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Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying parametric space exhibit constant curvature, which makes the geometry hyperbolic (negative) or spherical (positive). In this paper, we derive closed-form expressions for the components of the first and second fundamental forms regarding pairwise isotropic Gaussian-Markov random field manifolds, allowing the computation of the Gaussian, mean and principal curvatures. Computational simulations using Markov Chain Monte Carlo dynamics indicate that a change in the sign of the Gaussian curvature is related to the emergence of phase transitions in the field. Moreover, the curvatures are highly asymmetrical for positive and negative displacements in the inverse temperature parameter, suggesting the existence of irreversible geometric properties in the parametric space along the dynamics. Furthermore, these asymmetric changes in the curvature of the space induces an intrinsic notion of time in the evolution of the random field.

A reconfigurable intelligent surface (RIS) is a planar structure that is engineered to dynamically control the electromagnetic waves. In wireless communications, RISs have recently emerged as a promising technology for realizing programmable and reconfigurable wireless propagation environments through nearly passive signal transformations. With the aid of RISs, a wireless environment becomes part of the network design parameters that are subject to optimization. In this tutorial paper, we focus our attention on communication models for RISs. First, we review the communication models that are most often employed in wireless communications and networks for analyzing and optimizing RISs, and elaborate on their advantages and limitations. Then, we concentrate on models for RISs that are based on inhomogeneous sheets of surface impedance, and offer a step-by-step tutorial on formulating electromagnetically-consistent analytical models for optimizing the surface impedance. The differences between local and global designs are discussed and analytically formulated in terms of surface power efficiency and reradiated power flux through the Poynting vector. Finally, with the aid of numerical results, we discuss how approximate global designs can be realized by using locally passive RISs with zero electrical resistance (i.e., inhomogeneous reactance boundaries with no local power amplification), even for large angles of reflection and at high power efficiency.

In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics, which has emerged as an effective tool both to understand the influence of complex microstructures on the macro-mechanical response of engineering materials and to tailor-design innovative materials for specific applications through a proper modification of their microstructure. The computational framework presented in this thesis is based on the Virtual Element Method (VEM), a recently developed numerical technique able to provide robust numerical results even with highly-distorted meshes. The peculiar features of VEM have been exploited to analyse two-dimensional representations of heterogeneous materials microstructures. Ad-hoc polygonal multi-domain meshing strategies have been developed and tested to exploit the discretisation freedom that VEM allows. To further simplify the preprocessing stage of the analysis and reduce the total computational cost, a novel hybrid formulation for analysing multi-domain problems has been developed by combining the Virtual Element Method with the well-known Boundary Element Method (BEM). The hybrid approach has been used to study both composite material transverse behaviour in presence of inclusions with complex geometries and damage and crack propagation in the matrix phase. Numerical results are presented that demonstrate the potential of the developed framework.

Handed Shearing Auxetics (HSA) are a promising structure for making electrically driven robots with distributed compliance that convert a motors rotation and torque into extension and force. We overcame past limitations on the range of actuation, blocked force, and stiffness by focusing on two key design parameters: the point of an HSA's auxetic trajectory that is energetically preferred, and the number of cells along the HSAs length. Modeling the HSA as a programmable spring, we characterize the effect of both on blocked force, minimum energy length, spring constant, angle range and holding torque. We also examined the effect viscoelasticity has on actuation forces over time. By varying the auxetic trajectory point, we were able to make actuators that can push, pull, or do both. We expanded the range of forces possible from 5N to 150N, and the range of stiffness from 2 N/mm to 89 N/mm. For a fixed point on the auxetic trajectory, we found decreasing length can improve force output, at the expense of needing higher torques, and having a shorter throw. We also found that the viscoelastic effects can limit the amount of force a 3D printed HSA can apply over time.

The potential diagnostic applications of magnet-actuated capsules have been greatly increased in recent years. For most of these potential applications, accurate position control of the capsule have been highly demanding. However, the friction between the robot and the environment as well as the drag force from the tether play a significant role during the motion control of the capsule. Moreover, these forces especially the friction force are typically hard to model beforehand. In this paper, we first designed a magnet-actuated tethered capsule robot, where the driving magnet is mounted on the end of a robotic arm. Then, we proposed a learning-based approach to model the friction force between the capsule and the environment, with the goal of increasing the control accuracy of the whole system. Finally, several real robot experiments are demonstrated to showcase the effectiveness of our proposed approach.

We consider the problem of human deformation transfer, where the goal is to retarget poses between different characters. Traditional methods that tackle this problem require a clear definition of the pose, and use this definition to transfer poses between characters. In this work, we take a different approach and transform the identity of a character into a new identity without modifying the character's pose. This offers the advantage of not having to define equivalences between 3D human poses, which is not straightforward as poses tend to change depending on the identity of the character performing them, and as their meaning is highly contextual. To achieve the deformation transfer, we propose a neural encoder-decoder architecture where only identity information is encoded and where the decoder is conditioned on the pose. We use pose independent representations, such as isometry-invariant shape characteristics, to represent identity features. Our model uses these features to supervise the prediction of offsets from the deformed pose to the result of the transfer. We show experimentally that our method outperforms state-of-the-art methods both quantitatively and qualitatively, and generalises better to poses not seen during training. We also introduce a fine-tuning step that allows to obtain competitive results for extreme identities, and allows to transfer simple clothing.

We construct a new nonlinear finite volume (FV) scheme for highly anisotropic diffusion equations, that satisfies the discrete minimum-maximum principle. The construction relies on the linearized scheme satisfying less restrictive monotonicity conditions than those of an M-matrix, based on a weakly regular matrix splitting and using the Cartesian structure of the mesh (extension to quadrilateral meshes is also possible). The resulting scheme, obtained by expressing fluxes as nonlinear combinations of linear fluxes, has a larger stencil than other nonlinear positivity preserving or minimum-maximum principle preserving schemes. Its larger "linearized" stencil, closer to the actual complete stencil (that includes unknowns appearing in the convex combination coefficients), enables a faster convergence of the Picard iterations used to compute the solution of the scheme. Steady state dimensionless numerical tests as well as simulations of the highly anisotropic diffusion in electron radiation belts show a second order of convergence of the new scheme and confirm its computational efficiency compared to usual nonlinear FV schemes.

Swapping text in scene images while preserving original fonts, colors, sizes and background textures is a challenging task due to the complex interplay between different factors. In this work, we present SwapText, a three-stage framework to transfer texts across scene images. First, a novel text swapping network is proposed to replace text labels only in the foreground image. Second, a background completion network is learned to reconstruct background images. Finally, the generated foreground image and background image are used to generate the word image by the fusion network. Using the proposing framework, we can manipulate the texts of the input images even with severe geometric distortion. Qualitative and quantitative results are presented on several scene text datasets, including regular and irregular text datasets. We conducted extensive experiments to prove the usefulness of our method such as image based text translation, text image synthesis, etc.

In this work, we present a method for tracking and learning the dynamics of all objects in a large scale robot environment. A mobile robot patrols the environment and visits the different locations one by one. Movable objects are discovered by change detection, and tracked throughout the robot deployment. For tracking, we extend the Rao-Blackwellized particle filter of previous work with birth and death processes, enabling the method to handle an arbitrary number of objects. Target births and associations are sampled using Gibbs sampling. The parameters of the system are then learnt using the Expectation Maximization algorithm in an unsupervised fashion. The system therefore enables learning of the dynamics of one particular environment, and of its objects. The algorithm is evaluated on data collected autonomously by a mobile robot in an office environment during a real-world deployment. We show that the algorithm automatically identifies and tracks the moving objects within 3D maps and infers plausible dynamics models, significantly decreasing the modeling bias of our previous work. The proposed method represents an improvement over previous methods for environment dynamics learning as it allows for learning of fine grained processes.