Role of Wiener chaos expansion in modelling randomness for groundwater contamination flow

Pertinent mathematical modelling plays pivot role in making groundwater protection and reclamation policies. Uncertain parameters and several basic phenomena in almost all branches of engineering and science can be modelled efficiently with the help of Stochastic Partial Differential Equations (SPDEs) and their behaviour can be interpreted more accurately. The intent of the present study is to use an efficient numerical approach based on Wiener chaos expansion to understand the stochastic nature of variables associated with groundwater flow. First and second order moments of concentration profile are calculated and plotted graphically. Obtained results are in good agreement with those available in existing literature

Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks

Background: Numerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system’s dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states. Results: To demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions: The ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems

An improved stochastic modelling framework for biological networks

It has become very clear that stochasticity in biology is a rule rather than exception. Gillespie stochastic simulation algorithm (GSSA) (direct method) is the first algorithm proposed to model stochasticity in biochemical systems. However, the computational intractability of direct method has been identified as the main challenge for using it to model large biochemical systems. In this paper, a novel variant of the GSSA is proposed to address computational intractability of the direct method. The direct method is combined with a Mapping Reduction Method (MRM) to target a single run of the direct method to be accelerated by advancing the system through several reactions at each time step to replace the single reaction in GSSA. MRM is a framework for mimicking parallel processes occurring in large systems using a large number of threads that work together and seen as a single system. It is used for parallel problems to be processed across large datasets using a large number of nodes working together as a single system. Link between GSk3 and p53 in Alzheimer's disease (AD) is modelled using the proposed method and tested and validated by comparing it with the direct method

A simple Affymetrix ratio-transformation method yields comparable expression level quantifications with cDNA data

Gene expression profiling is rapidly evolving into a powerful technique for investigating tumor malignancies. The researchers are overwhelmed with the microarray-based platforms and methods that confer them the freedom to conduct large-scale gene expression profiling measurements. Simultaneously, investigations into cross-platform integration methods have started gaining momentum due to their underlying potential to help comprehend a myriad of broad biological issues in tumor diagnosis, prognosis, and therapy. However, comparing results from different platforms remains to be a challenging task as various inherent technical differences exist between the microarray platforms. In this paper, we explain a simple ratio-transformation method, which can provide some common ground for cDNA and Affymetrix platform towards cross-platform integration. The method is based on the characteristic data attributes of Affymetrix- and cDNA- platform. In the work, we considered seven childhood leukemia patients and their gene expression levels in either platform. With a dataset of 822 differentially expressed genes from both these platforms, we carried out a specific ratio-treatment to Affymetrix data, which subsequently showed an improvement in the relationship with the cDNA data

Prediction of lamb tenderness using combined quality parameters and meat surface characteristics

The objectives of the present study were: to investigate the predictability of cooked lamb tenderness from textural parameters extracted from lamb chops images using GLRM and GLDM techniques. To study the combined effects of texture features, marbling and ultimate pH on the prediction models

The influence of site aspect and pruning types on Pinot noir phenology and shoot growth

Aim: Managing the influence that terroir in vineyards has on vine development depends on improving our understanding the effect of the interaction of within-site variability, within-vine variability, and management practices (such as pruning types) on phenology and vine development. This study evaluates the consequence of site aspect and pruning management on budburst, leaf appearance rate, and shoot growth in Pinot noir vines. Methods and results: Two rows of 19-year-old Pinot noir vines were selected within a commercial vineyard with south, hilltop, and north-facing aspects (note: the north-facing slope is sun-facing in the Southern Hemisphere). Vines were either cane- or spur-pruned, retaining 20 nodes per vine. Budburst, shoot development, and leaf appearance were assessed, and vine trunk circumference was measured to quantify the accumulated differences in vine vigour. Hilltop plots had smaller trunk circumferences when compared to the south- and north-facing plots. Irrespective of topographical positions, budburst was earlier in cane-pruned vines compared to spur-pruned vines, but no differences were observed by the time of 12-leaf stage. The rate of shoot growth reflected the variations in topographical positions and trunk circumference. Cane-pruning exhibited more significant within-vine variation in budburst, budburst duration, and shoot growth when compared with spur-pruning. Shoots from hilltop vines were shorter relative to the vines at other plots for both pruning systems. Conclusions: The rate of shoot growth and development was associated more with site and vine vigour as determined by trunk circumference than pruning type. Spur-pruned vines had a later but more uniform budburst when compared to cane-pruned vines. Significance and impact of the study: Pruning type and within-site variability may lead to differences in canopy density and vine vigour, which can ultimately impact subsequent growth and development of the grapevine. Determining the influence of terroir within the vineyard on budburst, leaf appearance, and shoot growth variability will enable the development of improved phenology and growth models to describe within vineyard variability

Effect of molecular noise on the dynamics of tryptophan operon system in Escherichia coli

Noise in gene expression, or the variation in gene expression in an isogenic population under a homogeneous environment, has been of much interest in recent years. Differences in gene expression of two isogenic cells could be attributed to the variation in factors determining gene expression in these cells, such as transcription factors, the concentration of operators, RNA polymerase, the cell cycle, etc., which is termed extrinsic noise. However, variation could still persist even when all extrinsic noise is eliminated, due to the limited number of molecules for typical molecular species involved. The latter is termed intrinsic noise. However, the implications of stochastic gene expression are still not clear. There is very little knowledge about the consequences of stochasticity on particular systems. Here, we seek to better understand what differences may result from stochastic and deterministic kinetic approaches to modelling genetic regulatory systems by considering a model system of tryptophan (Trp) operon system in Escherichia coli. This genetic regulatory network is responsible for the production of tryptophan amino acid inside the cells. The molecular basis of the system is presented in the introduction part of the paper. The development and analysis of two stochastic models for the tryptophan operon system are discussed in section 2 and 3. In the first model we introduce molecular noise by setting up stochastic differential equations using the Langevin approach in which molecular fluctuation in the form of white noise is explicitly considered. The second stochastic model is based on the Gillespie method. Due to the lack of data on kinetic rates for elementary reaction steps of molecular processes, the implementation of the Gillespie method is carried out without decomposing the deterministic mechanism into detailed reaction steps. Simulation results from two versions of the stochastic regimes are compared to their deterministic counterpart. We found that intrinsic fluctuations resulted from molecular noise can destroy stable oscillatory behaviour. In this case, a new value for the bifurcation point is established, which is far from the corresponding deterministic bifurcation point. Moreover, we demonstrate that intrinsic noise can enable the system to obtain qualitatively different dynamics compared to when noise is absent. Specifically, stable sustained oscillations are obtained only when molecular noise is incorporated. Quantification of noise strength for key molecular species indicates that the transcription process exhibits high fluctuation levels which subsequently suggests that in order to reduce noise at the tryptophan output level, one may consider speeding up mRNA transcripts degradation

Modelling of circadian rhythms in Drosophila incorporating the interlocked PER/TIM and VRI/PDP1 feedback loops

Circadian rhythms of gene activity, metabolism, physiology and behaviour are observed in all the eukaryotes and some prokaryotes. In this study, we present a model to represent the transcriptional regulatory network essential for the circadian rhythmicity in Drosophila. The model incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not assumed to describe the regulation of genes, instead of the explicit reactions of binding and unbinding processes of transcription factors to promoters are modelled. The model simulates sustained circadian oscillations in mRNA and protein concentrations in constant darkness in agreement with experimental observations. It also simulates entrainment by light-dark cycles, disappearance of the rhythmicity in constant light and the shape of phase response curves resembling that of the experimental results. The model is robust over a wide range of parameter variations. In addition, the simulated E-box mutation, perS and perL mutants are similar to that observed in the experiments. The deficiency between the simulated mRNA levels and experimental observations in per01, tim01 andclkJrk mutants suggests some difference on the part of the model from reality

Validating a gene expression signature of invasive ductal carcinoma of the breast and detecting key genes using neural networks

Breast cancer is one of the leading causes of death in women in the world. It is a complex disease with challenges to accurate diagnosis due to cancer subtypes that are difficult to distinguish. The most common subtype is Invasive Ductal Carcinoma (IDC), a cancer in ductal cells that line the milk ducts in the breast. In depth understanding of the genetic basis of IDC can help treat it more effectively. Microarray based gene expression analysis is making new grounds in accurate diagnosis of diseases including cancer. Microarray experiments are designed to measure the expression levels of thousands of genes in various cells/tissues of interest and they are analysed to decipher a small set of genes that constitutes the gene signature of a particular disease. The few studies on breast cancer gene expression compare cancer subtypes but very few have compared gene expression between matched cancer and healthy tissues in the breast (Turashvili et al., 2007). The few studies that have compared different subtypes have little agreement on the gene signatures (Turashvili, 2007; Zhao et al., 2004, Sorlie, et al., 2001). Therefore, it is highly beneficial to further assess the validity of genes identified as differentially expressed, in order to boost confidence in the usefulness of the genes in various medical applications including diagnosis, prognosis and drug development. In this study, the validity of differentially expressed genes pertaining to a carefully conducted experiment on breast tissues affected by Invasive Ductal Carcinoma (IDL) and matched healthy tissues is conducted using neural networks and statistical methods. The data was obtained from NCBI database and deposited by Turashvili et al (2007) from their experiments on breast cancer. The original authors extracted a 326 gene signature for IDC using statistical methods. In our study, the ability of this gene set to discriminate the disease state from healthy state is investigated and validated using two sets of independent datasets. Our visual and qualitative exploration using Self organizing maps (SOM) followed by statistical tests indicated that the validation data supported 80% of the original gene signature. Another SOM results declared that the original gene set is able to classify patients as being healthy or having IDC. Original gene set was optimally clustered into two classes based on correlation of expression patterns of genes by SOM /Ward clustering. The two classes and genes in them were supported by 60% of the validation data. As an alternative, PCA was used to determine genes with correlated expressions in the original gene signature and 4 PCs accounted for 86% of the variation in the data with the first 2 PCs accounting for around 70%. Top most important 100 genes in PC1 and PC2 provided 52% support for the two SOM classes with PC1 dominating class 1 and PC2, class 2. Genes that were validated by independent data in the two SOM classes were used in conjunction with PC1 and PC2 to extract highly influential genes from the top 6%, 18% and 57% of the original genes represented by PC1 and PC2. These key genes may prove to be the most crucial in identifying ductal tumor from healthy tissues. Four new genes were among key genes that may shed more light onto the disease mechanism. The key genes as well as overall set of validated genes may provide further support to understand or refine genetic networks that these genes are part of in the next stage of our study

A literature review on wine production, quality, and machine learning: A report

This report is a literature review I have undertaken to survey the literature related to wine production and quality parameters, as a PI in a MBIE funded Pinot Noir research program, as an attempt to understand the intriguing world of wines and wine-making. This was written in rather unusual times, when there is a global pandemic, covid 19, and under various forms of government lockdowns. As there is hardly any serious attempts in AI applications in wine research space, we have reviewed machine learning and deep learning techniques in international agriculture in the later sections. The intention was to understand the extent of applications so that our future work would be an advancement not only in the novelty associated with wine research but also in new innovations that could be possible in future