Inverse Unfold Problem and Its Heuristic Solving

Unfold/fold transformations have been widely studied in various programming paradigms and are used in program transformations, theorem proving, and so on. This paper, by using an example, show that restoring an one-step unfolding is not easy, i.e., a challenging task, since some rules used by unfolding may be lost. We formalize this problem by regarding one-step program transformation as a relation. Next we discuss some issues on a specific framework, called pure-constructor systems, which constitute a subclass of conditional term rewriting systems. We show that the inverse of T preserves rewrite relations if T preserves rewrite relations and the signature. We propose a heuristic procedure to solve the problem, and show its successful examples. We improve the procedure, and show examples for which the improvement takes effect

Elaboration in Dependent Type Theory

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean's elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved

Convolutional Dictionary Learning through Tensor Factorization

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of the observed higher order input moments. However, in many domains, additional invariances such as shift invariances exist, enforced via models such as convolutional dictionary learning. In this paper, we develop novel tensor decomposition algorithms for parameter estimation of convolutional models. Our algorithm is based on the popular alternating least squares method, but with efficient projections onto the space of stacked circulant matrices. Our method is embarrassingly parallel and consists of simple operations such as fast Fourier transforms and matrix multiplications. Our algorithm converges to the dictionary much faster and more accurately compared to the alternating minimization over filters and activation maps

RNAiFold2T: Constraint Programming design of thermo-IRES switches

Motivation: RNA thermometers (RNATs) are cis-regulatory ele- ments that change secondary structure upon temperature shift. Often involved in the regulation of heat shock, cold shock and virulence genes, RNATs constitute an interesting potential resource in synthetic biology, where engineered RNATs could prove to be useful tools in biosensors and conditional gene regulation. Results: Solving the 2-temperature inverse folding problem is critical for RNAT engineering. Here we introduce RNAiFold2T, the first Constraint Programming (CP) and Large Neighborhood Search (LNS) algorithms to solve this problem. Benchmarking tests of RNAiFold2T against existent programs (adaptive walk and genetic algorithm) inverse folding show that our software generates two orders of magnitude more solutions, thus allow- ing ample exploration of the space of solutions. Subsequently, solutions can be prioritized by computing various measures, including probability of target structure in the ensemble, melting temperature, etc. Using this strategy, we rationally designed two thermosensor internal ribosome entry site (thermo-IRES) elements, whose normalized cap-independent transla- tion efficiency is approximately 50% greater at 42?C than 30?C, when tested in reticulocyte lysates. Translation efficiency is lower than that of the wild-type IRES element, which on the other hand is fully resistant to temperature shift-up. This appears to be the first purely computational design of functional RNA thermoswitches, and certainly the first purely computational design of functional thermo-IRES elements. Availability: RNAiFold2T is publicly available as as part of the new re- lease RNAiFold3.0 at https://github.com/clotelab/RNAiFold and http: //bioinformatics.bc.edu/clotelab/RNAiFold, which latter has a web server as well. The software is written in C++ and uses OR-Tools CP search engine.Comment: 24 pages, 5 figures, Intelligent Systems for Molecular Biology (ISMB 2016), to appear in journal Bioinformatics 201

Recognising the Clothing Categories from Free-Configuration Using Gaussian-Process-Based Interactive Perception

In this paper, we propose a Gaussian Process- based interactive perception approach for recognising highly- wrinkled clothes. We have integrated this recognition method within a clothes sorting pipeline for the pre-washing stage of an autonomous laundering process. Our approach differs from reported clothing manipulation approaches by allowing the robot to update its perception confidence via numerous interactions with the garments. The classifiers predominantly reported in clothing perception (e.g. SVM, Random Forest) studies do not provide true classification probabilities, due to their inherent structure. In contrast, probabilistic classifiers (of which the Gaussian Process is a popular example) are able to provide predictive probabilities. In our approach, we employ a multi-class Gaussian Process classification using the Laplace approximation for posterior inference and optimising hyper-parameters via marginal likelihood maximisation. Our experimental results show that our approach is able to recognise unknown garments from highly-occluded and wrinkled con- figurations and demonstrates a substantial improvement over non-interactive perception approaches