Mathematical models of eye movements

This is the author accepted manuscript. The final version is available from [the Institute of Mathematics and its ApplicationsSupported by the BBSRC grant no 36/MMI09774

Robust Structured Low-Rank Approximation on the Grassmannian

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identification and data series analysis. At the same time it has been shown how to control the rank of a structured approximation via matrix factorization approaches. The drawbacks of these methods either lie in the lack of robustness against outliers or in their static nature of repeated batch-processing. We present a Robust Structured Low-Rank Approximation method on the Grassmannian that on the one hand allows for fast re-initialization in an online setting due to subspace identification with manifolds, and that is robust against outliers due to a smooth approximation of the $\ell_p$-norm cost function on the other hand. The method is evaluated in online time series forecasting tasks on simulated and real-world data

Radial Basis Functions Network for Defect Sizing

An important aspect of non-destructive testing is the interpretation and classification of signal obtained by NDT methods such as eddy current and ultrasound. These signals are typically complex, non-stationary waveforms, with signals corresponding to a particular class of defect in a specimen having similar form and shape. However, distortions and noise introduced by the measurement system make the manual classification of these signals a time-consuming and unreliable process, with the results affected by operator fatigue and measurement quality. The design of traditional classifiers for this task also poses many difficulties, due to a number of parameters that influence measurement, and the limited understanding of the effect of these parameters on the signal. Recently, artificial neural networks have been applied to a variety of NDT problems, including signal classification, with encouraging results. Artificial neural networks consist of a dense interconnection of simple computational elements, whose interconnection strengths are determined using a predefined learning algorithm, specific to the network. These networks do not require an explicit mathematical modeling of the data they have to process, and are robust even in the presence of noisy data and data generated by strongly non-linear processes [1]. An example of a neural network that has been extensively used in NDT applications is the multilayer perception. However, the error backpropagation algorithm used for training the multilayer perceptron has several disadvantages, such as long training times and susceptibility to local minima. This paper presents a novel approach to defect sizing that involves the use of a radial basis functions network. The network has the advantages of having shorter training times and a parametric nature that allows network optimization on an analytic basis. The application of such a network in the inversion of ultrasonic data to obtain flaw sizing is described. Results from the sizing of defects in aluminium blocks are presented

Γ-stochastic neighbour embedding for feed-forward data visualization

t-distributed Stochastic Neighbour Embedding (t-SNE) is one of the most popular nonlinear dimension reduction techniques used in multiple application domains. In this paper we propose a variation on the embedding neighbourhood distribution, resulting in Γ-SNE, which can construct a feed-forward mapping using an RBF network. We compare the visualizations generated by Γ-SNE with those of t-SNE and provide empirical evidence suggesting the network is capable of robust interpolation and automatic weight regularization

RBF-TSS: Identification of Transcription Start Site in Human Using Radial Basis Functions Network and Oligonucleotide Positional Frequencies

Accurate identification of promoter regions and transcription start sites (TSS) in genomic DNA allows for a more complete understanding of the structure of genes and gene regulation within a given genome. Many recently published methods have achieved high identification accuracy of TSS. However, models providing more accurate modeling of promoters and TSS are needed. A novel identification method for identifying transcription start sites that improves the accuracy of TSS recognition for recently published methods is proposed. This method incorporates a metric feature based on oligonucleotide positional frequencies, taking into account the nature of promoters. A radial basis function neural network for identifying transcription start sites (RBF-TSS) is proposed and employed as a classification algorithm. Using non-overlapping chunks (windows) of size 50 and 500 on the human genome, the proposed method achieves an area under the Receiver Operator Characteristic curve (auROC) of 94.75% and 95.08% respectively, providing increased performance over existing TSS prediction methods

Complex temporal climate signals drive the emergence of human water-borne disease

Predominantly occurring in developing parts of the world, Buruli ulcer is a severely disabling mycobacterium infection which often leads to extensive necrosis of the skin. While the exact route of transmission remains uncertain, like many tropical diseases, associations with climate have been previously observed and could help identify the causative agent's ecological niche. In this paper, links between changes in rainfall and outbreaks of Buruli ulcer in French Guiana, an ultraperipheral European territory in the northeast of South America, were identified using a combination of statistical tests based on singular spectrum analysis, empirical mode decomposition and cross-wavelet coherence analysis. From this, it was possible to postulate for the first time that outbreaks of Buruli ulcer can be triggered by combinations of rainfall patterns occurring on a long (i.e., several years) and short (i.e., seasonal) temporal scale, in addition to stochastic events driven by the El Nino-Southern Oscillation that may disrupt or interact with these patterns. Long-term forecasting of rainfall trends further suggests the possibility of an upcoming outbreak of Buruli ulcer in French Guiana

Higuchi Dimension of Digital Images

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular direction along a line on an arbitrary angle through the image. The calculations must be made for the whole image. In this paper, a new method to overcome these limitations is proposed. 2D images are appropriately prepared in order to apply 1D signal analyses, originally developed to investigate nonlinear time series. The Higuchi dimension of these 1D signals is calculated using Higuchi's algorithm, and it is shown that both regions of interests and directional dependencies can be evaluated independently of the whole picture. A thorough validation of the proposed technique and a comparison of the new method to the Fourier dimension, a common two dimensional method for digital images, are given. The main result is that Higuchi's algorithm allows a direction dependent as well as direction independent analysis. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. Moreover, the proposed method is not restricted to Higuchi's algorithm, as any 1D method of analysis, can be applied

Indeterminacy of Reverse Engineering of Gene Regulatory Networks: The Curse of Gene Elasticity

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. A number of reverse engineering approaches have been developed to help uncover the regulatory networks giving rise to the observed gene expression profiles. However, this is an overspecified problem due to the fact that more than one genotype (network wiring) can give rise to the same phenotype. We refer to this phenomenon as “gene elasticity.” In this work, we study the effect of this particular problem on the pure, data-driven inference of gene regulatory networks.We simulated a four-gene network in order to produce “data” (protein levels) that we use in lieu of real experimental data. We then optimized the network connections between the four genes with a view to obtain the original network that gave rise to the data. We did this for two different cases: one in which only the network connections were optimized and the other in which both the network connections as well as the kinetic parameters (given as reaction probabilities in our case) were estimated. We observed that multiple genotypes gave rise to very similar protein levels. Statistical experimentation indicates that it is impossible to differentiate between the different networks on the basis of both equilibrium as well as dynamic data.We show explicitly that reverse engineering of GRNs from pure expression data is an indeterminate problem. Our results suggest the unsuitability of an inferential, purely data-driven approach for the reverse engineering transcriptional networks in the case of gene regulatory networks displaying a certain level of complexity