Pattern Reduction in Paper Cutting

A large part of the paper industry involves supplying customers with reels of specified width in specifed quantities. These 'customer reels' must be cut from a set of wider 'jumbo reels', in as economical a way as possible. The first priority is to minimize the waste, i.e. to satisfy the customer demands using as few jumbo reels as possible. This is an example of the one-dimensional cutting stock problem, which has an extensive literature. Greycon have developed cutting stock algorithms which they include in their software packages. Greycon's initial presentation to the Study Group posed several questions, which are listed below, along with (partial) answers arising from the work described in this report. (1) Given a minimum-waste solution, what is the minimum number of patterns required? It is shown in Section 2 that even when all the patterns appearing in minimum-waste solutions are known, determining the minimum number of patterns may be hard. It seems unlikely that one can guarantee to find the minimum number of patterns for large classes of realistic problems with only a few seconds on a PC available. (2) Given an n → n-1 algorithm, will it find an optimal solution to the minimum- pattern problem? There are problems for which n → n - 1 reductions are not possible although a more dramatic reduction is. (3) Is there an efficient n → n-1 algorithm? In light of Question 2, Question 3 should perhaps be rephrased as 'Is there an efficient algorithm to reduce n patterns?' However, if an algorithm guaranteed to find some reduction whenever one existed then it could be applied iteratively to minimize the number of patterns, and we have seen this cannot be done easily. (4) Are there efficient 5 → 4 and 4 → 3 algorithms? (5) Is it worthwhile seeking alternatives to greedy heuristics? In response to Questions 4 and 5, we point to the algorithm described in the report, or variants of it. Such approaches seem capable of catching many higher reductions. (6) Is there a way to find solutions with the smallest possible number of single patterns? The Study Group did not investigate methods tailored specifically to this task, but the algorithm proposed here seems to do reasonably well. It will not increase the number of singleton patterns under any circumstances, and when the number of singletons is high there will be many possible moves that tend to eliminate them. (7) Can a solution be found which reduces the number of knife changes? The algorithm will help to reduce the number of necessary knife changes because it works by bringing patterns closer together, even if this does not proceed fully to a pattern reduction. If two patterns are equal across some of the customer widths, the knives for these reels need not be changed when moving from one to the other

Phylogenetic relationships of African Caecilians (Amphibia: Gymnophiona): insights from mitochondrial rRNA gene sequences

Africa (excluding the Seychelles) has a diverse caecilian fauna, including the endemic family Scolecomorphidae and six endemic genera of the more cosmopolitan Caeciliidae. Previous molecular phylogenetic studies have not included any caecilians from the African mainland. Partial 12S and 16S mitochondrial gene sequences were obtained for two species of the endemic African Scolecomorphidae and five species and four genera of African Caeciliids, aligned against previously reported sequences for 16 caecilian species, and analysed using parsimony, maximum likelihood, Bayesian and distance methods. Results are in agreement with traditional taxonomy in providing support for the monophyly of the African Caeciliid genera Boulengerula and Schistometopum and for the Scolecomorphidae. They disagree in indicating that the Caeciliidae is paraphyletic with respect to the Scolecomorphidae. Although more data from morphology and/or molecules will be required to resolve details of the interrelationships of the African caecilian genera, the data provide strong support for at least two origins of caecilians in which the eye is reduced and covered with bone, and do not support the hypotheses that the caecilian assemblages of Africa, and of East and of West Africa are monophyletic

Evolution of the eyes of vipers with and without infrared-sensing pit organs

We examined lens and brille transmittance, photoreceptors, visual pigments, and visual opsin gene sequences of viperid snakes with and without infrared-sensing pit organs. Ocular media transmittance is high in both groups. Contrary to previous reports, small as well as large single cones occur in pit vipers. Non-pit vipers differ from pit vipers in having a twotiered retina, but few taxa have been examined for this poorly understood feature. All vipers sampled express rh1, sws1 and lws visual opsin genes. Opsin spectral tuning varies but not in accordance with the presence/absence of pit organs, and not always as predicted from gene sequences. The visual opsin genes were generally under purifying selection, with positive selection at spectral tuning amino acids in RH1 and SWS1 opsins, and at retinal pocket stabilization sites in RH1 or LWS (and without substantial differences between pit and nonpit vipers). Lack of evidence for sensory trade-off between viperid eyes (in the aspects examined) and pit organs might be explained by the high degree of neural integration of vision and infrared detection; the latter representing an elaboration of an existing sense with addition of a novel sense organ, rather than involving the evolution of a wholly novel sensory system

LGEM+^\text{+}: a first-order logic framework for automated improvement of metabolic network models through abduction

Scientific discovery in biology is difficult due to the complexity of the systems involved and the expense of obtaining high quality experimental data. Automated techniques are a promising way to make scientific discoveries at the scale and pace required to model large biological systems. A key problem for 21st century biology is to build a computational model of the eukaryotic cell. The yeast Saccharomyces cerevisiae is the best understood eukaryote, and genome-scale metabolic models (GEMs) are rich sources of background knowledge that we can use as a basis for automated inference and investigation. We present LGEM+, a system for automated abductive improvement of GEMs consisting of: a compartmentalised first-order logic framework for describing biochemical pathways (using curated GEMs as the expert knowledge source); and a two-stage hypothesis abduction procedure. We demonstrate that deductive inference on logical theories created using LGEM+, using the automated theorem prover iProver, can predict growth/no-growth of S. cerevisiae strains in minimal media. LGEM+ proposed 2094 unique candidate hypotheses for model improvement. We assess the value of the generated hypotheses using two criteria: (a) genome-wide single-gene essentiality prediction, and (b) constraint of flux-balance analysis (FBA) simulations. For (b) we developed an algorithm to integrate FBA with the logic model. We rank and filter the hypotheses using these assessments. We intend to test these hypotheses using the robot scientist Genesis, which is based around chemostat cultivation and high-throughput metabolomics.Comment: 15 pages, one figure, two tables, two algorithm

Phenotypic and genotypic monitoring of Schistosoma mansoni in Tanzanian schoolchildren five years into a preventative chemotherapy national control programme

We conducted combined in vitro PZQ efficacy testing with population genetic analyses of S. mansoni collected from children from two schools in 2010, five years after the introduction of a National Control Programme. Children at one school had received four annual PZQ treatments and the other school had received two mass treatments in total. We compared genetic differentiation, indices of genetic diversity, and estimated adult worm burden from parasites collected in 2010 with samples collected in 2005 (before the control programme began) and in 2006 (six months after the first PZQ treatment). Using 2010 larval samples, we also compared the genetic similarity of those with high and low in vitro sensitivity to PZQ

Chemotherapy versus supportive care in advanced non-small cell lung cancer: improved survival without detriment to quality of life

BACKGROUND: In 1995 a meta-analysis of randomised trials investigating the value of adding chemotherapy to primary treatment for non-small cell lung cancer (NSCLC) suggested a small survival benefit for cisplatin-based chemotherapy in each of the primary treatment settings. However, the metaanalysis included many small trials and trials with differing eligibility criteria and chemotherapy regimens. METHODS: The aim of the Big Lung Trial was to confirm the survival benefits seen in the meta-analysis and to assess quality of life and cost in the supportive care setting. A total of 725 patients were randomised to receive supportive care alone (n = 361) or supportive care plus cisplatin-based chemotherapy (n = 364). RESULTS: 65% of patients allocated chemotherapy (C) received all three cycles of treatment and a further 27% received one or two cycles. 74% of patients allocated no chemotherapy (NoC) received thoracic radiotherapy compared with 47% of the C group. Patients allocated C had a significantly better survival than those allocated NoC: HR 0.77 (95% CI 0.66 to 0.89, p = 0.0006), median survival 8.0 months for the C group v 5.7 months for the NoC group, a difference of 9 weeks. There were 19 (5%) treatment related deaths in the C group. There was no evidence that any subgroup benefited more or less fromchemotherapy. No significant differences were observed between the two groups in terms of the pre-defined primary and secondary quality of life end points, although large negative effects of chemotherapy were ruled out. The regimens used proved to be cost effective, the extra cost of chemotherapy being offset by longer survival. CONCLUSIONS: The survival benefit seen in this trial was entirely consistent with the NSCLC meta-analysis and subsequent similarly designed large trials. The information on quality of life and cost should enablepatients and their clinicians to make more informed treatment choices

LEGO: Automated Model Construction

Given any 3D body, how can it be built from LEGO bricks