Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

Dynamic Niche Clustering: a fuzzy variable radius niching technique for multimodal optimisation in GAs

This paper describes the recent developments and improvements made to the variable radius niching technique called Dynamic Niche Clustering (DNC). DNC is fitness sharing based technique that employs a separate population of overlapping fuzzy niches with independent radii which operate in the decoded parameter space, and are maintained alongside the normal GA population. We describe a speedup process that can be applied to the initial generation which greatly reduces the complexity of the initial stages. A split operator is also introduced that is designed to counteract the excessive growth of niches, and it is shown that this improves the overall robustness of the technique. Finally, the effect of local elitism is documented and compared to the performance of the basic DNC technique on a selection of 2D test functions. The paper is concluded with a view to future work to be undertaken on the technique.

A variable radius niching technique for speciation in genetic algorithms

In this paper, a continuation of a variable radius niche technique called Dynamic Niche Clustering developed by (Gan & Warwick, 1999) is presented. The technique employs a separate dynamic population of overlapping niches that coexists alongside the normal population. An empirical analysis of the updated methodology on a large group of standard optimisation test-bed functions is also given. The technique is shown to perform almost as well as standard fitness sharing with regards to stability and the accuracy of peak identification, but it outperforms standard fitness sharing with regards to time complexity. It is also shown that the technique is capable of forming niches of varying size depending on the characteristics of the underlying peak that the niche is populating.

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.

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.

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.

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.

Analysis of Direct Outdoor Air Cooling Efficency for Combined Variable Air Volume Air-conditioning System in Stores in Cold Climates of China

Direct outdoor air cooling contributes a lot not only to the improvement of the indoor air quality but also to the energy saving. Its full use will reduce the water chiller’s running time especially in some stores where cooling load keeps much higher and longer than that in other buildings. A novel air-conditioning system named Combined Variable Air Volume system (CVAV), combining a normal AHU with a separate outdoor air supply system, was proposed firstly by the authors. The most attractive feature of the system is its full utilization of cooling capacity and freshness of outdoor air in the transition period of the year round. On the basis of the obtain of the dynamic cooling loads of the typical shopping malls in different four cities located in cold climates in China with the aid of DOE-2, the possibility of increasing the amount of outdoor air volume of CVAV system in the transition period instead of operating the water chillers was confirmed. Moreover, a new concept, Direct Outdoor Air Cooling Efficiency (DOACE), was defined as the ratio of cooling capacity of outdoor air to the water chiller, indicating the degree of outdoor air’s utilization. And the DOACE of the CVAV was calculated and compared with that of conventional all-air constant volume air-conditioning systems, the results showed that CVAV bear much more energy saving potential with the 10%~19% higher DOACE and it is a kind of energy efficient systems and can improve the indoor air quality as well.