Scaling relationships of Gaussian processes

Asset returns conforming to a Gaussian random walk are characterised by the temporal independence of the moments of the distribution. Employing currency returns, this note demonstrates the conditions that are necessary for risk to be estimated in this manner.

Gaussian vault geometry : digital design and fabrication of scaled prototypes

This paper reports on three approaches to the translation of Gaussian surface models into scaled physical prototype models. Using the geometry of Eladio Dieste's Gaussian Vaults, the paper reports on the aspects encountered in the process of digital to physical prototype fabrication. The primary focus of the paper is on exploring the design geometry, investigating methods for preparing the geometry for fabrication and constructing physical prototypes. Three different approaches in the translation from digital to physical models are investigated: rapid prototyping, two dimensional surface models in paper and structural component models using Computer Numerical Controlled (CNC) fabrication. The three approaches identify a body of knowledge in the design and prototyping of Gaussian vaults. Finally the paper discusses the digital to. fabrication translation processes with regards to the characteristics, benefits and limitations of the three approaches of prototyping the ruled surface geometry of Gaussian Vaults.

Gaussian vault geometry : integrated approach in design and fabrication of physical prototypes

This paper reports the second part of a study on the digital design and fabrication of scaled architectural prototypes. The first paper reported techniques in the realization of a double curved vault surface, the Gaussian Vault. The aims of the research here further extend this body of knowledge to a better understanding of constructible components. It addresses the problem of fabricating complex curved forms through the integration of the basic building elements, skin and structure, to achieve a scaled physical prototype. The focus of the experimentation is to investigate the process from which a digital surface form is conceived, to its preparation for fabrication and eventual construction in the fashion of a scaled model or workable prototype.

Optimization of gaussian fuzzy membership functions and evaluation of the monotonicity property of fuzzy inference systems

In this paper, two issues relating to modeling of a monotonicity-preserving Fuzzy Inference System (FIS) are examined. The first is on designing or tuning of Gaussian Membership Functions (MFs) for a monotonic FIS. Designing Gaussian MFs for an FIS is difficult because of its spreading and curvature characteristics. In this study, the sufficient conditions are exploited, and the procedure of designing Gaussian MFs is formulated as a constrained optimization problem. The second issue is on the testing procedure for a monotonic FIS. As such, a testing procedure for a monotonic FIS model is proposed. Applicability of the proposed approach is demonstrated with a real world industrial application, i.e., Failure Mode and Effect Analysis. The results obtained are analysis and discussed. The outcomes show that the proposed approach is useful in designing a monotonicity-preserving FIS model.

Incremental learning of temporally-coherent gaussian mixture models

In this paper we address the problem of learning Gaussian Mixture Models (GMMs) incrementally. Unlike previous approaches which universally assume that new data comes in blocks representable by GMMs which are then merged with the current model estimate, our method works for the case when novel data points arrive oneby- one, while requiring little additional memory. We keep only two GMMs in the memory and no historical data. The current fit is updated with the assumption that the number of components is fixed, which is increased (or reduced) when enough evidence for a new component is seen. This is deduced from the change from the oldest fit of the same complexity, termed the Historical GMM, the concept of which is central to our method. The performance of the proposed method is demonstrated qualitatively and quantitatively on several synthetic data sets and video sequences of faces acquired in realistic imaging conditions

Incremental learning of temporally-coherent Gaussian mixture models

In this paper we address the problem of learning Gaussian Mixture Models (GMMs) incrementally. Unlike previous approaches which universally assume that new data comes in blocks representable by GMMs which are then merged with the current model estimate, our method works for the case when novel data points arrive one- by-one, while requiring little additional memory. We keep only two GMMs in the memory and no historical data. The current fit is updated with the assumption that the number of components is fixed which is increased (or reduced) when enough evidence for a new component is seen. This is deducedfrom the change from the oldest fit of the same complexity, termed the Historical GMM, the concept of which is central to our method. The performance of the proposed method is demonstrated qualitatively and quantitatively on several synthetic data sets and video sequences of faces acquired in realistic imaging conditions.