A greedy algorithm for dropping digits (Functional Pearl)

Consider the puzzle: given a number, remove $k$ digits such that the resulting number is as large as possible. Various techniques were employed to derive a linear-time solution to the puzzle: predicate logic was used to justify the structure of a greedy algorithm, a dependently-typed proof assistant was used to give a constructive proof of the greedy condition, and equational reasoning was used to calculate the greedy step as well as the final, linear-time optimisation

Longest segment of balanced parentheses -- an exercise in program inversion in a segment problem (Functional Pearl)

Given a string of parentheses, the task is to find the longest consecutive segment that is balanced, in linear time. We find this problem interesting because it involves a combination of techniques: the usual approach for solving segment problems, and a theorem for constructing the inverse of a function -- through which we derive an instance of shift-reduce parsing

Programming from Galois connection : principles and applications

"Technical Report No. TR-IIS-10-009"Problem statements often resort to superlatives such as in eg. “. . . the smallest such number”, “. . . the best approximation”, “. . . the longest such list” which lead to specifications made of two parts: one defining a broad class of solutions (the easy part) and the other requesting the optimal such solution (the hard part). This paper introduces a binary relational combinator which mirrors this linguistic structure and exploits its potential for calculating programs by optimization. This applies in particular to specifications written in the form of Galois connections, in which one of the adjoints delivers the optimal solution being sought. The framework encompasses re-factoring of results previously developed by Bird and de Moor for greedy and dynamic programming, in a way which makes them less technically involved and therefore easier to understand and play with

Programming from Galois connections

Problem statements often resort to superlatives such as in eg. “. . . the smallest such number”, “. . . the best approximation”, “. . . the longest such list” which lead to specifications made of two parts: one defining a broad class of solutions (the easy part) and the other requesting the optimal such solution (the hard part). This paper introduces a binary relational combinator which mirrors this linguistic structure and exploits its potential for calculating programs by optimization. This applies in particular to specifications written in the form of Galois connections, in which one of the adjoints delivers the optimal solution being sought. The framework encompasses re-factoring of results previously developed by Bird and de Moor for greedy and dynamic programming, in a way which makes them less technically involved and therefore easier to understand and play with.Mondrian Project funded by the Portuguese NSF under contract PTDC/EIA-CCO/108302/200

Duck (Anas platyrhynchos) linkage mapping by AFLP fingerprinting

Amplified fragment length polymorphism (AFLP) with multicolored fluorescent molecular markers was used to analyze duck (Anas platyrhynchos) genomic DNA and to construct the first AFLP genetic linkage map. These markers were developed and genotyped in 766 F2 individuals from six families from a cross between two different selected duck lines, brown Tsaiya and Pekin. Two hundred and ninety-six polymorphic bands (64% of all bands) were detected using 18 pairs of fluorescent TaqI/EcoRI primer combinations. Each primer set produced a range of 7 to 29 fragments in the reactions, and generated on average 16.4 polymorphic bands. The AFLP linkage map included 260 co-dominant markers distributed in 32 linkage groups. Twenty-one co-dominant markers were not linked with any other marker. Each linkage group contained three to 63 molecular markers and their size ranged between 19.0 cM and 171.9 cM. This AFLP linkage map provides important information for establishing a duck chromosome map, for mapping quantitative trait loci (QTL mapping) and for breeding applications

What are we measuring? A critique of range of motion methods currently in use for Dupuytren's disease and recommendations for practice

Background: Range of motion is the most frequently reported measure used in practice to evaluate outcomes. A goniometer is the most reliable tool to assess range of motion yet, the lack of consistency in reporting prevents comparison between studies. The aim of this study is to identify how range of motion is currently assessed and reported in Dupuytren’s disease literature. Following analysis recommendations for practice will be made to enable consistency in future studies for comparability. This paper highlights the variation in range of motion reporting in Dupuytren’s disease. Methods: A Participants, Intervention, Comparison, Outcomes and Study design format was used for the search strategy and search terms. Surgery, needle fasciotomy or collagenase injection for primary or recurrent Dupuytren’s disease in adults were included if outcomes were monitored using range of motion to record change. A literature search was performed in May 2013 using subject heading and free-text terms to also capture electronic publications ahead of print. In total 638 publications were identified and following screening 90 articles met the inclusion criteria. Data was extracted and entered onto a spreadsheet for analysis. A thematic analysis was carried out to establish any duplication, resulting in the final range of motion measures identified. Results: Range of motion measurement lacked clarity, with goniometry reportedly used in only 43 of the 90 studies, 16 stated the use of a range of motion protocol. A total of 24 different descriptors were identified describing range of motion in the 90 studies. While some studies reported active range of motion, others reported passive or were unclear. Eight of the 24 categories were identified through thematic analysis as possibly describing the same measure, ‘lack of joint extension’ and accounted for the most frequently used. Conclusions: Published studies lacked clarity in reporting range of motion, preventing data comparison and meta-analysis. Percentage change lacks context and without access to raw data, does not allow direct comparison of baseline characteristics. A clear description of what is being measured within each study was required. It is recommended that range of motion measuring and reporting for Dupuytren’s disease requires consistency to address issues that fall into 3 main categories:- Definition of terms Protocol statement Outcome reportin

Biomechanical analysis of the lumbar spine on facet joint force and intradiscal pressure - a finite element study

<p>Abstract</p> <p>Background</p> <p>Finite element analysis results will show significant differences if the model used is performed under various material properties, geometries, loading modes or other conditions. This study adopted an FE model, taking into account the possible asymmetry inherently existing in the spine with respect to the sagittal plane, with a more geometrically realistic outline to analyze and compare the biomechanical behaviour of the lumbar spine with regard to the facet force and intradiscal pressure, which are associated with low back pain symptoms and other spinal disorders. Dealing carefully with the contact surfaces of the facet joints at various levels of the lumbar spine can potentially help us further ascertain physiological behaviour concerning the frictional effects of facet joints under separate loadings or the responses to the compressive loads in the discs.</p> <p>Methods</p> <p>A lumbar spine model was constructed from processes including smoothing the bony outline of each scan image, stacking the boundary lines into a smooth surface model, and subsequent further processing in order to conform with the purpose of effective finite element analysis performance. For simplicity, most spinal components were modelled as isotropic and linear materials with the exception of spinal ligaments (bilinear). The contact behaviour of the facet joints and changes of the intradiscal pressure with different postures were analyzed.</p> <p>Results</p> <p>The results revealed that asymmetric responses of the facet joint forces exist in various postures and that such effect is amplified with larger loadings. In axial rotation, the facet joint forces were relatively larger in the contralateral facet joints than in the ipsilateral ones at the same level. Although the effect of the preloads on facet joint forces was not apparent, intradiscal pressure did increase with preload, and its magnitude increased more markedly in flexion than in extension and axial rotation.</p> <p>Conclusions</p> <p>Disc pressures showed a significant increase with preload and changed more noticeably in flexion than in extension or in axial rotation. Compared with the applied preloads, the postures played a more important role, especially in axial rotation; the facet joint forces were increased in the contralateral facet joints as compared to the ipsilateral ones at the same level of the lumbar spine.</p