Algorithmic embeddings

Stability of intersections of graphs in the plane and the van Kampen obstruction

A map φ : K → R2 of a graph K is approximable by embeddings, if for each ε > 0 there is an ε-close to φ embedding f : K → R2. Analogous notions were studied in computer science under the names of cluster planarity and weak simplicity. In this survey we present criteria for approximability by embeddings (P. Minc, 1997, M. Skopenkov, 2003) and their algorithmic corollaries. We introduce the van K...

Design of a parallel interconnect based on communication pattern considerations

An interconnect's versatility appears through its ability to support a variety of algorithmic patterns based on the physical or logical embeddings within its topology that match the desired algorithmic patterns. However, most such embeddings are available on a discrete basis, though a particular algorithm may require a variety of embeddings during diierent phases of its operation. To provide fo...

Algorithmic Applications of Low-Distortion Geometric Embeddings

Algorithmic and asymptotic properties of groups

This is a survey of the recent work in algorithmic and asymptotic properties of groups. I discuss Dehn functions of groups, complexity of the word problem, Higman embeddings, and constructions of finitely presented groups with extreme properties (monsters). Mathematics Subject Classification (2000). Primary 20F65; Secondary 20F10.

Learning Low-Dimensional Representations of Medical Concepts

We show how to learn low-dimensional representations (embeddings) of a wide range of concepts in medicine, including diseases (e.g., ICD9 codes), medications, procedures, and laboratory tests. We expect that these embeddings will be useful across medical informatics for tasks such as cohort selection and patient summarization. These embeddings are learned using a technique called neural languag...

Multiclass Learning by Probabilistic Embeddings

We describe a new algorithmic framework for learning multiclass categorization problems. In this framework a multiclass predictor is composed of a pair of embeddings that map both instances and labels into a common space. In this space each instance is assigned the label it is nearest to. We outline and analyze an algorithm, termed Bunching, for learning the pair of embeddings from labeled data...