Relative order defines a topology for recurrent networks

This paper uses techniques from control theory in the analysis of trained recurrent neural networks. Differential geometry is used as a framework, which allows the concept of relative order to be applied to neural networks. Any system possessing finite relative order has a left-inverse. Any recurrent network with finite relative order also has an inverse, which is shown to be a recurrent network.

Improved process topology for membrane distillation

In membrane distillation in a conventional membrane module, the enthalpies of vaporisation and condensation are supplied and removed by changes in the temperatures of the feed and permeate streams, respectively. Less than 5% of the feed can be distilled in a single pass, because the potential changes in the enthalpies of the liquid streams are much smaller than the enthalpy of vaporisation. Furthermore, the driving force for mass transfer reduces as the feed stream temperature and vapour pressure fall during distillation. These restrictions can be avoided if the enthalpy of vaporisation is uncoupled from the heat capacities of the feed and permeate streams. A specified distillation can then be effected continuously in a single module. Calculations are presented which estimate the performance of a flat plate unit in which the enthalpy of distillation is supplied and removed by the condensing and boiling of thermal fluids in separate circuits, and the imposed temperature difference is independent of position. Because the mass flux through the membrane is dependent on vapour pressure, membrane distillation is suited to applications with a high membrane temperature. The maximum mass flux in the proposed module geometry is predicted to be 30 kg/m2 per h at atmospheric pressure when the membrane temperature is 65°C. Operation at higher membrane temperatures is predicted to raise the mass flux, for example to 85 kg/m2 per h at a membrane temperature of 100°C. This would require pressurisation to 20 bar to prevent boiling at the heating plate of the feed channel. Pre-pressurisation of the membrane pores and control of the dissolved gas concentrations in the feed and the recyled permeate should be investigated as a means to achieve high temperature membrane distillation without pore penetration and wetting.

Crystallization of random aromatic copolyesters containing flexible spacer chains and side-groups

The crystallization behaviour of a series of random copolymers of varying chemical composition is reported. For polymers containing a high proportion of alternating rigid aromatic units and flexible spacers, conventional liquid crystalline and crystalline phase behaviour is observed. The introduction of a substantial fraction of a second shorter rigid unit containing side-chains leads to a broad endotherm in the d.s.c. scan covering some 150°C. Subsequent isothermal crystallization at any point within the broad endotherm leads to the generation of sharp endotherms at temperatures just above the recrystallization temperature. We attribute this behaviour to the crystallization of clusters of molecules containing similar random sequences. Such crystals are non-periodic along the chain direction.

Biaxial optical properties of thermotropic random copolyesters

The optical microstructures of thin sections of two liquid crystalline polymers are examined in the polarizing microscope. The polymers are random copolyesters based on hydroxybenzoic and hydroxynaphthoic acids (B-N), and hydroxybenzoic acid and ethylene terephthalate (B-ET). Sections cut from oriented samples, so as to include the extrusion direction, show microstructures in which there is no apparent preferred orientation of the axes describing the local optical anisotropy. The absence of preferred orientation in the microstructure, despite marked axial alignment of molecular chain segments as demonstrated by X-Ray diffraction, is interpreted in terms of the polymer having biaxial optical properties. The implication of optical biaxiality is that, although the mesophases are nematic, the orientation of the molecules is correlated about three (orthogonal) axes over distances greater than a micron. The structure is classified as a multiaxial nematic.

PDM 2006: Proceedings of the International Workshop on Data Mining

Recently major processor manufacturers have announced a dramatic shift in their paradigm to increase computing power over the coming years. Instead of focusing on faster clock speeds and more powerful single core CPUs, the trend clearly goes towards multi core systems. This will also result in a paradigm shift for the development of algorithms for computationally expensive tasks, such as data mining applications. Obviously, work on parallel algorithms is not new per se but concentrated efforts in the many application domains are still missing. Multi-core systems, but also clusters of workstations and even large-scale distributed computing infrastructures provide new opportunities and pose new challenges for the design of parallel and distributed algorithms. Since data mining and machine learning systems rely on high performance computing systems, research on the corresponding algorithms must be on the forefront of parallel algorithm research in order to keep pushing data mining and machine learning applications to be more powerful and, especially for the former, interactive. To bring together researchers and practitioners working in this exciting field, a workshop on parallel data mining was organized as part of PKDD/ECML 2006 (Berlin, Germany). The six contributions selected for the program describe various aspects of data mining and machine learning approaches featuring low to high degrees of parallelism: The first contribution focuses the classic problem of distributed association rule mining and focuses on communication efficiency to improve the state of the art. After this a parallelization technique for speeding up decision tree construction by means of thread-level parallelism for shared memory systems is presented. The next paper discusses the design of a parallel approach for dis- tributed memory systems of the frequent subgraphs mining problem. This approach is based on a hierarchical communication topology to solve issues related to multi-domain computational envi- ronments. The forth paper describes the combined use and the customization of software packages to facilitate a top down parallelism in the tuning of Support Vector Machines (SVM) and the next contribution presents an interesting idea concerning parallel training of Conditional Random Fields (CRFs) and motivates their use in labeling sequential data. The last contribution finally focuses on very efficient feature selection. It describes a parallel algorithm for feature selection from random subsets. Selecting the papers included in this volume would not have been possible without the help of an international Program Committee that has provided detailed reviews for each paper. We would like to also thank Matthew Otey who helped with publicity for the workshop.

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Spectrum of a Feinberg-Zee random hopping matrix

This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya, and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general class of random matrices whose spectra contain a hole around the origin. The presence of the hole forces substantial changes to the analysis.

Random-walk-based characterisation of multiple access interference in a DS/SSMA system

The problem of calculating the probability of error in a DS/SSMA system has been extensively studied for more than two decades. When random sequences are employed some conditioning must be done before the application of the central limit theorem is attempted, leading to a Gaussian distribution. The authors seek to characterise the multiple access interference as a random-walk with a random number of steps, for random and deterministic sequences. Using results from random-walk theory, they model the interference as a K-distributed random variable and use it to calculate the probability of error in the form of a series, for a DS/SSMA system with a coherent correlation receiver and BPSK modulation under Gaussian noise. The asymptotic properties of the proposed distribution agree with other analyses. This is, to the best of the authors' knowledge, the first attempt to propose a non-Gaussian distribution for the interference. The modelling can be extended to consider multipath fading and general modulation

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Random prism: an alternative to random forests

Ensemble learning techniques generate multiple classifiers, so called base classifiers, whose combined classification results are used in order to increase the overall classification accuracy. In most ensemble classifiers the base classifiers are based on the Top Down Induction of Decision Trees (TDIDT) approach. However, an alternative approach for the induction of rule based classifiers is the Prism family of algorithms. Prism algorithms produce modular classification rules that do not necessarily fit into a decision tree structure. Prism classification rulesets achieve a comparable and sometimes higher classification accuracy compared with decision tree classifiers, if the data is noisy and large. Yet Prism still suffers from overfitting on noisy and large datasets. In practice ensemble techniques tend to reduce the overfitting, however there exists no ensemble learner for modular classification rule inducers such as the Prism family of algorithms. This article describes the first development of an ensemble learner based on the Prism family of algorithms in order to enhance Prism’s classification accuracy by reducing overfitting.

Parallel random prism: a computationally efficient ensemble learner for classification

Generally classifiers tend to overfit if there is noise in the training data or there are missing values. Ensemble learning methods are often used to improve a classifier's classification accuracy. Most ensemble learning approaches aim to improve the classification accuracy of decision trees. However, alternative classifiers to decision trees exist. The recently developed Random Prism ensemble learner for classification aims to improve an alternative classification rule induction approach, the Prism family of algorithms, which addresses some of the limitations of decision trees. However, Random Prism suffers like any ensemble learner from a high computational overhead due to replication of the data and the induction of multiple base classifiers. Hence even modest sized datasets may impose a computational challenge to ensemble learners such as Random Prism. Parallelism is often used to scale up algorithms to deal with large datasets. This paper investigates parallelisation for Random Prism, implements a prototype and evaluates it empirically using a Hadoop computing cluster.