Proper Mergings of Stars and Chains are Counted by Sums of Antidiagonals in Certain Convolution Arrays -- The Details

A proper merging of two disjoint quasi-ordered sets $P$ and $Q$ is a quasi-order on the union of $P$ and $Q$ such that the restriction to $P$ or $Q$ yields the original quasi-order again and such that no elements of $P$ and $Q$ are identified. In this article, we determine the number of proper mergings in the case where $P$ is a star (i.e. an antichain with a smallest element adjoined), and $Q$ is a chain. We show that the lattice of proper mergings of an $m$-antichain and an $n$-chain, previously investigated by the author, is a quotient lattice of the lattice of proper mergings of an $m$-star and an $n$-chain, and we determine the number of proper mergings of an $m$-star and an $n$-chain by counting the number of congruence classes and by determining their cardinalities. Additionally, we compute the number of Galois connections between certain modified Boolean lattices and chains.Comment: 27 pages, 7 figures, 1 table. Jonathan Farley has solved Problem 4.18; added Section 4.4 to describe his solutio

Podoconiosis in East and West Gojam Zones, Northern Ethiopia

Background: Podoconiosis is a neglected tropical disease (NTD) that is prevalent in red clay soil-covered highlands of tropical Africa, Central and South America, and northern India. It is estimated that up to one million cases exist in Ethiopia. This study aimed to estimate the prevalence of podoconiosis in East and West Gojam Zones of Amhara Region in northern Ethiopia. Methodology/Principal Findings: A cross-sectional household survey was conducted in Debre Eliyas and Dembecha woredas (districts) in East and West Gojam Zones, respectively. The survey covered all 17,553 households in 20 kebeles (administrative subunits) randomly selected from the two woredas. A detailed structured interview was conducted on 1,704 cases of podoconiosis identified in the survey. Results: The prevalence of podoconiosis in the population aged 15 years and above was found to be 3.3% (95% CI, 3.2% to 3.6%). 87% of cases were in the economically active age group (15–64 years). On average, patients sought treatment five years after the start of the leg swelling. Most subjects had second (42.7%) or third (36.1%) clinical stage disease, 97.9% had mossy lesions, and 53% had open wounds. On average, patients had five episodes of acute adenolymphangitis (ALA) per year and spent a total of 90 days per year with ALA. The median age of first use of shoes and socks were 22 and 23 years, respectively. More men than women owned more than one pair of shoes (61.1% vs. 50.5%; x2 = 11.6 p = 0.001). At the time of interview, 23.6% of the respondents were barefoot, of whom about two-thirds were women. Conclusions: This study showed high prevalence of podoconiosis and associated morbidities such as ALA, mossy lesions and open wounds in northern Ethiopia. Predominance of cases at early clinical stage of podoconiosis indicates the potential for reversing the swelling and calls for disease prevention interventions

Towards a generalisation of formal concept analysis for data mining purposes

In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for K-Formal Concept Analysis, where K is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed

Further thoughts on precision

Background: There has been much discussion amongst automated software defect prediction researchers regarding use of the precision and false positive rate classifier performance metrics. Aim: To demonstrate and explain why failing to report precision when using data with highly imbalanced class distributions may provide an overly optimistic view of classifier performance. Method: Well documented examples of how dependent class distribution affects the suitability of performance measures. Conclusions: When using data where the minority class represents less than around 5 to 10 percent of data points in total, failing to report precision may be a critical mistake. Furthermore, deriving the precision values omitted from studies can reveal valuable insight into true classifier performancePeer reviewedFinal Accepted Versio

Effectiveness of a simple lymphoedema treatment regimen in podoconiosis management in southern Ethiopia: one year follow-up

Background: Podoconiosis is a non-filarial elephantiasis caused by long-term barefoot exposure to volcanic soils in endemic areas. Irritant silicate particles penetrate the skin, causing a progressive, debilitating lymphoedema of the lower leg, often starting in the second decade of life. A simple patient-led treatment approach appropriate for resource poor settings has been developed, comprising (1) education on aetiology and prevention of podoconiosis, (2) foot hygiene (daily washing with soap, water and an antiseptic), (3) the regular use of emollient, (4) elevation of the limb at night, and (5) emphasis on the consistent use of shoes and socks. Methodology/Principal Findings: We did a 12-month, non-comparative, longitudinal evaluation of 33 patients newly presenting to one clinic site of a non-government organization (the Mossy Foot Treatment & Prevention Association, MFTPA) in southern Ethiopia. Outcome measures used for the monitoring of disease progress were (1) the clinical staging system for podoconiosis, and (2) the Amharic Dermatology Life Quality Index (DLQI), both of which have been recently validated for use in this setting. Digital photographs were also taken at each visit. Twenty-seven patients completed follow up. Characteristics of patients completing follow-up were not significantly different to those not. Mean clinical stage and lower leg circumference decreased significantly (mean difference -0.67 (95% CI -0.38 to -0.96) and -2.00 (95% CI -1.26 to -2.74), respectively, p<0.001 for both changes). Mean DLQI diminished from 21 (out of a maximum of 30) to 6 (p<0.001). There was a non-significant change in proportion of patients with mossy lesions (p = 0.375). Conclusions/Significance: This simple, resource-appropriate regimen has a considerable impact both on clinical progression and self-reported quality of life of affected individuals. The regimen appears ideal for scaling up to other endemic regions in Ethiopia and internationally. We recommend that further research in the area include analysis of cost-effectiveness of the regimen

Content and changes in Provitamin A carotenoids during ripening of fruit from four popular Musa cultivars consumed in Eastern Democratic Republic of Congo

Poster presented at Nutrition Congress Africa 2012. Transforming the Nutrition Landscape in Africa. Bloemfontein (South Africa), 1-4 Oct 201

Infrared spectrum and stability of a π-type hydrogen-bonded complex between the OH and C2H2 reactants

A hydrogen-bonded complex between the hydroxyl radical and acetylene has been stabilized in the reactant channel well leading to the addition reaction and characterized by infrared action spectroscopy in the OH overtone region. Analysis of the rotational band structure associated with the a-type transition observed at 6885.53(1) cm−1 (origin) reveals a T-shaped structure with a 3.327(5) Å separation between the centers of mass of the monomer constituents. The OH (v = 1) product states populated following vibrational predissociation show that dissociation proceeds by two mechanisms: intramolecular vibrational to rotational energy transfer and intermolecular vibrational energy transfer. The highest observed OH product state establishes an upper limit of 956 cm−1 for the stability of the π-type hydrogen-bonded complex. The experimental results are in good accord with the intermolecular distance and well depth at the T-shaped minimum energy configuration obtained from complementary ab initio calculations, which were carried out at the restricted coupled cluster singles, doubles, noniterative triples level of theory with extrapolation to the complete basis set limit