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Wasserstein distances form a family of metrics on spaces of probability measures that have recently seen many applications. However, statistical analysis in these spaces is complex due to the nonlinearity of Wasserstein spaces. One potential solution to this problem is Linear Optimal Transport (LOT). This method allows one to find a Euclidean embedding, called {\it LOT embedding}, of measures in some Wasserstein spaces, but some information is lost in this embedding. So, to understand whether statistical analysis relying on LOT embeddings can make valid inferences about original data, it is helpful to quantify how well these embeddings describe that data. To answer this question, we present a decomposition of the {\it Fr\'echet variance} of a set of measures in the 2-Wasserstein space, which allows one to compute the percentage of variance explained by LOT embeddings of those measures. We then extend this decomposition to the Fused Gromov-Wasserstein setting. We also present several experiments that explore the relationship between the dimension of the LOT embedding, the percentage of variance explained by the embedding, and the classification accuracy of machine learning classifiers built on the embedded data. We use the MNIST handwritten digits dataset, IMDB-50000 dataset, and Diffusion Tensor MRI images for these experiments. Our results illustrate the effectiveness of low dimensional LOT embeddings in terms of the percentage of variance explained and the classification accuracy of models built on the embedded data. 

Language models are typically evaluated on their success at predicting the distribution of specific words in specific contexts. Yet linguistic knowledge also encodes relationships between contexts, allowing inferences between word distributions. We investigate the degree to which pre-trained transformer-based large language models (LLMs) represent such relationships, focusing on the domain of argument structure. We find that LLMs perform well in generalizing the distribution of a novel noun argument between related contexts that were seen during pre-training (e.g., the active object and passive subject of the verb spray), succeeding by making use of the semantically organized structure of the embedding space for word embeddings. However, LLMs fail at generalizations between related contexts that have not been observed during pre-training, but which instantiate more abstract, but well-attested structural generalizations (e.g., between the active object and passive subject of an arbitrary verb). Instead, in this case, LLMs show a bias to generalize based on linear order. This finding points to a limitation with current models and points to a reason for which their training is data-intensive.1

 

Climate change has led to a variety of disasters that have caused damage to infrastructure and the economy with societal impacts to human living. Understanding people’s emotions and stressors during disaster times will enable preparation strategies for mitigating further consequences. In this paper, we mine emotions and stressors encountered by people and shared on Twitter during Hurricane Harvey in 2017 as a showcase. In this work, we acquired a dataset of tweets from Twitter on Hurricane Harvey from 20 August 2017 to 30 August 2017. The dataset consists of around 400,000 tweets and is available on Kaggle. Next, a BERT-based model is employed to predict emotions associated with tweets posted by users. Then, natural language processing (NLP) techniques are utilized on negative-emotion tweets to explore the trends and prevalence of the topics discussed during the disaster event. Using Latent Dirichlet Allocation (LDA) topic modeling, we identified themes, enabling us to manually extract stressors termed as climate-change-related stressors. Results show that 20 climate-change-related stressors were extracted and that emotions peaked during the deadliest phase of the disaster. This indicates that tracking emotions may be a useful approach for studying environmentally determined well-being outcomes in light of understanding climate change impacts.

 

This paper presents a study on the characterization of density as a function of temperature for phase change materials (PCMs). More specifically, in this study we analyze organic alkane PCMs, often called paraffins. PCMs are materials that have the ability to absorb a substantial amount of heat during phase transition from solid to liquid, and therefore prove to be useful in thermal energy storage. The density of paraffin wax PCMs is largely dependent on temperature, and during the phase change process, the density decreases dramatically as the PCM transitions from solid to liquid. Consequently, the PCM experiences dramatic volumetric expansion during this transition. Besides the thermal energy storage uses of PCMs, this volumetric expansion that they exhibit is also used in thermal actuator applications, often referred to as wax motors. While density of PCMs does affect their thermal and mechanical performance, the property is not well-characterized within the literature. In this paper, we examine ten paraffin wax PCMs with varying meltingtemperatures and characterize their densities as a function of temperature. This characterization was done usinga piston and cylinder dilatometer test setup within a temperature-controlled thermal chamber that we designedand validated to the well-characterized density properties of water. The density and temperature relationships werefurther analyzed using piecewise linear regression analysis to develop mathematical models of density as it relates totemperature, which will be useful to those wishing to analyze designs in which PCMs are used, such as in PCM-filled heat sinks.