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We first present our view of detection and correction of syntactic errors. We then introduce a new correction method, based on heuristic criteria used to decide which correction should be preferred. Weighting of these criteria leads to a…
Statistical analysis of corpora provides an approach to quantitatively investigate natural languages. This approach has revealed that several power laws consistently emerge across different corpora and languages, suggesting universal…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
In this article we relate the construction of Ricci type symplectic connections by reduction to the construction of star product by reduction yielding rather explicit descriptions for the star product on the reduced space.
We analyze the syntactic sensitivity of Text-to-Speech (TTS) systems using methods inspired by psycholinguistic research. Specifically, we focus on the generation of intonational phrase boundaries, which can often be predicted by…
A sharp tension exists about the nature of human language between two opposite parties: those who believe that statistical surface distributions, in particular using measures like surprisal, provide a better understanding of language…
We hereby present a solution to a semantic textual similarity (STS) problem in which it is necessary to match two sentences containing, as the only distinguishing factor, highly specific information (such as names, addresses, identification…
This article presents a neural language architecture of sentence structure in the brain, in which sentences are temporal connection paths that interconnect neural structures underlying their words. Words remain 'in-situ', hence they are…
We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for…
Performance analysis has always been an afterthought during the application development process, focusing on application correctness first. The learning curve of the existing static and dynamic analysis tools are steep, which requires…
Let M be ternary, homogeneous and simple. We prove that if M is finitely constrained, then it is supersimple with finite SU-rank and dependence is $k$-trivial for some $k < \omega$ and for finite sets of real elements. Now suppose that, in…
Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is…
The brain's connectome and the vascular system are examples of physical networks whose tangible nature influences their structure, layout, and ultimately their function. The material resources required to build and maintain these networks…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
Recall that Janson showed that if the edges of the complete graph $K_n$ are assigned exponentially distributed independent random weights, then the expected length of a shortest path between a fixed pair of vertices is asymptotically equal…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
Word embeddings are a popular way to improve downstream performances in contemporary language modeling. However, the underlying geometric structure of the embedding space is not well understood. We present a series of explorations using…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
We introduce a new structure for a set of points in the plane and an angle $\alpha$, which is similar in flavor to a bounded-degree MST. We name this structure $\alpha$-MST. Let $P$ be a set of points in the plane and let $0 < \alpha \le…
Syntactic features play an essential role in identifying relationship in a sentence. Previous neural network models often suffer from irrelevant information introduced when subjects and objects are in a long distance. In this paper, we…