The Lost Melody Phenomenon

A typical phenomenon for machine models of transfinite computations is the existence of so-called lost melodies, i.e. real numbers $x$ such that the characteristic function of the set $\{x\}$ is computable while $x$ itself is not (a real having the first property is called recognizable). This was first observed by J. D. Hamkins and A. Lewis for infinite time Turing machine, then demonstrated by P. Koepke and the author for $ITRM$s. We prove that, for unresetting infinite time register machines introduced by P. Koepke, recognizability equals computability, i.e. the lost melody phenomenon does not occur. Then, we give an overview on our results on the behaviour of recognizable reals for $ITRM$s. We show that there are no lost melodies for ordinal Turing machines or ordinal register machines without parameters and that this is, under the assumption that $0^{\sharp}$ exists, independent of $ZFC$. Then, we introduce the notions of resetting and unresetting $\alpha$-register machines and give some information on the question for which of these machines there are lost melodies

Readers reading practices of EFL Yemeni students: recommendations for the 21st century

This paper investigates the reading practices of forty-five second year EFL Yemeni undergraduate students using the Four Resources Model of multiliteracy practices. The Four Resources Model of multiliteracy practices organizes reading practices into four key practices: code breaking, text participating, text uses and text analysing levels. Quantitative and qualitative methods, designed based on the Four Resources Model constructs, were used to collect data from a sample of students studying English as a Foreign Language at a university in Yemen. Quantitative data was collected through a questionnaire, while qualitative data was gathered using semi-structured interviews guided by the research objectives. The findings reveal that Yemeni students were medium users of the code breaker and text user practices whereas the meaning making and text analysis practices were reported to be used in low usage. On the whole, these early findings suggest that the reading practices and reading abilities of the Yemeni students are still limited even at the tertiary level and have not developed fully with regard to reading in English. This paper reports in detail, the use of the Four Resources Model as a tool to determine reading efficacy while examining the aforementioned findings. Discussion is put forward on the implications for teaching of reading and its approaches in a Yemeni context, especially in view of the students‟ reading needs at the tertiary level in Yemen

A constructive commutative quantum Lovasz Local Lemma, and beyond

The recently proven Quantum Lovasz Local Lemma generalises the well-known Lovasz Local Lemma. It states that, if a collection of subspace constraints are "weakly dependent", there necessarily exists a state satisfying all constraints. It implies e.g. that certain instances of the kQSAT quantum satisfiability problem are necessarily satisfiable, or that many-body systems with "not too many" interactions are always frustration-free. However, the QLLL only asserts existence; it says nothing about how to find the state. Inspired by Moser's breakthrough classical results, we present a constructive version of the QLLL in the setting of commuting constraints, proving that a simple quantum algorithm converges efficiently to the required state. In fact, we provide two different proofs, one using a novel quantum coupling argument, the other a more explicit combinatorial analysis. Both proofs are independent of the QLLL. So these results also provide independent, constructive proofs of the commutative QLLL itself, but strengthen it significantly by giving an efficient algorithm for finding the state whose existence is asserted by the QLLL. We give an application of the constructive commutative QLLL to convergence of CP maps. We also extend these results to the non-commutative setting. However, our proof of the general constructive QLLL relies on a conjecture which we are only able to prove in special cases.Comment: 43 pages, 2 conjectures, no figures; unresolved gap in the proof; see arXiv:1311.6474 or arXiv:1310.7766 for correct proofs of the symmetric cas

A configurable decoder for pin-limited applications

Pin limitation is the restriction imposed on an IC chip by the unavailability of a sufficient number of I/O pins. This impacts the design and performance of the chip, as the amount of information that can be passed through the boundary of the chip becomes limited. One area that would benefit from a reduction of the effect of pin limitation is reconfigurable architectures. In this work, we consider reconfigurable devices called Field Programmable Gate Arrays (FPGAs). Due to pin limitation, current FPGAs use a form of 1-hot decoder to select elements (one frame at a time) during partial reconfiguration. This results in a slow and coarse selection of elements for reconfiguration. We propose a module that performs a focused selection of only those elements that require reconfiguration. This reduces reconfiguration overheads and enables the speeds needed for dynamic reconfiguration. The problem is that of selecting subsets of an n-element set in a fast, focused and inexpensive manner. This thesis proposes such a configurable decoder that bridges the gap between the inexpensive, but inflexible, fixed 1-hot decoder, and the expensive, but flexible, pure LUT-based decoder. Our configurable decoder uses a LUT with a narrow output and a low cost in tandem with a special fixed decoder called a mapping unit that expands the output of the LUT to a desired n-bit output. We demonstrate several implementations of the mapping unit, each with different capabilities and trade-offs. A key result of this work is that for any gate cost G=O(n logk n) (where k is a constant), if a pure LUT-based solution produces λ independent subsets, then our method produces Ω(λ log n / log log n) independent subsets for the same cost. Our decoder also produces many more dependent subsets (that depend on the choice of the Ω( λ log n / log log n) independent subsets). We provide simulation results for the configurable decoder and predict future trends from the simulation data; these confirm the theoretical advantages of the proposed decoder. We illustrate the implementation of important subset classes on our configurable decoder and make key observations on a generalized variant