Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing implicit time-dependent information contained in the data. Such information is typically not directly observed but plays a key role in the learning task performance. In turn, lack of time dimension in knowledge encoding mechanisms for time-dependent data leads to frequent model updates, poor learning performance, and, as a result, subpar decision-making. Here we propose a new approach to a time-aware knowledge representation mechanism that notably focuses on implicit time-dependent topological information along multiple geometric dimensions. In particular, we propose a new approach, named Temporal MultiPersistence (TMP), which produces multidimensional topological fingerprints of the data by using the existing single parameter topological summaries. The main idea behind TMP is to merge the two newest directions in topological representation learning, that is, multi-persistence which simultaneously describes data shape evolution along multiple key parameters, and zigzag persistence to enable us to extract the most salient data shape information over time. We derive theoretical guarantees of TMP vectorizations and show its utility, in application to forecasting on benchmark traffic flow, Ethereum blockchain, and electrocardiogram datasets, demonstrating the competitive performance, especially, in scenarios of limited data records. In addition, our TMP method improves the computational efficiency of the state-of-the-art multipersistence summaries up to 59.5 times.

More than US$ 27 billion is estimated to have been paid-out in farm support in USA alone since 1991 in response to climate change impacts on agriculture, with costs likely continuing to rise. With the wider adoption of precision agriculture - an agriculture management strategy that involves gathering, processing and analyzing temporal, spatial and individual data - in both developed and developing countries, there is an increasing opportunity to harness accumulating, shareable, big data using artificial intelligence (AI) methods, collected from weather stations, field sensor networks, Internet-of-Things devices, unmanned aerial vehicles, and earth observational satellites. This requires smart algorithms tailored to agricultural data types, integrated into digital solutions that are viable, flexible, and scalable for wide deployment for a wide variety of agricultural users and decision-makers. We discuss a novel AI approach that addresses the real-world problem of developing a viable solution for reliably, timely, and cost-effectively forecasting crop status across large agricultural regions using Earth observational information in near-real-time. Our approach is based on extracting time-conditioned topological features which characterize complex spatio-temporal dependencies between crop production regions and integrating such topological signatures into Long Short Term Memory (LSTM). We discuss utility and limitations of the resulting zigzag persistence-based LSTM (ZZTop-LSTM) as a new tool for developing more informed crop insurance rate-making and accurate tracking of changing risk exposures and vulnerabilities within insurance risk areas.

This paper introduces an interactive visualization interface with a machine learning consensus analysis that enables the researchers to explore the impact of atmospheric and socioeconomic factors on COVID-19 clinical severity by employing multiple Recurrent Graph Neural Networks. We designed and implemented a visualization interface that leverages coordinated multi-views to support exploratory and predictive analysis of hospitalizations and other socio-geographic variables at multiple dimensions, simultaneously. By harnessing the strength of geometric deep learning, we build a consensus machine learning model to include knowledge from county-level records and investigate the complex interrelationships between global infectious disease, environment, and social justice. Additionally, we make use of unique NASA satellite-based observations which are not broadly used in the context of climate justice applications. Our current interactive interface focus on three US states (California, Pennsylvania, and Texas) to demonstrate its scientific value and presented three case studies to make qualitative evaluations.

In computer-aided drug discovery (CADD), virtual screening (VS) is used for comparing a library of compounds against known active ligands to identify the drug candidates that are most likely to bind to a molecular target. Most VS methods to date have focused on using canonical compound representations (e.g., SMILES strings, Morgan fingerprints) or generating alternative fingerprints of the compounds by training progressively more complex variational autoencoders (VAEs) and graph neural networks (GNNs). Although VAEs and GNNs led to significant improvements in VS performance, these methods suffer from reduced performance when scaling to large virtual compound datasets. The performance of these methods has shown only incremental improvements in the past few years. To address this problem, we developed a novel method using multiparameter persistence (MP) homology that produces topological fingerprints of the compounds as multidimensional vectors. Our primary contribution is framing the VS process as a new topology-based graph ranking problem by partitioning a compound into chemical substructures informed by the periodic properties of its atoms and extracting their persistent homology features at multiple resolution levels. We show that the margin loss fine-tuning of pretrained Triplet networks attains highly competitive results in differentiating between compounds in the embedding space and ranking their likelihood of becoming effective drug candidates. We further establish theoretical guarantees for the stability properties of our proposed MP signatures, and demonstrate that our models, enhanced by the MP signatures, outperform state-of-the-art methods on benchmark datasets by a wide and highly statistically significant margin (e.g., 93\% gain for Cleves-Jain and 54\% gain for DUD-E Diverse dataset).

There recently has been a surge of interest in developing a new class of deep learning (DL) architectures that integrate an explicit time dimension as a fundamental building block of learning and representation mechanisms. In turn, many recent results show that topological descriptors of the observed data, encoding information on the shape of the dataset in a topological space at different scales, that is, persistent homology of the data, may contain important complementary information, improving both performance and robustness of DL. As convergence of these two emerging ideas, we propose to enhance DL architectures with the most salient time-conditioned topological information of the data and introduce the concept of zigzag persistence into time-aware graph convolutional networks (GCNs). Zigzag persistence provides a systematic and mathematically rigorous framework to track the most important topological features of the observed data that tend to manifest themselves over time. To integrate the extracted time-conditioned topological descriptors into DL, we develop a new topological summary, zigzag persistence image, and derive its theoretical stability guarantees. We validate the new GCNs with a time-aware zigzag topological layer (Z-GCNETs), in application to traffic forecasting and Ethereum blockchain price prediction. Our results indicate that Z-GCNET outperforms 13 state-of-the-art methods on 4 time series datasets.

Given that persons with a prior history of respiratory diseases tend to demonstrate more severe illness from COVID-19 and, hence, are at higher risk of serious symptoms, ambient air quality data from NASA's satellite observations might provide a critical insight into which geographical areas may exhibit higher numbers of hospitalizations due to COVID-19, how the expected severity of COVID-19 and associated survival rates may vary across space in the future, and most importantly how given this information, health professionals can distribute vaccines in a more efficient, timely, and fair manner.

This paper introduces a new Estimation of Distribution Algorithm (EDA) based on the multivariate Boltzmann distribution. In this work, the design variables and the energy function of the Boltzmann distribution are continuous. Note that since the population has finite size, it can only approximate a continuous Boltzmann distribution with some error. In order to tackle this issue, the parameter estimators for the mean vector and covariance matrix of a Multivariate Normal Density that approximate the Boltzmann density, are derived by minimizing the Kullback-Leibler divergence. The algorithm introduced here uses one energy function for the mean estimator and another for the covariance matrix estimator. The first function places the probability mass around the most promising regions by assigning larger weights to individuals with higher fitness. However, the second function orients the covariance matrix along improving directions by assigning larger weights to individuals with lower fitness. Our proposal combines the conveniences of linear weights with a simple annealing schedule to regulate the exploration and exploitation of the search process. The resulting algorithm is named the Boltzmann Estimation of Multivariate Normal Algorithm (BEMNA). By applying the developed formulae the BEMNA is capable of adapting the structure of a density model to the promisory search directions. BEMNA is tested with a benchmark of 16 functions and contrasted with the AMaLGaM algorithm, a state of the art EDA. Statistical tests of the experimental data show the competitiveness of the proposed algorithm.

This paper introduces an Estimation of Distribution Algorithm (EDA), in which the parameters of the search distribution are updated by the natural gradient technique. The parameter updating is guided via the Kullback-Leibler divergence between the multivariate Normal and the Boltzmann densities. This approach makes sense because it is well-known that the Boltzmann function yields a reliable model to simulate particles near to optimum locations.

In this paper we introduce a method to build a large variety of multivariate density functions based on univariate distributions and promising direction vectors. The stochastic model constructed in our proposal simulates random vector towards directions with high probability of improving the population. Also, we provide two algorithms to use this ideas in the global optimization problem. The first one is a Hybrid Estimation of Distribution Algorithm and the second one is the Adaptive Basis of Evolution Strategy. Both algorithms are tested and show a good performance in a set of benchmark problems, even outperforming popular competitive algorithms. In the best of our knowledge, the central idea described here is not in previous literature about global optimization.