Non-ergodic effects in the Coulomb glass: specific heat

We present a numerical method for the investigation of non-ergodic effects in the Coulomb glass. For that, an almost complete set of low-energy many-particle states is obtained by a new algorithm. The dynamics of the sample is mapped to the graph formed by the relevant transitions between these states, that means by transitions with rates larger than the inverse of the duration of the measurement. The formation of isolated clusters in the graph indicates non-ergodicity. We analyze the connectivity of this graph in dependence on temperature, duration of measurement, degree of disorder, and dimensionality, studying how non-ergodicity is reflected in the specific heat.Comment: Submited Phys. Rev.

Random model trees: an effective and scalable regression method

We present and investigate ensembles of randomized model trees as a novel regression method. Such ensembles combine the scalability of tree-based methods with predictive performance rivaling the state of the art in numeric prediction. An extensive empirical investigation shows that Random Model Trees produce predictive performance which is competitive with state-of-the-art methods like Gaussian Processes Regression or Additive Groves of Regression Trees. The training and optimization of Random Model Trees scales better than Gaussian Processes Regression to larger datasets, and enjoys a constant advantage over Additive Groves of the order of one to two orders of magnitude

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Cooperation of Nature and Physiologically Inspired Mechanism in Visualisation

A novel approach of integrating two swarm intelligence algorithms is considered, one simulating the behaviour of birds flocking (Particle Swarm Optimisation) and the other one (Stochastic Diffusion Search) mimics the recruitment behaviour of one species of ants – Leptothorax acervorum. This hybrid algorithm is assisted by a biological mechanism inspired by the behaviour of blood flow and cells in blood vessels, where the concept of high and low blood pressure is utilised. The performance of the nature-inspired algorithms and the biologically inspired mechanisms in the hybrid algorithm is reflected through a cooperative attempt to make a drawing on the canvas. The scientific value of the marriage between the two swarm intelligence algorithms is currently being investigated thoroughly on many benchmarks and the results reported suggest a promising prospect (al-Rifaie, Bishop & Blackwell, 2011). We also discuss whether or not the ‘art works’ generated by nature and biologically inspired algorithms can possibly be considered as ‘computationally creative’

Generalized Network Psychometrics: Combining Network and Latent Variable Models

We introduce the network model as a formal psychometric model, conceptualizing the covariance between psychometric indicators as resulting from pairwise interactions between observable variables in a network structure. This contrasts with standard psychometric models, in which the covariance between test items arises from the influence of one or more common latent variables. Here, we present two generalizations of the network model that encompass latent variable structures, establishing network modeling as parts of the more general framework of Structural Equation Modeling (SEM). In the first generalization, we model the covariance structure of latent variables as a network. We term this framework Latent Network Modeling (LNM) and show that, with LNM, a unique structure of conditional independence relationships between latent variables can be obtained in an explorative manner. In the second generalization, the residual variance-covariance structure of indicators is modeled as a network. We term this generalization Residual Network Modeling (RNM) and show that, within this framework, identifiable models can be obtained in which local independence is structurally violated. These generalizations allow for a general modeling framework that can be used to fit, and compare, SEM models, network models, and the RNM and LNM generalizations. This methodology has been implemented in the free-to-use software package lvnet, which contains confirmatory model testing as well as two exploratory search algorithms: stepwise search algorithms for low-dimensional datasets and penalized maximum likelihood estimation for larger datasets. We show in simulation studies that these search algorithms performs adequately in identifying the structure of the relevant residual or latent networks. We further demonstrate the utility of these generalizations in an empirical example on a personality inventory dataset.Comment: Published in Psychometrik

Constraint-based sequence mining using constraint programming

The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the literature, but a general framework is still missing. We investigate the use of constraint programming as general framework for this task. We first identify four categories of constraints that are applicable to sequence mining. We then propose two constraint programming formulations. The first formulation introduces a new global constraint called exists-embedding. This formulation is the most efficient but does not support one type of constraint. To support such constraints, we develop a second formulation that is more general but incurs more overhead. Both formulations can use the projected database technique used in specialised algorithms. Experiments demonstrate the flexibility towards constraint-based settings and compare the approach to existing methods.Comment: In Integration of AI and OR Techniques in Constraint Programming (CPAIOR), 201