On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

Optimal path planning for nonholonomic robotics systems via parametric optimisation

Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping

Assessing the value of BMI and aerobic capacity as surrogate markers for the severity of left ventricular diastolic dysfunction in patients with type 2 diabetes who are obese

Left ventricular diastolic dysfunction (LVDD) is one of the earliest signs for abnormal cardiac function in patients with type 2 diabetes (T2DM). It is important to explore the risk factors that will assist in identifying the severity of the LVDD in this population. We examined the influences of fitness and fatness on the level of left ventricular (LV) impairment in patients with T2DM. Twenty-five patients (age: 64.0 ± 2.5 years, body mass index [BMI] = 36.0 ± 1.5 kg/m2, mean ± standard error of measurement) with T2DM and preserved systolic function, but impaired diastolic function, mitral valve (MV) E/e\u27, participated in the study. LV function was assessed using a stress echocardiograph, aerobic power was assessed with a sign- and symptom-limited graded exercise test, and the fatness level was assessed using Dual-energy X-ray absorptiometry and BMI. Patients in the higher 50% of BMI had higher lateral and septal MV E/e\u27 (∼34% and ∼25%, respectively, both P < 0.001), compared to those in the lower 50% of BMI, with no difference in LV ejection fraction (LVEF) (P > 0.05). In addition, a higher BMI correlated with a higher lateral (r = 0.62, P < 0.001) and septal (r = 0.56, P < 0.01) E/e\u27. There was no such relationship for VO2peak. BMI and VO2peak were not correlated with LV systolic function (ejection fraction). In individuals with T2DM and diastolic dysfunction, a higher BMI was associated with worsening diastolic function independent of their aerobic capacity. The data provide a simple and practical approach for clinicians to assist in the early identification and diagnostics of functional changes in the heart diastolic function in this population

Differential response to resistance training in CHF according to ACE genotype

The Angiotensin Converting Enzyme (ACE) gene may influence the risk of heart disease and the response to various forms of exercise training may be at least partly dependent on the ACE genotype. We aimed to determine the effect of ACE genotype on the response to moderate intensity circuit resistance training in chronic heart failure (CHF) patients. Methods: The relationship between ACE genotype and the response to 11 weeks of resistance exercise training was determined in 37 CHF patients (New York Heart Association Functional Class=2.3±0.5; left ventricular ejection fraction 28±7%; age 64±12 years; 32:5 male:female) who were randomised to either resistance exercise (n=19) or inactive control group (n=18). Outcome measures included V˙ O2peak, peak power output and muscle strength and endurance. ACE genotype was determined using standard methods. Results: At baseline, patients who were homozygous for the I allele had higher V˙ O2peak (p=0.02) and peak power (p=0.003) compared to patients who were homozygous for the D allele. Patients with the D allele, who were randomised to resistance training, compared to non-exercising controls, had greater peak power increases (ID pb0.001; DD pb0.001) when compared with patients homozygous for the I allele, who did not improve. No significant genotype-dependent changes were observed in V˙ O2peak, muscle strength, muscle endurance or lactate threshold. Conclusion: ACE genotype may have a role in exercise tolerance in CHF and could also influence the effectiveness of resistance training in this condition

Visualising text co-occurrence networks

We present a tool for automatically generating a visual summary of unstructured text data retrieved from documents, web sites or social media feeds. Unlike tools such as word clouds, we are able to visualise structures and topic relationships occurring in a document. These relationships are determined by a unique approach to co-occurrence analysis. The algorithm applies a decaying function to the distance between word pairs found in the original text such that words regularly occurring close to each other score highly, but even words occurring some distance apart will make a small contribution to the overall co-occurrence score. This is in contrast to other algorithms which simply count adjacent words or use a sliding window of fixed size. We show, with examples, how the network generated can be presented in tree or graph format. The tree format allows for the user to interact with the visualisation and expand or contract the data to a preferred level of detail. The tool is available as a web application and can be viewed using any modern web browse

Real-Time Observation of Organic Cation Reorientation in Methylammonium Lead Iodide Perovskites.

The introduction of a mobile and polarized organic moiety as a cation in 3D lead-iodide perovskites brings fascinating optoelectronic properties to these materials. The extent and the time scales of the orientational mobility of the organic cation and the molecular mechanism behind its motion remain unclear, with different experimental and computational approaches providing very different qualitative and quantitative description of the molecular dynamics. Here we use ultrafast 2D vibrational spectroscopy of methylammonium (MA) lead iodide to directly resolve the rotation of the organic cations within the MAPbI3 lattice. Our results reveal two characteristic time constants of motion. Using ab initio molecular dynamics simulations, we identify these as a fast (∼300 fs) "wobbling-in-a-cone" motion around the crystal axis and a relatively slow (∼3 ps) jump-like reorientation of the molecular dipole with respect to the iodide lattice. The observed dynamics are essential for understanding the electronic properties of perovskite materials.This work was supported by The Netherlands Organization for Scientific Research (NWO) through the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM) research program. A.A.B. also acknowledges a VENI grant from the NWO. A.A.B. is currently a Royal Society University Research Fellow. Z.S. and Z.C. acknowledge the ANR-2011-JS09-004-01-PvCoNano project and the EU Marie Curie Career Integration Grant (303824). A.A.B., Z.S., and Z.C. thank Dutch-French Academy for the support through van Gogh grant.This document is the Accepted Manuscript version of a Published Work that appeared in final form in The Journal of Physical Chemistry Letters, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.5b0155

Rigid Body Dynamics using Equimomental Systems of Point-Masses

The inertia matrix of any rigid body is the same as the inertia matrix of some system of four point-masses. In this work the possible disposition of these point-masses is investigated. It is found that every system of possible point-masses with the same inertia matrix can be parameterised by the elements of the orthogonal group in four dimensions modulo permutation of the points. It is shown that given a fixed inertia matrix, it is possible to find a system of point-masses with the same inertia matrix but where one of the points is located at some arbitrary point. It is also possible to place two point-masses on an arbitrary line or three of the points on an arbitrary plane. The possibility of placing some of the point- masses at infinity is also investigated. Applications of these ideas to rigid-body dynamics is considered. The equation of motion for a rigid body is derived in terms of a system of four point-masses. These turn out to be very simple when written in a 6-vector notation