A Graphical Language for Proof Strategies

Complex automated proof strategies are often difficult to extract, visualise, modify, and debug. Traditional tactic languages, often based on stack-based goal propagation, make it easy to write proofs that obscure the flow of goals between tactics and are fragile to minor changes in input, proof structure or changes to tactics themselves. Here, we address this by introducing a graphical language called PSGraph for writing proof strategies. Strategies are constructed visually by "wiring together" collections of tactics and evaluated by propagating goal nodes through the diagram via graph rewriting. Tactic nodes can have many output wires, and use a filtering procedure based on goal-types (predicates describing the features of a goal) to decide where best to send newly-generated sub-goals. In addition to making the flow of goal information explicit, the graphical language can fulfil the role of many tacticals using visual idioms like branching, merging, and feedback loops. We argue that this language enables development of more robust proof strategies and provide several examples, along with a prototype implementation in Isabelle

Proviola: A Tool for Proof Re-animation

To improve on existing models of interaction with a proof assistant (PA), in particular for storage and replay of proofs, we in- troduce three related concepts, those of: a proof movie, consisting of frames which record both user input and the corresponding PA response; a camera, which films a user's interactive session with a PA as a movie; and a proviola, which replays a movie frame-by-frame to a third party. In this paper we describe the movie data structure and we discuss a proto- type implementation of the camera and proviola based on the ProofWeb system. ProofWeb uncouples the interaction with a PA via a web- interface (the client) from the actual PA that resides on the server. Our camera films a movie by "listening" to the ProofWeb communication. The first reason for developing movies is to uncouple the reviewing of a formal proof from the PA used to develop it: the movie concept enables users to discuss small code fragments without the need to install the PA or to load a whole library into it. Other advantages include the possibility to develop a separate com- mentary track to discuss or explain the PA interaction. We assert that a combined camera+proviola provides a generic layer between a client (user) and a server (PA). Finally we claim that movies are the right type of data to be stored in an encyclopedia of formalized mathematics, based on our experience in filming the Coq standard library.Comment: Accepted for the 9th International Conference on Mathematical Knowledge Management (MKM 2010), 15 page

Sharing HOL4 and HOL Light proof knowledge

New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers. Certain conjectures can be proved directly from the dependencies induced by similar proofs in the other library. Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises. Such external help can be further combined with internal advice. We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

The CrowdHEALTH project and the Hollistic Health Records: Collective Wisdom Driving Public Health Policies.

Introduction: With the expansion of available Information and Communication Technology (ICT) services, a plethora of data sources provide structured and unstructured data used to detect certain health conditions or indicators of disease. Data is spread across various settings, stored and managed in different systems. Due to the lack of technology interoperability and the large amounts of health-related data, data exploitation has not reached its full potential yet. Aim: The aim of the CrowdHEALTH approach, is to introduce a new paradigm of Holistic Health Records (HHRs) that include all health determinants defining health status by using big data management mechanisms. Methods: HHRs are transformed into HHRs clusters capturing the clinical, social and human context with the aim to benefit from the collective knowledge. The presented approach integrates big data technologies, providing Data as a Service (DaaS) to healthcare professionals and policy makers towards a "health in all policies" approach. A toolkit, on top of the DaaS, providing mechanisms for causal and risk analysis, and for the compilation of predictions is developed. Results: CrowdHEALTH platform is based on three main pillars: Data & structures, Health analytics, and Policies. Conclusions: A holistic approach for capturing all health determinants in the proposed HHRs, while creating clusters of them to exploit collective knowledge with the aim of the provision of insight for different population segments according to different factors (e.g. location, occupation, medication status, emerging risks, etc) was presented. The aforementioned approach is under evaluation through different scenarios with heterogeneous data from multiple sources

CrowdHEALTH: Holistic Health Records and Big Data Analytics for Health Policy Making and Personalized Health.

Today's rich digital information environment is characterized by the multitude of data sources providing information that has not yet reached its full potential in eHealth. The aim of the presented approach, namely CrowdHEALTH, is to introduce a new paradigm of Holistic Health Records (HHRs) that include all health determinants. HHRs are transformed into HHRs clusters capturing the clinical, social and human context of population segments and as a result collective knowledge for different factors. The proposed approach also seamlessly integrates big data technologies across the complete data path, providing of Data as a Service (DaaS) to the health ecosystem stakeholders, as well as to policy makers towards a "health in all policies" approach. Cross-domain co-creation of policies is feasible through a rich toolkit, being provided on top of the DaaS, incorporating mechanisms for causal and risk analysis, and for the compilation of predictions

Inhibition of telomerase activity by HDV ribozyme in cancers

<p>Abstract</p> <p>Background</p> <p>Telomerase plays an important role in cell proliferation and carcinogenesis and is believed to be a good target for anti-cancer drugs. Elimination of template function of telomerase RNA may repress the telomerase activity.</p> <p>Methods</p> <p>A pseudo-knotted HDV ribozyme (g.RZ57) directed against the RNA component of human telomerase (hTR) was designed and synthesized. An in vitro transcription plasmid and a eukaryotic expression plasmid of ribozyme were constructed. The eukaryotic expression plasmid was induced into heptocellular carcinoma 7402 cells, colon cancer HCT116 cells and L02 hepatocytes respectively. Then we determine the cleavage activity of ribozyme against human telomerase RNA component (hTR) both in vitro and in vivo, and detect telomerase activity continuously.</p> <p>Results</p> <p>HDV ribozyme showed a specific cleavage activity against the telomerase RNA in vitro. The maximum cleavage ratio reached about 70.4%. Transfection of HDV ribozyme into 7402 cells and colon cancer cells HCT116 led to growth arrest and the spontaneous apoptosis of cells, and the telomerase activity dropped to 10% of that before.</p> <p>Conclussion</p> <p>HDV ribozyme (g.RZ57) is an effective strategy for gene therapy.</p

Human Telomerase Reverse Transcriptase (hTERT) Q169 Is Essential for Telomerase Function In Vitro and In Vivo

BACKGROUND:Telomerase is a reverse transcriptase that maintains the telomeres of linear chromosomes and preserves genomic integrity. The core components are a catalytic protein subunit, the telomerase reverse transcriptase (TERT), and an RNA subunit, the telomerase RNA (TR). Telomerase is unique in its ability to catalyze processive DNA synthesis, which is facilitated by telomere-specific DNA-binding domains in TERT called anchor sites. A conserved glutamine residue in the TERT N-terminus is important for anchor site interactions in lower eukaryotes. The significance of this residue in higher eukaryotes, however, has not been investigated. METHODOLOGY/PRINCIPAL FINDINGS:To understand the significance of this residue in higher eukaryotes, we performed site-directed mutagenesis on human TERT (hTERT) Q169 to create neutral (Q169A), conservative (Q169N), and non-conservative (Q169D) mutant proteins. We show that these mutations severely compromise telomerase activity in vitro and in vivo. The functional defects are not due to abrogated interactions with hTR or telomeric ssDNA. However, substitution of hTERT Q169 dramatically impaired the ability of telomerase to incorporate nucleotides at the second position of the template. Furthermore, Q169 mutagenesis altered the relative strength of hTERT-telomeric ssDNA interactions, which identifies Q169 as a novel residue in hTERT required for optimal primer binding. Proteolysis experiments indicate that Q169 substitution alters the protease-sensitivity of the hTERT N-terminus, indicating that a conformational change in this region of hTERT is likely critical for catalytic function. CONCLUSIONS/SIGNIFICANCE:We provide the first detailed evidence regarding the biochemical and cellular roles of an evolutionarily-conserved Gln residue in higher eukaryotes. Collectively, our results indicate that Q169 is needed to maintain the hTERT N-terminus in a conformation that is necessary for optimal enzyme-primer interactions and nucleotide incorporation. We show that Q169 is critical for the structure and function of human telomerase, thereby identifying a novel residue in hTERT that may be amenable to therapeutic intervention

Diminished Telomeric 3′ Overhangs Are Associated with Telomere Dysfunction in Hoyeraal-Hreidarsson Syndrome

BACKGROUND:Eukaryotic chromosomes end with telomeres, which in most organisms are composed of tandem DNA repeats associated with telomeric proteins. These DNA repeats are synthesized by the enzyme telomerase, whose activity in most human tissues is tightly regulated, leading to gradual telomere shortening with cell divisions. Shortening beyond a critical length causes telomere uncapping, manifested by the activation of a DNA damage response (DDR) and consequently cell cycle arrest. Thus, telomere length limits the number of cell divisions and provides a tumor-suppressing mechanism. However, not only telomere shortening, but also damaged telomere structure, can cause telomere uncapping. Dyskeratosis Congenita (DC) and its severe form Hoyeraal-Hreidarsson Syndrome (HHS) are genetic disorders mainly characterized by telomerase deficiency, accelerated telomere shortening, impaired cell proliferation, bone marrow failure, and immunodeficiency. METHODOLOGY/PRINCIPAL FINDINGS:We studied the telomere phenotypes in a family affected with HHS, in which the genes implicated in other cases of DC and HHS have been excluded, and telomerase expression and activity appears to be normal. Telomeres in blood leukocytes derived from the patients were severely short, but in primary fibroblasts they were normal in length. Nevertheless, a significant fraction of telomeres in these fibroblasts activated DDR, an indication of their uncapped state. In addition, the telomeric 3' overhangs are diminished in blood cells and fibroblasts derived from the patients, consistent with a defect in telomere structure common to both cell types. CONCLUSIONS/SIGNIFICANCE:Altogether, these results suggest that the primary defect in these patients lies in the telomere structure, rather than length. We postulate that this defect hinders the access of telomerase to telomeres, thus causing accelerated telomere shortening in blood cells that rely on telomerase to replenish their telomeres. In addition, it activates the DDR and impairs cell proliferation, even in cells with normal telomere length such as fibroblasts. This work demonstrates a telomere length-independent pathway that contributes to a telomere dysfunction disease

A Non-Canonical Function of Zebrafish Telomerase Reverse Transcriptase Is Required for Developmental Hematopoiesis

Although it is clear that telomerase expression is crucial for the maintenance of telomere homeostasis, there is increasing evidence that the TERT protein can have physiological roles that are independent of this central function. To further examine the role of telomerase during vertebrate development, the zebrafish telomerase reverse transcriptase (zTERT) was functionally characterized. Upon zTERT knockdown, zebrafish embryos show reduced telomerase activity and are viable, but develop pancytopenia resulting from aberrant hematopoiesis. The blood cell counts in TERT-depleted zebrafish embryos are markedly decreased and hematopoietic cell differentiation is impaired, whereas other somatic lineages remain morphologically unaffected. Although both primitive and definitive hematopoiesis is disrupted by zTERT knockdown, the telomere lengths are not significantly altered throughout early development. Induced p53 deficiency, as well as overexpression of the anti-apoptotic proteins Bcl-2 and E1B-19K, significantly relieves the decreased blood cells numbers caused by zTERT knockdown, but not the impaired blood cell differentiation. Surprisingly, only the reverse transcriptase motifs of zTERT are crucial, but the telomerase RNA-binding domain of zTERT is not required, for rescuing complete hematopoiesis. This is therefore the first demonstration of a non-canonical catalytic activity of TERT, which is different from “authentic” telomerase activity, is required for during vertebrate hematopoiesis. On the other hand, zTERT deficiency induced a defect in hematopoiesis through a potent and specific effect on the gene expression of key regulators in the absence of telomere dysfunction. These results suggest that TERT non-canonically functions in hematopoietic cell differentiation and survival in vertebrates, independently of its role in telomere homeostasis. The data also provide insights into a non-canonical pathway by which TERT functions to modulate specification of hematopoietic stem/progenitor cells during vertebrate development. (276 words