A unified framework for generalized multicategories

Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case, generalized multicategories are defined as the "lax algebras" or "Kleisli monoids" relative to a "monad" on a bicategory. However, the meanings of these words differ from author to author, as do the specific bicategories considered. We propose a unified framework: by working with monads on double categories and related structures (rather than bicategories), one can define generalized multicategories in a way that unifies all previous examples, while at the same time simplifying and clarifying much of the theory.Comment: 76 pages; final version, to appear in TA

Noise diffraction patterns eliminated in coherent optical systems

Lens rotation technique of noise diffraction pattern elimination spreads diffracted energy, normally concentrated over small area of image, over much larger annular area. Technique advantages include simplified lens selecting process, reduced clean room requirements, and low cost equipment requirements

Elimination of coherent noise in a coherent light imaging system

Optical imaging systems using coherent light introduce objectionable noise into the output image plane. Dust and bubbles on and in lenses cause most of the noise in the output image. This noise usually appears as bull's-eye diffraction patterns in the image. By rotating the lens about the optical axis these diffraction patterns can be essentially eliminated. The technique does not destroy the spatial coherence of the light and permits spatial filtering of the input plane

Tensor products of subspace lattices and rank one density

We show that, if $M$ is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, $L$ is a commutative subspace lattice and $P$ is the lattice of all projections on a separable infinite dimensional Hilbert space, then the lattice $L\otimes M\otimes P$ is reflexive. If $M$ is moreover an atomic Boolean subspace lattice while $L$ is any subspace lattice, we provide a concrete lattice theoretic description of $L\otimes M$ in terms of projection valued functions defined on the set of atoms of $M$. As a consequence, we show that the Lattice Tensor Product Formula holds for \Alg M and any other reflexive operator algebra and give several further corollaries of these results.Comment: 15 page

Heterologous vaccination of BNT162b2 in Ad26. COV2.S-vaccinated healthcare workers elicits long-term humoral immune response

Background. To date, there are no immunological data for the SARS-CoV-2 heterologous vaccination schedule in the South African (SA) population.Objectives. To assess and compare the immunogenicity and reactogenicity of the Jansen Ad26.COV2.S vaccine with the Pfizer/BioNTech- BNT162b2 booster following prime Ad26.COV2.S in 65 SA healthcare workers.Methods. In a prospective, quantitative, cross-sectional trial on individuals >18 years of age vaccinated with a single Ad26.COV2.S dose or single Ad26.COV2.S and a BNT162b2 single-dose/both doses booster, participants filled in a questionnaire on their demographics, type of vaccination, breakthrough infection/s (BTI/s), vaccine reactogenicity, prior SARS-CoV-2 infection and dates of vaccination. Qualitative analysis for presence/absence of anti-S (spike) immunoglobulin G (IgG) was performed using the Euroimmun anti-IgG enzyme-linked immunoassay kit, and anti-S IgG titres were quantitatively assessed using the Abbott IgG Quant II kit.Results. Between 28 October 2021 and 30 November 2021, 65 individuals were enrolled and assigned as either prime Ad26.COV2.S (n=18) or Ad26.COV2.S with a BNT162b2 supplement (n=47) at Charlotte Maxeke Johannesburg Academic Hospital, SA (mean age 45 years (95% confidence interval (CI) 29.5 - 58), 42 women (64.6%) and 23 men (35.4%)). The median IgG titre for the primed Ad26.COV2.S group was 4 272.55 (95% CI 68.40 - 10 351.40) and that for the BNT162b2 supplement group was 7 360.80 (95% CI 4 207.40 - 15 372.60). In the univariate model, the BNT162b2 supplement group showed a significant 1.99 times higher antibody titre factor (95% CI 0.045 - 5.553; p<0.005) than the Ad26.COV2.S group. In both univariate and multivariate models, age, time since prime vaccination, BTI and prior infection failed to show any statistically significant association (p>0.05) with antibody titres in both groups. However, sex (–55.381 (95% CI –76.984 - –13.498; p=0.018) in a multivariate model was found to have a statistically significant association with anti-S IgG titres observed in both groups. Participants who received their first dose of BNT162b2 9 - 10 months after their prime Ad26.COV2.S (n=44) had a higher degree of antibody response than those who received it earlier. Reactogenicity was observed to be manageable, with mild/moderate adverse effects in the study population.Conclusion. A BNT162b2 supplement given in single or two doses as booster in individuals primed with Ad26.COV2.S induced immunological response, with acceptable and manageable reactogenicity. This study provides novel evidence of the highest degree of antibody response in individuals who received a BNT162b2 first dose 9 - 10 months after prime Ad26.COV2.S, implying that a longer time gap between the two vaccines stimulates higher antibody response than a shorter gap, and that this antibody response can persist for as long as 6 months after the last BNT162b2 dose

Entry in the ADHD drugs market: Welfare impact of generics and me-toos

Recent decades have seen a growth in treatments for attention deficit hyperactivity disorder (ADHD) including many branded and generic drugs. In the early 2000's, new drug entry dramatically altered market shares. We estimate a demand system for ADHD drugs and assess the welfare impact of new drugs. We find that entry induced large welfare gains by reducing prices of substitute drugs, and by providing alternative delivery mechanisms for existing molecules. Our results suggest that the success of follow-on patented drugs may come from unanticipated innovations like delivery mechanisms, a factor ignored by proposals to retard new follow-on drug approvals

Complex paths for regular-to-chaotic tunneling rates

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical approach based on complex paths for the prediction of dynamical tunneling rates from regular tori to the chaotic region. This approach is demonstrated for the standard map giving excellent agreement with numerically determined tunneling rates.Comment: 5 pages, 4 figure

‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal

13C NMR visibility of rabbit muscle glycogen in vivo

The integrated 13C NMR intensity of the glycogen C1 resonance was measured in skeletal muscle (biceps femoris region) of nine rabbits under in vivo conditions. Concurrent chemical determinations of glycogen content showed that the in vivo signal was 1.02 ± 0.06 the intensity of analytical samples, where glycogen is known to be ~100% visible