Zara Ghodsi

From nature to maths

Many scientific fields consider accurate and reliable forecasting methods as important decision-making tools in the modern age amidst increasing volatility and uncertainty. As such there exists an opportune demand for theoretical developments which can result in more accurate forecasts. Inspired by Colonial Theory, this paper seeks to bring about considerable improvements to the field of time series analysis and forecasting by identifying certain core characteristics of Colonial Theory which are subsequently exploited in introducing a novel approach for the grouping step of subspace based methods. The proposed algorithm shows promising results in terms of improved performances in noise filtering and forecasting of time series. The reliability and validity of the proposed algorithm is evaluated and compared with popular forecasting models with the results being thoroughly evaluated for statistical significance and thereby adding more confidence and value to the findings of this research.

Bicoid Signal Extraction with a Selection of Parametric and Nonparametric Signal Processing Techniques

The maternal segmentation coordinate gene bicoid plays a significant role during Drosophila embryogenesis. The gradient of Bicoid, the protein encoded by this gene, determines most aspects of head and thorax development. This paper seeks to explore the applicability of a variety of signal processing techniques at extracting bicoid expression signal, and whether these methods can outperform the current model. We evaluate the use of six different powerful and widely-used models representing both parametric and nonparametric signal processing techniques to determine the most efficient method for signal extraction in bicoid. The results are evaluated using both real and simulated data. Our findings show that the Singular Spectrum Analysis technique proposed in this paper outperforms the synthesis diffusion degradation model for filtering the noisy protein profile of bicoid whilst the exponential smoothing technique was found to be the next best alternative followed by the autoregressive integrated moving average.

Optimizing Bicoid Signal Extraction

Signal extraction and analysis is of great importance, not only in fields such as economics and meteorology, but also in genetics and even biomedicine. There exists a range of parametric and nonparametric techniques which can perform signal extractions. However, the aim of this paper is to define a new approach for optimising signal extraction from bicoid gene expression profile. Having studied both parametric and nonparametric signal extraction techniques, we identified the lack of specific criteria enabling users to select the optimal signal extraction parameters. Exploiting the expression profile of bicoid gene, which is a maternal segmentation coordinate gene found in Drosophila melanogaster, we introduce a new approach for optimising the signal extraction using a nonparametric technique. The underlying criteria are based on the distribution of the residual, more specifically its skewness.

Mathematical approaches in studying bicoid gene

It is widely believed that in Drosophila melanogaster the pattern of Bicoid protein gradient plays a crucial role in the segmentation stage of embryo development. As a result of its fundamental role, modelling the Bicoid gradient has become increasingly popular for researchers from many different areas of study. The aim of this paper is to bring together the most prominent studies on this maternal gene and discuss how existing techniques for modelling this gradient have evolved over the years.

Forecasting energy data using Singular Spectrum Analysis in the presence of outlier(s)

The aim of this paper is to present a comparative study on the performance of the two different forecasting approaches of SSA in the presence of outliers. We examine this issue from different points of view. As our real data set, we have considered the well known WTI Spot Price series. The effect on forecasting process when confronted with outlier(s) in different parts of a time series is evaluated. Based on this study, we find evidence which suggests that the existence of outliers affect SSA reconstruction and forecasting results, and that VSSA forecasting performs better than RSSA in terms of the accuracy and robustness of forecasts.

Causality analysis detects the regulatory role of maternal effect genes in the early Drosophila embryo

In developmental studies, inferring regulatory interactions of segmentation genetic network play a vital role in unveiling the mechanism of pattern formation. As such, there exists an opportune demand for theoretical developments and new mathematical models which can result in a more accurate illustration of this genetic network. Accordingly, this paper seeks to extract the meaningful regulatory role of the maternal effect genes using a variety of causality detection techniques and to explore whether these methods can suggest a new analytical view to the gene regulatory networks. We evaluate the use of three different powerful and widely-used models representing time and frequency domain Granger causality and convergent cross mapping technique with the results being thoroughly evaluated for statistical significance. Our findings show that the regulatory role of maternal effect genes is detectable in different time classes and thereby the method is applicable to infer the possible regulatory interactions present among the other genes of this network.

A glance at the applications of Singular Spectrum Analysis in gene expression data.

In recent years Singular Spectrum Analysis (SSA) has been used to solve many biomedical issues and is currently accepted as a potential technique in quantitative genetics studies. Presented in this article is a review of recent published genetics studies which have taken advantage of SSA. Since Singular Value Decomposition (SVD) is an important stage of this technique which can also be used as an independent analytical method in gene expression data, we also briefly touch upon some areas of the application of SVD. The review finds that at present, the most prominent area of applying SSA in genetics is filtering and signal extraction, which proves that SSA can be considered as a valuable aid and promising method for genetics analysis.

Estimation of protein diffusion parameters: Estimation of protein diffusion parameters

Protein diffusion offers an essential and elegant mechanism for morphogen gradient formation. Morphogens are signalling molecules that emanate from a particular region of the cell and create a gradient which has an impact on most biological processes, cell signalling and embryonic development. Using a method that is based on Singular Spectrum Analysis, we estimate parameters introduced in the Synthesis Diffusion Degradation model which is a commonly applied model for a transcription factor known as Bicoid. Our findings, consistent with simulation results, indicate that the proposed method can be practically applied as an enhanced parameter estimation technique with reduced sensitivity to various levels of noise.

An enhanced version of Cochran-Armitage trend test for genome-wide association studies

Genome-wide association studies the evaluation of association between candidate gene and disease status is widely carried out using Cochran-Armitage trend test. However, only a small number of research papers have evaluated the distribution of p-values for the Cochran-Armitage trend test. In this paper, an enhanced version of Cochran-Armitage trend test based on bootstrap approach is introduced. The achieved results confirm that the distribution of p-values of the proposed approach fits better to the uniform distribution, and it is thus concluded that the proposed method, which needs less assumptions in comparison with the conventional method, can be successfully used to test the genetic association.

The impact of disaggregation on the forecasting performance of natural gas price

The aim of this paper is to evaluate the impact of disaggregating the data on the performance of two different versions of SSA methods, namely RSSA and VSSA. Using monthly data for natural gas prices in the United States residential sector with an out-of-sample period of 10:2010–5:2015, given an in-sample period of 1:2002–9:2010 we find evidence which suggests that data disaggregation improves SSA performance in terms of the accuracy and robustness of forecasts.