Jónathan Heras

GelJ – a tool for analyzing DNA fingerprint gel images

BackgroundDNA fingerprinting is a technique for comparing DNA patterns that has applications in a wide variety of contexts. Several commercial and freely-available tools can be used to analyze DNA fingerprint gel images; however, commercial tools are expensive and usually difficult to use; and, free tools support the basic functionality for DNA fingerprint analysis, but lack some instrumental features to obtain accurate results.ResultsIn this paper, we present GelJ, a feather-weight, user-friendly, platform-independent, open-source and free tool for analyzing DNA fingerprint gel images. Some of the outstanding features of GelJ are mechanisms for accurate lane- and band-detection, several options for computing migration models, a number of band- and curve-based similarity methods, different techniques for generating dendrograms, comparison of banding patterns from different experiments, and database support.ConclusionsGelJ is an easy to use tool for analyzing DNA fingerprint gel images. It combines the best characteristics of both free and commercial tools: GelJ is light and simple to use (as free programs), but it also includes the necessary features to obtain precise results (as commercial programs). In addition, GelJ incorporates new functionality that is not supported by any other tool.

Proof-Pattern Recognition and Lemma Discovery in ACL2

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.

Machine Learning in Proof General: Interfacing Interfaces

We present ML4PG - a machine learning extension for Proof General. It allows users to gather proof statistics related to shapes of goals, sequences of applied tactics, and proof tree structures from the libraries of interactive higher-order proofs written in Coq and SSReflect. The gathered data is clustered using the state-of-the-art machine learning algorithms available in MATLAB and Weka. ML4PG provides automated interfacing between Proof General and MATLAB/Weka. The results of clustering are used by ML4PG to provide proof hints in the process of interactive proof development.

Towards a certified computation of homology groups for digital images

In this paper we report on a project to obtain a verified computation of homology groups of digital images. The methodology is based on programming and executing inside the Coq proof assistant. Though more research is needed to integrate and make efficient more processing tools, we present some examples partially computed in Coq from real biomedical images.

Computing persistent homology within Coq/SSReflect

Persistent homology is one of the most active branches of computational algebraic topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this article, we report on the formal development of certified programs to compute persistent Betti numbers, an instrumental tool of persistent homology, using the Coq proof assistant together with the SSReflect extension. To this aim it has been necessary to formalize the underlying mathematical theory of these algorithms. This is another example showing that interactive theorem provers have reached a point where they are mature enough to tackle the formalization of nontrivial mathematical theories.

fKenzo: A user interface for computations in Algebraic Topology

a b s t r a c t fKenzo (= f riendly Kenzo) is a graphical user interface providing a user-friendly front-end for the Kenzo system, a Common Lisp pro- gram devoted to Algebraic Topology. The fKenzo system provides the user interface itself, an XML intermediary generator-translator and, finally the Kenzo kernel. We describe in this paper the main points of fKenzo, and we explain also the advantages and limita- tions of fKenzo with respect to Kenzo itself. The text is separated into two parts, trying to cover both the user and the developer perspectives.

Recycling Proof Patterns in Coq: Case Studies

Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the re-use of libraries by non-experts or across domains is a challenge. In this paper, we provide detailed case studies and evaluate the machine-learning tool ML4PG built to interactively data-mine the electronic libraries of proofs, and to provide user guidance on the basis of proof patterns found in the existing libraries.

Incidence simplicial matrices formalized in Coq/SSReflect

Simplicial complexes are at the heart of Computational Algebraic Topology, since they give a concrete, combinatorial description of otherwise rather abstract objects which makes many important topological computations possible. The whole theory has many applications such as coding theory, robotics or digital image analysis. In this paper we present a formalization in the Coq theorem prover of simplicial complexes and their incidence matrices as well as the main theorem that gives meaning to the definition of homology groups and is a first step towards their computation.

ML4PG in computer algebra verification

ML4PG is a machine-learning extension that provides statistical proof hints during the process of Coq/SSReflect proof development. In this paper, we use ML4PG to find proof patterns in the CoqEAL library - a library that was devised to verify the correctness of Computer Algebra algorithms. In particular, we use ML4PG to help us in the formalisation of an efficient algorithm to compute the inverse of triangular matrices.

Verifying an algorithm computing discrete vector fields for digital imaging

In this paper, we present a formalization of an algorithm to construct admissible discrete vector fields in the Coq theorem prover taking advantage of the SSReflect library. Discrete vector fields are a tool which has been welcomed in the homological analysis of digital images since it provides a procedure to reduce the amount of information but preserving the homological properties. In particular, thanks to discrete vector fields, we are able to compute, inside Coq, homological properties of biomedical images which otherwise are out of the reach of this system.