Reverse Derivative Categories

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.Comment: Extended version of paper to appear at CSL 202

Quantifying the performance of a hybrid anion exchanger/adsorbent for phosphorus removal using mass spectrometry coupled with batch kinetic trials

Increasingly stricter phosphorus discharge limits represent a significant challenge for the wastewater industry. Hybrid media comprising anionic exchange resins with dispersions of hydrated ferric oxide nanoparticles have been shown to selectively remove phosphorus from wastewaters, and display greater capacity and operational capability than both conventional treatment techniques and other ferric-based adsorbent materials. Spectrographic analyses of the internal surfaces of a hybrid media during kinetic experiments show that the adsorption of phosphorus is very rapid, utilising 54% of the total capacity of the media within the first 15 min and 95% within the first 60 min. These analyses demonstrate the importance of intraparticle diffusion on the overall rate in relation to the penetration of phosphorus. Operational capacity is a function of the target effluent phosphorus concentration and for 0.1 mg P L−1, this is , which is 8–13% of the exhaustive capacity. The adsorbed phosphorus can be selectively recovered, offering a potential route to recycle this important nutrient. The main implication of the work is that the ferric nanoparticle adsorbent can provide a highly effective means of achieving a final effluent phosphorus concentration of 0.1 mg P L−1, even when treating sewage effluent at 5 mg P L−1

Uncertainties in Theoretical HeI Emissivities: HII Regions, Primordial Abundance, and Cosmological Recombination

A number of recent works in astronomy and cosmology have relied upon theoretical He I emissivities, but we know of no effort to quantify the uncertainties in the atomic data. We analyze and assign uncertainties to all relevant atomic data, perform Monte Carlo analyses, and report standard deviations in the line emissivities. We consider two sets of errors, which we call "optimistic" and "pessimistic." We also consider three different conditions, corresponding to prototypical Galactic and extragalactic H II regions and the epoch of cosmological recombination. In the extragalactic H II case, the errors we obtain are comparable to or larger than the errors in some recent $Y_p$ calculations, including those derived from CMB observations. We demonstrate a systematic effect on primordial abundance calculations; this effect cannot be reduced by observing a large number of objects. In the cosmological recombination case, the errors are comparable to many of the effects considered in recent calculations.Comment: 5 pages, 3 figures, accepted to MNRAS Letter

A sampling strategy for genome sequencing the British terrestrial arthropod fauna

The Darwin Tree of Life (DToL) project aims to sequence and assemble high-quality genomes from all eukaryote species in Britain and Ireland, with the first phase of the project concentrating on family-level coverage plus species of particular ecological, biomedical or evolutionary interest. We summarise the processes involved in (1) assessing the UK arthropod fauna and the status of individual species on UK lists; (2) prioritising and collecting species for initial genome sequencing; (3) handling methods to ensure that high-quality genomic DNA is preserved; and (4) compiling standard operating procedures for processing specimens for genome sequencing, identification verification and voucher specimen curation. We briefly explore some lessons learned from the pilot phase of DToL and the impact of the Covid-19 pandemic

A systematic review of different models of home and community care services for older persons

<p>Abstract</p> <p>Background</p> <p>Costs and consumer preference have led to a shift from the long-term institutional care of aged older people to home and community based care. The aim of this review is to evaluate the outcomes of case managed, integrated or consumer directed home and community care services for older persons, including those with dementia.</p> <p>Methods</p> <p>A systematic review was conducted of non-medical home and community care services for frail older persons. MEDLINE, PsycINFO, CINAHL, AgeLine, Scopus and PubMed were searched from 1994 to May 2009. Two researchers independently reviewed search results.</p> <p>Results</p> <p>Thirty five papers were included in this review. Evidence from randomized controlled trials showed that case management improves function and appropriate use of medications, increases use of community services and reduces nursing home admission. Evidence, mostly from non-randomized trials, showed that integrated care increases service use; randomized trials reported that integrated care does not improve clinical outcomes. The lowest quality evidence was for consumer directed care which appears to increase satisfaction with care and community service use but has little effect on clinical outcomes. Studies were heterogeneous in methodology and results were not consistent.</p> <p>Conclusions</p> <p>The outcomes of each model of care differ and correspond to the model's focus. Combining key elements of all three models may maximize outcomes.</p

The functorial semantics of Lie theory

Ehresmann’s introduction of differentiable groupoids in the 1950s may be seen as a starting point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids and Lie groupoids) and sketch theory. This thesis uses tangent categories to build a bridge between these two lines of research, providing a structural account of Lie algebroids and the Lie functor. To accomplish this, we develop the theory of involution algebroids, which are a tangent-categorical sketch of Lie algebroids. We show that the category of Lie algebroids is precisely the category of involution algebroids in smooth manifolds, and that the category of Weil algebras is precisely the classifying category of an involution algebroid. This exhibits the category of Lie algebroids as a tangent-categorical functor category, and the Lie functor via precomposition with a functor ∂ : Weil1 → TGpd, bringing Lie algebroids and the Lie functor into the realm of functorial semantics

The genome sequence of the black needle fly, Leuctra nigra (Olivier, 1811) [version 1; peer review: 2 approved]

We present a genome assembly from an individual male Leuctra nigra (black needle fly; Arthropoda; Insecta; Plecoptera; Leuctridae). The genome sequence is 536.3 megabases in span. Most of the assembly is scaffolded into 13 chromosomal pseudomolecules, including the X sex chromosome. The mitochondrial genome has also been assembled and is 17.6 kilobases in length