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The morphing of 3D structures is suitable for i) future tunable material design for customizing material properties and ii) advanced manufacturing tools for fabricating 3D structures on a 2D plane. However, there is no inverse design method…
Legged machines are becoming increasingly agile and adaptive but they have so far lacked the morphological diversity of legged animals, which have been rearranged and reshaped to fill millions of niches. Unlike their biological…
Topological magnetism, characterized by topologically protected spin textures, offers rich physics and transformative prospects for spintronics. However, its stabilization typically demands external magnetic fields, preventing…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
Robotics is shifting from rigid, articulated systems to more sophisticated and heterogeneous mechanical structures. Soft robots, for example, have continuously deformable elements capable of large deformations. The flourishing of control…
We present a novel general model that unifies the kinematics of constant curvature and constant twist continuum manipulators. Combining this kinematics with energy-based physics, we derive a linear mapping from actuator configuration to…
We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
Model merging offers a scalable alternative to multi-task learning but often yields suboptimal performance on classification tasks. We attribute this degradation to a geometric misalignment between the merged encoder and static…
A common way to manipulate heavy objects is to maintain at least one point of the object in contact with the environment during the manipulation. When the object has a cylindrical shape or, in general, a curved edge, not only sliding and…
Convolutions are fundamental elements in deep learning architectures. Here, we present a theoretical framework for combining extrinsic and intrinsic approaches to manifold convolution through isometric embeddings into tori. In this way, we…
Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of…
Soft robotics is an emerging field of research where the robot body is composed of compliant and soft materials. It allows the body to bend, twist, and deform to move or to adapt its shape to the environment for grasping, all of which are…
Molecules with an odd number of electrons typically display paramagnetic behaviour in a uniform magnetic field. Single-molecule toroics -- a family of open shell lanthanide complexes -- instead display an unprecedented vanishing…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
A theoretical analysis of the unfolding pathway of simple modular proteins in length- controlled pulling experiments is put forward. Within this framework, we predict the first module to unfold in a chain of identical units, emphasizing the…
Performing long-term experimentation or large-scale data collection for machine learning in the field of soft robotics is challenging, due to the hardware robustness and experimental flexibility required. In this work, we propose a modular…
Computational methods that operate on three-dimensional molecular structure have the potential to solve important questions in biology and chemistry. In particular, deep neural networks have gained significant attention, but their…
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence…
Open source hardware has the potential to revolutionise the way we build scientific instruments; with the advent of readily-available 3D printers, mechanical designs can now be shared, improved and replicated faster and more easily than…