Visual place recognition (VPR) in condition-varying environments is still an open problem. Popular solutions are convolutional neural network (CNN)-based image descriptors, which have been shown to outperform traditional image descriptors based on hand-crafted visual features. However, there are two drawbacks of current CNN-based descriptors: (a) their high dimension and (b) lack of generalization, leading to low efficiency and poor performance in real robotic applications. In this paper, we propose to use a convolutional autoencoder (CAE) to tackle this problem. We employ a high-level layer of a pre-trained CNN to generate features and train a CAE to map the features to a low-dimensional space to improve the condition invariance property of the descriptor and reduce its dimension at the same time. We verify our method in four challenging real-world datasets involving significant illumination changes, and our method is shown to be superior to the state-of-the-art. The code of our work is publicly available at https://github.com/MedlarTea/CAE-VPR.

Dietary pattern analysis is typically based on dimension reduction and summarises the diet with a small number of scores. We assess ‘joint and individual variance explained’ (JIVE) as a method for extracting dietary patterns from longitudinal data that highlights elements of the diet that are associated over time. The Auckland Birthweight Collaborative Study, in which participants completed an FFQ at ages 3·5 (n 549), 7 (n 591) and 11 (n 617), is used as an example. Data from each time point are projected onto the directions of shared variability produced by JIVE to yield dietary patterns and scores. We assess the ability of the scores to predict future BMI and blood pressure measurements of the participants and make a comparison with principal component analysis (PCA) performed separately at each time point. The diet could be summarised with three JIVE patterns. The patterns were interpretable, with the same interpretation across age groups: a vegetable and whole grain pattern, a sweets and meats pattern and a cereal v. sweet drinks pattern. The first two PCA-derived patterns were similar across age groups and similar to the first two JIVE patterns. The interpretation of the third PCA pattern changed across age groups. Scores produced by the two techniques were similarly effective in predicting future BMI and blood pressure. We conclude that when data from the same participants at multiple ages are available, JIVE provides an advantage over PCA by extracting patterns with a common interpretation across age groups.

In this work we derive by $\Gamma$-convergence techniques a model for brittle fracture linearly elastic plates. Precisely, we start from a brittle linearly elastic thin film with positive thickness $\rho$ and study the limit as $\rho$ tends to $0$. The analysis is performed with no a priori restrictions on the admissible displacements and on the geometry of the fracture set. The limit model is characterized by a Kirchhoff-Love type of structure.

Starting from three-dimensional non-linear elasticity under the restriction of incompressibility, we derive reduced models to capture the behaviour of strings in response to external forces. Our Γ-convergence analysis of the constrained energy functionals in the limit of shrinking cross-sections gives rise to explicit one-dimensional limit energies. The latter depend on the scaling of the applied forces. The effect of local volume preservation is reflected either in their energy densities through a constrained minimization over the cross-section variables or in the class of admissible deformations. Interestingly, all scaling regimes allow for compression and/or stretching of the string. The main difficulty in the proof of the Γ-limit is to establish recovery sequences that accommodate the non-linear differential constraint imposed by the incompressibility. To this end, we modify classical constructions in the unconstrained case with the help of an inner perturbation argument tailored for 3d-1d dimension reduction problems.

Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades—under the same parametrisation—largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection—a non-linear least-squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.

One of today’s most propitious immersive technologies is virtual reality (VR). This term is colloquially associated with headsets that transport users to a bespoke, built-for-purpose immersive 3D virtual environment. It has given rise to the field of immersive analytics—a new field of research that aims to use immersive technologies for enhancing and empowering data analytics. However, in developing such a new set of tools, one has to ask whether the move from standard hardware setup to a fully immersive 3D environment is justified—both in terms of efficiency and development costs. To this end, in this paper, we present AeroVR—an immersive aerospace design environment with the objective of aiding the component aerodynamic design process by interactively visualizing performance and geometry. We decompose the design of such an environment into function structures, identify the primary and secondary tasks, present an implementation of the system, and verify the interface in terms of usability and expressiveness. We deploy AeroVR on a prototypical design study of a compressor blade for an engine.

We present an application of statistical graphical models to simulate economic variables for the purpose of risk calculations over long time horizons. We show that this approach is relatively easy to implement, and argue that it is appealing because of the transparent yet flexible means of achieving dimension reduction when many variables must be modelled. Using the United Kingdom data as an example, we demonstrate the development of an economic scenario generator that can be used by life insurance companies and pension funds.We compare different algorithms to select a graphical model, based on p-values, AIC, BIC and deviance. We find the economic scenario generator to yield reasonable results and relatively stable structures in our example, suggesting that it would be beneficial for actuaries to include graphical models in their toolkit.

In areas of application, including actuarial science and demography, it is increasingly common to consider a time series of curves; an example of this is age-specific mortality rates observed over a period of years. Given that age can be treated as a discrete or continuous variable, a dimension reduction technique, such as principal component analysis (PCA), is often implemented. However, in the presence of moderate-to-strong temporal dependence, static PCA commonly used for analyzing independent and identically distributed data may not be adequate. As an alternative, we consider a dynamic principal component approach to model temporal dependence in a time series of curves. Inspired by Brillinger’s (1974, Time Series: Data Analysis and Theory. New York: Holt, Rinehart and Winston) theory of dynamic principal components, we introduce a dynamic PCA, which is based on eigen decomposition of estimated long-run covariance. Through a series of empirical applications, we demonstrate the potential improvement of 1-year-ahead point and interval forecast accuracies that the dynamic principal component regression entails when compared with the static counterpart.

We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show that, as $h\searrow 0$, stationary points of the energy , for a rod $\Omega _h\subset {\open R}^3$ with cross-sectional diameter h, subconverge to stationary points of the Γ-limit of , provided that the bending energy of the sequence scales appropriately. This generalizes earlier results for homogeneous materials to the case of materials with (not necessarily periodic) inhomogeneities.

We derive asymptotic formulas for the solutions of the mixed boundary value problem forthe Poisson equation on the union of a thin cylindrical plate and several thin cylindricalrods. One of the ends of each rod is set into a hole in the plate and the other one issupplied with the Dirichlet condition. The Neumann conditions are imposed on the wholeremaining part of the boundary. Elements of the junction are assumed to have contrastingproperties so that the small parameter, i.e. the relative thickness,appears in the differential equation, too, while the asymptotic structures cruciallydepend on the contrastness ratio. Asymptotic error estimates are derived in anisotropicweighted Sobolev norms.

A 3D-2D dimension reduction for −Δ1 is obtained. A power law approximation from −Δp as p → 1 in terms of Γ-convergence, duality and asymptotics for least gradient functions has also been provided.

Dimension reduction of multivariate data was developed by Y. Guan for point processes with Gaussian random fields as covariates. The generalization to fibre and surface processes is straightforward. In inverse regression methods, we suggest slicing based on geometrical marks. An investigation of the properties of this method is presented in simulation studies of random marked sets. In a refined model for dimension reduction, the second-order central subspace is analyzed in detail. A real data pattern is tested for independence of a covariate.

The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). We consider all three cases.

The question, how does an organism maintain balance? provides a unifying theme tointroduce undergraduate students to the use of mathematics and modeling techniques inbiological research. The availability of inexpensive high speed motion capture camerasmakes it possible to collect the precise and reliable data that facilitates thedevelopment of relevant mathematical models. An in–house laboratory component ensures thatstudents have the opportunity to directly compare prediction to observation and motivatesthe development of projects that push the boundaries of the subject. The projects, bytheir nature, readily lend themselves to the formation of inter–disciplinary studentresearch teams. Thus students have the opportunity to learn skills essential for successin today’s workplace including productive team work, critical thinking, problem solving,project management, and effective communication.

We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint can give rise to a nonlocal functional as illustrated in an example.

We consider the Laplacian in a domain squeezedbetween two parallel curves in the plane,subject to Dirichlet boundary conditions on one of the curvesand Neumann boundary conditions on the other.We derive two-term asymptotics for eigenvaluesin the limit when the distance between the curves tends to zero.The asymptotics are uniform and local in the sense thatthe coefficients depend only on the extremal points wherethe ratio of the curvature radii of the Neumann boundaryto the Dirichlet one is the biggest.We also show that the asymptotics can be obtainedfrom a form of norm-resolvent convergencewhich takes into account the width-dependenceof the domain of definition of the operators involved.

We consider the Laplace operator in a thin tube of ${\mathbb R}^3$ with a Dirichlet condition on its boundary. We study asymptotically the spectrum ofsuch an operator as the thickness of the tube's cross section goes to zero. In particular weanalyse how the energy levels depend simultaneously on the curvature of the tube's central axisand on the rotation of the cross section with respect to the Frenet frame. The main argument is aΓ-convergence theorem for a suitable sequence of quadratic energies.