Parameter estimation for a point-source diffusion-decay morphogen model.

In this paper we present a novel method for finding unknown parameters for an unknown morphogen. We postulate the existence of an unknown morphogen in a given three-dimensional domain due to the spontaneous arrangement of a downstream species on the domain boundary for which data is known. Assuming a modified Helmholtz model for the morphogen and that it is produced from a single source in the domain, our method accurately estimates the source location and other model parameters. Notably, our method does not require the forward solution of the model to be computed which can often be a challenge for three-dimensional PDE model parameter fitting. Instead, an extension is made from the problem domain to an infinite domain and the analytic nature of the fundamental solution is exploited. We explore in this manuscript strategies for best conditioning the problem and rigorously explore the accuracy of the method on two test problems. Our tests focus on the effect of source location on accuracy but also the robustness of the algorithm to experimental noise.

Generating New Space-Filling Test Instances for Continuous Black-Box Optimization.

This article presents a method to generate diverse and challenging new test instances for continuous black-box optimization. Each instance is represented as a feature vector of exploratory landscape analysis measures. By projecting the features into a two-dimensional instance space, the location of existing test instances can be visualized, and their similarities and differences revealed. New instances are generated through genetic programming which evolves functions with controllable characteristics. Convergence to selected target points in the instance space is used to drive the evolutionary process, such that the new instances span the entire space more comprehensively. We demonstrate the method by generating two-dimensional functions to visualize its success, and ten-dimensional functions to test its scalability. We show that the method can recreate existing test functions when target points are co-located with existing functions, and can generate new functions with entirely different characteristics when target points are located in empty regions of the instance space. Moreover, we test the effectiveness of three state-of-the-art algorithms on the new set of instances. The results demonstrate that the new set is not only more diverse than a well-known benchmark set, but also more challenging for the tested algorithms. Hence, the method opens up a new avenue for developing test instances with controllable characteristics, necessary to expose the strengths and weaknesses of algorithms, and drive algorithm development.

Performance Analysis of Continuous Black-Box Optimization Algorithms via Footprints in Instance Space.

This article presents a method for the objective assessment of an algorithm's strengths and weaknesses. Instead of examining the performance of only one or more algorithms on a benchmark set, or generating custom problems that maximize the performance difference between two algorithms, our method quantifies both the nature of the test instances and the algorithm performance. Our aim is to gather information about possible phase transitions in performance, that is, the points in which a small change in problem structure produces algorithm failure. The method is based on the accurate estimation and characterization of the algorithm footprints, that is, the regions of instance space in which good or exceptional performance is expected from an algorithm. A footprint can be estimated for each algorithm and for the overall portfolio. Therefore, we select a set of features to generate a common instance space, which we validate by constructing a sufficiently accurate prediction model. We characterize the footprints by their area and density. Our method identifies complementary performance between algorithms, quantifies the common features of hard problems, and locates regions where a phase transition may lie.

Approximate Bayesian computation schemes for parameter inference of discrete stochastic models using simulated likelihood density.

BACKGROUND: Mathematical modeling is an important tool in systems biology to study the dynamic property of complex biological systems. However, one of the major challenges in systems biology is how to infer unknown parameters in mathematical models based on the experimental data sets, in particular, when the data are sparse and the regulatory network is stochastic. RESULTS: To address this issue, this work proposed a new algorithm to estimate parameters in stochastic models using simulated likelihood density in the framework of approximate Bayesian computation. Two stochastic models were used to demonstrate the efficiency and effectiveness of the proposed method. In addition, we designed another algorithm based on a novel objective function to measure the accuracy of stochastic simulations. CONCLUSIONS: Simulation results suggest that the usage of simulated likelihood density improves the accuracy of estimates substantially. When the error is measured at each observation time point individually, the estimated parameters have better accuracy than those obtained by a published method in which the error is measured using simulations over the entire observation time period.

A note on the relationship between turbulent coherent structures and phase correlation.

Various definitions of coherent structures exist in turbulence research, but a common assumption is that coherent structures have correlated spectral phases. As a result, randomization of phases is believed, generally, to remove coherent structures from the measured data. Here, we reexamine these assumptions using atmospheric turbulence measurements. Small-scale coherent structures are detected in the usual way using the wavelet transform. A considerable percentage of the detected structures are not phase correlated, although some of them are clearly organized in space and time. At larger scales, structures have even higher degree of spatiotemporal coherence but are also associated with weak phase correlation. A series of specific examples are shown to demonstrate this. These results warn about the vague terminology and assumptions around coherent structures, particularly for complex real-world turbulence.

Empirical evidence of climate change and urbanization impacts on warming stream temperatures.

Climate change and urbanization threaten streams and the biodiversity that rely upon them worldwide. Emissions of greenhouse gases are causing air and sea surface temperatures to increase, and even small areas of urbanization are degrading stream biodiversity, water quality and hydrology. However, empirical evidence of how increasing air temperatures and urbanization together affect stream temperatures over time and their relative influence on stream temperatures is limited. This study quantifies changes in stream temperatures in a region in South-East Australia with an urban-agricultural-forest landcover gradient and where increasing air temperatures have been observed. Using Random Forest models we identify air temperature and urbanization drive increasing stream temperatures and that their combined effects are larger than their individual effects occurring alone. Furthermore, we identify potential mitigation measures useful for waterway managers and policy makers. The results show that both local and global solutions are needed to reduce future increases to stream temperature.

Mathematical modelling of stem cell differentiation: the PU.1-GATA-1 interaction.

The transcription factors PU.1 and GATA-1 are known to be important in the development of blood progenitor cells. Specifically they are thought to regulate the differentiation of progenitor cells into the granulocyte/macrophage lineage and the erythrocyte/megakaryocite lineage. While several mathematical models have been proposed to investigate the interaction between the transcription factors in recent years, there is still debate about the nature of the progenitor state in the dynamical system, and whether the existing models adequately capture new knowledge about the interactions gleaned from experimental data. Further, the models utilise different formalisms to represent the genetic regulation, and it appears that the resulting dynamical system depends upon which formalism is adopted. In this paper we analyse the four existing models, and propose an alternative model which is shown to demonstrate a rich variety of dynamical systems behaviours found across the existing models, including both bistability and tristability required for modelling the undifferentiated progenitors.

Revisiting Facial Age Estimation With New Insights From Instance Space Analysis.

When demonstrating the effectiveness of a new algorithm, researchers are traditionally encouraged to compare their algorithm's performance against existing algorithms on well-studied benchmark test suites. In the absence of more nuanced methodologies, algorithm performance is typically summarized on average across the test suite examples. This paper highlights the potential bias of conclusions drawn by analyzing "on average" performance, and the opportunities offered by a recent testing methodology known as instance space analysis. To illustrate, we revisit our 2007 comparative study of algorithms for facial age estimation, and rigorously stress-test to challenge the original conclusions. The case study demonstrates how powerful visualizations offered by instance space analysis enable greater insights into unique strengths and weaknesses, and which algorithm should be used when and why. Inspired by such insights, a new algorithm is proposed, and its unique advantage is demonstrated. The bias often hidden in well-studied datasets, and the ramifications for drawing biased conclusions, are also illustrated in this case study. While focused on facial age estimation, the methodology and lessons learned from the case study are broadly applicable to any study seeking to draw conclusions about algorithm performance based on empirical results.

Relating instance hardness to classification performance in a dataset: a visual approach.

Machine Learning studies often involve a series of computational experiments in which the predictive performance of multiple models are compared across one or more datasets. The results obtained are usually summarized through average statistics, either in numeric tables or simple plots. Such approaches fail to reveal interesting subtleties about algorithmic performance, including which observations an algorithm may find easy or hard to classify, and also which observations within a dataset may present unique challenges. Recently, a methodology known as Instance Space Analysis was proposed for visualizing algorithm performance across different datasets. This methodology relates predictive performance to estimated instance hardness measures extracted from the datasets. However, the analysis considered an instance as being an entire classification dataset and the algorithm performance was reported for each dataset as an average error across all observations in the dataset. In this paper, we developed a more fine-grained analysis by adapting the ISA methodology. The adapted version of ISA allows the analysis of an individual classification dataset by a 2-D hardness embedding, which provides a visualization of the data according to the difficulty level of its individual observations. This allows deeper analyses of the relationships between instance hardness and predictive performance of classifiers. We also provide an open-access Python package named PyHard, which encapsulates the adapted ISA and provides an interactive visualization interface. We illustrate through case studies how our tool can provide insights about data quality and algorithm performance in the presence of challenges such as noisy and biased data.

Method for optimizing coating properties based on an evolutionary algorithm approach.

In industry as well as many areas of scientific research, data collected often contain a number of responses of interest for a chosen set of exploratory variables. Optimization of such multivariable multiresponse systems is a challenge well suited to genetic algorithms as global optimization tools. One such example is the optimization of coating surfaces with the required absolute and relative sensitivity for detecting analytes using devices such as sensor arrays. High-throughput synthesis and screening methods can be used to accelerate materials discovery and optimization; however, an important practical consideration for successful optimization of materials for arrays and other applications is the ability to generate adequate information from a minimum number of experiments. Here we present a case study to evaluate the efficiency of a novel evolutionary model-based multiresponse approach (EMMA) that enables the optimization of a coating while minimizing the number of experiments. EMMA plans the experiments and simultaneously models the material properties. We illustrate this novel procedure for materials optimization by testing the algorithm on a sol-gel synthetic route for production and optimization of a well studied amino-methyl-silane coating. The response variables of the coating have been optimized based on application criteria for micro- and macro-array surfaces. Spotting performance has been monitored using a fluorescent dye molecule for demonstration purposes and measured using a laser scanner. Optimization is achieved by exploring less than 2% of the possible experiments, resulting in identification of the most influential compositional variables. Use of EMMA to optimize control factors of a product or process is illustrated, and the proposed approach is shown to be a promising tool for simultaneously optimizing and modeling multivariable multiresponse systems.

Early classification of spatio-temporal events using partial information.

This paper investigates event extraction and early event classification in contiguous spatio-temporal data streams, where events need to be classified using partial information, i.e. while the event is ongoing. The framework incorporates an event extraction algorithm and an early event classification algorithm. We apply this framework to synthetic and real problems and demonstrate its reliability and broad applicability. The algorithms and data are available in the R package eventstream, and other code in the supplementary material.

Automatic age estimation based on facial aging patterns.

While recognition of most facial variations, such as identity, expression and gender, has been extensively studied, automatic age estimation has rarely been explored. In contrast to other facial variations, aging variation presents several unique characteristics which make age estimation a challenging task. This paper proposes an automatic age estimation method named AGES (AGing pattErn Subspace). The basic idea is to model the aging pattern, which is defined as the sequence of a particular individual' s face images sorted in time order, by constructing a representative subspace. The proper aging pattern for a previously unseen face image is determined by the projection in the subspace that can reconstruct the face image with minimum reconstruction error, while the position of the face image in that aging pattern will then indicate its age. In the experiments, AGES and its variants are compared with the limited existing age estimation methods (WAS and AAS) and some well-established classification methods (kNN, BP, C4.5, and SVM). Moreover, a comparison with human perception ability on age is conducted. It is interesting to note that the performance of AGES is not only significantly better than that of all the other algorithms, but also comparable to that of the human observers.

Mathematical modeling of GATA-switching for regulating the differentiation of hematopoietic stem cell.

BACKGROUND: Hematopoiesis is a highly orchestrated developmental process that comprises various developmental stages of the hematopoietic stem cells (HSCs). During development, the decision to leave the self-renewing state and selection of a differentiation pathway is regulated by a number of transcription factors. Among them, genes GATA-1 and PU.1 form a core negative feedback module to regulate the genetic switching between the cell fate choices of HSCs. Although extensive experimental studies have revealed the mechanisms to regulate the expression of these two genes, it is still unclear how this simple module regulates the genetic switching. METHODS: In this work we proposed a mathematical model to study the mechanisms of the GATA-PU.1 gene network in the determination of HSC differentiation pathways. We incorporated the mechanisms of GATA switch into the module, and developed a mathematical model that comprises three genes GATA-1, GATA-2 and PU.1. In addition, a novel multiple-objective optimization method was designed to infer unknown parameters in the proposed model by realizing different experimental observations. A stochastic model was also designed to describe the critical function of noise, due to the small copy numbers of molecular species, in determining the differentiation pathways. RESULTS: The proposed deterministic model has successfully realized three stable steady states representing the priming and different progenitor cells as well as genetic switching between the genetic states under various experimental conditions. Using different values of GATA-1 synthesis rate for the GATA-1 protein availability in the chromatin sites during the time period of GATA switch, stochastic simulations for the first time have realized different proportions of cells leading to different developmental pathways under various experimental conditions. CONCLUSIONS: Mathematical models provide testable predictions regarding the mechanisms and conditions for realizing different differentiation pathways of hematopoietic stem cells. This work represents the first attempt at using a discrete stochastic model to realize the decision of HSC differentiation pathways showing a multimodal distribution.

Stochastic modelling of biochemical systems of multi-step reactions using a simplified two-variable model.

BACKGROUND: A fundamental issue in systems biology is how to design simplified mathematical models for describing the dynamics of complex biochemical reaction systems. Among them, a key question is how to use simplified reactions to describe the chemical events of multi-step reactions that are ubiquitous in biochemistry and biophysics. To address this issue, a widely used approach in literature is to use one-step reaction to represent the multi-step chemical events. In recent years, a number of modelling methods have been designed to improve the accuracy of the one-step reaction method, including the use of reactions with time delay. However, our recent research results suggested that there are still deviations between the dynamics of delayed reactions and that of the multi-step reactions. Therefore, more sophisticated modelling methods are needed to accurately describe the complex biological systems in an efficient way. RESULTS: This work designs a two-variable model to simplify chemical events of multi-step reactions. In addition to the total molecule number of a species, we first introduce a new concept regarding the location of molecules in the multi-step reactions, which is the second variable to represent the system dynamics. Then we propose a simulation algorithm to compute the probability for the firing of the last step reaction in the multi-step events. This probability function is evaluated using a deterministic model of ordinary differential equations and a stochastic model in the framework of the stochastic simulation algorithm. The efficiency of the proposed two-variable model is demonstrated by the realization of mRNA degradation process based on the experimentally measured data. CONCLUSIONS: Numerical results suggest that the proposed new two-variable model produces predictions that match the multi-step chemical reactions very well. The successful realization of the mRNA degradation dynamics indicates that the proposed method is a promising approach to reduce the complexity of biological systems.

Face image modeling by multilinear subspace analysis with missing values.

Multilinear subspace analysis (MSA) is a promising methodology for pattern-recognition problems due to its ability in decomposing the data formed from the interaction of multiple factors. The MSA requires a large training set, which is well organized in a single tensor, which consists of data samples with all possible combinations of the contributory factors. However, such a "complete" training set is difficult (or impossible) to obtain in many real applications. The missing-value problem is therefore crucial to the practicality of the MSA but has been hardly investigated up to present. To solve the problem, this paper proposes an algorithm named M(2)SA, which is advantageous in real applications due to the following: 1) it inherits the ability of the MSA to decompose the interlaced semantic factors; 2) it does not depend on any assumptions on the data distribution; and 3) it can deal with a high percentage of missing values. M(2)SA is evaluated by face image modeling on two typical multifactorial applications, i.e., face recognition and facial age estimation. Experimental results show the effectiveness of M(2) SA even when the majority of the values in the training tensor are missing.

Identifying patterns in primary care consultations: a cluster analysis.

BACKGROUND: A literature review revealed that little is known about the systems context of general practice consultations and their outcomes. OBJECTIVES: To describe the systems context and resulting underlying patterns of primary care consultations in a local area. DESIGN: Cross-sectional multi-practice study based on a three-part questionnaire. Cluster analysis of data. SETTING: Stratified random sample of general practices and general practitioners--NSW-Central Coast, Australia. PARTICIPANTS: A total of 1104 adults attending 12 general practitioners between February and November 1999. RESULTS AND CONCLUSIONS: The study identified seven subgroups within the study population uniquely defined by variables from the health system, individual doctor and patient, consultation and consultation outcomes domains. A systems approach provides a framework in which to track and consider the important variables and their known and/or expected workings and thus offer a contextual framework to guide primary care reform.

Individual stable space: an approach to face recognition under uncontrolled conditions.

There usually exist many kinds of variations in face images taken under uncontrolled conditions, such as changes of pose, illumination, expression, etc. Most previous works on face recognition (FR) focus on particular variations and usually assume the absence of others. Instead of such a "divide and conquer" strategy, this paper attempts to directly address face recognition under uncontrolled conditions. The key is the individual stable space (ISS), which only expresses personal characteristics. A neural network named ISNN is proposed to map a raw face image into the ISS. After that, three ISS-based algorithms are designed for FR under uncontrolled conditions. There are no restrictions for the images fed into these algorithms. Moreover, unlike many other FR techniques, they do not require any extra training information, such as the view angle. These advantages make them practical to implement under uncontrolled conditions. The proposed algorithms are tested on three large face databases with vast variations and achieve superior performance compared with other 12 existing FR techniques.