One-Minute Derivation of the Conjugate Gradient Algorithm

One of the great triumphs in the history of numerical methods was the discovery of the Conjugate Gradient (CG) algorithm. It could solve a symmetric positive-definite system of linear equations of dimension N in exactly N steps. As many practical problems at that time belonged to this category, CG algorithm became rapidly popular. It remains popular even today due to its immense computational power. But despite its amazing computational ability, mathematics of this algorithm is not easy to learn. Lengthy derivations, redundant notations, and over-emphasis on formal presentation make it much difficult for a beginner to master this algorithm. This paper aims to serve as a starting point for such readers. It provides a curt, easy-to-follow but minimalist derivation of the algorithm by keeping the sufficient steps only, maintaining a uniform notation, and focusing entirely on the ease of reader

One-Minute Derivation of the Conjugate Gradient Algorithm

One of the great triumphs in the history of numerical methods was the discovery of the Conjugate Gradient (CG) algorithm. It could solve a symmetric positive-definite system of linear equations of dimension N in exactly N steps. As many practical problems at that time belonged to this category, CG algorithm became rapidly popular. It remains popular even today due to its immense computational power. But despite its amazing computational ability, mathematics of this algorithm is not easy to learn. Lengthy derivations, redundant notations, and over-emphasis on formal presentation make it much difficult for a beginner to master this algorithm. This paper aims to serve as a starting point for such readers. It provides a curt, easy-to-follow but minimalist derivation of the algorithm by keeping the sufficient steps only, maintaining a uniform notation, and focusing entirely on the ease of reader

Use of whole genome sequencing of commensal Escherichia coli in pigs for antimicrobial resistance surveillance, United Kingdom, 2018

BackgroundSurveillance of commensal Escherichia coli, a possible reservoir of antimicrobial resistance (AMR) genes, is important as they pose a risk to human and animal health. Most surveillance activities rely on phenotypic characterisation, but whole genome sequencing (WGS) presents an alternative.AimIn this retrospective study, we tested 515 E. coli isolated from pigs to evaluate the use of WGS to predict resistance phenotype.MethodsMinimum inhibitory concentration (MIC) was determined for nine antimicrobials of clinical and veterinary importance. Deviation from wild-type, fully-susceptible MIC was assessed using European Committee on Antimicrobial Susceptibility Testing (EUCAST) epidemiological cut-off (ECOFF) values. Presence of AMR genes and mutations were determined using APHA SeqFinder. Statistical two-by-two table analysis and Cohen's kappa (k) test were applied to assess genotype and phenotype concordance.ResultsOverall, correlation of WGS with susceptibility to the nine antimicrobials was 98.9% for test specificity, and 97.5% for the positive predictive value of a test. The overall kappa score (k = 0.914) indicated AMR gene presence was highly predictive of reduced susceptibility and showed excellent correlation with MIC. However, there was variation for each antimicrobial; five showed excellent correlation; four very good and one moderate. Suggested ECOFF adjustments increased concordance between genotypic data and kappa values for four antimicrobials.ConclusionWGS is a powerful tool for accurately predicting AMR that can be used for national surveillance purposes. Additionally, it can detect resistance genes from a wider panel of antimicrobials whose phenotypes are currently not monitored but may be of importance in the future

Investigations of different strategies for high frequency regeneration of Dendrobium malones ‘Victory’

Regeneration of orchid, Dendrobium malones “Victory”, has been established by direct differentiation and through callus formation. With direct thin leaf section differentiation method, the number of protocorm like bodies (PLBs) formed from Thin Section (TS) explants obtainedfrom a single leaf was 10 times more than that from a single whole leaf, in a short time period. This therefore suggested that the proliferation potential is distributed all along the seedling leaves and morphogenically competent cells were not limited in the basal ends or the tips of the leaves in TS of orchid leaf cultures. Full MS media supplemented with auxins/cytokinins either in single orin combination along with peptone, yeast extract, casein hydrolysate (each at 100 mg/l), banana powder (40 g/l), 15% coconut water and 2% sucrose have shown excellent results for high frequency regeneration in orchid cultures. In many higher plants, regenerating leaves responded by developing proliferative loci in some “Predetermined Regenerative” cells in the dermal layers by tissue culture methods

Can Tobacco consumption explain the association between SEP and chronic periodontitis in adults living in a deprived area of the UK? A secondary analysis of the ELOHI study data.

Aim: To assess whether there are social inequalities on periodontitis at the population level in a deprived area of the United Kingdom (UK) and further elucidate the relationship between socio-economic position, plaque accumulation, tobacco smoking, and chronic periodontitis in a representative sample of adults living in a multicultural and socially deprived area. Methods: The present sub study used the cross-sectional data previously collected in the East London Oral Health Inequality (ELOHI) study, conducted in the outer northeast boroughs of London, UK. A stratified two-staged sampling was performed which consisted of a sample of 2149 adults (16-65 years of age). Participants underwent an oral examination and answered a supervised questionnaire in their own homes. Data regarding information on the explanatory variables: socio-economic position (SEP), oral health behaviour and indicators were obtained from the ELOHI study. The main outcome variable for the present sub study was chronic periodontitis (presence of at least one site of a tooth with a pocket depth (PD) ≥4mm). Statistical analysis included conceptual hierarchical modelling and mediation analysis. The level of statistical significance was set at 0.05. Results: The prevalence of periodontitis in this area of East London was very high, 80.5% among males and 82% among females although these differences were not statistically significant. Hierarchical conceptual modelling analysis demonstrated that those in the manual/routine occupations category were 2.21 (95% CI 1.64-2.989) more likely to have chronic periodontitis than those in the professional category. The difference between those in the intermediate and the professional and managerial occupations category were not statistically significant after adjusting for demographic and behavioural variables. The results of mediation analysis, using the four steps proposed by Baron and Kenny demonstrated that the association between socio-economic position and periodontitis was partially mediated through smoking. Conclusion: A social gradient in periodontal diseases in part mediated by tobacco consumption may exist even in areas where there are highly socially deprived communities was identified. SEP as measured by NS-SEC was found to be associated with the chronic periodontitis experience (PD ≥ 4mm) with individuals placed higher in the NS-SEC ranking demonstrating a lesser risk of disease as compared to a lower NS-SEC ranking

Antimicrobial resistance characteristics and fitness of Gram-negative fecal bacteria from volunteers treated with minocycline or amoxicillin.

A yearlong study was performed to examine the effect of antibiotic administration on the bacterial gut flora. Gram-negative facultative anaerobic bacteria were recovered from the feces of healthy adult volunteers administered amoxicillin, minocycline or placebo, and changes determined in antimicrobial resistance (AMR) gene carriage. Seventy percent of the 1039 facultative anaerobic isolates recovered were identified by MALDI-TOF as Escherichia coli. A microarray used to determine virulence and resistance gene carriage demonstrated that AMR genes were widespread in all administration groups, with the most common resistance genes being bla TEM, dfr, strB, tet(A), and tet(B). Following amoxicillin administration, an increase in the proportion of amoxicillin resistant E. coli and a three-fold increase in the levels of bla TEM gene carriage was observed, an effect not observed in the other two treatment groups. Detection of virulence genes, including stx1A, indicated not all E. coli were innocuous commensals. Approximately 150 E. coli collected from 6 participants were selected for pulse field gel electrophoresis (PFGE), and a subset used for characterisation of plasmids and Phenotypic Microarrays (PM). PFGE indicated some E. coli clones had persisted in volunteers for up to 1 year, while others were transient. Although there were no unique characteristics associated with plasmids from persistent or transient isolates, PM assays showed transient isolates had greater adaptability to a range of antiseptic biocides and tetracycline; characteristics which were lost in some, but not all persistent isolates. This study indicates healthy individuals carry bacteria harboring resistance to a variety of antibiotics and biocides in their intestinal tract. Antibiotic administration can have a temporary effect of selecting bacteria, showing co-resistance to multiple antibiotics, some of which can persist within the gut for up to 1 year

The hopes of West African refugees during resettlement in northern Sweden: a 6-year prospective qualitative study of pathways and agency thoughts

<p>Abstract</p> <p>Background</p> <p>Little is known about how positive phenomena can support resettlement of refugees in a new country. The aim of this study was to examine the hopeful thinking in a group of West African quota refugees at arrival and after 6 years in Sweden and compare these thoughts to the views of resettlement support professionals.</p> <p>Method</p> <p>The primary study population comprised 56 adult refugees and 13 resettlement professionals. Qualitative data were collected from the refugees by questionnaires on arrival and 6 years later. Data were collected from the resettlement professionals by interview about 3 years after arrival of the refugees. Snyder's cognitive model of hope was used to inform the comparative data analyses.</p> <p>Results</p> <p>Hopes regarding education were in focus for the refugees shortly after arrival, but thoughts on family reunion were central later in the resettlement process. During the later stages of the resettlement process, the unresponsiveness of the support organization to the family reunion problem became as issue for the refugees. The professionals reported a complex mix of "silent agency thoughts" underlying the local resettlement process as a contributing reason for this unresponsiveness.</p> <p>Conclusion</p> <p>Hopes regarding education and family reunion were central in the resettlement of West African refugees in Sweden. These thoughts were not systematically followed up by the support organization; possibly the resources for refugees were not fully released. More studies are needed to further investigate the motivational factors underpinning host community support of refugees' hopes and plans.</p