Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Do turning biases by the 7-spot ladybird, Coccinella septempunctata, increase their foraging efficiency?

The hypothesis that foraging male and female Coccinella septempunctata L. would exhibit a turning bias when walking along a branched linear wire in a Y-maze was tested. Individuals were placed repeatedly in the maze. Approximately 45% of all individuals tested displayed significant turning biases, with a similar number of individuals biased to the left and right. In the maze right-handed individuals turned right at 84.4% of turns and the left-handed individuals turned left at 80.2% of turns. A model of the searching efficiency of C. septempunctata in dichotomous branched environments showed that model coccinellids with greater turning biases discovered a higher proportion of the plant for a given number of searches than those with no bias. A modification of the model to investigate foraging efficiency, by calculating the mean time taken by individuals to find randomly distributed aphid patches, suggested that on four different sizes of plants, with a variety of aphid patch densities, implementing a turning bias was a significantly more efficient foraging strategy than no bias. In general the benefits to foraging of implementing a turning bias increased with the degree of the bias. It may be beneficial for individuals in highly complex branched environments to have a turning bias slightly lower than 100% in order to benefit from increased foraging efficiency without walking in circles. Foraging bias benefits increased with increasing plant size and decreasing aphid density. In comparisons of two different plant morphologies, one with a straight stem and side branches and one with a symmetrically branched morphology, there were few significant differences in the effects of turning biases on foraging efficiency between morphologies

On the evolutionary origins of obesity: a new hypothesis

Obesity is an escalating threat of pandemic proportions, currently affecting billions of people worldwide and exerting a devastating socioeconomic influence in industrialized countries. Despite intensive efforts to curtail obesity, results have proved disappointing. Although it is well recognized that obesity is a result of gene-environment interactions and that predisposition to obesity lies predominantly in our evolutionary past, there is much debate as to the precise nature of how our evolutionary past contributed to obesity. The “thrifty genotype” hypothesis suggests that obesity in industrialized countries is a throwback to our ancestors having undergone positive selection for genes that favored energy storage as a consequence of the cyclical episodes of famine and surplus after the advent of farming 10 000 years ago. Conversely, the “drifty genotype” hypothesis contends that the prevalence of thrifty genes is not a result of positive selection for energy-storage genes but attributable to genetic drift resulting from the removal of predative selection pressures. Both theories, however, assume that selection pressures the ancestors of modern humans living in western societies faced were the same. Moreover, neither theory adequately explains the impact of globalization and changing population demographics on the genetic basis for obesity in developed countries, despite clear evidence for ethnic variation in obesity susceptibility and related metabolic disorders. In this article, we propose that the modern obesity pandemic in industrialized countries is a result of the differential exposure of the ancestors of modern humans to environmental factors that began when modern humans left Africa around 70 000 years ago and migrated through the globe, reaching the Americas around 20 000 years ago. This article serves to elucidate how an understanding of ethnic differences in genetic susceptibility to obesity and the metabolic syndrome, in the context of historic human population redistribution, could be used in the treatment of obesity in industrialized countries

Evaluation of positioning error-induced pixel shifts on satellite linear push-broom imagery

Georeferencing is one of the major tasks of satellite-borne remote sensing. Compared to traditional indirect methods, direct georeferencing through a Global Positioning System/inertial navigation system requires fewer and simpler steps to obtain exterior orientation parameters of remotely sensed images. However, the pixel shift caused by geographic positioning error, which is generally derived from boresight angle as well as terrain topography variation, can have a great impact on the precision of georeferencing. The distribution of pixel shifts introduced by the positioning error on a satellite linear push-broom image is quantitatively analyzed. We use the variation of the object space coordinate to simulate different kinds of positioning errors and terrain topography. Then a total differential method was applied to establish a rigorous sensor model in order to mathematically obtain the relationship between pixel shift and positioning error. Finally, two simulation experiments are conducted using the imaging parameters of Chang’ E-1 satellite to evaluate two different kinds of positioning errors. The experimental results have shown that with the experimental parameters, the maximum pixel shift could reach 1.74 pixels. The proposed approach can be extended to a generic application for imaging error modeling in remote sensing with terrain variation.

Local adaptation in migrated interior Douglas-fir seedlings is mediated by ectomycorrhizas and other soil factors

Separating edaphic impacts on tree distributions from those of climate and geography is notoriously difficult. Aboveground and belowground factors play important roles, and determining their relative contribution to tree success will greatly assist in refining predictive models and forestry strategies in a changing climate. In a common glasshouse, seedlings of interior Douglas-fir (Pseudotsuga menziesii var. glauca) from multiple populations were grown in multiple forest soils. Fungicide was applied to half of the seedlings to separate soil fungal and nonfungal impacts on seedling performance. Soils of varying geographic and climatic distance from seed origin were compared, using a transfer function approach. Seedling height and biomass were optimized following seed transfer into drier soils, whereas survival was optimized when elevation transfer was minimised. Fungicide application reduced ectomycorrhizal root colonization by c. 50%, with treated seedlings exhibiting greater survival but reduced biomass. Local adaptation of Douglas-fir populations to soils was mediated by soil fungi to some extent in 56% of soil origin by response variable combinations. Mediation by edaphic factors in general occurred in 81% of combinations. Soil biota, hitherto unaccounted for in climate models, interacts with biogeography to influence plant ranges in a changing climate.

Host and habitat filtering in seedling root-associated fungal communities: taxonomic and functional diversity are altered in ‘novel’ soils

Climatic and land use changes have significant consequences for the distribution of tree species, both through natural dispersal processes and following management prescriptions. Responses to these changes will be expressed most strongly in seedlings near current species range boundaries. In northern temperate forest ecosystems, where changes are already being observed, ectomycorrhizal fungi contribute significantly to successful tree establishment. We hypothesised that communities of fungal symbionts might therefore play a role in facilitating, or limiting, host seedling range expansion. To test this hypothesis, ectomycorrhizal communities of interior Douglas-fir and interior lodgepole pine seedlings were analysed in a common greenhouse environment following growth in five soils collected along an ecosystem gradient. Currently, Douglas-fir’s natural distribution encompasses three of the five soils, whereas lodgepole pine’s extends much further north. Host filtering was evident amongst the 29 fungal species encountered: 7 were shared, 9 exclusive to Douglas-fir and 13 exclusive to lodgepole pine. Seedlings of both host species formed symbioses with each soil fungal community, thus Douglas-fir did so even where those soils came from outside its current distribution. However, these latter communities displayed significant taxonomic and functional differences to those found within the host distribution, indicative of habitat filtering. In contrast, lodgepole pine fungal communities displayed high functional similarity across the soil gradient. Taxonomic and/or functional shifts in Douglas-fir fungal communities may prove ecologically significant during the predicted northward migration of this species; especially in combination with changes in climate and management operations, such as seed transfer across geographical regions for forestry purposes.

Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology

Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.