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Two meromorphic functions $ f $ and $ g $ are said to share a value $ s\in\mathbb{C}\cup\{\infty\} $ $ CM $ $ (IM) $ provided that $ f(z)-s $ and $ g(z)-s $ have the same set of zeros counting multiplicities (ignoring multiplicities). We…
We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…
We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any…
With the development of web technology, multi-modal or multi-view data has surged as a major stream for big data, where each modal/view encodes individual property of data objects. Often, different modalities are complementary to each…
Temporal knowledge graph completion aims to infer the missing facts in temporal knowledge graphs. Current approaches usually embed factual knowledge into continuous vector space and apply geometric operations to learn potential patterns in…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to…
The creation of social ties is largely determined by the entangled effects of people's similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making…
Deep functional maps have recently emerged as a successful paradigm for non-rigid 3D shape correspondence tasks. An essential step in this pipeline consists in learning feature functions that are used as constraints to solve for a…
We prove the following two results 1. For a proper holomorphic function $ f : X \to D$ of a complex manifold $X$ on a disc such that $\{df = 0 \} \subset f^{-1}(0)$, we construct, in a functorial way, for each integer $p$, a geometric…
Model merging aims to cheaply combine individual task-specific models into a single multitask model. In this work, we view past merging methods as leveraging different notions of a ''task parameter subspace'' in which models are matched…
A certain signed adjacency matrix of the hypercube, which Hao Huang used last year to resolve the sensitivity conjecture, is closely related to the unique, 4-cycle free, 2-fold cover of the hypercube. We develop a framework in which this…
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
The mainstream approach to the development of ontologies is merging ontologies encoding different information, where one of the major difficulties is that the heterogeneity motivates the ontology merging but also limits high-quality merging…
An invertible polynomial is a quasihomogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search…
This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a…
Model merging provides a way of cheaply combining individual models to produce a model that inherits each individual's capabilities. While some merging methods can approach the performance of multitask training, they are often heuristically…
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric…
Recently, the forward-backward and Douglas-Rachford envelope functions were proposed in the literature. The stationary points of these envelope functions have a close relationship with the solutions of the possibly nonsmooth optimization…
Considering the variability of amplitude and phase patterns in electrocardiogram (ECG) signals due to cardiac activity and individual differences, existing entropy-based studies have not fully utilized these two patterns and lack…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…