A colimit decomposition for homotopy algebras in Cat

Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosicky observed a key point to be that each homotopy colimit in simplicial sets admits a decomposition into a homotopy sifted colimit of finite coproducts, and asked the author whether a similar decomposition holds in the 2-category of categories Cat. Our purpose in the present paper is to show that this is the case.Comment: Some notation changed; small amount of exposition added in intr

Student Participation in Mathematics Discourse in a Standards-based Middle Grades Classroom

The vision of K-12 standards-based mathematics reform embraces a greater emphasis on students’ ability to communicate their understandings of mathematics by utilizing adaptive reasoning (i.e., reflection, explanation, and justification of thinking) through mathematics discourse. However, recent studies suggest that many students lack the socio-cognitive capacity needed to succeed in learner-centered, discussion-intensive mathematics classrooms. A multiple case study design was used to examine the nature of participation in mathematics discourse among two low- and two high-performing sixth grade female students while solving rational number tasks in a standards-based classroom. Data collected through classroom observations, student interviews, and student work samples were analyzed via a multiple-cycle coding process that yielded several important within-case and cross-case findings. Within-case analyses revealed that (a) students’ access to participation was mediated by the degree of space they were afforded and how they attempted to utilize that space, as well as the meaning they were able to construct through providing and listening to explanations; and (b) participation was greatly influenced by peer interactional tendencies that either promoted or impeded productive contributions, as well as teacher interactions that helped to offset some of the problems related to unequal access to participation. Cross-case findings suggested that (a) students’ willingness to contribute to task discussions was related to their goal orientations as well as the degree of social risk perceived with providing incorrect solutions before their peers; and (b) differences between the kinds of peer and teacher interactions that low- and high-performers engaged in were directly related to the types of challenges they faced during discussion of these tasks. An important implication of this study’s findings is that the provision of space and meaning for students to participate equitably in rich mathematics discourse depends greatly on teacher interaction, especially in small-group instructional settings where unequal peer status often leads to unequal peer interactions. Research and practice should continue to focus on addressing ways in which students can learn how to help provide adequate space and meaning in small-group mathematics discussion contexts so that all students involved are allowed access to an optimally rich learning experience

On the 2-categories of weak distributive laws

A weak mixed distributive law (also called weak entwining structure) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generalizes a mixed distributive law due to Beck. We show that a weak mixed distributive law can be described as a compatible pair of a monad and a comonad, in 2-categories extending, respectively, the 2-category of comonads and the 2-category of monads. Based on this observation, we define a 2-category whose 0-cells are weak mixed distributive laws. In a 2-category K which admits Eilenberg-Moore constructions both for monads and comonads, and in which idempotent 2-cells split, we construct a fully faithful 2-functor from this 2-category of weak mixed distributive laws to K^{2 x 2}.Comment: 15 pages LaTeX source, final version to appear in Comm. Algebr

Accuracy of Patient-Specific Organ Dose Estimates Obtained Using an Automated Image Segmentation Algorithm

The overall goal of this work is to develop a rapid, accurate, and automated software tool to estimate patient-specific organ doses from computed tomography (CT) scans using simulations to generate dose maps combined with automated segmentation algorithms. This work quantified the accuracy of organ dose estimates obtained by an automated segmentation algorithm. We hypothesized that the autosegmentation algorithm is sufficiently accurate to provide organ dose estimates, since small errors delineating organ boundaries will have minimal effect when computing mean organ dose. A leave-one-out validation study of the automated algorithm was performed with 20 head-neck CT scans expertly segmented into nine regions. Mean organ doses of the automatically and expertly segmented regions were computed from Monte Carlo-generated dose maps and compared. The automated segmentation algorithm estimated the mean organ dose to be within 10% of the expert segmentation for regions other than the spinal canal, with the median error for each organ region below 2%. In the spinal canal region, the median error was -7%, with a maximum absolute error of 28% for the single-atlas approach and 11% for the multiatlas approach. The results demonstrate that the automated segmentation algorithm can provide accurate organ dose estimates despite some segmentation errors

Characterizing Van Kampen Squares via Descent Data

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Precautionary labelling of foods for allergen content: are we ready for a global framework?

© 2014 Allen et al.; licensee BioMed Central Ltd.Food allergy appears to be on the rise with the current mainstay of treatment centred on allergen avoidance. Mandatory allergen labelling has improved the safety of food for allergic consumers. However an additional form of voluntary labelling (termed precautionary allergen labelling) has evolved on a wide range of packaged goods, in a bid by manufacturers to minimise risk to customers, and the negative impact on business that might result from exposure to trace amounts of food allergen present during cross-contamination during production. This has resulted in near ubiquitous utilisation of a multitude of different precautionary allergen labels with subsequent confusion amongst many consumers as to their significance. The global nature of food production and manufacturing makes harmonisation of allergen labelling regulations across the world a matter of increasing importance. Addressing inconsistencies across countries with regards to labelling legislation, as well as improvement or even banning of precautionary allergy labelling are both likely to be significant steps forward in improved food safety for allergic families. This article outlines the current status of allergen labelling legislation around the world and reviews the value of current existing precautionary allergen labelling for the allergic consumer. We strongly urge for an international framework to be considered to help roadmap a solution to the weaknesses of the current systems, and discuss the role of legislation in facilitating this

Thermodynamic graph-rewriting

We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy cost function. The idea is that the generators define the qualitative dynamics, by showing which transformations are possible, while the energy patterns and cost function specify the long-term probability $\pi$ of any reachable graph. Given the generators and energy patterns, we construct a finite set of rules which (i) has the same qualitative transition system as the generators; and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which $\pi$ is the unique fixed point. The construction relies on the use of site graphs and a technique of `growth policy' for quantitative rule refinement which is of independent interest. This division of labour between the qualitative and long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the examples in S4 and S5). It also guarantees thermodynamical consistency (AKA detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications

Nets, relations and linking diagrams

In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the composition of spans over appropriate categories of relations, and study the underlying algebraic structures.Comment: 15 pages, Proceedings of 5th Conference on Algebra and Coalgebra in Computer Science (CALCO), Warsaw, Poland, 3-6 September 201

Faecal carriage of multi-drug resistant Enterobacteriaceae in hospitalized children at University Teaching Hospital Sylvanus Olympio of Lomé, Togo

Background: High prevalence of infections and associated antibiotherapy may put children at increased risk for development of multidrug-resistance (MDR), mostly to bacterial infections. The objective of this study therefore was to determine the prevalence of gastrointestinal carriage of MDR Enterobacteriaceae among hospitalized children in the Paediatric department of Sylvanus Olympio University Hospital, Lomé, Togo.Methodology: A descriptive cross-sectional study was carried out on randomly selected hospitalized children in the Paediatric wards of the hospital from November 03 to November 10, 2020, after obtaining informed consent from their parents/guardians. Rectal swabs and stool samples were collected from each participant and cultured for isolation of members of the family Enterobacteriaceae on Hektoen enteric agar containing 4 µg/L cefotaxime, which was incubated aerobically at 37oC for 24 hours. The isolates were identified using in-house biochemical tests. Antibiotic susceptibility test (AST) of each isolate to a panel of antibiotics including ertapenem and imipenem was done by the disc diffusion method and interpreted according to the European Committee on Antimicrobial Susceptibility Testing (EUCAST) clinical breakpoints version 2020 V.1.1. ESBL production was detected by the double-disc synergy test of amoxicillin and clavulanic acid, and resistance to carbapenem was inferred by resistance to ertapenem and imipenem discs in the AST. Multi-drug resistance (MDR) was defined as resistance to at least three families of antibiotics. Statistical analysis of data was carried out on Excel 2010 and EPI INFO 7.2 and p value < 0.05 was considered to be statistical significance. Results: A total of 70 hospitalized children during the study period were randomly recruited with an average age of 4 years 3 days and a range of 1 day to 18 years. The male gender was predominant (54.3%) with a M: F ratio of 1.2. Samples were culture positive in 85.7% (60/70) and a total of 72 species of Enterobacteriaceae were isolated in 93.3% (56/60) of these cultures. Escherichia coli was the most frequently isolated species(56.9%, 41/72). More than 90% (65/72) of the isolates were resistant to ampicillin, 58.3% (42/72) to third generation cephalosporins, 59.7% (43/72) to fourth generation cephalosporins, 43% (31/72) to aminoglycosides, 55.6% (40/72) were multi-drug resistant, 48.6% (35/72) were ESBL-producing strains, and 6.9% (5/72) were carbapenem resistant. Eighty-three percent (29/35) of ESBL-producing and all the carbapenem resistant isolates (5/5) were recovered from children on antibiotic therapy. The prevalence of ESBL-producing phenotypes among culture-positive children on antibiotic treatment (72.5%, 29/40) was significantly higher than among culture-positive children not on antibiotic treatment (20.0%, 4/20), indicating that antibiotic therapy was significantly associated with carriage of MDR isolates (OR=10.545, 95% CI=2.882-38.590, p=0.0002). Conclusion: The high faecal carriage rate of MDR Enterobacteriaceae, which are all ESBL-producing strains, in this study is worrying. There is urgent need to develop measures to monitor and limit the spread of these MDR organisms in children and the community in Togo

Generalised Compositional Theories and Diagrammatic Reasoning

This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G. Chirabella, R. Spekken