Multi-Task Time Series Analysis applied to Drug Response Modelling

Time series models such as dynamical systems are frequently fitted to a cohort of data, ignoring variation between individual entities such as patients. In this paper we show how these models can be personalised to an individual level while retaining statistical power, via use of multi-task learning (MTL). To our knowledge this is a novel development of MTL which applies to time series both with and without control inputs. The modelling framework is demonstrated on a physiological drug response problem which results in improved predictive accuracy and uncertainty estimation over existing state-of-the-art models.Comment: To appear in AISTATS 201

The second and third Sonine coefficients of a freely cooling granular gas revisited

In its simplest statistical-mechanical description, a granular fluid can be modeled as composed of smooth inelastic hard spheres (with a constant coefficient of normal restitution $\alpha$) whose velocity distribution function obeys the Enskog-Boltzmann equation. The basic state of a granular fluid is the homogeneous cooling state, characterized by a homogeneous, isotropic, and stationary distribution of scaled velocities, $F(\mathbf{c})$. The behavior of $F(\mathbf{c})$ in the domain of thermal velocities ($c\sim 1$) can be characterized by the two first non-trivial coefficients ($a_2$ and $a_3$) of an expansion in Sonine polynomials. The main goals of this paper are to review some of the previous efforts made to estimate (and measure in computer simulations) the $\alpha$-dependence of $a_2$ and $a_3$, to report new computer simulations results of $a_2$ and $a_3$ for two-dimensional systems, and to investigate the possibility of proposing theoretical estimates of $a_2$ and $a_3$ with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change

Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates corrections in the theory of tidal despinning and libration damping. We prove that when the inclination is low and phase lags are linear in frequency, the Kaula series is equivalent to a corrected version of the MacDonald method. The correction to MacDonald's approach would be to set the phase lag of the integral bulge proportional to the instantaneous frequency. The equivalence of descriptions gets violated by a nonlinear frequency-dependence of the lag. We explain that both the MacDonald- and Darwin-torque-based derivations of the popular formula for the tidal despinning rate are limited to low inclinations and to the phase lags being linear in frequency. The Darwin-torque-based derivation, though, is general enough to accommodate both a finite inclination and the actual rheology. Although rheologies with Q scaling as the frequency to a positive power make the torque diverge at a zero frequency, this reveals not the impossible nature of the rheology, but a flaw in mathematics, i.e., a common misassumption that damping merely provides lags to the terms of the Fourier series for the tidal potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the magnitudes of the terms, too, get changed. Reinstating of this detail tames the infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial text overlap with arXiv:0712.105

Effects of Dietary Fibre (Pectin) and/or Increased Protein (Casein or Pea) on Satiety, Body Weight, Adiposity and Caecal Fermentation in High Fat Diet-Induced Obese Rats

We thank the University of Aberdeen MRF staff for the daily care of experimental rats, body weight, food intake and MRI measurements. We also thank the Analytical Department of the Rowett Institute for Nutrition and Health for the proximate analyses, glucose determinations and SCFA GC. Funding: This work was funded by the Scottish Government Rural and Environment Science and Analytical Services Division. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin

Remote Actuation of Magnetic Nanoparticles For Cancer Cell Selective Treatment Through Cytoskeletal Disruption

Motion of micron and sub-micron size magnetic particles in alternating magnetic fields can activate mechanosensitive cellular functions or physically destruct cancer cells. However, such effects are usually observed with relatively large magnetic particles (>250 nm) that would be difficult if at all possible to deliver to remote sites in the body to treat disease. Here we show a completely new mechanism of selective toxicity of superparamagnetic nanoparticles (SMNP) of 7 to 8 nm in diameter to cancer cells. These particles are coated by block copolymers, which facilitates their entry into the cells and clustering in the lysosomes, where they are then magneto-mechanically actuated by remotely applied alternating current (AC) magnetic fields of very low frequency (50 Hz). Such fields and treatments are safe for surrounding tissues but produce cytoskeletal disruption and subsequent death of cancer cells while leaving healthy cells intact

Energy cost and return for hunting in African wild dogs and Cheetahs

African wild dogs (Lycaon pictus) are reported to hunt with energetically costly long chase distances. We used high-resolution GPS and inertial technology to record 1,119 high-speed chases of all members of a pack of six adult African wild dogs in northern Botswana. Dogs performed multiple short, high-speed, mostly unsuccessful chases to capture prey, while cheetahs (Acinonyx jubatus) undertook even shorter, higher-speed hunts. We used an energy balance model to show that the energy return from group hunting and feeding substantially outweighs the cost of multiple short chases, which indicates that African wild dogs are more energetically robust than previously believed. Comparison with cheetah illustrates the trade-off between sheer athleticism and high individual kill rate characteristic of cheetahs, and the energetic robustness of frequent opportunistic group hunting and feeding by African wild dogs

Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited

This report is a review of Darwin's classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) the capture into a 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.Comment: 30 pages, 7 figures, corrected typo