Batch Nonlinear Continuous-Time Trajectory Estimation as Exactly Sparse Gaussian Process Regression

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any nonlinear, time-varying stochastic differential equation driven by white noise; this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models (e.g., `constant-velocity'). We show that this class of prior results in an inverse kernel matrix (i.e., covariance matrix between all pairs of measurement times) that is exactly sparse (block-tridiagonal) and that this can be exploited to carry out GP regression (and interpolation) very efficiently. When the prior is based on a linear, time-varying stochastic differential equation and the measurement model is also linear, this GP approach is equivalent to classical, discrete-time smoothing (at the measurement times); when a nonlinearity is present, we iterate over the whole trajectory to maximize accuracy. We test the approach experimentally on a simultaneous trajectory estimation and mapping problem using a mobile robot dataset.Comment: Submitted to Autonomous Robots on 20 November 2014, manuscript # AURO-D-14-00185, 16 pages, 7 figure

Normalizing connections and the energy-momentum method

The block diagonalization method for determining the stability of relative equilibria is discussed from the point of view of connections. We construct connections whose horizontal and vertical decompositions simultaneosly put the second variation of the augmented Hamiltonian and the symplectic structure into normal form. The cotangent bundle reduction theorem provides the setting in which the results are obtained

A block diagonalization theorem in the energy-momentum method

We prove a geometric generalization of a block diagonalization theorem first found by the authors for rotating elastic rods. The result here is given in the general context of simple mechanical systems with a symmetry group acting by isometries on a configuration manifold. The result provides a choice of variables for linearized dynamics at a relative equilibrium which block diagonalizes the second variation of an augmented energy these variables effectively separate the rotational and internal vibrational modes. The second variation of the effective Hamiltonian is block diagonal. separating the modes completely. while the symplectic form has an off diagonal term which represents the dynamic interaction between these modes. Otherwise, the symplectic form is in a type of normal form. The result sets the stage for the development of useful criteria for bifurcation as well as the stability criteria found here. In addition, the techniques should apply to other systems as well, such as rotating fluid masses

Population aging, unemployment and house prices in South Africa

Abstract: This paper examines the joint dynamics between house prices, population aging and unemployment in South Africa. It uses provincial level dataset to compare the demographic effects of house prices across different housing segments over the period from 1995 to 2015. When heterogeneity, endogeneity and spatial effects are controlled for, the analysis finds that on average in the past 22 years, population aging have contributed to the decline of the South African house prices by 6.28 and 7.52 basis point in the large and medium housing segments, respectively while the small segment has remained unaffected. Likewise, unemployment appears to have played a significant role in slowing down the growth rate of house prices across segments but to a lesser extent. While the response of real house prices to demographic shift is consistent with the life cycle hypothesis, the insensitivity of small house prices to aging might reveal the mitigating effect of the retirees’ relocation from larger segment houses to smaller ones. The relocation effect might induce higher demand of small segment houses which drives up their prices and offsets the detrimental effect of aging. These findings suggest that, increasing the incentive to prolong the retirement age or engage elderly population in other income generating activities to meet their increasing financial needs given the meagre social security system, is likely to sustain the growth prospective of housing value in South Africa

Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

Enhancing EFL Learning in Cameroon’s Language Centres through Content and Language Integrated Learning

This study seeks to determine how Content and Language Integrated Learning (CLIL), already applied successfully in other parts of the world, could be adapted to teaching English as a foreign language in language centres in Cameroon. The problem identified was the fact that 43 out of 64 students leave language centres with a lot of general English but with little or no language abilities relevant to their fields of experience, whether academic or professional. The results revealed that the implementation of CLIL had a positive impact on learners’ development of diverse skills necessary for their success in academic and/or professional settings since there was a remarkable improvement in students’ performance in the experimental group (93%) as opposed to the limited (lower) performance of the control group (56.4%), providing therefore factual evidence of the effectiveness of the CLIL approach over other conventional approaches in meeting students’ needs and interests after training

Corruption's effect on BRICS countries' economic growth: a panel data analysis

Purpose: The theoretical debate of corruption's impact on economic growth remains unsettled, making it an empirical question. This study aims to investigate corruption's effect on BRICS countries' economic growth. Design/methodology/approach: A panel dataset on BRICS countries spanning 1996 to 2020 was used. Bias-corrected estimators in small dynamic panels were employed to estimate a growth model as a linear-quadratic function of corruption that accounts for cross-sectional dependence, endogeneity and unobserved heterogeneity due to country and time-specific characteristics. Findings: The results indicate that corruption is detrimental to economic growth in BRICS countries; the quadratic relationship implies corruption is less prevalent in some countries than others. Thus, governments of BRICS countries are encouraged to embark on anti-corruption policies to boost their economic performance. Originality/value: An important limitation of corruption studies is the difficulty in measuring real corruption experiences due to the secretive nature of corruption and the fact that corruption is known not to leave a paper trail. For the uncertainty of the index estimates, the analysis used a continuous corruption composite score measuring the standard deviation of the extent to which public power is exercised for public gain. Furthermore, estimation and inference are robust to small dynamic panels with a general form of cross-sectional dependence

Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature