Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Large-scale phenotyping of patients with long COVID post-hospitalization reveals mechanistic subtypes of disease

One in ten severe acute respiratory syndrome coronavirus 2 infections result in prolonged symptoms termed long coronavirus disease (COVID), yet disease phenotypes and mechanisms are poorly understood1. Here we profiled 368 plasma proteins in 657 participants ≥3 months following hospitalization. Of these, 426 had at least one long COVID symptom and 233 had fully recovered. Elevated markers of myeloid inflammation and complement activation were associated with long COVID. IL-1R2, MATN2 and COLEC12 were associated with cardiorespiratory symptoms, fatigue and anxiety/depression; MATN2, CSF3 and C1QA were elevated in gastrointestinal symptoms and C1QA was elevated in cognitive impairment. Additional markers of alterations in nerve tissue repair (SPON-1 and NFASC) were elevated in those with cognitive impairment and SCG3, suggestive of brain–gut axis disturbance, was elevated in gastrointestinal symptoms. Severe acute respiratory syndrome coronavirus 2-specific immunoglobulin G (IgG) was persistently elevated in some individuals with long COVID, but virus was not detected in sputum. Analysis of inflammatory markers in nasal fluids showed no association with symptoms. Our study aimed to understand inflammatory processes that underlie long COVID and was not designed for biomarker discovery. Our findings suggest that specific inflammatory pathways related to tissue damage are implicated in subtypes of long COVID, which might be targeted in future therapeutic trials

Sample preparation method for scanning force microscopy

We present a method of sample preparation for studies of ion implantation on metal surfaces. The method, employing a mechanical mask, is specially adapted for samples analysed by Scanning Force Microscopy. It was successfully tested on polycrystallyne copper substrates implanted with phosphorus ions at an acceleration voltage of 39keV. The changes of the electrical properties of the surface were measured by Kelvin Probe Force Microscopy and the surface composition was analysed by Auger Electron Spectroscopy.552561Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Soil health in agricultural systems

Soil health is presented as an integrative property that reflects the capacity of soil to respond to agricultural intervention, so that it continues to support both the agricultural production and the provision of other ecosystem services. The major challenge within sustainable soil management is to conserve ecosystem service delivery while optimizing agricultural yields. It is proposed that soil health is dependent on the maintenance of four major functions: carbon transformations; nutrient cycles; soil structure maintenance; and the regulation of pests and diseases. Each of these functions is manifested as an aggregate of a variety of biological processes provided by a diversity of interacting soil organisms under the influence of the abiotic soil environment. Analysis of current models of the soil community under the impact of agricultural interventions (particularly those entailing substitution of biological processes with fossil fuel-derived energy or inputs) confirms the highly integrative pattern of interactions within each of these functions and leads to the conclusion that measurement of individual groups of organisms, processes or soil properties does not suffice to indicate the state of the soil health. A further conclusion is that quantifying the flow of energy and carbon between functions is an essential but non-trivial task for the assessment and management of soil health