Related papers: Representation Theorems Obtained by Miningacross W…
We propose an explanatory and computational theory of transformative discoveries in science. The theory is derived from a recurring theme found in a diverse range of scientific change, scientific discovery, and knowledge diffusion theories…
The notions of a {\em 2-precontact space}\/ and a {\em 2-contact space}\/ are introduced. Using them, new representation theorems for precontact and contact algebras are proved. It is shown that there are bijective correspondences between…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
In this paper, we prove the existence of fundamental relations between information theory and estimation theory for network-coded flows. When the network is represented by a directed graph G=(V, E) and under the assumption of uncorrelated…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
Presented is a novel methodology for determining representational structure, which builds upon the existing Spotlight Resonance method. This new tool is used to gain insight into how discrete representations can emerge and organise in…
Identifying latent representations or causal structures is important for good generalization and downstream task performance. However, both fields have been developed rather independently. We observe that several methods in both…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
We propose a joint event and temporal relation extraction model with shared representation learning and structured prediction. The proposed method has two advantages over existing work. First, it improves event representation by allowing…
Network representation learning has exploded recently. However, existing studies usually reconstruct networks as sequences or matrices, which may cause information bias or sparsity problem during model training. Inspired by a cognitive…
Understanding how reliable information emerges in interconnected populations is a challenge in social science, network theory and data analysis. Many existing approaches model treat truth as an external reference or a property of individual…
Many recent methods for unsupervised or self-supervised representation learning train feature extractors by maximizing an estimate of the mutual information (MI) between different views of the data. This comes with several immediate…
Representing and navigating hierarchy is a fundamental primitive of reasoning. Large language models have demonstrated proficiency in a wide variety of tasks requiring hierarchical reasoning, but there exists limited analysis on how the…