Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we propose Hyperbolic Delaunay Geometric Alignment (HyperDGA) - a similarity score for comparing datasets in a hyperbolic space. The core idea is counting the edges of the hyperbolic Delaunay graph connecting datapoints across the given sets. We provide an empirical investigation on synthetic and real-life biological data and demonstrate that HyperDGA outperforms the hyperbolic version of classical distances between sets. Furthermore, we showcase the potential of HyperDGA for evaluating latent representations inferred by a Hyperbolic Variational Auto-Encoder.

Interactive perception enables robots to manipulate the environment and objects to bring them into states that benefit the perception process. Deformable objects pose challenges to this due to manipulation difficulty and occlusion in vision-based perception. In this work, we address such a problem with a setup involving both an active camera and an object manipulator. Our approach is based on a sequential decision-making framework and explicitly considers the motion regularity and structure in coupling the camera and manipulator. We contribute a method for constructing and computing a subspace, called Dynamic Active Vision Space (DAVS), for effectively utilizing the regularity in motion exploration. The effectiveness of the framework and approach are validated in both a simulation and a real dual-arm robot setup. Our results confirm the necessity of an active camera and coordinative motion in interactive perception for deformable objects.

“Hot flow in the cold

changes shape in a dead world

comes matter to life”

Programmable matter that allows free shape transfiguration and locomotionon command promises ubiquitous access to objects or functions of interest.Current approaches for the autonomous reshaping of solid objects (smartmaterials, soft actuators, modular robotics) are limited in spatial resolution andshape. Solid-liquid phase change pumping as a mechanism for the contactlesstransfiguring and locomotion of solid objects is introduced. Thin objects aredeformed into any intended shape with sub-millimeter resolution and the abilityto freely change their topology is demonstrated, including adding or removingholes, splitting and merging. The unique locomotion of objects throughmillimeter-sized constrictions narrower than their body size is demonstrated,followed by restoring the original shape. This approach opens up avenues fordeveloping autonomous programmable matter with free shape transfiguration.

Physical interaction with textiles, such as assistivedressing or household tasks, requires advanced dexterous skills.The complexity of textile behavior during stretching and pullingis influenced by the material properties of the yarn and bythe textile’s construction technique, which are often unknownin real-world settings. Moreover, identification of physicalproperties of textiles through sensing commonly available onrobotic platforms remains an open problem. To address this,we introduce Elastic Context (EC), a method to encode theelasticity of textiles using stress-strain curves adapted fromtextile engineering for robotic applications. We employ EC tolearn generalized elastic behaviors of textiles and examine theeffect of EC dimension on accurate force modeling of real-worldnon-linear elastic behaviors.

Water oxidation is the holy grail reaction of natural and artificial photosynthesis. How to design an efficient water-oxidation catalyst remains a long-term challenge for solar fuel production. The rate of water oxidation in photosystem II by the oxygen-evolving complex (OEC) Mn4CaO5 cluster is as high as 100-400 s−1. Mimicking the structures of the OEC is a straightforward strategy to design water-oxidation catalysts. However, the high efficiency of the OEC relies on not only its highly active site but also its holistic system for well-organized electron transfer and proton transport. Lacking such a holistic functional system makes δ-MnO2 a poor water-oxidation catalyst, although the local structure of δ-MnO2 is similar to that of the Mn4CaO5 cluster. Electrocatalysts simultaneously imitating the catalytically active sites, fast electron transfer, and promoted proton transport in a natural OEC have been rarely reported. The significance of the synergy of a holistic system is underrated in the design of water-oxidation catalysts. In this work, we fabricated holistic functional biomimetic composites of two-dimensional manganese oxide nanosheets and pyridyl-modified graphene (MnOx-NS/py-G) for electrocatalytic water oxidation. MnOx-NS/py-G simultaneously imitates the synergy of catalytically active sites, fast electron transfer, and promoted proton transport in a natural OEC, resulting in overall 600 times higher activity than that of typical δ-MnO2. This work demonstrates the significance of holistic functional biomimetic design and guides the development of highly active electrocatalysts for small molecule activation related to solar energy storage.

Energy shortage and environmental pollution limit the sustainable development of human beings. Water, as a clean and renewable resource, provides a solution for sustainable energy conversion from water oxidation catalysis. Lessons should be learned from nature to explore efficient artificial catalysts. In this chapter, we will review recent major progress in natural photosynthesis, from the structure and functions to the mechanisms for the water-oxidizing center of the biological enzyme. Later, the development of molecular and material water oxidation catalysts is discussed, with a focus on the mechanisms and rational catalyst design.

We introduce an algorithm for active function approximation based on nearest neighbor regression. Our Active Nearest Neighbor Regressor (ANNR) relies on the Voronoi-Delaunay framework from computational geometry to subdivide the space into cells with constant estimated function value and select novel query points in a way that takes the geometry of the function graph into account. We consider the recent state-of-the-art active function approximator called DEFER, which is based on incremental rectangular partitioning of the space, as the main baseline. The ANNR addresses a number of limitations that arise from the space subdivision strategy used in DEFER. We provide a computationally efficient implementation of our method, as well as theoretical halting guarantees. Empirical results show that ANNR outperforms the baseline for both closed-form functions and real-world examples, such as gravitational wave parameter inference and exploration of the latent space of a generative model.

Exploration of efficient water oxidation catalysts (WOCs) is the primary challenge in conversion of renewable energy into fuels. Here we report a molecularly well-defined heterogeneous WOC with Aza-fused, pi-conjugated, microporous polymer (Aza-CMP) coordinated single cobalt sites (Aza-CMP-Co). The single cobalt sites in Aza-CMP-Co exhibited superior activity under alkaline and near-neutral conditions. Moreover, the molecular nature of the isolated catalytic sites makes Aza-CMP-Co a reliable model for studying the heterogeneous water oxidation mechanism. By a combination of experimental and theoretical results, a pH-dependent nucleophilic attack pathway for O-O bond formation was proposed. Under alkaline conditions, the intramolecular hydroxyl nucleophilic attack (IHNA) process with which the adjacent -OH group nucleophilically attacks Co4+=O was identified as the rate-determining step. This process leads to lower activation energy and accelerated kinetics than those of the intermolecular water nucleophilic attack (WNA) pathway. This study provides significant insights into the crucial function of electrolyte pH in water oxidation catalysis and enhancement of water oxidation activity by regulation of the IHNA pathway.

Isolation of RuIII-bda (17-electron specie) complex with an aqua ligand (2-electron donor) is challenging due to violation of the 18-electron rule. Although considerable efforts have been dedicated to mechanistic studies of water oxidation by the Ru-bda family, the structure and initial formation of the RuIII-bda aqua complex are still controversial. Herein, we challenge this often overlooked step by designing a pocket-shape Ru-based complex 1. The computational studies showed that 1 possesses the crucial hydrophobicity at the RuV(O) state as well as similar probability of access of terminal O to solvent water molecules when compared with classic Ru-bda catalysts. Through characterization of single-crystal structures at the RuII and RuIII states, a pseudo seven-coordinate “ready-to-go” aqua ligand with RuIII...O distance of 3.62 Å was observed. This aqua ligand was also found to be part of a formed hydrogen-bonding network, providing a good indication of how the RuIII-OH2 complex is formed.

The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because Voronoi cells rapidly increase in complexity as dimensions grow, making the necessary explicit computations infeasible. We define a variant of the VDE deemed Compactified Voronoi Density Estimator (CVDE), suitable for higher dimensions. We propose computationally efficient algorithms for numerical approximation of the CVDE and formally prove convergence of the estimated density to the original one. We implement and empirically validate the CVDE through a comparison with the Kernel Density Estimator (KDE). Our results indicate that the CVDE outperforms the KDE on sound and image data.