon Markov decision processes with finite state and finite action space. Illustrative numerical experiments with the proposed algorithm are shown for problems in flow control of communication networks and capacity switching in semiconductor fabrication.

A four-timescale algorithm for constrained stochastic optimization of RED

The overall performance of random early detection (RED) routers in the Internet is determined by the settings of their associated parameters. The non-availability of a functional relationship between the RED performance and its parameters makes it difficult to implement optimization techniques directly in order to optimize the RED parameters. In this paper, we formulate a generic optimization framework using a stochastically bounded delay metric to dynamically adapt the RED parameters. The constrained optimization problem thus formulated is solved using traditional nonlinear programming techniques. Here, we implement the barrier and penalty function approaches, respectively. We adopt a second-order nonlinear optimization framework and propose a novel four-timescale stochastic approximation algorithm to estimate the gradient and Hessian of the barrier and penalty objectives and update the RED parameters. A convergence analysis of the proposed algorithm is briefly sketched. We perform simulations to evaluate the performance of our algorithm with both barrier and penalty objectives and compare these with RED and a variant of it in the literature. We observe an improvement in performance using our proposed algorithm over RED, and the above variant of it.