In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Most algorithms for representation learning and link prediction in relational data have been designed for static data. However, the data they are applied to usually evolves with time, such as friend graphs in social networks or user interactions with items in recommender systems. This is also the case for knowledge bases, which contain facts such as (US, has president, B. Obama, [2009-2017]) that are valid only at certain points in time. For the problem of link prediction under temporal constraints, i.e., answering queries of the form (US, has president, ?, 2012), we propose a solution inspired by the canonical decomposition of tensors of order 4.
 We introduce new regularization schemes and present an extension of ComplEx that achieves state-of-the-art performance. Additionally, we propose a new dataset for knowledge base completion constructed from Wikidata, larger than previous benchmarks by an order of magnitude, as a new reference for evaluating temporal and non-temporal link prediction methods.
We propose new tensor decompositions and associated regularizers to obtain state of the art performances on temporal knowledge base completion.

Hierarchical label structures widely exist in many machine learning tasks, ranging from those with explicit label hierarchies such as image classification to the ones that have latent label hierarchies such as semantic segmentation. Unfortunately, state-of-the-art methods often utilize cross-entropy loss which in-explicitly assumes the independence among class labels. Motivated by the fact that class members from the same hierarchy need to be similar to each others, we design a new training diagram called Hierarchical Complement Objective Training (HCOT). In HCOT, in addition to maximizing the probability of the ground truth class, we also neutralize the probabilities of rest of the classes in a hierarchical fashion, making the model take advantage of the label hierarchy explicitly. We conduct our method on both image classification and semantic segmentation. Results show that HCOT outperforms state-of-the-art models in CIFAR100, Imagenet, and PASCAL-context. Our experiments also demonstrate that HCOT can be applied on tasks with latent label hierarchies, which is a common characteristic in many machine learning tasks.
We propose Hierarchical Complement Objective Training, a novel training paradigm to effectively leverage category hierarchy in the labeling space on both image classification and semantic segmentation.

Key equatorial climate phenomena such as QBO and ENSO have never been adequately explained as deterministic processes. This in spite of recent research showing growing evidence of predictable behavior. This study applies the fundamental Laplace tidal equations with simplifying assumptions along the equator — i.e. no Coriolis force and a small angle approximation. The solutions to the partial differential equations are highly non-linear related to Navier-Stokes and only search approaches can be used to fit to the data.

Analytical Formulation of Equatorial Standing Wave Phenomena: Application to QBO and ENSO