Metal-organic frameworks (MOFs), composed of metal nodes and inorganic linkers are promising for a wide range of applications due to their unique periodic frameworks that can be flexibly tuned. Understanding of the structure-activity relationships can facilitate the development and application of MOFs nanomaterials. Transmission electron microscopy (TEM) is a one-of-a-kind technique capable of characterizing MOFs microstructures at the atomic scale. Besides, in-situ TEM set-ups make it possible to direct visualize the microstructural evolution of MOFs in real time, which enables monitoring transitions of MOFs during growth as well as under working conditions. However, MOFs are so sensitive to the high-energy electron beam which makes TEM-based characterizing methods challenging. In this review, we first introduce the main damage mechanisms for MOFs under electron beam irradiation and two strategies to minimize the damages: low-dose TEM and cryo-TEM. Then, we discuss the techniques combined with the two strategies to analyze the MOFs’ microstructure, including three-dimensional electron diffraction, direct detection electron counting camera, and iDPC-STEM. Groundbreaking milestones and research advances with respect to static characterization of MOFs structures are highlighted. In-situ TEM studies are exemplary reviewed to provide insights into MOFs dynamics induced by various stimuli. Additionally, perspectives on promising techniques that may further facilitate the MOFs study using TEM are analyzed.

Hopfield Neural Networks (HNNs) are recurrent neural networks used to implement associative memory. Their main feature is their ability to pattern recognition, optimization, or image segmentation. However, sometimes it is not easy to provide the users with good explanations about the results obtained with them due to mainly the large number of changes in the state of neurons (and their weights) produced during a problem of machine learning. There are currently limited techniques to visualize, verbalize, or abstract HNNs. This paper outlines how we can construct automatic video generation systems to explain their execution. This work constitutes a novel approach to get explainable artificial intelligence systems in general and HNNs in particular building on the theory of data-to-text systems and software visualization approaches. We present a complete methodology to build these kinds of systems. Software architecture is also designed, implemented, and tested. Technical details about the implementation are also detailed and explained. Finally, we apply our approach for creating a complete explainer video about the execution of HNNs on a small recognition problem.

The understanding of water quality and its underlying processes is important for the protection of aquatic environments enabling the rare opportunity of access to a domain expert. Hence, an explainable AI (XAI) framework is proposed that is applicable to multivariate time series resulting in explanations that are interpretable by a domain expert. The XAI combines in three steps a data-driven choice of a distance measure with explainable cluster analysis through supervised decision trees. The multivariate time series consists of water quality measurements, including nitrate, electrical conductivity, and twelve other environmental parameters. The relationships between water quality and the environmental parameters are investigated by identifying similar days within a cluster and dissimilar days between clusters. The XAI does not depend on prior knowledge about data structure, and its explanations are tendentially contrastive. The relationships in the data can be visualized by a topographic map representing high-dimensional structures. Two comparable decision-based XAIs were unable to provide meaningful and relevant explanations from the multivariate time series data. Open-source code in R for the three steps of the XAI framework is provided.

Variational Auto-Encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the Simplicial Auto-Encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a data set better than a standard VAE.

We propose a novel framework for understanding quantum phenomena through the lens of a modified electromagnetic spacetime governed by Einstein field equations. By assuming the existence of an electromagnetic spacetime that adheres to these modified geodesic and Einstein field equations, provided the field equations satisfy the Coulomb force law in weak-field approximations, we explore the derivation of Maxwell’s equations and highlight the necessity of incorporating spin to validate these equations. We derive the wave equation for the normalized transverse metric and establish its equivalence with the de Broglie wave proposition, suggesting a relationship between this metric and the particle's wavefunction. This approach offers a classical explanation for several quantum phenomena, including the double-slit experiment, entanglement, tunneling, non-locality, and wavefunction collapse. Additionally, it posits a method to visualize atomic orbital structures in line with quantum mechanical predictions. These findings suggest that the foundational principles of quantum mechanics can be interpreted as linearized approximations of general relativity applied to electromagnetic spacetime. While this theory does not yet extend to the correlations between general relativity, quantum electrodynamics (QED), and quantum chromodynamics (QCD), it provides a valuable visualization tool for physicists and advances our understanding of the unresolved challenges linking quantum mechanics with general relativity.