Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

Cells respond to various biochemical and physical cues during wound–healing and tumour progression. In vitro assays used to study these processes are typically conducted in one particular geometry and it is unclear how the assay geometry affects the capacity of cell populations to spread, or whether the relevant mechanisms, such as cell motility and cell proliferation, are somehow sensitive to the geometry of the assay. In this work we use a circular barrier assay to characterise the spreading of cell populations in two different geometries. Assay 1 describes a tumour–like geometry where a cell population spreads outwards into an open space. Assay 2 describes a wound–like geometry where a cell population spreads inwards to close a void. We use a combination of discrete and continuum mathematical models and automated image processing methods to obtain independent estimates of the effective cell diffusivity, D, and the effective cell proliferation rate, λ. Using our parameterised mathematical model we confirm that our estimates of D and λ accurately predict the time–evolution of the location of the leading edge and the cell density profiles for both assay 1 and assay 2. Our work suggests that the effective cell diffusivity is up to 50% lower for assay 2 compared to assay 1, whereas the effective cell proliferation rate is up to 30% lower for assay 2 compared to assay 1.

Teaching fractions to adult learners enrolled in a civil construction course : knowledge, action and materials action in tandem

This paper investigates the teaching and learning of fractions to Indigenous adult learners in a Civil Construction Certificate Course. More specifically it explores why the use of materials is critical to building knowledge and understanding. This focus is important for two reasons. First, it allows for considerations of a trainer’s approach for teaching fractions and, second it provides insights into how adult learners can be supported with representing their practical experiences of fractions to make generalisation thus building on their knowledge and learning experiences. The paper draws on teaching episodes from an Australian Research Council funded Linkage project that investigates how mathematics is taught and learned in Certificate Courses, here, Certificate 11 in Civil Construction. Action research and decolonising methods (Smith, 1999) were used to conduct the research. Video excerpts which feature one trainer and three students are analysed and described. Findings from the data indicate that adult learners need to be supported with materials to assist with building their capacity to know and apply understandings of fractions in a range of contexts, besides construction. Without materials and where fractions are taught via pen and paper tasks, students are less likely to retain and apply fraction ideas to their Certificate Course. Further they are less likely to understand decimals because of limited understanding of fractions.

How much information can be obtained from tracking the position of the leading edge in a scratch assay?

Moving cell fronts are an essential feature of wound healing, development and disease. The rate at which a cell front moves is driven, in part, by the cell motility, quantified in terms of the cell diffusivity $D$, and the cell proliferation rate �$\lambda$. Scratch assays are a commonly-reported procedure used to investigate the motion of cell fronts where an initial cell monolayer is scratched and the motion of the front is monitored over a short period of time, often less than 24 hours. The simplest way of quantifying a scratch assay is to monitor the progression of the leading edge. Leading edge data is very convenient since, unlike other methods, it is nondestructive and does not require labeling, tracking or counting individual cells amongst the population. In this work we study short time leading edge data in a scratch assay using a discrete mathematical model and automated image analysis with the aim of investigating whether such data allows us to reliably identify $D$ and $\lambda$�. Using a naıve calibration approach where we simply scan the relevant region of the ($D$;$\lambda$�) parameter space, we show that there are many choices of $D$ and $\lambda$� for which our model produces indistinguishable short time leading edge data. Therefore, without due care, it is impossible to estimate $D$ and $\lambda$� from this kind of data. To address this, we present a modified approach accounting for the fact that cell motility occurs over a much shorter time scale than proliferation. Using this information we divide the duration of the experiment into two periods, and we estimate $D$ using data from the first period, while we estimate �$\lambda$ using data from the second period. We confirm the accuracy of our approach using in silico data and a new set of in vitro data, which shows that our method recovers estimates of $D$ and $\lamdba$� that are consistent with previously-reported values except that that our approach is fast, inexpensive, nondestructive and avoids the need for cell labeling and cell counting.

Methods for isolation and cultivation of filamentous fungi

Filamentous fungi are important organisms for basic discovery, industry, and human health. Their natural growth environments are extremely variable, a fact reflected by the numerous methods developed for their isolation and cultivation. Fungal culture in the laboratory is usually carried out on agar plates, shake flasks, and bench top fermenters starting with an inoculum that typically features fungal spores. Here we discuss the most popular methods for the isolation and cultivation of filamentous fungi for various purposes with the emphasis on enzyme production and molecular microbiology.

ORIGO stepping stones common core mathematics Grade 5 practice book

ORIGO Stepping Stones is written and developed by a team of experts to provide teachers with a world-class elementary math program. Our expert team of authors and consultants are utilizing all available educational research to create a unique program that has never before been available to teachers. The full color Student Practice Book provides practice pages that support previous and current lessons.

Object tracking via non-Euclidean geometry : a Grassmann approach

A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image. In this paper, we first propose a tracking approach based on affine subspaces (constructed from several images) which are able to accommodate the abovementioned variations. We use affine subspaces not only to represent the object, but also the candidate areas that the object may occupy. We furthermore propose a novel approach to measure affine subspace-to-subspace distance via the use of non-Euclidean geometry of Grassmann manifolds. The tracking problem is then considered as an inference task in a Markov Chain Monte Carlo framework via particle filtering. Quantitative evaluation on challenging video sequences indicates that the proposed approach obtains considerably better performance than several recent state-of-the-art methods such as Tracking-Learning-Detection and MILtrack.

Random projections on manifolds of symmetric positive definite matrices for image classification

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account manifold geometry is typically done via (1) embedding the manifolds in tangent spaces, or (2) embedding into Reproducing Kernel Hilbert Spaces (RKHS). While embedding into tangent spaces allows the use of existing Euclidean-based learning algorithms, manifold shape is only approximated which can cause loss of discriminatory information. The RKHS approach retains more of the manifold structure, but may require non-trivial effort to kernelise Euclidean-based learning algorithms. In contrast to the above approaches, in this paper we offer a novel solution that allows SPD matrices to be used with unmodified Euclidean-based learning algorithms, with the true manifold shape well-preserved. Specifically, we propose to project SPD matrices using a set of random projection hyperplanes over RKHS into a random projection space, which leads to representing each matrix as a vector of projection coefficients. Experiments on face recognition, person re-identification and texture classification show that the proposed approach outperforms several recent methods, such as Tensor Sparse Coding, Histogram Plus Epitome, Riemannian Locality Preserving Projection and Relational Divergence Classification.

Matching image sets via adaptive multi convex hull

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image set. Existing multi-model approaches extract local models by clustering each image set individually only once, with fixed clusters used for matching with various image sets. This may not be optimal for discrimination, as undesirable environmental conditions (eg. illumination and pose variations) may result in the two closest clusters representing different characteristics of an object (eg. frontal face being compared to non-frontal face). To address the above problem, we propose a novel approach to enhance nearest points based methods by integrating affine/convex hull classification with an adapted multi-model approach. We first extract multiple local convex hulls from a query image set via maximum margin clustering to diminish the artificial variations and constrain the noise in local convex hulls. We then propose adaptive reference clustering (ARC) to constrain the clustering of each gallery image set by forcing the clusters to have resemblance to the clusters in the query image set. By applying ARC, noisy clusters in the query set can be discarded. Experiments on Honda, MoBo and ETH-80 datasets show that the proposed method outperforms single model approaches and other recent techniques, such as Sparse Approximated Nearest Points, Mutual Subspace Method and Manifold Discriminant Analysis.

Dictionary learning and sparse coding on Grassmann manifolds : an extrinsic solution

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis.

Physical inactivity remains the greatest public health problem of the 21st century : evidence, improved methods and solutions using the '7 investments that work' as a framework

In 2009, BJSM's first editorial argued that ‘Physical inactivity is the greatest public health problem of the 21st century’.1 The data supporting that claim have not yet been challenged. Now, 5 years after BJSM published its first dedicated ‘Physical Activity is Medicine’ theme issue (http://bjsm.bmj.com/content/43/1.toc) we are pleased to highlight 23 new contributions from six countries. This issue contains an analysis of the cost of physical inactivity from the US Centre for Diseases Control.2 We also report the cost-effectiveness of one particular physical activity intervention for adults.3

Multi-shot person re-identification via relational stein divergence

Person re-identification is particularly challenging due to significant appearance changes across separate camera views. In order to re-identify people, a representative human signature should effectively handle differences in illumination, pose and camera parameters. While general appearance-based methods are modelled in Euclidean spaces, it has been argued that some applications in image and video analysis are better modelled via non-Euclidean manifold geometry. To this end, recent approaches represent images as covariance matrices, and interpret such matrices as points on Riemannian manifolds. As direct classification on such manifolds can be difficult, in this paper we propose to represent each manifold point as a vector of similarities to class representers, via a recently introduced form of Bregman matrix divergence known as the Stein divergence. This is followed by using a discriminative mapping of similarity vectors for final classification. The use of similarity vectors is in contrast to the traditional approach of embedding manifolds into tangent spaces, which can suffer from representing the manifold structure inaccurately. Comparative evaluations on benchmark ETHZ and iLIDS datasets for the person re-identification task show that the proposed approach obtains better performance than recent techniques such as Histogram Plus Epitome, Partial Least Squares, and Symmetry-Driven Accumulation of Local Features.

A comparison of spatially explicit landscape representation methods and their relationship to stream condition

1. Biodiversity, water quality and ecosystem processes in streams are known to be influenced by the terrestrial landscape over a range of spatial and temporal scales. Lumped attributes (i.e. per cent land use) are often used to characterise the condition of the catchment; however, they are not spatially explicit and do not account for the disproportionate influence of land located near the stream or connected by overland flow. 2. We compared seven landscape representation metrics to determine whether accounting for the spatial proximity and hydrological effects of land use can be used to account for additional variability in indicators of stream ecosystem health. The landscape metrics included the following: a lumped metric, four inverse-distance-weighted (IDW) metrics based on distance to the stream or survey site and two modified IDW metrics that also accounted for the level of hydrologic activity (HA-IDW). Ecosystem health data were obtained from the Ecological Health Monitoring Programme in Southeast Queensland, Australia and included measures of fish, invertebrates, physicochemistry and nutrients collected during two seasons over 4 years. Linear models were fitted to the stream indicators and landscape metrics, by season, and compared using an information-theoretic approach. 3. Although no single metric was most suitable for modelling all stream indicators, lumped metrics rarely performed as well as other metric types. Metrics based on proximity to the stream (IDW and HA-IDW) were more suitable for modelling fish indicators, while the HA-IDW metric based on proximity to the survey site generally outperformed others for invertebrates, irrespective of season. There was consistent support for metrics based on proximity to the survey site (IDW or HA-IDW) for all physicochemical indicators during the dry season, while a HA-IDW metric based on proximity to the stream was suitable for five of the six physicochemical indicators in the post-wet season. Only one nutrient indicator was tested and results showed that catchment area had a significant effect on the relationship between land use metrics and algal stable isotope ratios in both seasons. 4. Spatially explicit methods of landscape representation can clearly improve the predictive ability of many empirical models currently used to study the relationship between landscape, habitat and stream condition. A comparison of different metrics may provide clues about causal pathways and mechanistic processes behind correlative relationships and could be used to target restoration efforts strategically.

Human-centred methods for design of mobile social technologies : a case study of agile ridesharing

Social contexts are possible information sources that can foster connections between mobile application users, but they are also minefields of privacy concerns and have great potential for misinterpretation. This research establishes a framework for guiding the design of context-aware mobile social applications from a socio-technical perspective. Agile ridesharing was chosen as the test domain for the research because its success relies upon effectively connecting people through mobile technologies.

The continuing decline of science and mathematics enrolments in Australian high schools

Is there a crisis in Australian science and mathematics education? Declining enrolments in upper secondary Science and Mathematics courses have gained much attention from the media, politicians and high-profile scientists over the last few years, yet there is no consensus amongst stakeholders about either the nature or the magnitude of the changes. We have collected raw enrolment data from the education departments of each of the Australian states and territories from 1992 to 2012 and analysed the trends for Biology, Chemistry, Physics, two composite subject groups (Earth Sciences and Multidisciplinary Sciences), as well as entry, intermediate and advanced Mathematics. The results of these analyses are discussed in terms of participation rates, raw enrolments and gender balance. We have found that the total number of students in Year 12 increased by around 16% from 1992 to 2012 while the participation rates for most Science and Mathematics subjects, as a proportion of the total Year 12 cohort, fell (Biology (-10%), Chemistry (-5%), Physics (-7%), Multidisciplinary Science (-5%), intermediate Mathematics (-11%), advanced Mathematics (-7%) in the same period. There were increased participation rates in Earth Sciences (+0.3%) and entry Mathematics (+11%). In each case the greatest rates of change occurred prior to 2001 and have been slower and steadier since. We propose that the broadening of curriculum offerings, further driven by students' self-perception of ability and perceptions of subject difficulty and usefulness, are the most likely cause of the changes in participation. While these continuing declines may not amount to a crisis, there is undoubtedly serious cause for concern.