A Universal Machine for Biform Theory Graphs

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time. We pick up on the idea of biform theories and interpret it in the MMTt/OMDoc framework which introduced the foundations-as-theories approach, and can thus represent both logics and programming languages as theories. This yields a formal, modular framework of biform theory graphs which mixes specifications and implementations sharing the module system and typing information. We present automated knowledge management work flows that interface to existing specification/programming tools and enable an OpenMath Machine, that operationalizes biform theories, evaluating expressions by exhaustively applying the implementations of the respective operators. We evaluate the new biform framework by adding implementations to the OpenMath standard content dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final publication is available at http://link.springer.com

Automated Generation of User Guidance by Combining Computation and Deduction

Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an emerging generation of educational mathematics assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction, is the most reliable technology used to check user input. However ATP is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck then the system should be able to suggest possible next steps. The key idea of Lucas Interpretation is to compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides the next steps. User guidance is generated by combining deduction and computation: the latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas Interpretation so that open questions can adequately be addressed, and prerequisites for further work are provided.Comment: In Proceedings THedu'11, arXiv:1202.453

A static higher-order dependency pair framework

We revisit the static dependency pair method for proving termination of higher-order term rewriting and extend it in a number of ways: (1) We introduce a new rewrite formalism designed for general applicability in termination proving of higher-order rewriting, Algebraic Functional Systems with Meta-variables. (2) We provide a syntactically checkable soundness criterion to make the method applicable to a large class of rewrite systems. (3) We propose a modular dependency pair framework for this higher-order setting. (4) We introduce a fine-grained notion of formative and computable chains to render the framework more powerful. (5) We formulate several existing and new termination proving techniques in the form of processors within our framework. The framework has been implemented in the (fully automatic) higher-order termination tool WANDA

Guidelines for the use of flow cytometry and cell sorting in immunological studies (third edition)

The third edition of Flow Cytometry Guidelines provides the key aspects to consider when performing flow cytometry experiments and includes comprehensive sections describing phenotypes and functional assays of all major human and murine immune cell subsets. Notably, the Guidelines contain helpful tables highlighting phenotypes and key differences between human and murine cells. Another useful feature of this edition is the flow cytometry analysis of clinical samples with examples of flow cytometry applications in the context of autoimmune diseases, cancers as well as acute and chronic infectious diseases. Furthermore, there are sections detailing tips, tricks and pitfalls to avoid. All sections are written and peer-reviewed by leading flow cytometry experts and immunologists, making this edition an essential and state-of-the-art handbook for basic and clinical researchers

Guidelines for the use of flow cytometry and cell sorting in immunological studies (third edition)

The third edition of Flow Cytometry Guidelines provides the key aspects to consider when performing flow cytometry experiments and includes comprehensive sections describing phenotypes and functional assays of all major human and murine immune cell subsets. Notably, the Guidelines contain helpful tables highlighting phenotypes and key differences between human and murine cells. Another useful feature of this edition is the flow cytometry analysis of clinical samples with examples of flow cytometry applications in the context of autoimmune diseases, cancers as well as acute and chronic infectious diseases. Furthermore, there are sections detailing tips, tricks and pitfalls to avoid. All sections are written and peer-reviewed by leading flow cytometry experts and immunologists, making this edition an essential and state-of-the-art handbook for basic and clinical researchers

Formally Verified Computation of Enclosures of Solutions of Ordinary Differential Equations

Ordinary differential equations (ODEs) are ubiquitous when mod-eling continuous dynamics. Classical numerical methods compute ap-proximations of the solution, however without any guarantees on the quality of the approximation. Nevertheless, methods have been devel-oped that are supposed to compute enclosures of the solution. In this paper, we demonstrate that enclosures of the solution can be verified with a high level of rigor: We implement a functional algo-rithm that computes enclosures of solutions of ODEs in the interactive theorem prover Isabelle/HOL, where we formally verify (and have me-chanically checked) the safety of the enclosures against the existing theory of ODEs in Isabelle/HOL. Our algorithm works with dyadic rational numbers with statically fixed precision and is based on the well-known Euler method. We ab-stract discretization and round-off errors in the domain of affine forms

Verso l’identificazione del feromone sessuale di Contarinia sorghicola (Coquillet)

La contaminai delle spighette del sorgo, Contarinia sorghicola (Coquillett) (Diptera, Cecidomyiidae), è uno degli insetti più dannosi del sorgo nel mondo. tale studio è stato rivolto all'identificazione del feromone sessuale di C. sorghicola con lo scopo di poterlo utilizzare in un sistema di monitoraggio e controllo. Gli estratti GC-EAD degli estratti in esano di ovopositori recisi hanno rivelato la presenza di due "candidati" componenti del feromone sessuale specifico