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Tverberg's theorem says that a set with sufficiently many points in $\mathbb{R}^d$ can always be partitioned into $m$ parts so that the $(m-1)$-simplex is the (nerve) intersection pattern of the convex hulls of the parts. In…
In this paper, we discuss a method for identifying a seed word that would best represent a class of named entities in a graphical representation of words and their similarities. Word networks, or word graphs, are representations of…
This paper connects a series of papers dealing with taxonomic word embeddings. It begins by noting that there are different types of semantic relatedness and that different lexical representations encode different forms of relatedness. A…
We present a deterministic algorithm for Russian inflection. This algorithm is implemented in a publicly available web-service www.passare.ru which provides functions for inflection of single words, word matching and synthesis of…
The relationship between words in a sentence often tells us more about the underlying semantic content of a document than its actual words, individually. In this work, we propose two novel algorithms, called Flexible Lexical Chain II and…
The phenomenon of human language is widely studied from various points of view. It is interesting not only for social scientists, antropologists or philosophers, but also for those, interesting in the network dynamics. In several recent…
Word embedding has become ubiquitous and is widely used in various natural language processing (NLP) tasks, such as web retrieval, web semantic analysis, and machine translation, and so on. Unfortunately, training the word embedding in a…
Much like sentences are composed of words, words themselves are composed of smaller units. For example, the English word questionably can be analyzed as question+able+ly. However, this structural decomposition of the word does not directly…
Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some…
Machine learning about language can be improved by supplying it with specific knowledge and sources of external information. We present here a new version of the linked open data resource ConceptNet that is particularly well suited to be…
We develop an approach for unsupervised learning of associations between co-occurring perceptual events using a large graph. We applied this approach to successfully solve the image captcha of China's railroad system. The approach is based…
In this paper we propose a graph-community detection approach to identify cross-document relationships at the topic segment level. Given a set of related documents, we automatically find these relationships by clustering segments with…
We prove that the invariably generating graph of a finite group can have an arbitrarily large number of connected components with at least two vertices.
Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…
The paper presents a linguistic and computational model aiming at making the morphological structure of the lexicon emerge from the formal and semantic regularities of the words it contains. The model is word-based. The proposed…
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…
Information on any given topic is often scattered across the web. Previously this scatter has been characterized through the distribution of a set of facts (i.e. pieces of information) across web pages, showing that typically a few pages…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Large language models (LLMs) have recently shown strong potential in modeling relational structures. However, existing approaches remain fundamentally graph-centric: they focus on processing pairwise graph structures into tokens that LLMs…
The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…