Replica analysis of overfitting in regression models for time-to-event data

Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine presents us with data of unprecedented dimensionality, these data cannot yet be used effectively for clinical outcome prediction. Standard error measures in maximum likelihood regression, such as p-values and z-scores, are blind to overfitting, and even for Cox's proportional hazards model (the main tool of medical statisticians), one finds in literature only rules of thumb on the number of samples required to avoid overfitting. In this paper we present a mathematical theory of overfitting in regression models for time-to-event data, which aims to increase our quantitative understanding of the problem and provide practical tools with which to correct regression outcomes for the impact of overfitting. It is based on the replica method, a statistical mechanical technique for the analysis of heterogeneous many-variable systems that has been used successfully for several decades in physics, biology, and computer science, but not yet in medical statistics. We develop the theory initially for arbitrary regression models for time-to-event data, and verify its predictions in detail for the popular Cox model.Comment: 37 pages, 9 figure

Motion in Quantum Gravity

We tackle the question of motion in Quantum Gravity: what does motion mean at the Planck scale? Although we are still far from a complete answer we consider here a toy model in which the problem can be formulated and resolved precisely. The setting of the toy model is three dimensional Euclidean gravity. Before studying the model in detail, we argue that Loop Quantum Gravity may provide a very useful approach when discussing the question of motion in Quantum Gravity.Comment: 30 pages, to appear in the book "Mass and Motion in General Relativity", proceedings of the C.N.R.S. School in Orleans, France, eds. L. Blanchet, A. Spallicci and B. Whitin

Dissecting and reprogramming the folding and assembly of tandem-repeat proteins.

Studying protein folding and protein design in globular proteins presents significant challenges because of the two related features, topological complexity and co-operativity. In contrast, tandem-repeat proteins have regular and modular structures composed of linearly arrayed motifs. This means that the biophysics of even giant repeat proteins is highly amenable to dissection and to rational design. Here we discuss what has been learnt about the folding mechanisms of tandem-repeat proteins. The defining features that have emerged are: (i) accessibility of multiple distinct routes between denatured and native states, both at equilibrium and under kinetic conditions; (ii) different routes are favoured for folding compared with unfolding; (iii) unfolding energy barriers are broad, reflecting stepwise unravelling of an array repeat by repeat; (iv) highly co-operative unfolding at equilibrium and the potential for exceptionally high thermodynamic stabilities by introducing consensus residues; (v) under force, helical-repeat structures are very weak with non-co-operative unfolding leading to elasticity and buffering effects. This level of understanding should enable us to create repeat proteins with made-to-measure folding mechanisms, in which one can dial into the sequence the order of repeat folding, number of pathways taken, step size (co-operativity) and fine-structure of the kinetic energy barriers.We acknowledge funding from the Medical Research Council of the UK (grant G1002329) and the Leverhulme Trust. AP is funded by a BBSRC Doctoral Training Program studentship. LSI acknowledges support of a Fellowship from the Medical Research Foundation.This is the accepted manuscript. The final version is available at http://www.biochemsoctrans.org/content/43/5/881

Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions

We report a combined experimental and theoretical study of the melting curve and the structural behavior of vanadium under extreme pressure and temperature. We performed powder x-ray diffraction experiments up to 120 GPa and 4000 K, determining the phase boundary of the bcc-to-rhombohedral transition and melting temperatures at different pressures. Melting temperatures have also been established from the observation of temperature plateaus during laser heating, and the results from the density-functional theory calculations. Results obtained from our experiments and calculations are fully consistent and lead to an accurate determination of the melting curve of vanadium. These results are discussed in comparison with previous studies. The melting temperatures determined in this study are higher than those previously obtained using the speckle method, but also considerably lower than those obtained from shock-wave experiments and linear muffin-tin orbital calculations. Finally, a high-pressure high-temperature equation of state up to 120 GPa and 2800 K has also been determined

A Sliding Mode Control Architecture for Human-Manipulator Cooperative Surface Treatment Tasks

© 2018 IEEE. This paper presents a control architecture readily suitable for surface treatment tasks such as polishing, grinding, finishing or deburring as carried out by a human operator, with the added benefit of accuracy, recurrence and physical strength as administered by a robotic manipulator partner. The shared strategy effectively couples the human operator propioceptive abilities and fine skills through his interactions with the autonomous physical agent. The novel proposed control scheme is based on task prioritization and a non-conventional sliding mode control, which is considered to benefit from its inherent robustness and low computational cost. The system relies on two force sensors, one located between the last link of the robot and the surface treatment tool, and the other located in some place of the robot end-effector: the former is used to suitably accomplish the conditioning task, while the latter is used by the operator to manually guide the robotic tool. When the operator chooses to cease guiding the tool, the robot motion safely switches back to an automatic reference tracking. The paper presents the theories for the novel collaborative controller, whilst its effectiveness for robotic surface treatment is substantiated by experimental results using a redundant 7R manipulator and a mock-up conditioning tool

Identification and “in silico” Structural Analysis of the Glutamine-rich Protein Qrp (YheA) in Staphylococcus Aureus

Background: YlbF and YmcA are two essential proteins for the formation of biofilm, sporulation, and competence in Bacillus subtilis. In these two proteins, a new protein domain called com_ylbF was recently discovered, but its role and protein function has not yet been established. Objective: In this study, we identified and performed an “in silico” structural analysis of the YheA protein, another com_ylbF-containing protein, in the opportunistic pathogen Staphylococcus aureus. Methods: The search of the yheA gene was performed using BLAST-P and tBLASn algorithms. The three-dimensional (3D) models of YheA, as well as YlbF and YmcA proteins, were built using the I-TASSER and Quark programs. The identification of the native YheA in Staphylococcus aureus was carried out through chromatography using the FPLC system. Results: We found that YheA protein is more widely distributed in Gram-positive bacteria than YlbF and YmcA. Two new and important characteristics for YheA and other com_ylbF-containing proteins were found: a highly conserved 3D structure and the presence of a putative conserved motif located in the central region of the domain, which could be involved in its function. Additionally, we established that Staphylococcus aureus expresses YheA protein in both planktonic growth and biofilm. Finally, we suggest renaming YheA as glutamine-rich protein (Qrp) in S. aureus. Conclusion: The Grp (YheA), YlbF, and YmcA proteins adopt a highly conserved three-dimensional structure, harboring a protein-specific putative motif within the com_ylbF domain, which possibly favors the interaction with their substrates. Finally, Staphylococcus aureus expresses the Grp (YheA) protein in both planktonic and biofilm growth. </jats:sec

An adaptive observer-based controller design for active damping of a DC network with a constant power load

This article explores a nonlinear, adaptive controller aimed at increasing the stability margin of a direct-current (dc), small-scale, electrical network containing an unknown constant power load (CPL). Due to its negative incremental impedance, this load reduces the effective damping of the network, which may lead to voltage oscillations and even to voltage collapse. To overcome this drawback, we consider the incorporation of a controlled dc-dc power converter in parallel with the CPL. The design of the control law for the converter is particularly challenging due to the existence of unmeasured states and unknown parameters. We propose a standard input-output linearization stage, to which a suitably tailored adaptive observer is added. The good performance of the controller is validated through experiments on a small-scale network

Synaptotagmin-1 membrane binding is driven by the C2B domain and assisted cooperatively by the C2A domain

Synaptotagmin interaction with anionic lipid (phosphatidylserine/phosphatidylinositol) containing membranes, both in the absence and presence of calcium ions (Ca2+), is critical to its central role in orchestrating neurotransmitter release. The molecular surfaces involved, namely the conserved polylysine motif in the C2B domain and Ca2+-binding aliphatic loops on both C2A and C2B domains, are known. Here we use surface force apparatus combined with systematic mutational analysis of the functional surfaces to directly measure Syt1-membrane interaction and fully map the site-binding energetics of Syt1 both in the absence and presence of Ca2+. By correlating energetics data with the molecular rearrangements measured during confinement, we find that both C2 domains cooperate in membrane binding, with the C2B domain functioning as the main energetic driver, and the C2A domain acting as a facilitator

Computer-Generated Ovaries to Assist Follicle Counting Experiments

Precise estimation of the number of follicles in ovaries is of key importance in the field of reproductive biology, both from a developmental point of view, where follicle numbers are determined at specific time points, as well as from a therapeutic perspective, determining the adverse effects of environmental toxins and cancer chemotherapeutics on the reproductive system. The two main factors affecting follicle number estimates are the sampling method and the variation in follicle numbers within animals of the same strain, due to biological variability. This study aims at assessing the effect of these two factors, when estimating ovarian follicle numbers of neonatal mice. We developed computer algorithms, which generate models of neonatal mouse ovaries (simulated ovaries), with characteristics derived from experimental measurements already available in the published literature. The simulated ovaries are used to reproduce in-silico counting experiments based on unbiased stereological techniques; the proposed approach provides the necessary number of ovaries and sampling frequency to be used in the experiments given a specific biological variability and a desirable degree of accuracy. The simulated ovary is a novel, versatile tool which can be used in the planning phase of experiments to estimate the expected number of animals and workload, ensuring appropriate statistical power of the resulting measurements. Moreover, the idea of the simulated ovary can be applied to other organs made up of large numbers of individual functional units

Intergenerational change and familial aggregation of body mass index

The relationship between parental BMI and that of their adult offspring, when increased adiposity can become a clinical issue, is unknown. We investigated the intergenerational change in body mass index (BMI) distribution, and examined the sex-specific relationship between parental and adult offspring BMI. Intergenerational change in the distribution of adjusted BMI in 1,443 complete families (both parents and at least one offspring) with 2,286 offspring (1,263 daughters and 1,023 sons) from the west of Scotland, UK, was investigated using quantile regression. Familial correlations were estimated from linear mixed effects regression models. The distribution of BMI showed little intergenerational change in the normal range (\25 kg/m2), decreasing overweightness (25– \30 kg/m2) and increasing obesity (C30 kg/m2). Median BMI was static across generations in males and decreased in females by 0.4 (95% CI: 0.0, 0.7) kg/m2; the 95th percentileincreased by 2.2 (1.1, 3.2) kg/m2 in males and 2.7 (1.4, 3.9) kg/m2 in females. Mothers’ BMI was more strongly associated with daughters’ BMI than was fathers’ (correlation coefficient (95% CI): mothers 0.31 (0.27, 0.36), fathers 0.19 (0.14, 0.25); P = 0.001). Mothers’ and fathers’ BMI were equally correlated with sons’ BMI (correlation coefficient: mothers 0.28 (0.22, 0.33), fathers 0.27 (0.22, 0.33). The increase in BMI between generations was concentrated at the upper end of the distribution. This, alongside the strong parent-offspring correlation, suggests that the increase in BMI is disproportionally greater among offspring of heavier parents. Familial influences on BMI among middle-aged women appear significantly stronger from mothers than father