Representing Scott sets in algebraic settings

We prove that for every Scott set $S$ there are $S$-saturated real closed fields and models of Presburger arithmetic

Extracting Biomolecular Interactions Using Semantic Parsing of Biomedical Text

We advance the state of the art in biomolecular interaction extraction with three contributions: (i) We show that deep, Abstract Meaning Representations (AMR) significantly improve the accuracy of a biomolecular interaction extraction system when compared to a baseline that relies solely on surface- and syntax-based features; (ii) In contrast with previous approaches that infer relations on a sentence-by-sentence basis, we expand our framework to enable consistent predictions over sets of sentences (documents); (iii) We further modify and expand a graph kernel learning framework to enable concurrent exploitation of automatically induced AMR (semantic) and dependency structure (syntactic) representations. Our experiments show that our approach yields interaction extraction systems that are more robust in environments where there is a significant mismatch between training and test conditions.Comment: Appearing in Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI-16

Zariski Closures and Subgroup Separability

The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a free or surface group.Comment: Final version. To appear in Selecta Mat

Variations on Algebra: monadicity and generalisations of equational theories

Dedicated to Rod Burstal

A Few Considerations on Structural and Logical Composition in Specification Theories

Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms. In this short abstract, we collect results of our work in progress on describing and systematizing the algebraic assumptions in specification theories.Comment: In Proceedings FIT 2010, arXiv:1101.426

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

Numerical algebraic geometry for model selection and its application to the life sciences

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.Comment: References added, additional clarification