Different Approaches to Proof Systems

The classical approach to proof complexity perceives proof systems as deterministic, uniform, surjective, polynomial-time computable functions that map strings to (propositional) tautologies. This approach has been intensively studied since the late 70’s and a lot of progress has been made. During the last years research was started investigating alternative notions of proof systems. There are interesting results stemming from dropping the uniformity requirement, allowing oracle access, using quantum computations, or employing probabilism. These lead to different notions of proof systems for which we survey recent results in this paper

How can I encourage multi-stakeholder narrative and reflection on the use of ICT in Teacher Professional Development programmes in Rwanda?

This is an action research enquiry into how I can improve my practice to encourage multi-stakeholder narrative and reflection on the use of Information and Communication Technology (ICT) in Teacher Professional Development (TPD) programmes in Rwanda. I examine the complexity of the ICT-TPD landscape in the Africa Region. I describe two action research cycles in which I attempt to encourage reflection on ICT in professional development in Rwanda. In each cycle I explore the potential of an Activity Theory lens for probing the issues and examining the perspectives of the stakeholder community of teachers, teacher educators, curriculum developers and researchers affiliated to national ICT in TPD programmes and initiatives. I integrate a “Most Significant Change” narrative technique to engage participants in telling stories of significant change in their practice with technology integration. Through the rigour of the action research living theory approach I come to a number of conclusions about my own values and how I actually live my values in practice as I engage with partners in discourse and reflection for mutual learning on the issues of ICT integration in Teacher Professional Development

Wadge Degrees of ω\omega-Languages of Petri Nets

We prove that $\omega$-languages of (non-deterministic) Petri nets and $\omega$-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of $\omega$-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of $\omega$-languages of (non-deterministic) Turing machines which also form the class of effective analytic sets. In particular, for each non-null recursive ordinal $\alpha < \omega\_1^{{\rm CK}}$ there exist some ${\bf \Sigma}^0\_\alpha$-complete and some ${\bf \Pi}^0\_\alpha$-complete $\omega$-languages of Petri nets, and the supremum of the set of Borel ranks of $\omega$-languages of Petri nets is the ordinal $\gamma\_2^1$, which is strictly greater than the first non-recursive ordinal $\omega\_1^{{\rm CK}}$. We also prove that there are some ${\bf \Sigma}\_1^1$-complete, hence non-Borel, $\omega$-languages of Petri nets, and that it is consistent with ZFC that there exist some $\omega$-languages of Petri nets which are neither Borel nor ${\bf \Sigma}\_1^1$-complete. This answers the question of the topological complexity of $\omega$-languages of (non-deterministic) Petri nets which was left open in [DFR14,FS14].Comment: arXiv admin note: text overlap with arXiv:0712.1359, arXiv:0804.326

Computer simulation of shear flows of granular material

The purpose of this paper is to present results from computer simulations of Couette flows of granular materials and to examine the detailed rheological behavior inherent in these simulations. Comparison is made with the experimental results of Bagnold (1954) and Savage and Sayed (1980, 1982) as well as with the various theoretical constitutive models

Open-Source Telemedicine Platform for Wireless Medical Video Communication

An m-health system for real-time wireless communication of medical video based on open-source software is presented. The objective is to deliver a low-cost telemedicine platform which will allow for reliable remote diagnosis m-health applications such as emergency incidents, mass population screening, and medical education purposes. The performance of the proposed system is demonstrated using five atherosclerotic plaque ultrasound videos. The videos are encoded at the clinically acquired resolution, in addition to lower, QCIF, and CIF resolutions, at different bitrates, and four different encoding structures. Commercially available wireless local area network (WLAN) and 3.5G high-speed packet access (HSPA) wireless channels are used to validate the developed platform. Objective video quality assessment is based on PSNR ratings, following calibration using the variable frame delay (VFD) algorithm that removes temporal mismatch between original and received videos. Clinical evaluation is based on atherosclerotic plaque ultrasound video assessment protocol. Experimental results show that adequate diagnostic quality wireless medical video communications are realized using the designed telemedicine platform. HSPA cellular networks provide for ultrasound video transmission at the acquired resolution, while VFD algorithm utilization bridges objective and subjective ratings

Logics of Finite Hankel Rank

We discuss the Feferman-Vaught Theorem in the setting of abstract model theory for finite structures. We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the Feferman-Vaught Theorem. The largest logic known to satisfy a Feferman-Vaught Theorem for product-like operations is CFOL, first order logic with modular counting quantifiers. For sum-like operations it is CMSOL, the corresponding monadic second order logic. We discuss whether there are maximal logics satisfying Feferman-Vaught Theorems for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th birthday. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23534-9_1