Predictive Modelling using Neuroimaging Data in the Presence of Confounds

When training predictive models from neuroimaging data, we typically have available non-imaging variables such as age and gender that affect the imaging data but which we may be uninterested in from a clinical perspective. Such variables are commonly referred to as 'confounds'. In this work, we firstly give a working definition for confound in the context of training predictive models from samples of neuroimaging data. We define a confound as a variable which affects the imaging data and has an association with the target variable in the sample that differs from that in the population-of-interest, i.e., the population over which we intend to apply the estimated predictive model. The focus of this paper is the scenario in which the confound and target variable are independent in the population-of-interest, but the training sample is biased due to a sample association between the target and confound. We then discuss standard approaches for dealing with confounds in predictive modelling such as image adjustment and including the confound as a predictor, before deriving and motivating an Instance Weighting scheme that attempts to account for confounds by focusing model training so that it is optimal for the population-of-interest. We evaluate the standard approaches and Instance Weighting in two regression problems with neuroimaging data in which we train models in the presence of confounding, and predict samples that are representative of the population-of-interest. For comparison, these models are also evaluated when there is no confounding present. In the first experiment we predict the MMSE score using structural MRI from the ADNI database with gender as the confound, while in the second we predict age using structural MRI from the IXI database with acquisition site as the confound. Considered over both datasets we find that none of the methods for dealing with confounding gives more accurate predictions than a baseline model which ignores confounding, although including the confound as a predictor gives models that are less accurate than the baseline model. We do find, however, that different methods appear to focus their predictions on specific subsets of the population-of-interest, and that predictive accuracy is greater when there is no confounding present. We conclude with a discussion comparing the advantages and disadvantages of each approach, and the implications of our evaluation for building predictive models that can be used in clinical practice

Transition Property for α\alpha-Power Free Languages with α≥2\alpha\geq 2 and k≥3k\geq 3 Letters

In 1985, Restivo and Salemi presented a list of five problems concerning power free languages. Problem $4$ states: Given $\alpha$-power-free words $u$ and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$ states: Given $\alpha$-power-free words $u$ and $v$, find a transition word $w$, if it exists. Let $\Sigma_k$ denote an alphabet with $k$ letters. Let $L_{k,\alpha}$ denote the $\alpha$-power free language over the alphabet $\Sigma_k$, where $\alpha$ is a rational number or a rational "number with $+$". If $\alpha$ is a "number with $+$" then suppose $k\geq 3$ and $\alpha\geq 2$. If $\alpha$ is "only" a number then suppose $k=3$ and $\alpha>2$ or $k>3$ and $\alpha\geq 2$. We show that: If $u\in L_{k,\alpha}$ is a right extendable word in $L_{k,\alpha}$ and $v\in L_{k,\alpha}$ is a left extendable word in $L_{k,\alpha}$ then there is a (transition) word $w$ such that $uwv\in L_{k,\alpha}$. We also show a construction of the word $w$

Convergence in measure under Finite Additivity

We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained

High prevalence of subclinical hypothyroidism in pregnant women in South India

Background: Thyroid dysfunction is one of the commonest endocrinopathies seen in pregnancy and affects both maternal and fetal outcomes. There is little data available on its prevalence in Indian pregnant women. This study was conducted at Bhaskar medical college and hospital situated in a rural/suburban area near Hyderabad, Telengana, India. The aim of the study was to find out the prevalence of thyroid disease among pregnant women.  Methods: All consecutive pregnant women registered from January 2014 to December 2014 were included in the study. Morning samples of serum were tested for T3, T4 and TSH.  Results: A total of 1340 women were included in the study. 260 pregnant women (19.41%) had TSH values more than 3.0 mIU/L, the cut-off value used for upper limit of normal in this study. Out of these, 216 had normal T4 value, hence labeled as subclinical hypothyroidism and 44 had low T4, hence termed overt hypothyroidism. Three pregnant women had overt hyperthyroidism and 11 had subclinical hyperthyroidism. Nine women had low T4 values-Isolated hypothyroidism.Conclusions: Prevalence of thyroid disease in pregnancy was found to be higher in our patients, more so the sub clinical hypothyroidism

A [4Fe-4S]-Fe(CO)(CN)-L-cysteine intermediate is the first organometallic precursor in [FeFe] hydrogenase H-cluster bioassembly.

Biosynthesis of the [FeFe] hydrogenase active site (the 'H-cluster') requires the interplay of multiple proteins and small molecules. Among them, the radical S-adenosylmethionine enzyme HydG, a tyrosine lyase, has been proposed to generate a complex that contains an Fe(CO)2(CN) moiety that is eventually incorporated into the H-cluster. Here we describe the characterization of an intermediate in the HydG reaction: a [4Fe-4S][(Cys)Fe(CO)(CN)] species, 'Complex A', in which a CO, a CN- and a cysteine (Cys) molecule bind to the unique 'dangler' Fe site of the auxiliary [5Fe-4S] cluster of HydG. The identification of this intermediate-the first organometallic precursor to the H-cluster-validates the previously hypothesized HydG reaction cycle and provides a basis for elucidating the biosynthetic origin of other moieties of the H-cluster

Truncated and Helix-Constrained Peptides with High Affinity and Specificity for the cFos Coiled-Coil of AP-1

Protein-based therapeutics feature large interacting surfaces. Protein folding endows structural stability to localised surface epitopes, imparting high affinity and target specificity upon interactions with binding partners. However, short synthetic peptides with sequences corresponding to such protein epitopes are unstructured in water and promiscuously bind to proteins with low affinity and specificity. Here we combine structural stability and target specificity of proteins, with low cost and rapid synthesis of small molecules, towards meeting the significant challenge of binding coiled coil proteins in transcriptional regulation. By iteratively truncating a Jun-based peptide from 37 to 22 residues, strategically incorporating i-->i+4 helix-inducing constraints, and positioning unnatural amino acids, we have produced short, water-stable, alpha-helical peptides that bind cFos. A three-dimensional NMR-derived structure for one peptide (24) confirmed a highly stable alpha-helix which was resistant to proteolytic degradation in serum. These short structured peptides are entropically pre-organized for binding with high affinity and specificity to cFos, a key component of the oncogenic transcriptional regulator Activator Protein-1 (AP-1). They competitively antagonized the cJun–cFos coiled-coil interaction. Truncating a Jun-based peptide from 37 to 22 residues decreased the binding enthalpy for cJun by ~9 kcal/mol, but this was compensated by increased conformational entropy (TDS ≤ 7.5 kcal/mol). This study demonstrates that rational design of short peptides constrained by alpha-helical cyclic pentapeptide modules is able to retain parental high helicity, as well as high affinity and specificity for cFos. These are important steps towards small antagonists of the cJun-cFos interaction that mediates gene transcription in cancer and inflammatory diseases

Invariant Distribution of Promoter Activities in Escherichia coli

Cells need to allocate their limited resources to express a wide range of genes. To understand how Escherichia coli partitions its transcriptional resources between its different promoters, we employ a robotic assay using a comprehensive reporter strain library for E. coli to measure promoter activity on a genomic scale at high-temporal resolution and accuracy. This allows continuous tracking of promoter activity as cells change their growth rate from exponential to stationary phase in different media. We find a heavy-tailed distribution of promoter activities, with promoter activities spanning several orders of magnitude. While the shape of the distribution is almost completely independent of the growth conditions, the identity of the promoters expressed at different levels does depend on them. Translation machinery genes, however, keep the same relative expression levels in the distribution across conditions, and their fractional promoter activity tracks growth rate tightly. We present a simple optimization model for resource allocation which suggests that the observed invariant distributions might maximize growth rate. These invariant features of the distribution of promoter activities may suggest design constraints that shape the allocation of transcriptional resources

Fluctuation induces evolutionary branching in a modeled microbial ecosystem

The impact of environmental fluctuation on species diversity is studied with a model of the evolutionary ecology of microorganisms. We show that environmental fluctuation induces evolutionary branching and assures the consequential coexistence of multiple species. Pairwise invasibility analysis is applied to illustrate the speciation process. We also discuss how fluctuation affects species diversity.Comment: 4 pages, 4 figures. Submitted to Physical Review Letter