Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Empirical investigation of the usefulness of Gateway constructs in process models

Process modeling grammars are used to create scripts of a business domain that a process-aware information system is intended to support. A key grammatical construct of such grammars is known as a Gateway. A Gateway construct is used to describe scenarios in which the workflow of a process diverges or converges according to relevant conditions. Gateway constructs have been subjected to much academic discussion about their meaning, role and usefulness, and have been linked to both process-modeling errors and process-model understandability. This paper examines perceptual discriminability effects of Gateway constructs on an individual's abilities to interpret process models. We compare two ways of expressing two convergence and divergence patterns – Parallel Split and Simple Merge – implemented in a process modeling grammar. On the basis of an experiment with 98 students, we provide empirical evidence that Gateway constructs aid the interpretation of process models due to a perceptual discriminability effect, especially when models are complex. We discuss the emerging implications for research and practice, in terms of revisions to grammar specifications, guideline development and design choices in process modeling.

From conceptual process models to running workflows : a holistic approach for the configuration of enterprise systems

The configuration of comprehensive Enterprise Systems to meet the specific requirements of an organisation up to today is consuming significant resources. The results of failing implementation projects are severe and may even threaten the organisation’s existence. This paper proposes a method which aims at increasing the efficiency of Enterprise Systems implementations. First, we argue that existing process modelling languages that feature different degrees of abstraction for different user groups exist and are used for different purposes which makes it necessary to integrate them. We describe how to do this using the meta models of the involved languages. Second, we motivate that an integrated process model based on the integrated meta model needs to be configurable and elaborate on the mechanisms by which this model configuration can be achieved. We introduce a business example using SAP modelling techniques to illustrate the proposed method.

Modelling surface and shallow groundwater interactions in an ungauged subtropical coastal catchment using the SWAT model, Elimbah Creek, southeast Queensland, Australia

The study presented here applies the highly parameterised semi-distributed U.S. Department of Agriculture Soil and Water Assessment Tool (SWAT) to an Australian subtropical catchment. SWAT has been applied to numerous catchments worldwide and is considered to be a useful tool that is under ongoing development with contributions coming from different research groups in different parts of the world. In a preliminary run the SWAT model application for the Elimbah Creek catchment has estimated water yield for the catchment and has quantified the different sources. For the modelling period of April 1999 to September 2009 the results show that the main sources of water in Elimbah Creek are total surface runoff and lateral flow (65%). Base-flow contributes 36% to the total runoff. On a seasonal basis modelling results show a shift in the source of water contributing to Elimbah Creek from surface runoff and lateral flow during intense summer storms to base-flow conditions during dry months. Further calibration and validation of these results will confirm that SWAT provides an alternative to Australian water balance models.

Designing Innovative Business Models : A Design Catalyst Learning Resource

The term Design Led Innovation is emerging as a fundamental business process, which is rapidly being adopted by large as well as small to medium sized firms. The value that design brings to an organisation is a different way of thinking, of framing situations and possibilities, doing things and tackling problems: essentially a cultural transformation of the way the firm undertakes its business. Being Design Led is increasingly being seen by business as a driver of company growth, allowing firms to provide a strong point of difference to its stakeholders. Achieving this Design Led process, requires strong leadership to enable the organisation to develop a clear vision for top line growth. Specifically, based on deep customer insights and expanded through customer and stakeholder engagements, the outcomes of which are then adopted by all aspects of the business. To achieve this goal, several tools and processes are available, which need to be linked to new organisational capabilities within a business transformation context. The Design Led Innovation Team focuses on embedding tools and processes within an organisation and matching this with design leadership qualities to enable companies to create breakthrough innovation and achieve sustained growth, through ultimately transforming their business model. As all information for these case studies was derived from publicly accessed data, this resource is not intended to be used as reference material, but rather is a learning tool for designers to begin to consider and explore businesses at a strategic level. It is not the results that are key, but rather the process and philosophies that were used to create these case studies and disseminate this way of thinking amongst the design community. It is this process of unpacking a business guided by the framework of Osterwalder’s Business Model Canvas* which provides an important tool for designers to gain a greater perspective of a company’s true innovation potential.

Compaction control of topography and fault network structure along strike-slip faults in sedimentary basins

Strike-slip faults commonly display structurally complex areas of positive or negative topography. Understanding the development of such areas has important implications for earthquake studies and hydrocarbon exploration. Previous workers identified the key factors controlling the occurrence of both topographic modes and the related structural styles. Kinematic and stress boundary conditions are of first-order relevance. Surface mass transport and material properties affect fault network structure. Experiments demonstrate that dilatancy can generate positive topography even under simple-shear boundary conditions. Here, we use physical models with sand to show that the degree of compaction of the deformed rocks alone can determine the type of topography and related surface fault network structure in simple-shear settings. In our experiments, volume changes of ∼5% are sufficient to generate localized uplift or subsidence. We discuss scalability of model volume changes and fault network structure and show that our model fault zones satisfy geometrical similarity with natural flower structures. Our results imply that compaction may be an important factor in the development of topography and fault network structure along strike-slip faults in sedimentary basins.

The rise of birds and mammals: are microevolutionary processes sufficient for macroevolution?

It is a basis of darwinian evolution that the microevolutionary mechanisms that can be studied in the present are sufficient to account for macroevolution. However, this idea needs to be tested explicitly, as highlighted here by the example of the superceding of dinosaurs and pterosaurs by birds and placental mammals that occurred near the Cretaceous/Tertiary boundary approximately 65 million years ago. A major problem for testing the sufficiency of microevolutionary processes is that independent ideas (such as the existence of an extraterrestrial impact, and the extinction of dinosaurs) were linked without the evidence for each idea being evaluated separately. Here, we suggest and discuss five testable models for the times and divergences of modern mammals and birds. Determination of the model that best represents these events will enable the role of microevolutionary mechanisms to be evaluated. The question of the sufficiency of microevolutionary processes for macroevolution is solvable, and available evidence supports an important role for biological processes in the initial decline of dinosaurs and pterosaurs.

Genome-scale phylogeny and the detection of systematic biases

Phylogenetic inference from sequences can be misled by both sampling (stochastic) error and systematic error (nonhistorical signals where reality differs from our simplified models). A recent study of eight yeast species using 106 concatenated genes from complete genomes showed that even small internal edges of a tree received 100% bootstrap support. This effective negation of stochastic error from large data sets is important, but longer sequences exacerbate the potential for biases (systematic error) to be positively misleading. Indeed, when we analyzed the same data set using minimum evolution optimality criteria, an alternative tree received 100% bootstrap support. We identified a compositional bias as responsible for this inconsistency and showed that it is reduced effectively by coding the nucleotides as purines and pyrimidines (RY-coding), reinforcing the original tree. Thus, a comprehensive exploration of potential systematic biases is still required, even though genome-scale data sets greatly reduce sampling error.

A description of the Mei2-like protein family; structure, phylogenetic distribution and biological context

The Schizosaccharomyces pombe Mei2 gene encodes an RNA recognition motif (RRM) protein that stimulates meiosis upon binding a specific non-coding RNA and subsequent accumulation in a “mei2-dot” in the nucleus. We present here the first systematic characterization of the family of proteins with characteristic Mei2-like amino acid sequences. Mei2-like proteins are an ancient eukaryotic protein family with three identifiable RRMs. The C-terminal RRM (RRM3) is unique to Mei2-like proteins and is the most highly conserved of the three RRMs. RRM3 also contains conserved sequence elements at its C-terminus not found in other RRM domains. Single copy Mei2-like genes are present in some fungi, in alveolates such as Paramecium and in the early branching eukaryote Entamoeba histolytica, while plants contain small families of Mei2-like genes. While the C-terminal RRM is highly conserved between plants and fungi, indicating conservation of molecular mechanisms, plant Mei2-like genes have changed biological context to regulate various aspects of developmental pattern formation.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

A two-stage approach for generating topic models

Topic modeling has been widely utilized in the fields of information retrieval, text mining, text classification etc. Most existing statistical topic modeling methods such as LDA and pLSA generate a term based representation to represent a topic by selecting single words from multinomial word distribution over this topic. There are two main shortcomings: firstly, popular or common words occur very often across different topics that bring ambiguity to understand topics; secondly, single words lack coherent semantic meaning to accurately represent topics. In order to overcome these problems, in this paper, we propose a two-stage model that combines text mining and pattern mining with statistical modeling to generate more discriminative and semantic rich topic representations. Experiments show that the optimized topic representations generated by the proposed methods outperform the typical statistical topic modeling method LDA in terms of accuracy and certainty.