Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

Fuzzy Connectedness Image Segmentation in Graph Cut Formulation: A Linear-Time Algorithm and a Comparative Analysis

A deep theoretical analysis of the graph cut image segmentation framework presented in this paper simultaneously translates into important contributions in several directions. The most important practical contribution of this work is a full theoretical description, and implementation, of a novel powerful segmentation algorithm, GC(max). The output of GC(max) coincides with a version of a segmentation algorithm known as Iterative Relative Fuzzy Connectedness, IRFC. However, GC(max) is considerably faster than the classic IRFC algorithm, which we prove theoretically and show experimentally. Specifically, we prove that, in the worst case scenario, the GC(max) algorithm runs in linear time with respect to the variable M=|C|+|Z|, where |C| is the image scene size and |Z| is the size of the allowable range, Z, of the associated weight/affinity function. For most implementations, Z is identical to the set of allowable image intensity values, and its size can be treated as small with respect to |C|, meaning that O(M)=O(|C|). In such a situation, GC(max) runs in linear time with respect to the image size |C|. We show that the output of GC(max) constitutes a solution of a graph cut energy minimization problem, in which the energy is defined as the a"" (a) norm ayenF (P) ayen(a) of the map F (P) that associates, with every element e from the boundary of an object P, its weight w(e). This formulation brings IRFC algorithms to the realm of the graph cut energy minimizers, with energy functions ayenF (P) ayen (q) for qa[1,a]. Of these, the best known minimization problem is for the energy ayenF (P) ayen(1), which is solved by the classic min-cut/max-flow algorithm, referred to often as the Graph Cut algorithm. We notice that a minimization problem for ayenF (P) ayen (q) , qa[1,a), is identical to that for ayenF (P) ayen(1), when the original weight function w is replaced by w (q) . Thus, any algorithm GC(sum) solving the ayenF (P) ayen(1) minimization problem, solves also one for ayenF (P) ayen (q) with qa[1,a), so just two algorithms, GC(sum) and GC(max), are enough to solve all ayenF (P) ayen (q) -minimization problems. We also show that, for any fixed weight assignment, the solutions of the ayenF (P) ayen (q) -minimization problems converge to a solution of the ayenF (P) ayen(a)-minimization problem (ayenF (P) ayen(a)=lim (q -> a)ayenF (P) ayen (q) is not enough to deduce that). An experimental comparison of the performance of GC(max) and GC(sum) algorithms is included. This concentrates on comparing the actual (as opposed to provable worst scenario) algorithms' running time, as well as the influence of the choice of the seeds on the output.

Analyzing the Complexity and Reliability of Switch-Frequency-Reconfigurable Antennas Using Graph Models

This paper addresses the functional reliability and the complexity of reconfigurable antennas using graph models. The correlation between complexity and reliability for any given reconfigurable antenna is defined. Two methods are proposed to reduce failures and improve the reliability of reconfigurable antennas. The failures are caused by the reconfiguration technique or by the surrounding environment. These failure reduction methods proposed are tested and examples are given which verify these methods.

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Particle Competition and Cooperation in Networks for Semi-Supervised Learning

Semi-supervised learning is one of the important topics in machine learning, concerning with pattern classification where only a small subset of data is labeled. In this paper, a new network-based (or graph-based) semi-supervised classification model is proposed. It employs a combined random-greedy walk of particles, with competition and cooperation mechanisms, to propagate class labels to the whole network. Due to the competition mechanism, the proposed model has a local label spreading fashion, i.e., each particle only visits a portion of nodes potentially belonging to it, while it is not allowed to visit those nodes definitely occupied by particles of other classes. In this way, a "divide-and-conquer" effect is naturally embedded in the model. As a result, the proposed model can achieve a good classification rate while exhibiting low computational complexity order in comparison to other network-based semi-supervised algorithms. Computer simulations carried out for synthetic and real-world data sets provide a numeric quantification of the performance of the method.

Efficient Forest Data Structure for Evolutionary Algorithms Applied to Network Design

The design of a network is a solution to several engineering and science problems. Several network design problems are known to be NP-hard, and population-based metaheuristics like evolutionary algorithms (EAs) have been largely investigated for such problems. Such optimization methods simultaneously generate a large number of potential solutions to investigate the search space in breadth and, consequently, to avoid local optima. Obtaining a potential solution usually involves the construction and maintenance of several spanning trees, or more generally, spanning forests. To efficiently explore the search space, special data structures have been developed to provide operations that manipulate a set of spanning trees (population). For a tree with n nodes, the most efficient data structures available in the literature require time O(n) to generate a new spanning tree that modifies an existing one and to store the new solution. We propose a new data structure, called node-depth-degree representation (NDDR), and we demonstrate that using this encoding, generating a new spanning forest requires average time O(root n). Experiments with an EA based on NDDR applied to large-scale instances of the degree-constrained minimum spanning tree problem have shown that the implementation adds small constants and lower order terms to the theoretical bound.

Collaborative fuzzy clustering algorithms: some refinements and design guidelines

There are some variants of the widely used Fuzzy C-Means (FCM) algorithm that support clustering data distributed across different sites. Those methods have been studied under different names, like collaborative and parallel fuzzy clustering. In this study, we offer some augmentation of the two FCM-based clustering algorithms used to cluster distributed data by arriving at some constructive ways of determining essential parameters of the algorithms (including the number of clusters) and forming a set of systematically structured guidelines such as a selection of the specific algorithm depending on the nature of the data environment and the assumptions being made about the number of clusters. A thorough complexity analysis, including space, time, and communication aspects, is reported. A series of detailed numeric experiments is used to illustrate the main ideas discussed in the study.

Riverbed: A Novel User-Steered Image Segmentation Method Based on Optimum Boundary Tracking

This paper presents an optimum user-steered boundary tracking approach for image segmentation, which simulates the behavior of water flowing through a riverbed. The riverbed approach was devised using the image foresting transform with a never-exploited connectivity function. We analyze its properties in the derived image graphs and discuss its theoretical relation with other popular methods such as live wire and graph cuts. Several experiments show that riverbed can significantly reduce the number of user interactions (anchor points), as compared to live wire for objects with complex shapes. This paper also includes a discussion about how to combine different methods in order to take advantage of their complementary strengths.

Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

A survey of evolutionary algorithms for decision-tree induction

This paper presents a survey of evolutionary algorithms that are designed for decision-tree induction. In this context, most of the paper focuses on approaches that evolve decision trees as an alternate heuristics to the traditional top-down divide-and-conquer approach. Additionally, we present some alternative methods that make use of evolutionary algorithms to improve particular components of decision-tree classifiers. The paper's original contributions are the following. First, it provides an up-to-date overview that is fully focused on evolutionary algorithms and decision trees and does not concentrate on any specific evolutionary approach. Second, it provides a taxonomy, which addresses works that evolve decision trees and works that design decision-tree components by the use of evolutionary algorithms. Finally, a number of references are provided that describe applications of evolutionary algorithms for decision-tree induction in different domains. At the end of this paper, we address some important issues and open questions that can be the subject of future research.

Automatic design of decision-tree induction algorithms tailored to flexible-receptor docking data

Background: This paper addresses the prediction of the free energy of binding of a drug candidate with enzyme InhA associated with Mycobacterium tuberculosis. This problem is found within rational drug design, where interactions between drug candidates and target proteins are verified through molecular docking simulations. In this application, it is important not only to correctly predict the free energy of binding, but also to provide a comprehensible model that could be validated by a domain specialist. Decision-tree induction algorithms have been successfully used in drug-design related applications, specially considering that decision trees are simple to understand, interpret, and validate. There are several decision-tree induction algorithms available for general-use, but each one has a bias that makes it more suitable for a particular data distribution. In this article, we propose and investigate the automatic design of decision-tree induction algorithms tailored to particular drug-enzyme binding data sets. We investigate the performance of our new method for evaluating binding conformations of different drug candidates to InhA, and we analyze our findings with respect to decision tree accuracy, comprehensibility, and biological relevance. Results: The empirical analysis indicates that our method is capable of automatically generating decision-tree induction algorithms that significantly outperform the traditional C4.5 algorithm with respect to both accuracy and comprehensibility. In addition, we provide the biological interpretation of the rules generated by our approach, reinforcing the importance of comprehensible predictive models in this particular bioinformatics application. Conclusions: We conclude that automatically designing a decision-tree algorithm tailored to molecular docking data is a promising alternative for the prediction of the free energy from the binding of a drug candidate with a flexible-receptor.

The contribution of HGAL/GCET2 in immunohistological algorithms: a comparative study in 424 cases of nodal diffuse large B-cell lymphoma

Diffuse large B-cell lymphoma can be subclassified into at least two molecular subgroups by gene expression profiling: germinal center B-cell like and activated B-cell like diffuse large B-cell lymphoma. Several immunohistological algorithms have been proposed as surrogates to gene expression profiling at the level of protein expression, but their reliability has been an issue of controversy. Furthermore, the proportion of misclassified cases of germinal center B-cell subgroup by immunohistochemistry, in all reported algorithms, is higher compared with germinal center B-cell cases defined by gene expression profiling. We analyzed 424 cases of nodal diffuse large B-cell lymphoma with the panel of markers included in the three previously described algorithms: Hans, Choi, and Tally. To test whether the sensitivity of detecting germinal center B-cell cases could be improved, the germinal center B-cell marker HGAL/GCET2 was also added to all three algorithms. Our results show that the inclusion of HGAL/GCET2 significantly increased the detection of germinal center B-cell cases in all three algorithms (P<0.001). The proportions of germinal center B-cell cases in the original algorithms were 27%, 34%, and 19% for Hans, Choi, and Tally, respectively. In the modified algorithms, with the inclusion of HGAL/GCET2, the frequencies of germinal center B-cell cases were increased to 38%, 48%, and 35%, respectively. Therefore, HGAL/GCET2 protein expression may function as a marker for germinal center B-cell type diffuse large B-cell lymphoma. Consideration should be given to the inclusion of HGAL/GCET2 analysis in algorithms to better predict the cell of origin. These findings bear further validation, from comparison to gene expression profiles and from clinical/therapeutic data. Modern Pathology (2012) 25, 1439-1445; doi: 10.1038/modpathol.2012.119; published online 29 June 2012

Algebraic-graph method for identification of islanding in power system grids

In this paper, a new algebraic-graph method for identification of islanding in power system grids is proposed. The proposed method identifies all the possible cases of islanding, due to the loss of a equipment, by means of a factorization of the bus-branch incidence matrix. The main features of this new method include: (i) simple implementation, (ii) high speed, (iii) real-time adaptability, (iv) identification of all islanding cases and (v) identification of the buses that compose each island in case of island formation. The method was successfully tested on large-scale systems such as the reduced south Brazilian system (45 buses/72 branches) and the south-southeast Brazilian system (810 buses/1340 branches). (C) 2011 Elsevier Ltd. All rights reserved.

Network-based stochastic semisupervised learning

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.

Cash balance management: A comparison between genetic algorithms and particle swarm optimization

This work aimed to apply genetic algorithms (GA) and particle swarm optimization (PSO) in cash balance management using Miller-Orr model, which consists in a stochastic model that does not define a single ideal point for cash balance, but an oscillation range between a lower bound, an ideal balance and an upper bound. Thus, this paper proposes the application of GA and PSO to minimize the Total Cost of cash maintenance, obtaining the parameter of the lower bound of the Miller-Orr model, using for this the assumptions presented in literature. Computational experiments were applied in the development and validation of the models. The results indicated that both the GA and PSO are applicable in determining the cash level from the lower limit, with best results of PSO model, which had not yet been applied in this type of problem.